]> uoa-corpus

Speech and Accessibility Group Logo  UoAMathCorpus

UoAMathCorpus is a collection of representative mathematical expressions in MathML developed by the Speech and Accessibility Lab., University of Athens (UoA). It includes a Greek text with math section. UoAMathCorpus has been designed as a research tool for eAccessiblity.

You can download UoAMathCorpus from: Download .docx file.

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1.    Fractions

1.1       Simple

1 1 2 + 1 3 1 4 + 1 5 =ln2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgk HiTmaalaaabaGaaGymaaqaaiaaikdaaaGaey4kaSYaaSaaaeaacaaI XaaabaGaaG4maaaacqGHsisldaWcaaqaaiaaigdaaeaacaaI0aaaai abgUcaRmaalaaabaGaaGymaaqaaiaaiwdaaaGaeyOeI0IaeS47IWKa eyypa0JaciiBaiaac6gacaaIYaaaaa@46F3@

1 1 3 + 1 5 1 7 + 1 9 = π 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgk HiTmaalaaabaGaaGymaaqaaiaaiodaaaGaey4kaSYaaSaaaeaacaaI XaaabaGaaGynaaaacqGHsisldaWcaaqaaiaaigdaaeaacaaI3aaaai abgUcaRmaalaaabaGaaGymaaqaaiaaiMdaaaGaeyOeI0IaeS47IWKa eyypa0ZaaSaaaeaacqaHapaCaeaacaaI0aaaaaaa@46E8@

1 2 1 5 + 1 8 1 11 + 1 14 = π 3 9 + 1 3 ln2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGOmaaaacqGHsisldaWcaaqaaiaaigdaaeaacaaI1aaa aiabgUcaRmaalaaabaGaaGymaaqaaiaaiIdaaaGaeyOeI0YaaSaaae aacaaIXaaabaGaaGymaiaaigdaaaGaey4kaSYaaSaaaeaacaaIXaaa baGaaGymaiaaisdaaaGaeyOeI0IaeS47IWKaeyypa0ZaaSaaaeaacq aHapaCdaGcaaqaaiaaiodaaSqabaaakeaacaaI5aaaaiabgUcaRmaa laaabaGaaGymaaqaaiaaiodaaaGaciiBaiaac6gacaaIYaaaaa@4F15@

1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 += π 2 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOmaaaaaaGccqGHRaWkdaWc aaqaaiaaigdaaeaacaaIYaWaaWbaaSqabeaacaaIYaaaaaaakiabgU caRmaalaaabaGaaGymaaqaaiaaiodadaahaaWcbeqaaiaaikdaaaaa aOGaey4kaSYaaSaaaeaacaaIXaaabaGaaGinamaaCaaaleqabaGaaG OmaaaaaaGccqGHRaWkcqWIVlctcqGH9aqpdaWcaaqaaiabec8aWnaa CaaaleqabaGaaGOmaaaaaOqaaiaaiAdaaaaaaa@49DD@

1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 += π 4 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGinaaaaaaGccqGHRaWkdaWc aaqaaiaaigdaaeaacaaIYaWaaWbaaSqabeaacaaI0aaaaaaakiabgU caRmaalaaabaGaaGymaaqaaiaaiodadaahaaWcbeqaaiaaisdaaaaa aOGaey4kaSYaaSaaaeaacaaIXaaabaGaaGinamaaCaaaleqabaGaaG inaaaaaaGccqGHRaWkcqWIVlctcqGH9aqpdaWcaaqaaiabec8aWnaa CaaaleqabaGaaGinaaaaaOqaaiaaiMdacaaIWaaaaaaa@4AA4@

1 1 6 + 1 2 6 + 1 3 6 + 1 4 6 += π 6 945 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOnaaaaaaGccqGHRaWkdaWc aaqaaiaaigdaaeaacaaIYaWaaWbaaSqabeaacaaI2aaaaaaakiabgU caRmaalaaabaGaaGymaaqaaiaaiodadaahaaWcbeqaaiaaiAdaaaaa aOGaey4kaSYaaSaaaeaacaaIXaaabaGaaGinamaaCaaaleqabaGaaG OnaaaaaaGccqGHRaWkcqWIVlctcqGH9aqpdaWcaaqaaiabec8aWnaa CaaaleqabaGaaGOnaaaaaOqaaiaaiMdacaaI0aGaaGynaaaaaaa@4B71@

1 1 6 + 1 2 6 + 1 3 6 + 1 4 6 += 31 π 6 30,240 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOnaaaaaaGccqGHRaWkdaWc aaqaaiaaigdaaeaacaaIYaWaaWbaaSqabeaacaaI2aaaaaaakiabgU caRmaalaaabaGaaGymaaqaaiaaiodadaahaaWcbeqaaiaaiAdaaaaa aOGaey4kaSYaaSaaaeaacaaIXaaabaGaaGinamaaCaaaleqabaGaaG OnaaaaaaGccqGHRaWkcqWIVlctcqGH9aqpdaWcaaqaaiaaiodacaaI XaGaeqiWda3aaWbaaSqabeaacaaI2aaaaaGcbaGaaG4maiaaicdaca GGSaGaaGOmaiaaisdacaaIWaaaaaaa@4F04@

1 1 3 + 1 3 3 1 5 3 1 7 3 += 3 π 3 2 128 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaG4maaaaaaGccqGHRaWkdaWc aaqaaiaaigdaaeaacaaIZaWaaWbaaSqabeaacaaIZaaaaaaakiabgk HiTmaalaaabaGaaGymaaqaaiaaiwdadaahaaWcbeqaaiaaiodaaaaa aOGaeyOeI0YaaSaaaeaacaaIXaaabaGaaG4namaaCaaaleqabaGaaG 4maaaaaaGccqGHRaWkcqWIVlctcqGH9aqpdaWcaaqaaiaaiodacqaH apaCdaahaaWcbeqaaiaaiodaaaGcdaGcaaqaaiaaikdaaSqabaaake aacaaIXaGaaGOmaiaaiIdaaaaaaa@4D15@

1 1×3 + 1 3×5 + 1 5×7 + 1 7×9 += 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymaiabgEna0kaaiodaaaGaey4kaSYaaSaaaeaacaaI XaaabaGaaG4maiabgEna0kaaiwdaaaGaey4kaSYaaSaaaeaacaaIXa aabaGaaGynaiabgEna0kaaiEdaaaGaey4kaSYaaSaaaeaacaaIXaaa baGaaG4naiabgEna0kaaiMdaaaGaey4kaSIaeS47IWKaeyypa0ZaaS aaaeaacaaIXaaabaGaaGOmaaaaaaa@4F7A@

1 1 2 × 3 2 + 1 3 2 × 5 2 + 1 5 2 × 7 2 + 1 7 2 × 9 2 += π 2 8 16 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOmaaaakiabgEna0kaaioda daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaaIXaaaba GaaG4mamaaCaaaleqabaGaaGOmaaaakiabgEna0kaaiwdadaahaaWc beqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaaIXaaabaGaaGynam aaCaaaleqabaGaaGOmaaaakiabgEna0kaaiEdadaahaaWcbeqaaiaa ikdaaaaaaOGaey4kaSYaaSaaaeaacaaIXaaabaGaaG4namaaCaaale qabaGaaGOmaaaakiabgEna0kaaiMdadaahaaWcbeqaaiaaikdaaaaa aOGaey4kaSIaeS47IWKaeyypa0ZaaSaaaeaacqaHapaCdaahaaWcbe qaaiaaikdaaaGccqGHsislcaaI4aaabaGaaGymaiaaiAdaaaaaaa@5B75@

β+ γ δ ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdiMaey 4kaSYaaSaaaeaacqaHZoWzaeaacqaH0oazaaGaeyOeI0IaeqyTduga aa@3E6A@

β+γ δ+ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHYoGycqGHRaWkcqaHZoWzaeaacqaH0oazcqGHRaWkcqaH1oqzaaaa aa@3E5F@

βγ δ +ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHYoGycqGHsislcqaHZoWzaeaacqaH0oazaaGaey4kaSIaeqyTduga aa@3E6A@

α+β+γ+δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey 4kaSIaeqOSdiMaey4kaSIaeq4SdCMaey4kaSIaeqiTdqgaaa@3F29@

α+ β γ +δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey 4kaSYaaSaaaeaacqaHYoGyaeaacqaHZoWzaaGaey4kaSIaeqiTdqga aa@3E57@

α β+γ+δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHXoqyaeaacqaHYoGycqGHRaWkcqaHZoWzcqGHRaWkcqaH0oazaaaa aa@3E57@

α+β γ+δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHXoqycqGHRaWkcqaHYoGyaeaacqaHZoWzcqGHRaWkcqaH0oazaaaa aa@3E57@

( α+β )( γ+δ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHXoqycqGHRaWkcqaHYoGyaiaawIcacaGLPaaacqGHflY1daqadaqa aiabeo7aNjabgUcaRiabes7aKbGaayjkaiaawMcaaaaa@43A3@  

χ+ ψ 2 κ+1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHhpWycqGHRaWkcqaHipqEdaahaaWcbeqaaiaaikdaaaaakeaacqaH 6oWAcqGHRaWkcaaIXaaaaaaa@3EB0@

χ+ ψ 2 κ +1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey 4kaSYaaSaaaeaacqaHipqEdaahaaWcbeqaaiaaikdaaaaakeaacqaH 6oWAaaGaey4kaSIaaGymaaaa@3EB0@

β×( γ+δ ) ε 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHYoGycqGHxdaTdaqadaqaaiabeo7aNjabgUcaRiabes7aKbGaayjk aiaawMcaaaqaaiabew7aLnaaCaaaleqabaGaaGOmaaaaaaaaaa@4206@

 

1.2       Complex

1 1 2π + 1 3 2π + 1 5 2π + 1 7 2π += ( 2 2π 1 ) π 2π Β π 2( 2π )! MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOmaiabec8aWbaaaaGccqGH RaWkdaWcaaqaaiaaigdaaeaacaaIZaWaaWbaaSqabeaacaaIYaGaeq iWdahaaaaakiabgUcaRmaalaaabaGaaGymaaqaaiaaiwdadaahaaWc beqaaiaaikdacqaHapaCaaaaaOGaey4kaSYaaSaaaeaacaaIXaaaba GaaG4namaaCaaaleqabaGaaGOmaiabec8aWbaaaaGccqGHRaWkcqWI VlctcqGH9aqpdaWcaaqaamaabmaabaGaaGOmamaaCaaaleqabaGaaG Omaiabec8aWbaakiabgkHiTiaaigdaaiaawIcacaGLPaaacqaHapaC daahaaWcbeqaaiaaikdacqaHapaCaaGccqqHsoGqdaWgaaWcbaGaeq iWdahabeaaaOqaaiaaikdadaqadaqaaiaaikdacqaHapaCaiaawIca caGLPaaacaGGHaaaaaaa@6129@

1 1 2π 1 2 2π + 1 3 2π 1 4 2π += ( 2 2π1 1 ) π 2π Β π ( 2π )! MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOmaiabec8aWbaaaaGccqGH sisldaWcaaqaaiaaigdaaeaacaaIYaWaaWbaaSqabeaacaaIYaGaeq iWdahaaaaakiabgUcaRmaalaaabaGaaGymaaqaaiaaiodadaahaaWc beqaaiaaikdacqaHapaCaaaaaOGaeyOeI0YaaSaaaeaacaaIXaaaba GaaGinamaaCaaaleqabaGaaGOmaiabec8aWbaaaaGccqGHRaWkcqWI VlctcqGH9aqpdaWcaaqaamaabmaabaGaaGOmamaaCaaaleqabaGaaG Omaiabec8aWjabgkHiTiaaigdaaaGccqGHsislcaaIXaaacaGLOaGa ayzkaaGaeqiWda3aaWbaaSqabeaacaaIYaGaeqiWdahaaOGaeuOKdi 0aaSbaaSqaaiabec8aWbqabaaakeaadaqadaqaaiaaikdacqaHapaC aiaawIcacaGLPaaacaGGHaaaaaaa@6225@

1 1 2π+1 1 3 2π+1 + 1 5 2π+1 1 7 2π+1 += π 2π+1 Ε π 2 2π+2 ( 2π )! MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGymamaaCaaaleqabaGaaGOmaiabec8aWjabgUcaRiaa igdaaaaaaOGaeyOeI0YaaSaaaeaacaaIXaaabaGaaG4mamaaCaaale qabaGaaGOmaiabec8aWjabgUcaRiaaigdaaaaaaOGaey4kaSYaaSaa aeaacaaIXaaabaGaaGynamaaCaaaleqabaGaaGOmaiabec8aWjabgU caRiaaigdaaaaaaOGaeyOeI0YaaSaaaeaacaaIXaaabaGaaG4namaa CaaaleqabaGaaGOmaiabec8aWjabgUcaRiaaigdaaaaaaOGaey4kaS IaeS47IWKaeyypa0ZaaSaaaeaacqaHapaCdaahaaWcbeqaaiaaikda cqaHapaCcqGHRaWkcaaIXaaaaOGaeuyLdu0aaSbaaSqaaiabec8aWb qabaaakeaacaaIYaWaaWbaaSqabeaacaaIYaGaeqiWdaNaey4kaSIa aGOmaaaakmaabmaabaGaaGOmaiabec8aWbGaayjkaiaawMcaaiaacg caaaaaaa@6707@

( α+χ ) ν = α ν +ν α ν1 χ+ ν(ν1) 2! α ν2 χ 2 + ν(ν1)(ν2) 3! α ν3 χ 3 + MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaqada qaaiabeg7aHjabgUcaRiabeE8aJbGaayjkaiaawMcaamaaCaaaleqa baGaeqyVd4gaaOGaeyypa0JaeqySde2aaWbaaSqabeaacqaH9oGBaa GccqGHRaWkcqaH9oGBcqaHXoqydaahaaWcbeqaaiabe27aUjabgkHi TiaaigdaaaGccqaHhpWycqGHRaWkdaWcaaqaaiabe27aUjaacIcacq aH9oGBcqGHsislcaaIXaGaaiykaaqaaiaaikdacaGGHaaaaiabeg7a HnaaCaaaleqabaGaeqyVd4MaeyOeI0IaaGOmaaaakiabeE8aJnaaCa aaleqabaGaaGOmaaaaaOqaaiabgUcaRmaalaaabaGaeqyVd4Maaiik aiabe27aUjabgkHiTiaaigdacaGGPaGaaiikaiabe27aUjabgkHiTi aaikdacaGGPaaabaGaaG4maiaacgcaaaGaeqySde2aaWbaaSqabeaa cqaH9oGBcqGHsislcaaIZaaaaOGaeq4Xdm2aaWbaaSqabeaacaaIZa aaaOGaey4kaSIaeS47IWeaaaa@74A0@

α χ = e χlnα =1+χlnα+ ( χlnα ) 2 2! + ( χlnα ) 3 3! + MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaW baaSqabeaacqaHhpWyaaGccqGH9aqpcaWGLbWaaWbaaSqabeaacqaH hpWyciGGSbGaaiOBaiabeg7aHbaakiabg2da9iaaigdacqGHRaWkcq aHhpWyciGGSbGaaiOBaiabeg7aHjabgUcaRmaalaaabaWaaeWaaeaa cqaHhpWyciGGSbGaaiOBaiabeg7aHbGaayjkaiaawMcaamaaCaaale qabaGaaGOmaaaaaOqaaiaaikdacaGGHaaaaiabgUcaRmaalaaabaWa aeWaaeaacqaHhpWyciGGSbGaaiOBaiabeg7aHbGaayjkaiaawMcaam aaCaaaleqabaGaaG4maaaaaOqaaiaaiodacaGGHaaaaiabgUcaRiab l+Uimbaa@5FA6@

lnχ=2{ ( χ1 χ+1 )+ 1 3 ( χ1 χ+1 ) 3 + 1 5 ( χ1 χ+1 ) 5 + } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac6 gacqaHhpWycqGH9aqpcaaIYaWaaiWaaeaadaqadaqaamaalaaabaGa eq4XdmMaeyOeI0IaaGymaaqaaiabeE8aJjabgUcaRiaaigdaaaaaca GLOaGaayzkaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaG4maaaadaqa daqaamaalaaabaGaeq4XdmMaeyOeI0IaaGymaaqaaiabeE8aJjabgU caRiaaigdaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIZaaaaOGa ey4kaSYaaSaaaeaacaaIXaaabaGaaGynaaaadaqadaqaamaalaaaba Gaeq4XdmMaeyOeI0IaaGymaaqaaiabeE8aJjabgUcaRiaaigdaaaaa caGLOaGaayzkaaWaaWbaaSqabeaacaaI1aaaaOGaey4kaSIaeS47IW eacaGL7bGaayzFaaaaaa@5FF9@

2sinμπ π ( sinχ 1 μ 2 2sin2χ 2 2 μ 2 + 3sin3χ 3 2 μ 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIYaGaci4CaiaacMgacaGGUbGaeqiVd0MaeqiWdahabaGaeqiWdaha amaabmaabaWaaSaaaeaaciGGZbGaaiyAaiaac6gacqaHhpWyaeaaca aIXaGaeyOeI0IaeqiVd02aaWbaaSqabeaacaaIYaaaaaaakiabgkHi TmaalaaabaGaaGOmaiGacohacaGGPbGaaiOBaiaaikdacqaHhpWyae aacaaIYaWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaeqiVd02aaWba aSqabeaacaaIYaaaaaaakiabgUcaRmaalaaabaGaaG4maiGacohaca GGPbGaaiOBaiaaiodacqaHhpWyaeaacaaIZaWaaWbaaSqabeaacaaI YaaaaOGaeyOeI0IaeqiVd02aaWbaaSqabeaacaaIYaaaaaaakiabgk HiTiabl+UimbGaayjkaiaawMcaaaaa@64A9@

1+ χ 1+ χ 1+ χ 1+ χ 1+ χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgU caRmaalaaabaGaeq4XdmgabaGaaGymaiabgUcaRmaalaaabaGaeq4X dmgabaGaaGymaiabgUcaRmaalaaabaGaeq4XdmgabaGaaGymaiabgU caRmaalaaabaGaeq4XdmgabaGaaGymaiabgUcaRmaalaaabaGaeq4X dmgabaGaeSOjGSeaaaaaaaaaaaaaaaa@480D@

φ΄(χ)+φ(χ)×ψ+ζ χ×ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aHgpGAcaWGeoGaaiikaiabeE8aJjaacMcacqGHRaWkcqaHgpGAcaGG OaGaeq4XdmMaaiykaiabgEna0kabeI8a5jabgUcaRiabeA7a6bqaai abeE8aJjabgEna0kabeI8a5baaaaa@4DAF@

χ= β± β 2 4αγ 2α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey ypa0ZaaSaaaeaacqGHsislcqaHYoGycqGHXcqSdaGcaaqaaiabek7a InaaCaaaleqabaGaaGOmaaaakiabgkHiTiaaisdacqGHflY1cqaHXo qycqGHflY1cqaHZoWzaSqabaaakeaacaaIYaGaeyyXICTaeqySdega aaaa@4E23@

 

2.    Roots

2.1       Simple

β γ +δε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaada Wcaaqaaiabek7aIbqaaiabeo7aNbaaaSqabaGccqGHRaWkcqaH0oaz cqGHsislcqaH1oqzaaa@3E8F@

β γ+δ ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaada Wcaaqaaiabek7aIbqaaiabeo7aNjabgUcaRiabes7aKbaaaSqabaGc cqGHsislcqaH1oqzaaa@3E8F@

β γ ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaada Wcaaqaaiabek7aIbqaaiabeo7aNbaacqGHsislcqaH1oqzaSqabaaa aa@3BFE@

β+γ + δ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaacq aHYoGycqGHRaWkcqaHZoWzaSqabaGccqGHRaWkcqaH0oazdaahaaWc beqaaiaaikdaaaaaaa@3DB6@

β +γ δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada Gcaaqaaiabek7aIbWcbeaakiabgUcaRiabeo7aNbqaaiabes7aKbaa aaa@3BFB@

 

2.2       Complex

π 2 π 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada Gcaaqaaiabec8aWbWcbeaaaOqaaiaaikdaaaGaeyiyIK7aaOaaaeaa daWcaaqaaiabec8aWbqaaiaaikdaaaaaleqaaaaa@3D10@

1+ 2+ 2+ 2+ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaaca aIXaGaey4kaSYaaOaaaeaacaaIYaGaey4kaSYaaOaaaeaacaaIYaGa ey4kaSYaaOaaaeaacaaIYaGaey4kaSIaeSOjGSealeqaaaqabaaabe aaaeqaaaaa@3DDB@

d( χ,ψ )= ( χ 1 ψ 1 ) 2 + ( χ 2 ψ 2 ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaabm aabaGaeq4XdmMaaiilaiabeI8a5bGaayjkaiaawMcaaiabg2da9maa kaaabaWaaeWaaeaacqaHhpWydaWgaaWcbaGaaGymaaqabaGccqGHsi slcqaHipqEdaWgaaWcbaGaaGymaaqabaaakiaawIcacaGLPaaadaah aaWcbeqaaiaaikdaaaGccqGHRaWkdaqadaqaaiabeE8aJnaaBaaale aacaaIYaaabeaakiabgkHiTiabeI8a5naaBaaaleaacaaIYaaabeaa aOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaeqaaaaa@502E@

Σ= α β 2π×φ(χ)× 1+ [ φ'(χ) ] 2 dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4OdmLaey ypa0Zaa8qmaeaacaaIYaGaeqiWdaNaey41aqRaeqOXdOMaaiikaiab eE8aJjaacMcacqGHxdaTdaGcaaqaaiaaigdacqGHRaWkdaWadaqaai abeA8aQjaacEcacaGGOaGaeq4XdmMaaiykaaGaay5waiaaw2faamaa CaaaleqabaGaaGOmaaaaaeqaaOGaamizaiabeE8aJbWcbaGaeqySde gabaGaeqOSdiganiabgUIiYdaaaa@5608@

σ= [ ( χ χ ¯ ) 2 ν ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0ZaaOaaaeaadaWadaqaamaalaaabaWaaabqaeaadaqadaqaaiab eE8aJjabgkHiTmaanaaabaGaeq4XdmgaaaGaayjkaiaawMcaamaaCa aaleqabaGaaGOmaaaaaeqabeqdcqGHris5aaGcbaGaeqyVd4gaaaGa ay5waiaaw2faaaWcbeaaaaa@4586@

 

3.    Derivatives

3.1       Simple

Ω= Ω ¯ Ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOaIyRaeu yQdCLaeyypa0ZaaSaaaeaacuqHPoWvgaqeaaqaaiabfM6axbaaaaa@3D35@

υ τ ( χ,τ )=( Λ( χ )υ( χ,τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaS baaSqaaiabes8a0bqabaGcdaqadaqaaiabeE8aJjaacYcacqaHepaD aiaawIcacaGLPaaacqGH9aqpcqGHhis0daqadaqaaiabfU5amnaabm aabaGaeq4XdmgacaGLOaGaayzkaaGaey4bIeTaeqyXdu3aaeWaaeaa cqaHhpWycaGGSaGaeqiXdqhacaGLOaGaayzkaaaacaGLOaGaayzkaa aaaa@513A@

Δ υ( χ )= Κ,σ υ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey4bIe9aaS baaSqaaiabfs5aebqabaGccqaHfpqDdaqadaqaaiabeE8aJbGaayjk aiaawMcaaiabg2da9iabgEGirpaaBaaaleaacqqHAoWscaGGSaGaeq 4Wdmhabeaakiabew8a1baa@468F@

0 υ ν = υ ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOaIy7aaW baaSqabeaacaaIWaaaaOGaeqyXdu3aaSbaaSqaaiabe27aUbqabaGc cqGH9aqpcqaHfpqDdaWgaaWcbaGaeqyVd4gabeaaaaa@40B4@

2 υ ν = 1 κ ( 1 υ ν 1 υ ν1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOaIy7aaW baaSqabeaacaaIYaaaaOGaeqyXdu3aaSbaaSqaaiabe27aUbqabaGc cqGH9aqpdaWcaaqaaiaaigdaaeaacqaH6oWAaaWaaeWaaeaacqGHci ITdaahaaWcbeqaaiaaigdaaaGccqaHfpqDdaWgaaWcbaGaeqyVd4ga beaakiabgkHiTiabgkGi2oaaCaaaleqabaGaaGymaaaakiabew8a1n aaBaaaleaacqaH9oGBcqGHsislcaaIXaaabeaaaOGaayjkaiaawMca aaaa@4FC0@

α Δ η Δ ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aau WaaeaacqGHhis0daWgaaWcbaGaeuiLdqeabeaakiabeE7aOnaaDaaa leaacqqHuoaraeaacqaH9oGBaaaakiaawMa7caGLkWoaaaa@42E0@

d 2 υ d λ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqyXduhabaGaamizaiabeU7a SnaaCaaaleqabaGaaGOmaaaaaaaaaa@3D30@

( Φ( τ,υ( τ ) ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey4bIe9aae WaaeaacqqHMoGrdaqadaqaaiabes8a0jaacYcacqaHfpqDdaqadaqa aiabes8a0bGaayjkaiaawMcaaaGaayjkaiaawMcaaaGaayjkaiaawM caaaaa@4393@

υ ¨ ( τ )=Φ( τ,υ( τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyXduNbam aadaqadaqaaiabes8a0bGaayjkaiaawMcaaiabg2da9iabgEGirlab fA6agnaabmaabaGaeqiXdqNaaiilaiabew8a1naabmaabaGaeqiXdq hacaGLOaGaayzkaaaacaGLOaGaayzkaaaaaa@482F@

| Η( τ,χ ) |φ( τ ) | χ | α +γ( τ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaacq GHhis0cqqHxoasdaqadaqaaiabes8a0jaacYcacqaHhpWyaiaawIca caGLPaaaaiaawEa7caGLiWoacqGHKjYOcqaHgpGAdaqadaqaaiabes 8a0bGaayjkaiaawMcaamaaemaabaGaeq4XdmgacaGLhWUaayjcSdWa aWbaaSqabeaacqaHXoqyaaGccqGHRaWkcqaHZoWzdaqadaqaaiabes 8a0bGaayjkaiaawMcaaaaa@5507@

φ ( υ ν )0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqOXdOMbau aadaqadaqaaiabew8a1naaBaaaleaacqaH9oGBaeqaaaGccaGLOaGa ayzkaaGaeyOKH4QaaGimaaaa@3FA5@

υ ˜ ν | φ ( υ ν ), υ ˜ ν | MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaauWaaeaacu aHfpqDgaacamaaBaaaleaacqaH9oGBaeqaaaGccaGLjWUaayPcSdGa eyyzIm7aaqWaaeaadaaadaqaaiqbeA8aQzaafaWaaeWaaeaacqaHfp qDdaWgaaWcbaGaeqyVd4gabeaaaOGaayjkaiaawMcaaiaacYcacuaH fpqDgaacamaaBaaaleaacqaH9oGBaeqaaaGccaGLPmIaayPkJaaaca GLhWUaayjcSdaaaa@4F15@

ξ υ 1 τ ξ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITdaahaaWcbeqaaiabe67a4baakiabew8a1naaBaaaleaacaaI XaaabeaaaOqaaiabgkGi2kabes8a0naaCaaaleqabaGaeqOVdGhaaa aaaaa@413A@

ιΔυ υ τ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyUdKMaey iLdqKaeqyXduNaeyOeI0IaeqyXdu3aaSbaaSqaaiabes8a0bqabaGc cqaHgpGAaaa@4140@

Δ ω υ+κ×υ=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyiLdq0aaS baaSqaaiabeM8a3bqabaGccqaHfpqDcqGHRaWkcqaH6oWAcqGHxdaT cqaHfpqDcqGH9aqpcaaIWaaaaa@435A@

χ=ρ× χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey ypa0JaeqyWdiNaey41aqRafq4XdmMbauaaaaa@3E4E@

υ ω | ω=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqGaaeaada WcaaqaaiabgkGi2kabew8a1bqaaiabgkGi2kabeM8a3baaaiaawIa7 amaaBaaaleaacqaHjpWDcqGH9aqpcaaIWaaabeaaaaa@41B6@

2 υ v 2 λ 2 υ=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITdaahaaWcbeqaaiaaikdaaaGccqaHfpqDaeaacqGHciITcaWG 2bWaaWbaaSqabeaacaaIYaaaaaaakiabgkHiTiabeU7aSnaaCaaale qabaGaaGOmaaaakiabew8a1jabg2da9iaaicdaaaa@4496@

χ ξ γ 2 ( τ )lnρ= γ 2 ( τ ) χ ξ ρ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITaeaacqGHciITcqaHhpWydaWgaaWcbaGaeqOVdGhabeaaaaGc cqaHZoWzdaWgaaWcbaGaaGOmaaqabaGcdaqadaqaaiabes8a0bGaay jkaiaawMcaaiGacYgacaGGUbGaeqyWdiNaeyypa0Jaeq4SdC2aaSba aSqaaiaaikdaaeqaaOWaaeWaaeaacqaHepaDaiaawIcacaGLPaaada WcaaqaaiabeE8aJnaaBaaaleaacqaH+oaEaeqaaaGcbaGaeqyWdi3a aWbaaSqabeaacaaIYaaaaaaaaaa@5364@

1 ρ sin ωπ ω 0 ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaeqyWdihaaiGacohacaGGPbGaaiOBamaalaaabaGaeqyY dCNaeqiWdahabaGaeqyYdC3aaSbaaSqaaiaaicdaaeqaaaaakmaala aabaGaeyOaIylabaGaeyOaIyRaeqyYdChaaaaa@465A@

υ( 0 )= υ ( 1 )= υ ( 0 )= υ ( 1 )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aae WaaeaacaaIWaaacaGLOaGaayzkaaGaeyypa0JafqyXduNbauaadaqa daqaaiaaigdaaiaawIcacaGLPaaacqGH9aqpcuaHfpqDgaGbamaabm aabaGaaGimaaGaayjkaiaawMcaaiabg2da9iqbew8a1zaasaWaaeWa aeaacaaIXaaacaGLOaGaayzkaaGaeyypa0JaaGimaaaa@4B25@

υ ( 4 ) ( τ )=φ( τ,υ( τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaW baaSqabeaadaqadaqaaiaaisdaaiaawIcacaGLPaaaaaGcdaqadaqa aiabes8a0bGaayjkaiaawMcaaiabg2da9iabeA8aQnaabmaabaGaeq iXdqNaaiilaiabew8a1naabmaabaGaeqiXdqhacaGLOaGaayzkaaaa caGLOaGaayzkaaaaaa@4960@

2 u 2 Ξ( τ,σ )=Γ( τ,σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITdaahaaWcbeqaaiaaikdaaaaakeaacqGHciITcaWG1bWaaWba aSqabeaacaaIYaaaaaaakiabf65aynaabmaabaGaeqiXdqNaaiilai abeo8aZbGaayjkaiaawMcaaiabg2da9iabgkHiTiabfo5ahnaabmaa baGaeqiXdqNaaiilaiabeo8aZbGaayjkaiaawMcaaaaa@4C14@

| υ |=max{ υ , υ , υ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaada qbdaqaaiabew8a1bGaayzcSlaawQa7aaGaay5bSlaawIa7aiabg2da 9iGac2gacaGGHbGaaiiEamaacmaabaWaauWaaeaacqaHfpqDaiaawM a7caGLkWoacaGGSaWaauWaaeaacuaHfpqDgaqbaaGaayzcSlaawQa7 aiaacYcadaqbdaqaaiqbew8a1zaagaaacaGLjWUaayPcSdaacaGL7b GaayzFaaaaaa@5455@

( υ * ) ( τ )= ( Τ υ * ) ( τ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHfpqDdaahaaWcbeqaaiaacQcaaaaakiaawIcacaGLPaaadaahaaWc beqaaOGamai4gkdiIUGaaGzaVRGamai4gkdiIcaadaqadaqaaiabes 8a0bGaayjkaiaawMcaaiabg2da9maabmaabaGaeuiPdqLaeqyXdu3a aWbaaSqabeaacaGGQaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaaki adacUHYaIOliaaygW7kiadacUHYaIOaaWaaeWaaeaacqaHepaDaiaa wIcacaGLPaaaaaa@56D5@

 

3.2       Complex

d dτ ( | υ ˙ ( τ ) | π( τ )2 υ ˙ ( τ ) )=Φ( τ,υ( τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbaabaGaamizaiabes8a0baadaqadaqaamaaemaabaGafqyXduNb aiaadaqadaqaaiabes8a0bGaayjkaiaawMcaaaGaay5bSlaawIa7am aaCaaaleqabaGaeqiWda3aaeWaaeaacqaHepaDaiaawIcacaGLPaaa cqGHsislcaaIYaaaaOGafqyXduNbaiaadaqadaqaaiabes8a0bGaay jkaiaawMcaaaGaayjkaiaawMcaaiabg2da9iabgEGirlabfA6agnaa bmaabaGaeqiXdqNaaiilaiabew8a1naabmaabaGaeqiXdqhacaGLOa GaayzkaaaacaGLOaGaayzkaaaaaa@5C89@

d dτ ( υ 2 +2 Ω Φ( υ )dχ )+2 υ τ 2 =2( ( α τ , υ τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWcaa qaaiaadsgaaeaacaWGKbGaeqiXdqhaamaabmaabaWaauWaaeaacqGH his0cqaHfpqDaiaawMa7caGLkWoadaahaaWcbeqaaiaaikdaaaGccq GHRaWkcaaIYaWaa8quaeaacqqHMoGrdaqadaqaaiabew8a1bGaayjk aiaawMcaaiaadsgacqaHhpWyaSqaaiabfM6axbqab0Gaey4kIipaaO GaayjkaiaawMcaaiabgUcaRiaaikdadaqbdaqaamaalaaabaGaeyOa IyRaeqyXduhabaGaeyOaIyRaeqiXdqhaaaGaayzcSlaawQa7amaaCa aaleqabaGaaGOmaaaaaOqaaiabg2da9iaaikdadaqadaqaamaabmaa baWaaSaaaeaacqGHciITcqaHXoqyaeaacqGHciITcqaHepaDaaGaai ilamaalaaabaGaeyOaIyRaeqyXduhabaGaeyOaIyRaeqiXdqhaaaGa ayjkaiaawMcaaaGaayjkaiaawMcaaaaaaa@6DCB@

τ ( υ τ )Δ υ τ + φ ( υ ) υ τ = α τ +Δαυ υ τ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWcaa qaaiabgkGi2cqaaiabgkGi2kabes8a0baadaqadaqaamaalaaabaGa eyOaIyRaeqyXduhabaGaeyOaIyRaeqiXdqhaaaGaayjkaiaawMcaai abgkHiTiabgs5aenaalaaabaGaeyOaIyRaeqyXduhabaGaeyOaIyRa eqiXdqhaaiabgUcaRiqbeA8aQzaafaWaaeWaaeaacqaHfpqDaiaawI cacaGLPaaadaWcaaqaaiabgkGi2kabew8a1bqaaiabgkGi2kabes8a 0baaaeaacqGH9aqpcqGHsisldaWcaaqaaiabgkGi2kabeg7aHbqaai abgkGi2kabes8a0baacqGHRaWkcqGHuoarcqaHXoqycqGHsislcqaH fpqDcqGHsisldaWcaaqaaiabgkGi2kabew8a1bqaaiabgkGi2kabes 8a0baaaaaa@6DD3@

d dτ ( Α 3 2 α 2 + Α dα dτ 2 )γ Δυ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbaabaGaamizaiabes8a0baadaqadaqaamaafmaabaGaeuyKde0a aWbaaSqabeaadaWcaaqaaiaaiodaaeaacaaIYaaaaaaakiabeg7aHb GaayzcSlaawQa7amaaCaaaleqabaGaaGOmaaaakiabgUcaRmaafmaa baGaeuyKde0aaSaaaeaacaWGKbGaeqySdegabaGaamizaiabes8a0b aaaiaawMa7caGLkWoadaahaaWcbeqaaiaaikdaaaaakiaawIcacaGL PaaacqGHKjYOcqaHZoWzdaqbdaqaaiabgs5aejabew8a1bGaayzcSl aawQa7amaaCaaaleqabaGaaGOmaaaaaaa@5A3C@

υ μ τ + ν μ τ + υ ¯ μ χ = φ ¯ μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITcqaHfpqDdaWgaaWcbaGaeqiVd0gabeaaaOqaaiabgkGi2kab es8a0baacqGHRaWkdaWcaaqaaiabgkGi2kabe27aUnaaBaaaleaacq aH8oqBaeqaaaGcbaGaeyOaIyRaeqiXdqhaaiabgUcaRmaalaaabaGa eyOaIyRafqyXduNbaebadaWgaaWcbaGaeqiVd0gabeaaaOqaaiabgk Gi2kabeE8aJbaacqGH9aqpcuaHgpGAgaqeamaaBaaaleaacqaH8oqB aeqaaaaa@556F@

sup 0τΤ [ ( υ ν υ ) τ ]+ sup 0τΤ [ ( θ ν θ ) τ ] Γ( λ ν+1 1 8 + μ ν+1 1 8 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWfqa qaaiGacohacaGG1bGaaiiCaaWcbaGaaGimaiabgsMiJkabes8a0jab gsMiJkabfs6aubqabaGcdaWadaqaamaalaaabaGaeyOaIy7aaeWaae aacqaHfpqDdaWgaaWcbaGaeqyVd4gabeaakiabgkHiTiabew8a1bGa ayjkaiaawMcaaaqaaiabgkGi2kabes8a0baaaiaawUfacaGLDbaacq GHRaWkdaWfqaqaaiGacohacaGG1bGaaiiCaaWcbaGaaGimaiabgsMi Jkabes8a0jabgsMiJkabfs6aubqabaGcdaWadaqaamaalaaabaGaey OaIy7aaeWaaeaacqaH4oqCdaWgaaWcbaGaeqyVd4gabeaakiabgkHi TiabeI7aXbGaayjkaiaawMcaaaqaaiabgkGi2kabes8a0baaaiaawU facaGLDbaaaeaacqGHKjYOcqqHtoWrdaqadaqaaiabeU7aSnaaDaaa leaacqaH9oGBcqGHRaWkcaaIXaaabaGaeyOeI0YaaSaaaeaacaaIXa aabaGaaGioaaaaaaGccqGHRaWkcqaH8oqBdaqhaaWcbaGaeqyVd4Ma ey4kaSIaaGymaaqaaiabgkHiTmaalaaabaGaaGymaaqaaiaaiIdaaa aaaaGccaGLOaGaayzkaaaaaaa@7DF6@

d[ φ(χ) τ(χ) ] dx = τ(χ)× d[ φ(χ) ] dx φ(χ)× d[ τ(χ) ] dx [ τ(χ) ] 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbWaamWaaeaadaWcaaqaaiabeA8aQjaacIcacqaHhpWycaGGPaaa baGaeqiXdqNaaiikaiabeE8aJjaacMcaaaaacaGLBbGaayzxaaaaba GaamizaiaadIhaaaGaeyypa0ZaaSaaaeaacqaHepaDcaGGOaGaeq4X dmMaaiykaiabgEna0oaalaaabaGaamizamaadmaabaGaeqOXdOMaai ikaiabeE8aJjaacMcaaiaawUfacaGLDbaaaeaacaWGKbGaamiEaaaa cqGHsislcqaHgpGAcaGGOaGaeq4XdmMaaiykaiabgEna0oaalaaaba GaamizamaadmaabaGaeqiXdqNaaiikaiabeE8aJjaacMcaaiaawUfa caGLDbaaaeaacaWGKbGaamiEaaaaaeaadaWadaqaaiabes8a0jaacI cacqaHhpWycaGGPaaacaGLBbGaayzxaaWaaWbaaSqabeaacaaIYaaa aaaaaaa@6F41@

 

4.    Exponentials & Indicators

4.1       Simple

δ Κ,σ >0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaS baaSqaaiabfQ5aljaacYcacqaHdpWCaeqaaOGaeyOpa4JaaGimaaaa @3D7A@

β σ Κ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aa0 baaSqaaiabeo8aZbqaaiabfQ5albaakiabgcMi5kaaicdaaaa@3D86@

χ σ = ΚΜ β σ Κ χ Κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiabeo8aZbqabaGccqGH9aqpdaaeqbqaaiabek7aInaaDaaa leaacqaHdpWCaeaacqqHAoWsaaGccqaHhpWydaWgaaWcbaGaeuOMdS eabeaaaeaacqqHAoWscqGHiiIZcqqHCoqtaeqaniabggHiLdaaaa@4997@

{ χ Κ } Κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaacq aHhpWydaWgaaWcbaGaeuOMdSeabeaaaOGaay5Eaiaaw2haamaaBaaa leaacqqHAoWsaeqaaaaa@3D27@

υ Κ =φ( χ Κ ),ΚΜ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaS baaSqaaiabfQ5albqabaGccqGH9aqpcqaHgpGAdaqadaqaaiabeE8a JnaaBaaaleaacqqHAoWsaeqaaaGccaGLOaGaayzkaaGaaiilaiabgc GiIiabfQ5aljabgIGiolabfY5anbaa@4701@

1 υ ν = υ ν υ ν1 κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOaIy7aaW baaSqabeaacaaIXaaaaOGaeqyXdu3aaWbaaSqabeaacqaH9oGBaaGc cqGH9aqpdaWcaaqaaiabew8a1naaCaaaleqabaGaeqyVd4gaaOGaey OeI0IaeqyXdu3aaWbaaSqabeaacqaH9oGBcqGHsislcaaIXaaaaaGc baGaeqOUdSgaaaaa@48CE@

Φ Κ,σ ( υ )= σ Ε κ Α σ σ ( υ κ υ σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOPdy0aaS baaSqaaiabfQ5aljaacYcacqaHdpWCaeqaaOWaaeWaaeaacqaHfpqD aiaawIcacaGLPaaacqGH9aqpdaaeqbqaaiabfg5abnaaCaaaleqaba Gaeq4WdmNafq4WdmNbauaaaaGcdaqadaqaaiabew8a1naaBaaaleaa cqaH6oWAaeqaaOGaeyOeI0IaeqyXdu3aaSbaaSqaaiqbeo8aZzaafa aabeaaaOGaayjkaiaawMcaaaWcbaGafq4WdmNbauaacqGHiiIZcqqH voqrdaWgaaadbaGaeqOUdSgabeaaaSqab0GaeyyeIuoaaaa@57C5@

α | υ | χ 2 υ,υ Φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaq WaaeaacqaHfpqDaiaawEa7caGLiWoadaqhaaWcbaGaeq4XdmgabaGa aGOmaaaakiabgsMiJoaaamaabaGaeqyXduNaaiilaiabew8a1bGaay zkJiaawQYiamaaBaaaleaacqqHMoGraeqaaaaa@4892@

Γ 6 = δ 3 θ+ δ 7 2 θ 2 + δ 5 2 θ+1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aaS baaSqaaiaaiAdaaeqaaOGaeyypa0JaeqiTdq2aaWbaaSqabeaacaaI ZaaaaOGaeqiUdeNaey4kaSIaeqiTdq2aaWbaaSqabeaadaWcaaqaai aaiEdaaeaacaaIYaaaaaaakiabeI7aXnaaCaaaleqabaGaaGOmaaaa kiabgUcaRiabes7aKnaaCaaaleqabaWaaSaaaeaacaaI1aaabaGaaG OmaaaaaaGccqaH4oqCcqGHRaWkcaaIXaaaaa@4C3A@

υ ¯ Δ 0 = υ Δ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyXduNbae badaqhaaWcbaGaeuiLdqeabaGaaGimaaaakiabg2da9iabew8a1naa DaaaleaacqqHuoaraeaacaaIWaaaaaaa@3F47@

θ 2 υ ν = κ 1 ( 1 υ ν 1 υ ν1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUde3aaW baaSqabeaacaaIYaaaaOGaeqyXdu3aaWbaaSqabeaacqaH9oGBaaGc cqGH9aqpcqaH6oWAdaahaaWcbeqaaiabgkHiTiaaigdaaaGcdaqada qaaiabgkGi2oaaCaaaleqabaGaaGymaaaakiabew8a1naaCaaaleqa baGaeqyVd4gaaOGaeyOeI0IaeyOaIy7aaWbaaSqabeaacaaIXaaaaO GaeqyXdu3aaWbaaSqabeaacqaH9oGBcqGHsislcaaIXaaaaaGccaGL OaGaayzkaaaaaa@5127@

χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaauWaaeaacq aHhpWyaiaawMa7caGLkWoaaaa@3AD5@

α η Δ ν+1 χ Γ π Μ Δ ν+1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aau WaaeaacqaH3oaAdaqhaaWcbaGaeuiLdqeabaGaeqyVd4Maey4kaSIa aGymaaaaaOGaayzcSlaawQa7aiabeE8aJjabgsMiJkabfo5ahnaaBa aaleaacqaHapaCaeqaaOGaeuiNd00aa0baaSqaaiabfs5aebqaaiab e27aUjabgUcaRiaaigdaaaaaaa@4E81@

Φ 2 ( τ,χ )=| sinωτ | | χ | 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOPdy0aaS baaSqaaiaaikdaaeqaaOWaaeWaaeaacqaHepaDcaGGSaGaeq4Xdmga caGLOaGaayzkaaGaeyypa0ZaaqWaaeaaciGGZbGaaiyAaiaac6gacq aHjpWDcqaHepaDaiaawEa7caGLiWoadaabdaqaaiabeE8aJbGaay5b SlaawIa7amaaCaaaleqabaGaaG4maaaaaaa@4E6D@

Η( τ,χ )= | χ | 1+α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4LdG0aae WaaeaacqaHepaDcaGGSaGaeq4XdmgacaGLOaGaayzkaaGaeyypa0Ja eyOeI0YaaqWaaeaacqaHhpWyaiaawEa7caGLiWoadaahaaWcbeqaai aaigdacqGHRaWkcqaHXoqyaaaaaa@474E@

γ= log 2λ ( 2μ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdCMaey ypa0JaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaikdacqaH7oaBaeqa aOWaaeWaaeaacaaIYaGaeqiVd0gacaGLOaGaayzkaaaaaa@4215@

1 2 μ< 2 π 1 λ π MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGOmaaaacqGHKjYOcqaH8oqBcqGH8aapcaaIYaWaaWba aSqabeaacqaHapaCdaahaaadbeqaaiabgkHiTaaaliabgkHiTiaaig daaaGccqaH7oaBdaahaaWcbeqaaiabec8aWnaaCaaameqabaGaeyOe I0caaaaaaaa@4624@

| υ | π( τ ) >1 | υ | π( τ ) π ρ( υ ) | υ | π( τ ) π + MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaacq aHfpqDaiaawEa7caGLiWoadaWgaaWcbaGaeqiWda3aaeWaaeaacqaH epaDaiaawIcacaGLPaaaaeqaaOGaeyOpa4JaaGymaiabgkDiEpaaem aabaGaeqyXduhacaGLhWUaayjcSdWaa0baaSqaaiabec8aWnaabmaa baGaeqiXdqhacaGLOaGaayzkaaaabaGaeqiWda3aaWbaaWqabeaacq GHsislaaaaaOGaeyizImQaeqyWdi3aaeWaaeaacqaHfpqDaiaawIca caGLPaaacqGHKjYOdaabdaqaaiabew8a1bGaay5bSlaawIa7amaaDa aaleaacqaHapaCdaqadaqaaiabes8a0bGaayjkaiaawMcaaaqaaiab ec8aWnaaCaaameqabaGaey4kaScaaaaaaaa@66AC@

Β Τ 1,π( τ ) = Β ˜ Τ 1,π( τ ) Ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOKdi0aa0 baaSqaaiabfs6aubqaaiaaigdacaGGSaGaeqiWda3aaeWaaeaacqaH epaDaiaawIcacaGLPaaaaaGccqGH9aqpcuqHsoGqgaacamaaDaaale aacqqHKoavaeaacaaIXaGaaiilaiabec8aWnaabmaabaGaeqiXdqha caGLOaGaayzkaaaaaOGaeyyLIuSaeSyhHe6aaWbaaSqabeaacqqHDo Gtaaaaaa@4F54@

υ( χ,τ )= γ 1 ( τ )+ γ 2 ( τ )lnρ+ υ 0 ( χ,τ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aae WaaeaacqaHhpWycaGGSaGaeqiXdqhacaGLOaGaayzkaaGaeyypa0Ja eq4SdC2aaSbaaSqaaiaaigdaaeqaaOWaaeWaaeaacqaHepaDaiaawI cacaGLPaaacqGHRaWkcqaHZoWzdaWgaaWcbaGaaGOmaaqabaGcdaqa daqaaiabes8a0bGaayjkaiaawMcaaiGacYgacaGGUbGaeqyWdiNaey 4kaSIaeqyXdu3aaSbaaSqaaiaaicdaaeqaaOWaaeWaaeaacqaHhpWy caGGSaGaeqiXdqhacaGLOaGaayzkaaaaaa@581A@

| υ 1 |Γ | χ | Im λ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaacq aHfpqDdaWgaaWcbaGaaGymaaqabaaakiaawEa7caGLiWoacqGHKjYO cqqHtoWrdaabdaqaaiabeE8aJbGaay5bSlaawIa7amaaCaaaleqaba Gaciysaiaac2gacqaH7oaBdaWgaaadbaGaaGymaaqabaaaaaaa@4850@

Imλ( τ )=β+α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciysaiaac2 gacqaH7oaBdaqadaqaaiabes8a0bGaayjkaiaawMcaaiabg2da9iab ek7aIjabgUcaRiabeg7aHbaa@41E1@

Im λ Ν 0 ( τ 0 )= β 1 +2μ+ λ 1 ν 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciysaiaac2 gacqaH7oaBdaWgaaWcbaGaeuyNd40aaSbaaWqaaiaaicdaaeqaaaWc beaakmaabmaabaGaeqiXdq3aaSbaaSqaaiaaicdaaeqaaaGccaGLOa GaayzkaaGaeyypa0JaeyOeI0IaeqOSdi2aaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaaGOmaiabeY7aTjabgUcaRiabeU7aSnaaBaaaleaaca aIXaaabeaakiabgkHiTmaalaaabaGaeqyVd4gabaGaaGOmaaaaaaa@4F1B@

φ ^ = κ 0 φ+ Λ 1 υ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqOXdOMbaK aacqGH9aqpcqaH6oWAdaWgaaWcbaGaaGimaaqabaGccqaHgpGAcqGH RaWkcqqHBoatdaWgaaWcbaGaaGymaaqabaGccqaHfpqDaaa@4238@

Λ Σ δ = Α δ + Ρ δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4MdWKaeu 4Odm1aaSbaaSqaaiabes7aKbqabaGccqGH9aqpcqqHroqqdaWgaaWc baGaeqiTdqgabeaakiabgUcaRiabfg6asnaaBaaaleaacqaH0oazae qaaaaa@4340@

ι ( 1 ) μ1 Λυ υ τ =φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyUdK2aae WaaeaacqGHsislcaaIXaaacaGLOaGaayzkaaWaaWbaaSqabeaacqaH 8oqBcqGHsislcaaIXaaaaOGaeu4MdWKaeqyXduNaeyOeI0IaeqyXdu 3aaSbaaSqaaiabes8a0bqabaGccqGH9aqpcqaHgpGAaaa@491A@

χ 0 +χ+ χ 2 + χ 3 + χ 4 + χ 5 + χ 6 ++ χ ν1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaW baaSqabeaacaaIWaaaaOGaey4kaSIaeq4XdmMaey4kaSIaeq4Xdm2a aWbaaSqabeaacaaIYaaaaOGaey4kaSIaeq4Xdm2aaWbaaSqabeaaca aIZaaaaOGaey4kaSIaeq4Xdm2aaWbaaSqabeaacaaI0aaaaOGaey4k aSIaeq4Xdm2aaWbaaSqabeaacaaI1aaaaOGaey4kaSIaeq4Xdm2aaW baaSqabeaacaaI2aaaaOGaey4kaSIaeSOjGSKaey4kaSIaeq4Xdm2a aWbaaSqabeaacqaH9oGBcqGHsislcaaIXaaaaaaa@5528@

( χ+ψ+ζ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHhpWycqGHRaWkcqaHipqEcqGHRaWkcqaH2oGEaiaawIcacaGLPaaa daahaaWcbeqaaiaaikdaaaaaaa@3F6F@

( χ+ψ ) 2 +ζ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHhpWycqGHRaWkcqaHipqEaiaawIcacaGLPaaadaahaaWcbeqaaiaa ikdaaaGccqGHRaWkcqaH2oGEaaa@3F79@

χ+ ( ψ+ζ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey 4kaSYaaeWaaeaacqaHipqEcqGHRaWkcqaH2oGEaiaawIcacaGLPaaa daahaaWcbeqaaiaaikdaaaaaaa@3F6F@

χ+ψ+ ζ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey 4kaSIaeqiYdKNaey4kaSIaeqOTdO3aaWbaaSqabeaacaaIYaaaaaaa @3DE6@

χ 0 + χ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiaaicdaaeqaaOGaey4kaSIaeq4Xdm2aaSbaaSqaaiaaigda aeqaaaaa@3C1E@

χ ˙ + χ ¨ + χ ˜ + χ ^ + χ + χ + χ + χ * MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4XdmMbai aacqGHRaWkcuaHhpWygaWaaiabgUcaRiqbeE8aJzaaiaGaey4kaSIa fq4XdmMbaKaacqGHRaWkcuaHhpWygaGbaiabgUcaRiqbeE8aJzaasa Gaey4kaSIafq4XdmMbauaacqGHRaWkcqaHhpWydaahaaWcbeqaaiaa cQcaaaaaaa@4B1B@

α 1,1 + α 2,2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaW baaSqabeaacaaIXaGaaiilaiaaigdaaaGccqGHRaWkcqaHXoqydaah aaWcbeqaaiaaikdacaGGSaGaaGOmaaaaaaa@3EC9@

υ,υ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaacq aHfpqDcaGGSaGaeqyXduhacaGLPmIaayPkJaWaaSbaaSqaaiabeA8a Qbqabaaaaa@3DEE@

κ α κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabuaeaacq aHXoqydaWgaaWcbaGaeqOUdSgabeaaaeaacqaH6oWAcqGHiiIZcqWI DesOaeqaniabggHiLdaaaa@4032@

ι=1 Ν α 2 +β+ γ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaacq aHXoqydaahaaWcbeqaaiaaikdaaaaabaGaeqyUdKMaeyypa0JaaGym aaqaaiabf25aobqdcqGHris5aOGaey4kaSIaeqOSdiMaey4kaSIaeq 4SdC2aaWbaaSqabeaacaaIYaaaaaaa@459E@

ε ε ε χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaW baaSqabeaacqaH1oqzdaahaaadbeqaaiabew7aLnaaCaaabeqaaiab eE8aJbaaaaaaaaaa@3D20@

ε ε ε χ ε ε χ ε χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaW baaSqabeaacqaH1oqzdaahaaadbeqaaiabew7aLnaaCaaabeqaaiab eE8aJbaaaaaaaOGaeyyXICTaeqyTdu2aaWbaaSqabeaacqaH1oqzda ahaaadbeqaaiabeE8aJbaaaaGccqGHflY1cqaH1oqzdaahaaWcbeqa aiabeE8aJbaaaaa@4AB3@

ε ( ε ε χ + ε χ +χ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaW baaSqabeaadaqadaqaaiabew7aLnaaCaaameqabaGaeqyTdu2aaWba aeqabaGaeq4XdmgaaaaaliabgUcaRiabew7aLnaaCaaameqabaGaeq 4XdmgaaSGaey4kaSIaeq4XdmgacaGLOaGaayzkaaaaaaaa@45C6@

ι=1 ν α ι =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaacq aHXoqydaWgaaWcbaGaeqyUdKgabeaaaeaacqaH5oqAcqGH9aqpcaaI XaaabaGaeqyVd4ganiabggHiLdGccqGH9aqpcaaIXaaaaa@429B@

ι=1 ν α ι + β ι =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaacq aHXoqydaWgaaWcbaGaeqyUdKgabeaakiabgUcaRiabek7aInaaBaaa leaacqaH5oqAaeqaaaqaaiabeM7aPjabg2da9iaaigdaaeaacqaH9o GBa0GaeyyeIuoakiabg2da9iaaigdaaaa@4703@

1+χ+ χ 2 + χ 3 + χ 4 ++ χ ν1 += 1 1+χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgU caRiabeE8aJjabgUcaRiabeE8aJnaaCaaaleqabaGaaGOmaaaakiab gUcaRiabeE8aJnaaCaaaleqabaGaaG4maaaakiabgUcaRiabeE8aJn aaCaaaleqabaGaaGinaaaakiabgUcaRiablAciljabgUcaRiabeE8a JnaaCaaaleqabaGaeqyVd4MaeyOeI0IaaGymaaaakiabgUcaRiablA ciljabg2da9maalaaabaGaaGymaaqaaiaaigdacqGHRaWkcqaHhpWy aaaaaa@534F@

χ χ 2 2 + χ 3 3 χ 4 4 + χ 5 5 ±=log( 1+χ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey OeI0YaaSaaaeaacqaHhpWydaahaaWcbeqaaiaaikdaaaaakeaacaaI YaaaaiabgUcaRmaalaaabaGaeq4Xdm2aaWbaaSqabeaacaaIZaaaaa GcbaGaaG4maaaacqGHsisldaWcaaqaaiabeE8aJnaaCaaaleqabaGa aGinaaaaaOqaaiaaisdaaaGaey4kaSYaaSaaaeaacqaHhpWydaahaa WcbeqaaiaaiwdaaaaakeaacaaI1aaaaiabgglaXkablAciljabg2da 9iGacYgacaGGVbGaai4zamaabmaabaGaaGymaiabgUcaRiabeE8aJb GaayjkaiaawMcaaaaa@54F3@

( α+β ) 3 = α 3 +3 α 2 β+3α β 2 + β 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHXoqycqGHRaWkcqaHYoGyaiaawIcacaGLPaaadaahaaWcbeqaaiaa iodaaaGccqGH9aqpcqaHXoqydaahaaWcbeqaaiaaiodaaaGccqGHRa WkcaaIZaGaeyyXICTaeqySde2aaWbaaSqabeaacaaIYaaaaOGaeyyX ICTaeqOSdiMaey4kaSIaaG4maiabgwSixlabeg7aHjabgwSixlabek 7aInaaCaaaleqabaGaaGOmaaaakiabgUcaRiabek7aInaaCaaaleqa baGaaG4maaaaaaa@5868@

χ 1 κ + χ 2 κ + χ 3 κ ++ χ ν κ =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aa0 baaSqaaiaaigdaaeaacqaH6oWAaaGccqGHRaWkcqaHhpWydaqhaaWc baGaaGOmaaqaaiabeQ7aRbaakiabgUcaRiabeE8aJnaaDaaaleaaca aIZaaabaGaeqOUdSgaaOGaey4kaSIaeSOjGSKaey4kaSIaeq4Xdm2a a0baaSqaaiabe27aUbqaaiabeQ7aRbaakiabg2da9iaaicdaaaa@4ECD@

χ κ 1 + χ κ 2 + χ κ 3 + χ κ ν =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiabeQ7aRnaaCaaameqabaGaaGymaaaaaSqabaGccqGHRaWk cqaHhpWydaWgaaWcbaGaeqOUdS2aaWbaaWqabeaacaaIYaaaaaWcbe aakiabgUcaRiabeE8aJnaaBaaaleaacqaH6oWAdaahaaadbeqaaiaa iodaaaaaleqaaOGaey4kaSIaeSOjGSKaeq4Xdm2aaSbaaSqaaiabeQ 7aRnaaCaaameqabaGaeqyVd4gaaaWcbeaakiabg2da9iaaicdaaaa@4ECB@

χ κ 1 + χ κ 2 + χ κ 3 ++ χ κ ν =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiabeQ7aRnaaBaaameaacaaIXaaabeaaaSqabaGccqGHRaWk cqaHhpWydaWgaaWcbaGaeqOUdS2aaSbaaWqaaiaaikdaaeqaaaWcbe aakiabgUcaRiabeE8aJnaaBaaaleaacqaH6oWAdaWgaaadbaGaaG4m aaqabaaaleqaaOGaey4kaSIaeSOjGSKaey4kaSIaeq4Xdm2aaSbaaS qaaiabeQ7aRnaaBaaameaacqaH9oGBaeqaaaWcbeaakiabg2da9iaa icdaaaa@4FA9@

χ 2 ψ χ 2 ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaW baaSqabeaacaaIYaWaaWbaaWqabeaacqaHipqEaaaaaOGaeyiyIKRa eq4Xdm2aaWbaaSqabeaacaaIYaWaaWbaaWqabeaacqaHipqEaaaaaa aa@4100@

α χ 2 +βχ+γ=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey yXICTaeq4Xdm2aaWbaaSqabeaacaaIYaaaaOGaey4kaSIaeqOSdiMa eyyXICTaeq4XdmMaey4kaSIaeq4SdCMaeyypa0JaaGimaaaa@4757@                       

log3 (χ+ψ) 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ gacaGGNbGaaG4maiaacIcacqaHhpWycqGHRaWkcqaHipqEcaGGPaWa aWbaaSqabeaacaaIZaaaaaaa@402E@

log 2 χ2logχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ gacaGGNbWaaWbaaSqabeaacaaIYaaaaOGaeq4XdmMaeyiyIKRaaGOm aiabgwSixlGacYgacaGGVbGaai4zaiabeE8aJbaa@44C5@

logχ logα = log α χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGSbGaai4BaiaacEgacqaHhpWyaeaaciGGSbGaai4BaiaacEgacqaH XoqyaaGaeyypa0JaciiBaiaac+gacaGGNbWaaSbaaSqaaiabeg7aHb qabaGccqaHhpWyaaa@465F@

χ ¯ +χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4XdmMbae bacqGHRaWkcqaHhpWyaaa@3A5F@

arg( ζ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyyaiaack hacaGGNbWaaeWaaeaacqaH2oGEaiaawIcacaGLPaaaaaa@3C05@

 

4.2       Complex

υ ( 0 ) = ζ=1 ν ξ ζ ( 1 ) ρ ζ ( υ ( ι ) ) = ζ=1 ν ξ ζ ( 2 ) ρ ζ ( υ ( 2 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaW baaSqabeaadaqadaqaaiaaicdaaiaawIcacaGLPaaaaaGccqGH9aqp daaeWbqaaiabe67a4naaBaaaleaacqaH2oGEaeqaaOWaaWbaaSqabe aadaqadaqaaiaaigdaaiaawIcacaGLPaaaaaGccqaHbpGCdaWgaaWc baGaeqOTdOhabeaakmaabmaabaGaeqyXdu3aaWbaaSqabeaadaqada qaaiabeM7aPbGaayjkaiaawMcaaaaaaOGaayjkaiaawMcaaaWcbaGa eqOTdONaeyypa0JaaGymaaqaaiabe27aUbqdcqGHris5aOGaeyypa0 ZaaabCaeaacqaH+oaEdaWgaaWcbaGaeqOTdOhabeaakmaaCaaaleqa baWaaeWaaeaacaaIYaaacaGLOaGaayzkaaaaaOGaeqyWdi3aaSbaaS qaaiabeA7a6bqabaGcdaqadaqaaiabew8a1naaCaaaleqabaWaaeWa aeaacaaIYaaacaGLOaGaayzkaaaaaaGccaGLOaGaayzkaaaaleaacq aH2oGEcqGH9aqpcaaIXaaabaGaeqyVd4ganiabggHiLdaaaa@6B92@

| υ | = ορισμος ( κ=1 ν υ κ 2 ) 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaacq aHfpqDaiaawEa7caGLiWoadaWfGaqaaiabg2da9aWcbeqaaiabe+7a Vjabeg8aYjabeM7aPjabeo8aZjabeY7aTjabe+7aVjabek8awbaakm aabmaabaWaaabCaeaacqaHfpqDdaqhaaWcbaGaeqOUdSgabaGaaGOm aaaaaeaacqaH6oWAcqGH9aqpcaaIXaaabaGaeqyVd4ganiabggHiLd aakiaawIcacaGLPaaadaahaaWcbeqaamaalaaabaGaaGymaaqaaiaa ikdaaaaaaaaa@5747@

0 | ξ ι ( 1 ) ( τ,χ ) |dχ Γ( φ ( 0 ) Λ 1 ( + ) + α ( 0 ) Λ 1 ( + ) + η ( 0 ) Λ 1 ( + ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWdXb qaamaaemaabaGaeqOVdG3aaSbaaSqaaiabeM7aPbqabaGcdaahaaWc beqaamaabmaabaGaaGymaaGaayjkaiaawMcaaaaakmaabmaabaGaeq iXdqNaaiilaiabeE8aJbGaayjkaiaawMcaaaGaay5bSlaawIa7aiaa dsgacqaHhpWyaSqaaiaaicdaaeaacqGHEisPa0Gaey4kIipakiabgs MiJcqaaiabfo5ahnaabmaabaWaauWaaeaacqaHgpGAdaahaaWcbeqa amaabmaabaGaaGimaaGaayjkaiaawMcaaaaaaOGaayzcSlaawQa7am aaBaaaleaacqqHBoatdaahaaadbeqaaiaaigdaaaWcdaqadaqaaiab l2riHoaaCaaameqabaGaey4kaScaaaWccaGLOaGaayzkaaaabeaaki abgUcaRmaafmaabaGaeqySde2aaWbaaSqabeaadaqadaqaaiaaicda aiaawIcacaGLPaaaaaaakiaawMa7caGLkWoadaWgaaWcbaGaeu4MdW 0aaWbaaWqabeaacaaIXaaaaSWaaeWaaeaacqWIDesOdaahaaadbeqa aiabgUcaRaaaaSGaayjkaiaawMcaaaqabaGccqGHRaWkdaqbdaqaai abeE7aOnaaCaaaleqabaWaaeWaaeaacaaIWaaacaGLOaGaayzkaaaa aaGccaGLjWUaayPcSdWaaSbaaSqaaiabfU5amnaaCaaameqabaGaaG ymaaaalmaabmaabaGaeSyhHe6aaWbaaWqabeaacqGHRaWkaaaaliaa wIcacaGLPaaaaeqaaaGccaGLOaGaayzkaaaaaaa@7CA4@

Β ˜ 1 ( Τ )= max ι=1,ν max ξι sup Γ ξ Γ ξ | υ ι |dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuOKdiKbaG aadaWgaaWcbaGaaGymaaqabaGcdaqadaqaaiabfs6aubGaayjkaiaa wMcaaiabg2da9maaxababaGaciyBaiaacggacaGG4baaleaacqaH5o qAcqGH9aqpcaaIXaGaaiilaiablAciljabe27aUbqabaGcdaWfqaqa aiGac2gacaGGHbGaaiiEaaWcbaGaeqOVdGNaeyiyIKRaeqyUdKgabe aakmaaxababaGaci4CaiaacwhacaGGWbaaleaacqqHtoWrdaWgaaad baGaeqOVdGhabeaaaSqabaGcdaWdrbqaamaaemaabaGaeqyXdu3aaS baaSqaaiabeM7aPbqabaaakiaawEa7caGLiWoacaWGKbGaeqiXdqha leaacqqHtoWrdaWgaaadbaGaeqOVdGhabeaaaSqab0Gaey4kIipaaa a@6484@

{ ε λ } λ=1 ν+μ2κ ={ { ε ι } ιΑ , { ε ξ } ξ Α } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaacq aH1oqzdaWgaaWcbaGaeq4UdWgabeaakmaaCaaaleqabaGccWaGGBOm Gi6ccaaMb8UccWaGGBOmGikaaaGaay5Eaiaaw2haamaaDaaaleaacq aH7oaBcqGH9aqpcaaIXaaabaGaeqyVd4Maey4kaSIaeqiVd0MaeyOe I0IaaGOmaiabeQ7aRbaakiabg2da9maacmaabaWaaiWaaeaacqaH1o qzdaWgaaWcbaGaeqyUdKgabeaaaOGaay5Eaiaaw2haamaaBaaaleaa cqaH5oqAcqGHjiYZcqqHroqqaeqaaOGaaiilamaacmaabaGaeqyTdu 2aaSbaaSqaaiabe67a4bqabaGcdaahaaWcbeqaaOGamai4gkdiIcaa aiaawUhacaGL9baadaWgaaWcbaGaeqOVdGNaeyycI8SafuyKdeKbau aaaeqaaaGccaGL7bGaayzFaaaaaa@6B00@

υ ε (ν+1,μ+1) υ+ κ=1 ν ψ κ υ κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey4bIeTaeq yXdu3aaSbaaSqaaiabew7aLbqabaGcdaGdKaWcbaGaaiikaiabe27a UjabgUcaRiaaigdacaGGSaGaeqiVd0Maey4kaSIaaGymaiaacMcaae qakiaawkziaiabgEGirlabew8a1jabgUcaRmaaqahabaGaey4bIe9a aSbaaSqaaiabeI8a5naaBaaameaacqaH6oWAaeqaaaWcbeaakiabew 8a1naaBaaaleaacqaH6oWAaeqaaaqaaiabeQ7aRjabg2da9iaaigda aeaacqaH9oGBa0GaeyyeIuoaaaa@5A14@

wsep,1 μκ ={ ( ε, { ε ξ } ξ=1 μ ) wsep μκ : ε 2 ε μ 0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyyeHe8aa0 baaSqaaiaadEhacaWGZbGaamyzaiaadchacaGGSaGaaGymaaqaaiab eY7aTjablYJi6iabeQ7aRbaakiabg2da9maacmaabaWaaeWaaeaacq aH1oqzcaGGSaWaaiWaaeaacuaH1oqzgaqbamaaBaaaleaacqaH+oaE aeqaaaGccaGL7bGaayzFaaWaa0baaSqaaiabe67a4jabg2da9iaaig daaeaacqaH8oqBaaaakiaawIcacaGLPaaacqGHiiIZcqGHresWdaqh aaWcbaGaam4DaiaadohacaWGLbGaamiCaaqaaiabeY7aTjablYJi6i abeQ7aRbaakiaacQdadaWcaaqaaiabew7aLnaaCaaaleqabaGaaGOm aaaaaOqaaiabew7aLnaaBaaaleaacqaH8oqBaeqaaOWaaWbaaSqabe aakiadacUHYaIOaaaaaiabgkziUkaaicdaaiaawUhacaGL9baaaaa@6C40@

ε 1 ={ ε,{ ε 0,2 , ε 0,5 ,ε, ε 1,2 , ε 1,5 | logε | } } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaigdaaeqaaOGaeyypa0ZaaiWaaeaacqaH1oqzcaGGSaWa aiWaaeaacqaH1oqzdaahaaWcbeqaaiaaicdacaGGSaGaaGOmaaaaki aacYcacqaH1oqzdaahaaWcbeqaaiaaicdacaGGSaGaaGynaaaakiaa cYcacqaH1oqzcaGGSaGaeqyTdu2aaWbaaSqabeaacaaIXaGaaiilai aaikdaaaGccaGGSaWaaSaaaeaacqaH1oqzdaahaaWcbeqaaiaaigda caGGSaGaaGynaaaaaOqaamaaemaabaGaciiBaiaac+gacaGGNbGaeq yTdugacaGLhWUaayjcSdaaaaGaay5Eaiaaw2haaaGaay5Eaiaaw2ha aaaa@5C76@

υ μ ν + ν μ ν +κ d υ μ ν dχ =κ× φ μ ν + υ μ ν1 + ν μ ν1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aa0 baaSqaaiabeY7aTbqaaiabe27aUbaakiabgUcaRiabe27aUnaaDaaa leaacqaH8oqBaeaacqaH9oGBaaGccqGHRaWkcqaH6oWAdaWcaaqaai aadsgacqaHfpqDdaqhaaWcbaGaeqiVd0gabaGaeqyVd4gaaaGcbaGa amizaiabeE8aJbaacqGH9aqpcqaH6oWAcqGHxdaTcqaHgpGAdaqhaa WcbaGaeqiVd0gabaGaeqyVd4gaaOGaey4kaSIaeqyXdu3aa0baaSqa aiabeY7aTbqaaiabe27aUjabgkHiTiaaigdaaaGccqGHRaWkcqaH9o GBdaqhaaWcbaGaeqiVd0gabaGaeqyVd4MaeyOeI0IaaGymaaaaaaa@673F@

Ω | κ μ ξ | 2 dχ+κ ν=1 ξ | κ μ ν | 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8quaeaada abdaqaaiabeQ7aRnaaDaaaleaacqaH8oqBaeaacqaH+oaEaaaakiaa wEa7caGLiWoadaahaaWcbeqaaiaaikdaaaGccaWGKbGaeq4XdmMaey 4kaSIaeqOUdS2aaabCaeaadaabdaqaaiabeQ7aRnaaDaaaleaacqaH 8oqBaeaacqaH9oGBaaaakiaawEa7caGLiWoadaahaaWcbeqaaiaaik daaaaabaGaeqyVd4Maeyypa0JaaGymaaqaaiabe67a4bqdcqGHris5 aaWcbaGaeuyQdCfabeqdcqGHRiI8aaaa@594F@

sgn ξΙ( δ 1 , δ 2 ) α ξ Γ ι 1 ε ξ dχ =sgn ξΙ( δ 1 , δ 2 ) α ξ Γ ι 2 ε ξ dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacE gacaGGUbWaaabuaeaacqaHXoqydaWgaaWcbaGaeqOVdGhabeaakmaa pefabaGaeqyTdu2aaSbaaSqaaiabe67a4bqabaGccaWGKbGaeq4Xdm galeaacqqHtoWrdaWgaaadbaGaeqyUdK2aaSbaaeaacaaIXaaabeaa aeqaaaWcbeqdcqGHRiI8aaWcbaGaeqOVdGNaeyicI4SaeuyMdK0aae WaaeaacqaH0oazdaWgaaadbaGaaGymaaqabaWccaGGSaGaeqiTdq2a aSbaaWqaaiaaikdaaeqaaaWccaGLOaGaayzkaaaabeqdcqGHris5aO Gaeyypa0JaeyOeI0Iaci4CaiaacEgacaGGUbWaaabuaeaacqaHXoqy daWgaaWcbaGaeqOVdGhabeaakmaapefabaGaeqyTdu2aaSbaaSqaai abe67a4bqabaGccaWGKbGaeq4XdmgaleaacqqHtoWrdaWgaaadbaGa eqyUdK2aaSbaaeaacaaIYaaabeaaaeqaaaWcbeqdcqGHRiI8aaWcba GaeqOVdGNaeyicI4SaeuyMdK0aaeWaaeaacqaH0oazdaWgaaadbaGa aGymaaqabaWccaGGSaGaeqiTdq2aaSbaaWqaaiaaikdaaeqaaaWcca GLOaGaayzkaaaabeqdcqGHris5aaaa@7AC3@

φ( Φ σ κ )= φ( Φ σ κ ) φ κ ( Φ σ κ ) 0 + φ κ ( Φ σ κ ) χ κ χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdO2aae WaaeaacqqHMoGrdaqhaaWcbaGaeq4WdmhabaGaeqOUdSgaaaGccaGL OaGaayzkaaGaeyypa0ZaaGbaaeaacqaHgpGAdaqadaqaaiabfA6agn aaDaaaleaacqaHdpWCaeaacqaH6oWAaaaakiaawIcacaGLPaaacqGH sislcqaHgpGAdaWgaaWcbaGaeqOUdSgabeaakmaabmaabaGaeuOPdy 0aa0baaSqaaiabeo8aZbqaaiabeQ7aRbaaaOGaayjkaiaawMcaaaWc baWaa4akaWqabeaacqGHsgIRaSGaayPKHaGaaGimaaGccaGL44pacq GHRaWkdaagaaqaaiabeA8aQnaaBaaaleaacqaH6oWAaeqaaOWaaeWa aeaacqqHMoGrdaqhaaWcbaGaeq4WdmhabaGaeqOUdSgaaaGccaGLOa GaayzkaaaaleaacqaHhpWydaahaaadbeqaaiabeQ7aRbaaaOGaayjo +dGaeyOKH4Qaeq4Xdmgaaa@6DCC@

φ(χ)=φ(α)+φ'(α)×(χα)++ φ ν (α) ν × (χα) ν + φ (ν+1) ( γ ) ν+1 × ( χα ) (ν+1) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdOMaai ikaiabeE8aJjaacMcacqGH9aqpcqaHgpGAcaGGOaGaeqySdeMaaiyk aiabgUcaRiabeA8aQjaacEcacaGGOaGaeqySdeMaaiykaiabgEna0k aacIcacqaHhpWycqGHsislcqaHXoqycaGGPaGaey4kaSIaeSOjGSKa ey4kaSYaaSaaaeaacqaHgpGAdaahaaWcbeqaaiabe27aUbaakiaacI cacqaHXoqycaGGPaaabaGaeqyVd4gaaiabgEna0kaacIcacqaHhpWy cqGHsislcqaHXoqycaGGPaWaaWbaaSqabeaacqaH9oGBaaGccqGHRa WkdaWcaaqaaiabeA8aQnaaCaaaleqabaGaaiikaiabe27aUjabgUca RiaaigdacaGGPaaaaOWaaeWaaeaacqaHZoWzaiaawIcacaGLPaaaae aacqaH9oGBcqGHRaWkcaaIXaaaaiabgEna0oaabmaabaGaeq4XdmMa eyOeI0IaeqySdegacaGLOaGaayzkaaWaaWbaaSqabeaacaGGOaGaeq yVd4Maey4kaSIaaGymaiaacMcaaaaaaa@7E3F@

2 υ χψ =( χ 2 ψ 2 )×{ τ×φ"(τ)+3×φ'(τ) } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITdaahaaWcbeqaaiaaikdaaaGccqaHfpqDaeaacqGHciITcqaH hpWycqGHciITcqaHipqEaaGaeyypa0ZaaeWaaeaacqaHhpWydaahaa WcbeqaaiaaikdaaaGccqGHsislcqaHipqEdaahaaWcbeqaaiaaikda aaaakiaawIcacaGLPaaacqGHxdaTdaGadaqaaiabes8a0jabgEna0k abeA8aQjaackcacaGGOaGaeqiXdqNaaiykaiabgUcaRiaaiodacqGH xdaTcqaHgpGAcaGGNaGaaiikaiabes8a0jaacMcaaiaawUhacaGL9b aaaaa@6040@

log( 1+χ )log( 1χ )=log 1+χ 1χ = ι=1 χ 2ι1 2ι1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ gacaGGNbWaaeWaaeaacaaIXaGaey4kaSIaeq4XdmgacaGLOaGaayzk aaGaeyOeI0IaciiBaiaac+gacaGGNbWaaeWaaeaacaaIXaGaeyOeI0 Iaeq4XdmgacaGLOaGaayzkaaGaeyypa0JaciiBaiaac+gacaGGNbWa aSaaaeaacaaIXaGaey4kaSIaeq4XdmgabaGaaGymaiabgkHiTiabeE 8aJbaacqGH9aqpdaaeWbqaamaalaaabaGaeq4Xdm2aaWbaaSqabeaa caaIYaGaeyyXICTaeqyUdKMaeyOeI0IaaGymaaaaaOqaaiaaikdacq GHflY1cqaH5oqAcqGHsislcaaIXaaaaaWcbaGaeqyUdKMaeyypa0Ja aGymaaqaaiabg6HiLcqdcqGHris5aaaa@67C3@

Δ χ ν ω= 0λν κ 1 ++ κ ν =λ κ 1 +2 κ 2 ++ν κ ν =ν κ 1 ,, κ ν 0 Δ υ λ ω× n! ( Δ χ 1 υ ) κ 1 ( Δ χ ν υ ) κ ν κ 1 ! (1!) κ 1 κ ν ! ( ν! ) κ ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdq0aa0 baaSqaaiabeE8aJbqaaiabe27aUbaakiabeM8a3jabg2da9maaqaba baWaaabeaeaacqqHuoardaqhaaWcbaGaeqyXduhabaGaeq4UdWgaaO GaeqyYdCNaey41aq7aaSaaaeaacaWGUbGaaiyiamaabmaabaGaeuiL dq0aa0baaSqaaiabeE8aJbqaaiaaigdaaaGccqaHfpqDaiaawIcaca GLPaaadaahaaWcbeqaaiabeQ7aRnaaCaaameqabaGaaGymaaaaaaGc cqWIMaYsdaqadaqaaiabfs5aenaaDaaaleaacqaHhpWyaeaacqaH9o GBaaGccqaHfpqDaiaawIcacaGLPaaadaahaaWcbeqaaiabeQ7aRnaa BaaameaacqaH9oGBaeqaaaaaaOqaaiabeQ7aRnaaBaaaleaacaaIXa aabeaakiaacgcacaGGOaGaaGymaiaacgcacaGGPaWaaWbaaSqabeaa cqaH6oWAdaWgaaadbaGaaGymaaqabaaaaOGaeSOjGSKaeqOUdS2aaS baaSqaaiabe27aUbqabaGccaGGHaWaaeWaaeaacqaH9oGBcaGGHaaa caGLOaGaayzkaaWaaWbaaSqabeaacqaH6oWAdaWgaaadbaGaeqyVd4 gabeaaaaaaaaWceaqabeaacqaH6oWAdaWgaaadbaGaaGymaaqabaWc cqGHRaWkcqWIMaYscqGHRaWkcqaH6oWAdaWgaaadbaGaeqyVd4gabe aaliabg2da9iabeU7aSbqaaiabeQ7aRnaaBaaameaacaaIXaaabeaa liabgUcaRiaaikdacqaH6oWAdaWgaaadbaGaaGOmaaqabaWccqGHRa WkcqWIMaYscqGHRaWkcqaH9oGBcqaH6oWAdaWgaaadbaGaeqyVd4ga beaaliabg2da9iabe27aUbqaaiabeQ7aRnaaBaaameaacaaIXaaabe aaliaacYcacqWIMaYscaGGSaGaeqOUdS2aaSbaaWqaaiabe27aUbqa baWccqGHLjYScaaIWaaaaeqaniabggHiLdaaleaacaaIWaGaeyizIm Qaeq4UdWMaeyizImQaeqyVd4gabeqdcqGHris5aaaa@AA4F@

1ιν α ι =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabeaeaacq aHXoqydaWgaaWcbaGaeqyUdKgabeaaaeaacaaIXaGaeyizImQaeqyU dKMaeyizImQaeqyVd4gabeqdcqGHris5aOGaeyypa0JaaGymaaaa@44A0@

κ=1 ( 1 ) κ+1 ( κ+1 )×ln(κ+1) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaada WcaaqaamaabmaabaGaeyOeI0IaaGymaaGaayjkaiaawMcaamaaCaaa leqabaGaeqOUdSMaey4kaSIaaGymaaaaaOqaamaabmaabaGaeqOUdS Maey4kaSIaaGymaaGaayjkaiaawMcaaiabgEna0kGacYgacaGGUbGa aiikaiabeQ7aRjabgUcaRiaaigdacaGGPaaaaaWcbaGaeqOUdSMaey ypa0JaaGymaaqaaiabg6HiLcqdcqGHris5aaaa@515F@

κ=11 28 (κ10)×sin[ π κ10 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaaca GGOaGaeqOUdSMaeyOeI0IaaGymaiaaicdacaGGPaGaey41aqRaci4C aiaacMgacaGGUbWaamWaaeaadaWcaaqaaiabec8aWbqaaiabeQ7aRj abgkHiTiaaigdacaaIWaaaaaGaay5waiaaw2faaaWcbaGaeqOUdSMa eyypa0JaaGymaiaaigdaaeaacaaIYaGaaGioaaqdcqGHris5aaaa@5014@

 

 

5.    Integrals

5.1       Simple

0 Τ Φ 2 ( τ,χ )dτ Δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaacq qHMoGrdaWgaaWcbaGaaGOmaaqabaGcdaqadaqaaiabes8a0jaacYca cqaHhpWyaiaawIcacaGLPaaacaWGKbGaeqiXdqhaleaacaaIWaaaba GaeuiPdqfaniabgUIiYdGccqGHLjYScqqHuoaraaa@48A5@

0 Τ η( τ )dτ =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaacq aH3oaAdaqadaqaaiabes8a0bGaayjkaiaawMcaaiaadsgacqaHepaD aSqaaiaaicdaaeaacqqHKoava0Gaey4kIipakiabg2da9iaaicdaaa a@4412@

υ Δ,υ 0 Φ = ΚΜ υ Κ Κ Δ υ 0 ( χ )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaacq aHfpqDdaqhaaWcbaGaeuiLdqKaaiilaiabew8a1bqaaiaaicdaaaaa kiaawMYicaGLQmcadaWgaaWcbaGaeuOPdyeabeaakiabg2da9iabgk HiTmaaqafabaGaeqyXdu3aaSbaaSqaaiabfQ5albqabaGcdaWdrbqa aiabgs5aejabew8a1naaCaaaleqabaGaaGimaaaakmaabmaabaGaeq 4XdmgacaGLOaGaayzkaaGaamizaiabeE8aJbWcbaGaeuOMdSeabeqd cqGHRiI8aaWcbaGaeuOMdSKaeyicI4SaeuiNd0eabeqdcqGHris5aa aa@59BC@

υ τ ,υ + Ω υ( χ,τ )×υ( χ )dχ = Ω φ( χ,τ )υ( χ )dχ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaaada qaaiabew8a1naaBaaaleaacqaHepaDaeqaaOGaaiilaiabew8a1bGa ayzkJiaawQYiaiabgUcaRmaapefabaGaey4bIeTaeqyXdu3aaeWaae aacqaHhpWycaGGSaGaeqiXdqhacaGLOaGaayzkaaGaey41aqRaey4b IeTaeqyXdu3aaeWaaeaacqaHhpWyaiaawIcacaGLPaaacaWGKbGaeq 4XdmgaleaacqGHPoWvaeqaniabgUIiYdaakeaacqGH9aqpdaWdrbqa aiabeA8aQnaabmaabaGaeq4XdmMaaiilaiabes8a0bGaayjkaiaawM caaiabew8a1naabmaabaGaeq4XdmgacaGLOaGaayzkaaGaamizaiab eE8aJbWcbaGaeyyQdCfabeqdcqGHRiI8aaaaaa@6B09@

α( β,υ )= Ω β( χ )υ( χ )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqaHYoGycaGGSaGaeqyXduhacaGLOaGaayzkaaGaeyypa0Za a8quaeaacqGHhis0cqaHYoGydaqadaqaaiabeE8aJbGaayjkaiaawM caaiabgwSixlabgEGirlabew8a1naabmaabaGaeq4XdmgacaGLOaGa ayzkaaGaamizaiabeE8aJbWcbaGaeuyQdCfabeqdcqGHRiI8aaaa@53F3@

Ω φ( χ,τ )υ( χ )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8quaeaacq aHgpGAdaqadaqaaiabeE8aJjaacYcacqaHepaDaiaawIcacaGLPaaa cqaHfpqDdaqadaqaaiabeE8aJbGaayjkaiaawMcaaiaadsgacqaHhp WyaSqaaiabfM6axbqab0Gaey4kIipaaaa@48E8@

Κ ( υ( χ, τ ν+1 )υ( χ, τ ν ) )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8quaeaada qadaqaaiabew8a1naabmaabaGaeq4XdmMaaiilaiabes8a0naaBaaa leaacqaH9oGBcqGHRaWkcaaIXaaabeaaaOGaayjkaiaawMcaaiabgk HiTiabew8a1naabmaabaGaeq4XdmMaaiilaiabes8a0naaBaaaleaa cqaH9oGBaeqaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaGaamizai abeE8aJbWcbaGaeuOMdSeabeqdcqGHRiI8aaaa@533B@

Κ Δ υ 0 ( χ )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa8 quaeaacqGHuoarcqaHfpqDdaahaaWcbeqaaiaaicdaaaGcdaqadaqa aiabeE8aJbGaayjkaiaawMcaaiaadsgacqaHhpWyaSqaaiabfQ5alb qab0Gaey4kIipaaaa@44A0@

Λ Κ, σ = Κ, σ Ιdχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4MdW0aaS baaSqaaiabfQ5aljaacYcacuaHdpWCgaGbaaqabaGccqGH9aqpdaWd rbqaaiabfM5ajjaadsgacqaHhpWyaSqaaiabfQ5aljaacYcacuaHdp WCgaGbaaqab0Gaey4kIipaaaa@46E8@

τ ν τ ν+1 Δυ( χ,τ )dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaacq GHuoarcqaHfpqDdaqadaqaaiabeE8aJjaacYcacqaHepaDaiaawIca caGLPaaacaWGKbGaeqiXdqhaleaacqaHepaDdaWgaaadbaGaeqyVd4 gabeaaaSqaaiabes8a0naaBaaameaacqaH9oGBcqGHRaWkcaaIXaaa beaaa0Gaey4kIipaaaa@4CED@

0 Τ | υ( τ ) | 2 dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada abdaqaaiabew8a1naabmaabaGaeqiXdqhacaGLOaGaayzkaaaacaGL hWUaayjcSdWaaWbaaSqabeaacaaIYaaaaOGaamizaiabes8a0bWcba GaaGimaaqaaiabfs6aubqdcqGHRiI8aaaa@4678@

0 Τ | υ ˙ ( τ ) | 2 dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada abdaqaaiqbew8a1zaacaWaaeWaaeaacqaHepaDaiaawIcacaGLPaaa aiaawEa7caGLiWoadaahaaWcbeqaaiaaikdaaaGccaWGKbGaeqiXdq haleaacaaIWaaabaGaeuiPdqfaniabgUIiYdaaaa@4681@

0 Τ υ φdτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaacu aHfpqDgaqbaiabeA8aQjaadsgacqaHepaDaSqaaiaaicdaaeaacqqH Koava0Gaey4kIipaaaa@40DE@

0 Τ | υ ˜ ( τ ) | π dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada abdaqaaiqbew8a1zaaiaWaaeWaaeaacqaHepaDaiaawIcacaGLPaaa aiaawEa7caGLiWoadaahaaWcbeqaaiabec8aWnaaCaaameqabaGaey OeI0caaaaakiaadsgacqaHepaDaSqaaiaaicdaaeaacqqHKoava0Ga ey4kIipaaaa@48A3@

0 Τ Φ( τ,χ )dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaacq qHMoGrdaqadaqaaiabes8a0jaacYcacqaHhpWyaiaawIcacaGLPaaa caWGKbGaeqiXdqhaleaacaaIWaaabaGaeuiPdqfaniabgUIiYdGccq GHsgIRcqGHEisPaaa@47E5@

0 Τ 0 1 γ( τ )| υ( τ ) |dσ dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada WdXbqaaiabeo7aNnaabmaabaGaeqiXdqhacaGLOaGaayzkaaWaaqWa aeaacqaHfpqDdaqadaqaaiabes8a0bGaayjkaiaawMcaaaGaay5bSl aawIa7aiaadsgacqaHdpWCaSqaaiaaicdaaeaacaaIXaaaniabgUIi YdGccaWGKbGaeqiXdqhaleaacaaIWaaabaGaeuiPdqfaniabgUIiYd aaaa@510E@

1 μ 0 Τ Φ 1 ( τ,λ υ ¯ )dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaeqiVd0gaamaapehabaGaeuOPdy0aaSbaaSqaaiaaigda aeqaaOWaaeWaaeaacqaHepaDcaGGSaGaeq4UdWMafqyXduNbaebaai aawIcacaGLPaaacaWGKbGaeqiXdqhaleaacaaIWaaabaGaeuiPdqfa niabgUIiYdaaaa@49CB@

Ω ρ 2 dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8quaeaacq aHbpGCdaahaaWcbeqaaiabgkHiTiaaikdaaaGccaWGKbGaeq4Xdmga leaacqqHPoWvaeqaniabgUIiYdaaaa@400F@

1 6 σ 1 σ( 3 σ 2 )η( σ )α( σ )dσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGOnaaaadaWdXbqaaiabeo8aZnaabmaabaGaaG4maiab gkHiTiabeo8aZnaaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaai abeE7aOnaabmaabaGaeq4WdmhacaGLOaGaayzkaaGaeqySde2aaeWa aeaacqaHdpWCaiaawIcacaGLPaaacaWGKbGaeq4WdmhaleaacqaHdp WCaeaacaaIXaaaniabgUIiYdaaaa@50A4@

λ max 0τ1 0 1 Γ( τ,σ )η( σ )ψ( σ,β )dσ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdW2aaC beaeaaciGGTbGaaiyyaiaacIhaaSqaaiaaicdacqGHKjYOcqaHepaD cqGHKjYOcaaIXaaabeaakmaapehabaGaeu4KdC0aaeWaaeaacqaHep aDcaGGSaGaeq4WdmhacaGLOaGaayzkaaGaeq4TdG2aaeWaaeaacqaH dpWCaiaawIcacaGLPaaacqaHipqEdaqadaqaaiabeo8aZjaacYcacq aHYoGyaiaawIcacaGLPaaacaWGKbGaeq4WdmhaleaacaaIWaaabaGa aGymaaqdcqGHRiI8aaaa@5B7B@

1 2 λ sup υΥ( ρ ) 0 1 | υ( σ ) |dσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaaGOmaaaacqaH7oaBdaWfqaqaaiGacohacaGG1bGaaiiC aaWcbaGaeqyXduNaeyicI4SaeuyPdu1aaeWaaeaacqaHbpGCaiaawI cacaGLPaaaaeqaaOWaa8qCaeaadaabdaqaaiabew8a1naabmaabaGa eq4WdmhacaGLOaGaayzkaaaacaGLhWUaayjcSdGaamizaiabeo8aZb WcbaGaaGimaaqaaiaaigdaa0Gaey4kIipaaaa@5336@

0 1 τ Ξ( τ,σ )υ( σ )dσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada WcaaqaaiabgkGi2cqaaiabgkGi2kabes8a0baacqqHEoawdaqadaqa aiabes8a0jaacYcacqaHdpWCaiaawIcacaGLPaaacqaHfpqDdaqada qaaiabeo8aZbGaayjkaiaawMcaaiaadsgacqaHdpWCaSqaaiaaicda aeaacaaIXaaaniabgUIiYdaaaa@4D7A@

τ 1 υ σdσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada qbdaqaaiqbew8a1zaagaaacaGLjWUaayPcSdGaeq4WdmNaamizaiab eo8aZbWcbaGaeqiXdqhabaGaaGymaaqdcqGHRiI8aaaa@444A@

Η η ( χ+2 )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8quaeaacq aH3oaAaSqaaiabfE5aibqab0Gaey4kIipakmaabmaabaGaeq4XdmMa ey4kaSIaaGOmaaGaayjkaiaawMcaaiaadsgacqaHhpWyaaa@42E2@

1 ε χ 2 χ1 dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qmaeaacq aH1oqzdaahaaWcbeqaaiabeE8aJnaaCaaameqabaGaaGOmaaaaliab gkHiTiabeE8aJjabgkHiTiaaigdaaaGccaWGKbGaeq4Xdmgaleaaca aIXaaabaGaeyOhIukaniabgUIiYdaaaa@45C2@

dχ χ =logχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaada WcaaqaaiaadsgacqaHhpWyaeaacqaHhpWyaaaaleqabeqdcqGHRiI8 aOGaeyypa0JaciiBaiaac+gacaGGNbGaeq4Xdmgaaa@41F0@

 

 

5.2       Complex

τ ν τ ν+1 Κ υ τ ( χ,τ )dχ dτ σ Ε Κ τ ν τ ν+1 σ υ( χ,τ )× ν Κ,σ ( χ ) δ γ ( χ )dτ = τ ν τ ν+1 Κ φ( χ,τ )dχ dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWdXb qaamaapefabaGaeqyXdu3aaSbaaSqaaiabes8a0bqabaGcdaqadaqa aiabeE8aJjaacYcacqaHepaDaiaawIcacaGLPaaacaWGKbGaeq4Xdm galeaacqqHAoWsaeqaniabgUIiYdGccaWGKbGaeqiXdqhaleaacqaH epaDdaWgaaadbaGaeqyVd4gabeaaaSqaaiabes8a0naaBaaameaacq aH9oGBcqGHRaWkcaaIXaaabeaaa0Gaey4kIipakiabgkHiTaqaamaa qafabaWaa8qCaeaadaWdrbqaaiabgEGirlabew8a1naabmaabaGaeq 4XdmMaaiilaiabes8a0bGaayjkaiaawMcaaiabgEna0kabe27aUnaa BaaaleaacqqHAoWscaGGSaGaeq4WdmhabeaakmaabmaabaGaeq4Xdm gacaGLOaGaayzkaaGaeqiTdq2aaSbaaSqaaiabeo7aNbqabaGcdaqa daqaaiabeE8aJbGaayjkaiaawMcaaiaadsgacqaHepaDaSqaaiabeo 8aZbqab0Gaey4kIipaaSqaaiabes8a0naaBaaameaacqaH9oGBaeqa aaWcbaGaeqiXdq3aaSbaaWqaaiabe27aUjabgUcaRiaaigdaaeqaaa qdcqGHRiI8aaWcbaGaeq4WdmNaeyicI4SaeuyLdu0aaSbaaWqaaiab fQ5albqabaaaleqaniabggHiLdGccqGH9aqpaeaadaWdXbqaamaape fabaGaeqOXdO2aaeWaaeaacqaHhpWycaGGSaGaeqiXdqhacaGLOaGa ayzkaaGaamizaiabeE8aJbWcbaGaeuOMdSeabeqdcqGHRiI8aOGaam izaiabes8a0bWcbaGaeqiXdq3aaSbaaWqaaiabe27aUbqabaaaleaa cqaHepaDdaWgaaadbaGaeqyVd4Maey4kaSIaaGymaaqabaaaniabgU IiYdaaaaa@A76F@

2 ( Δ α υ( χ, τ ν ) )= 1 κ 2 τ ν1 τ ν τη τ ( Δ α υ ) ττ ( χ,τ )dσ dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOaIy7aaW baaSqabeaacaaIYaaaaOWaaeWaaeaacqqHuoardaahaaWcbeqaaiab eg7aHbaakiabew8a1naabmaabaGaeq4XdmMaaiilaiabes8a0naaBa aaleaacqaH9oGBaeqaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaGa eyypa0ZaaSaaaeaacaaIXaaabaGaeqOUdS2aaWbaaSqabeaacaaIYa aaaaaakmaapehabaWaa8qCaeaadaqadaqaaiabfs5aenaaCaaaleqa baGaeqySdegaaOGaeqyXduhacaGLOaGaayzkaaWaaSbaaSqaaiabes 8a0jabes8a0bqabaGcdaqadaqaaiabeE8aJjaacYcacqaHepaDaiaa wIcacaGLPaaacaWGKbGaeq4WdmhaleaacqaHepaDcqGHsislcqaH3o aAaeaacqaHepaDa0Gaey4kIipakiaadsgacqaHepaDaSqaaiabes8a 0naaBaaameaacqaH9oGBcqGHsislcaaIXaaabeaaaSqaaiabes8a0n aaBaaameaacqaH9oGBaeqaaaqdcqGHRiI8aaaa@7456@

1 κ Κ 1 ( τ ν τ ν+1 Δυ( χ,τ )dτ )dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaeqOUdSgaamaapefabaGaeyOaIy7aaWbaaSqabeaacaaI XaaaaOWaaeWaaeaadaWdXbqaaiabgs5aejabew8a1naabmaabaGaeq 4XdmMaaiilaiabes8a0bGaayjkaiaawMcaaiaadsgacqaHepaDaSqa aiabes8a0naaBaaameaacqaH9oGBaeqaaaWcbaGaeqiXdq3aaSbaaW qaaiabe27aUjabgUcaRiaaigdaaeqaaaqdcqGHRiI8aaGccaGLOaGa ayzkaaGaamizaiabeE8aJbWcbaGaeuOMdSeabeqdcqGHRiI8aaaa@59B2@

1 κ 2 Κ τ ν1 τ ν τ ν1 τ σ σ+κ Δ d 2 υ d λ 2 ( χ,λ )dλ dσ dτ dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaeqOUdS2aaWbaaSqabeaacaaIYaaaaaaakmaapefabaWa a8qCaeaadaWdXbqaamaapehabaGaeyiLdq0aaSaaaeaacaWGKbWaaW baaSqabeaacaaIYaaaaOGaeqyXduhabaGaamizaiabeU7aSnaaCaaa leqabaGaaGOmaaaaaaGcdaqadaqaaiabeE8aJjaacYcacqaH7oaBai aawIcacaGLPaaacaWGKbGaeq4UdWgaleaacqaHdpWCaeaacqaHdpWC cqGHRaWkcqaH6oWAa0Gaey4kIipakiaadsgacqaHdpWCaSqaaiabes 8a0naaBaaameaacqaH9oGBcqGHsislcaaIXaaabeaaaSqaaiabes8a 0bqdcqGHRiI8aOGaamizaiabes8a0bWcbaGaeqiXdq3aaSbaaWqaai abe27aUjabgkHiTiaaigdaaeqaaaWcbaGaeqiXdq3aaSbaaWqaaiab e27aUbqabaaaniabgUIiYdGccaWGKbGaeq4XdmgaleaacqqHAoWsae qaniabgUIiYdaaaa@73A5@

υ Γ 1 ( ( 0 Τ | υ ˙ | π( τ ) dτ ) 1 π +1+| υ ¯ | ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaauWaaeaacq aHfpqDaiaawMa7caGLkWoacqGHKjYOcqqHtoWrdaWgaaWcbaGaaGym aaqabaGcdaqadaqaamaabmaabaWaa8qCaeaadaabdaqaaiqbew8a1z aacaaacaGLhWUaayjcSdWaaWbaaSqabeaacqaHapaCdaqadaqaaiab es8a0bGaayjkaiaawMcaaaaakiaadsgacqaHepaDaSqaaiaaicdaae aacqqHKoava0Gaey4kIipaaOGaayjkaiaawMcaamaaCaaaleqabaWa aSaaaeaacaaIXaaabaGaeqiWda3aaWbaaWqabeaacqGHsislaaaaaa aakiabgUcaRiaaigdacqGHRaWkdaabdaqaaiqbew8a1zaaraaacaGL hWUaayjcSdaacaGLOaGaayzkaaaaaa@5EF4@

Ξ ( υ ),ν = 0 Τ ( | υ ˙ ( τ ) | π( τ )2 υ ˙ ( τ ), υ ˙ ( τ ) )dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaacu qHEoawgaqbamaabmaabaGaeqyXduhacaGLOaGaayzkaaGaaiilaiab e27aUbGaayzkJiaawQYiaiabg2da9maapehabaWaaeWaaeaadaabda qaaiqbew8a1zaacaWaaeWaaeaacqaHepaDaiaawIcacaGLPaaaaiaa wEa7caGLiWoadaahaaWcbeqaaiabec8aWnaabmaabaGaeqiXdqhaca GLOaGaayzkaaGaeyOeI0IaaGOmaaaakiqbew8a1zaacaWaaeWaaeaa cqaHepaDaiaawIcacaGLPaaacaGGSaGafqyXduNbaiaadaqadaqaai abes8a0bGaayjkaiaawMcaaaGaayjkaiaawMcaaiaadsgacqaHepaD aSqaaiaaicdaaeaacqqHKoava0Gaey4kIipaaaa@630C@

Γ 5 ( 0 Τ | υ ˙ ( τ ) | π( τ ) dτ ) α+1 π MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aaS baaSqaaiaaiwdaaeqaaOWaaeWaaeaadaWdXbqaamaaemaabaGafqyX duNbaiaadaqadaqaaiabes8a0bGaayjkaiaawMcaaaGaay5bSlaawI a7amaaCaaaleqabaGaeqiWda3aaeWaaeaacqaHepaDaiaawIcacaGL PaaaaaGccaWGKbGaeqiXdqhaleaacaaIWaaabaGaeuiPdqfaniabgU IiYdaakiaawIcacaGLPaaadaahaaWcbeqaamaalaaabaGaeqySdeMa ey4kaSIaaGymaaqaaiabec8aWnaaCaaameqabaGaeyOeI0caaaaaaa aaaa@5511@

φ ( υ ν ), υ ν υ = 0 Τ [ ( | υ ˙ ν ( τ ) | π( τ )2 υ ˙ ν ( τ ), υ ˙ ν ( τ ) υ ˙ ( τ ) ) +( Φ( τ, υ ν ( τ ) ), υ ν ( τ )υ( τ ) ) ]dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaacu aHgpGAgaqbamaabmaabaGaeqyXdu3aaSbaaSqaaiabe27aUbqabaaa kiaawIcacaGLPaaacaGGSaGaeqyXdu3aaSbaaSqaaiabe27aUbqaba GccqGHsislcqaHfpqDaiaawMYicaGLQmcacqGH9aqpdaWdXbqaamaa dmaaeaqabeaadaqadaqaamaaemaabaGafqyXduNbaiaadaWgaaWcba GaeqyVd4gabeaakmaabmaabaGaeqiXdqhacaGLOaGaayzkaaaacaGL hWUaayjcSdWaaWbaaSqabeaacqaHapaCdaqadaqaaiabes8a0bGaay jkaiaawMcaaiabgkHiTiaaikdaaaGccuaHfpqDgaGaamaaBaaaleaa cqaH9oGBaeqaaOWaaeWaaeaacqaHepaDaiaawIcacaGLPaaacaGGSa GafqyXduNbaiaadaWgaaWcbaGaeqyVd4gabeaakmaabmaabaGaeqiX dqhacaGLOaGaayzkaaGaeyOeI0IafqyXduNbaiaadaqadaqaaiabes 8a0bGaayjkaiaawMcaaaGaayjkaiaawMcaaaqaaiabgUcaRmaabmaa baGaey4bIeTaeuOPdy0aaeWaaeaacqaHepaDcaGGSaGaeqyXdu3aaS baaSqaaiabe27aUbqabaGcdaqadaqaaiabes8a0bGaayjkaiaawMca aaGaayjkaiaawMcaaiaacYcacqaHfpqDdaWgaaWcbaGaeqyVd4gabe aakmaabmaabaGaeqiXdqhacaGLOaGaayzkaaGaeyOeI0IaeqyXdu3a aeWaaeaacqaHepaDaiaawIcacaGLPaaaaiaawIcacaGLPaaaaaGaay 5waiaaw2faaiaadsgacqaHepaDaSqaaiaaicdaaeaacqqHKoava0Ga ey4kIipaaaa@95D3@

0 Τ 0 1 ( Γ( συ( τ ) )Γ( 0 ),υ( τ ) )dσ dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaada WdXbqaamaabmaabaGaey4bIeTaeu4KdC0aaeWaaeaacqaHdpWCcqaH fpqDdaqadaqaaiabes8a0bGaayjkaiaawMcaaaGaayjkaiaawMcaai abgkHiTiabgEGirlabfo5ahnaabmaabaGaaGimaaGaayjkaiaawMca aiaacYcacqaHfpqDdaqadaqaaiabes8a0bGaayjkaiaawMcaaaGaay jkaiaawMcaaiaadsgacqaHdpWCaSqaaiaaicdaaeaacaaIXaaaniab gUIiYdGccaWGKbGaeqiXdqhaleaacaaIWaaabaGaeuiPdqfaniabgU IiYdaaaa@5C9D@

( Ω ( | α |+ξ=1 λ ρ 2( β+| α |+ξλ ) | Δ α λ υ τ ξ | 2 + | υ | 2 ) ε 2γτ dχdτ ) 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaada WdrbqaamaabmaabaWaaabCaeaacqaHbpGCdaahaaWcbeqaaiaaikda daqadaqaaiabek7aIjabgUcaRmaaemaabaGaeqySdegacaGLhWUaay jcSdGaey4kaSIaeqOVdGNaeyOeI0Iaeq4UdWgacaGLOaGaayzkaaaa aOWaaqWaaeaacqqHuoardaahaaWcbeqaaiabeg7aHbaakiabeU7aSj abew8a1naaBaaaleaacqaHepaDdaahaaadbeqaaiabe67a4baaaSqa baaakiaawEa7caGLiWoadaahaaWcbeqaaiaaikdaaaGccqGHRaWkda abdaqaaiabew8a1bGaay5bSlaawIa7amaaCaaaleqabaGaaGOmaaaa aeaadaabdaqaaiabeg7aHbGaay5bSlaawIa7aiabgUcaRiabe67a4j abg2da9iaaigdaaeaacqaH7oaBa0GaeyyeIuoaaOGaayjkaiaawMca aiabew7aLnaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7aNjabes8a0b aakiaadsgacqaHhpWycaWGKbGaeqiXdqhaleaacqqHPoWvdaWgaaad baGaeyOhIukabeaaaSqab0Gaey4kIipaaOGaayjkaiaawMcaamaaCa aaleqabaWaaSaaaeaacaaIXaaabaGaaGOmaaaaaaaaaa@7FE2@

| π |,| ρ |=0 μ ( 1 ) | π | Ω α πρ ( ·,τ ) Δ ρ υ Δ Π υ ¯ dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaada qadaqaaiabgkHiTiaaigdaaiaawIcacaGLPaaadaahaaWcbeqaamaa emaabaGaeqiWdahacaGLhWUaayjcSdaaaOWaa8quaeaacqaHXoqyda WgaaWcbaGaeqiWdaNaeqyWdihabeaakmaabmaabaGaeS4JPFMaaiil aiabes8a0bGaayjkaiaawMcaaiabfs5aenaaCaaaleqabaGaeqyWdi haaOGaeqyXdu3aa0aaaeaacqqHuoardaahaaWcbeqaaiabfc6aqbaa kiabew8a1baacaWGKbGaeq4XdmgaleaacqqHPoWvaeqaniabgUIiYd aaleaadaabdaqaaiabec8aWbGaay5bSlaawIa7aiaacYcadaabdaqa aiabeg8aYbGaay5bSlaawIa7aiabg2da9iaaicdaaeaacqaH8oqBa0 GaeyyeIuoaaaa@6AB6@

ξ=0 μ1 Γ Β ξ υ ξ υ ¯ ν ξ dσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaada Wdrbqaaiabfk5acnaaBaaaleaacqaH+oaEaeqaaOGaeqyXdu3aaSaa aeaacqGHciITdaahaaWcbeqaaiabe67a4baakiqbew8a1zaaraaaba GaeyOaIyRaeqyVd42aaWbaaSqabeaacqaH+oaEaaaaaOGaamizaiab eo8aZbWcbaGaeu4KdCeabeqdcqGHRiI8aaWcbaGaeqOVdGNaeyypa0 JaaGimaaqaaiabeY7aTjabgkHiTiaaigdaa0GaeyyeIuoaaaa@5501@

Γ 1 Κ [ υ 2 + | gradυ | 2 + | α |=2 | Δ α υ 1 | 2 ]d χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aaS baaSqaaiaaigdaaeqaaOWaa8quaeaadaWadaqaaiabew8a1naaCaaa leqabaGaaGOmaaaakiabgUcaRmaaemaabaGaam4zaiaadkhacaWGHb Gaamizaiabew8a1bGaay5bSlaawIa7amaaCaaaleqabaGaaGOmaaaa kiabgUcaRmaaqafabaWaaqWaaeaacqqHuoardaahaaWcbeqaaiabeg 7aHbaakiabew8a1naaBaaaleaacaaIXaaabeaaaOGaay5bSlaawIa7 amaaCaaaleqabaGaaGOmaaaaaeaadaabdaqaaiabeg7aHbGaay5bSl aawIa7aiabg2da9iaaikdaaeqaniabggHiLdaakiaawUfacaGLDbaa caWGKbGafq4XdmMbauaaaSqaaiqbfQ5alzaafaaabeqdcqGHRiI8aa aa@6167@

0 1 ( χ ψ ζ 10 )dζ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qmaeaada qadaqaaiabeE8aJnaaCaaaleqabaGaeqiYdKhaaOGaeyOeI0YaaSaa aeaacqaH2oGEaeaacaaIXaGaaGimaaaaaiaawIcacaGLPaaacaWGKb GaeqOTdOhaleaacaaIWaaabaGaaGymaaqdcqGHRiI8aaaa@45AF@

0 1 0 1 ψ 2 1dχdψ = 0 π 2 0 1 ρdρdθ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qmaeaada WdXaqaaiaaigdacaWGKbGaeq4XdmMaamizaiabeI8a5bWcbaGaaGim aaqaamaakaaabaGaaGymaiabgkHiTiabeI8a5naaCaaameqabaGaaG OmaaaaaeqaaaqdcqGHRiI8aaWcbaGaaGimaaqaaiaaigdaa0Gaey4k Iipakiabg2da9maapedabaWaa8qmaeaacqaHbpGCcaWGKbGaeqyWdi NaamizaiabeI7aXbWcbaGaaGimaaqaaiaaigdaa0Gaey4kIipaaSqa aiaaicdaaeaadaWcaaqaaiabec8aWbqaaiaaikdaaaaaniabgUIiYd aaaa@581C@

[ cos χ 2× χ ] dχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaada WadaqaamaalaaabaGaci4yaiaac+gacaGGZbWaaOaaaeaacqaHhpWy aSqabaaakeaacaaIYaGaey41aq7aaOaaaeaacqaHhpWyaSqabaaaaa GccaGLBbGaayzxaaaaleqabeqdcqGHRiI8aOGaamizaiabeE8aJbaa @45FC@

 

6.    Limits

6.1       Simple

lim ν | υ ν υ | π( τ ) =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkziUkabg6HiLcqabaGc daabdaqaaiabew8a1naaBaaaleaacqaH9oGBaeqaaOGaeyOeI0Iaeq yXduhacaGLhWUaayjcSdWaaSbaaSqaaiabec8aWnaabmaabaGaeqiX dqhacaGLOaGaayzkaaaabeaakiabg2da9iaaicdaaaa@4EAC@

lim ν ρ( υ ν υ )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkziUkabg6HiLcqabaGc cqaHbpGCdaqadaqaaiabew8a1naaBaaaleaacqaH9oGBaeqaaOGaey OeI0IaeqyXduhacaGLOaGaayzkaaGaeyypa0JaaGimaaaa@4992@

lim ν ρ( υ ν )=ρ( υ ν ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkziUkabg6HiLcqabaGc cqaHbpGCdaqadaqaaiabew8a1naaBaaaleaacqaH9oGBaeqaaaGcca GLOaGaayzkaaGaeyypa0JaeqyWdi3aaeWaaeaacqaHfpqDdaWgaaWc baGaeqyVd4gabeaaaOGaayjkaiaawMcaaaaa@4D22@

limsup ν Ξ ( υ ν ) Ξ ( υ ), υ ν υ =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaciGGZbGaaiyDaiaacchaaSqaaiabe27aUjab gkziUkabg6HiLcqabaGcdaaadaqaaiqbf65ayzaafaWaaeWaaeaacq aHfpqDdaWgaaWcbaGaeqyVd4gabeaaaOGaayjkaiaawMcaaiabgkHi Tiqbf65ayzaafaWaaeWaaeaacqaHfpqDaiaawIcacaGLPaaacaGGSa GaeqyXdu3aaSbaaSqaaiabe27aUbqabaGccqGHsislcqaHfpqDaiaa wMYicaGLQmcacqGH9aqpcaaIWaaaaa@5849@

[ Α lim χ+0 φ( χ ) χ ] 1 <λ< [ Β lim χ φ( χ ) χ ] 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaacq qHroqqdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaeq4XdmMaeyOK H4Qaey4kaSIaaGimaaqabaGcdaWcaaqaaiabeA8aQnaabmaabaGaeq 4XdmgacaGLOaGaayzkaaaabaGaeq4XdmgaaaGaay5waiaaw2faamaa CaaaleqabaGaeyOeI0IaaGymaaaakiabgYda8iabeU7aSjabgYda8m aadmaabaGaeuOKdi0aaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiab eE8aJjabgkziUkabg6HiLcqabaGcdaWcaaqaaiabeA8aQnaabmaaba Gaeq4XdmgacaGLOaGaayzkaaaabaGaeq4XdmgaaaGaay5waiaaw2fa amaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@6210@

[ Α lim χ φ( χ ) χ ] 1 <λ< [ Β lim χ+0 φ( χ ) χ ] 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaacq qHroqqdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaeq4XdmMaeyOK H4QaeyOhIukabeaakmaalaaabaGaeqOXdO2aaeWaaeaacqaHhpWyai aawIcacaGLPaaaaeaacqaHhpWyaaaacaGLBbGaayzxaaWaaWbaaSqa beaacqGHsislcaaIXaaaaOGaeyipaWJaeq4UdWMaeyipaWZaamWaae aacqqHsoGqdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaeq4XdmMa eyOKH4Qaey4kaSIaaGimaaqabaGcdaWcaaqaaiabeA8aQnaabmaaba Gaeq4XdmgacaGLOaGaayzkaaaabaGaeq4XdmgaaaGaay5waiaaw2fa amaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@6210@

λ lim Δτ0 1 Δτ [ ( Τυ )( τ+Δτ )( Τυ )( τ ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdW2aaC beaeaaciGGSbGaaiyAaiaac2gaaSqaaiabgs5aejabes8a0jabgkzi UkaaicdaaeqaaOWaaSaaaeaacaaIXaaabaGaeyiLdqKaeqiXdqhaam aadmaabaWaaeWaaeaacqqHKoavcqaHfpqDaiaawIcacaGLPaaadaqa daqaaiabes8a0jabgUcaRiabgs5aejabes8a0bGaayjkaiaawMcaai abgkHiTmaabmaabaGaeuiPdqLaeqyXduhacaGLOaGaayzkaaWaaeWa aeaacqaHepaDaiaawIcacaGLPaaaaiaawUfacaGLDbaaaaa@5BBD@

lim Δτ0 ( Τ 2 υ )( τ+Δτ )( Τ 2 υ )( τ ) Δτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabfs5aejabes8a0jabgkziUkaaicda aeqaaOWaaSaaaeaadaqadaqaaiabfs6aunaaBaaaleaacaaIYaaabe aakiabew8a1bGaayjkaiaawMcaamaabmaabaGaeqiXdqNaey4kaSIa euiLdqKaeqiXdqhacaGLOaGaayzkaaGaeyOeI0YaaeWaaeaacqqHKo avdaWgaaWcbaGaaGOmaaqabaGccqaHfpqDaiaawIcacaGLPaaadaqa daqaaiabes8a0bGaayjkaiaawMcaaaqaaiabfs5aejabes8a0baaaa a@593D@

lim ν 0 1 | ( Τ 1 υ ν )( τ )( Τ 1 υ 0 )( τ ) |dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkziUkabg6HiLcqabaGc daWdXbqaamaaemaabaWaaeWaaeaacqqHKoavdaWgaaWcbaGaaGymaa qabaGccqaHfpqDdaWgaaWcbaGaeqyVd4gabeaaaOGaayjkaiaawMca amaabmaabaGaeqiXdqhacaGLOaGaayzkaaGaeyOeI0YaaeWaaeaacq qHKoavdaWgaaWcbaGaaGymaaqabaGccqaHfpqDdaWgaaWcbaGaaGim aaqabaaakiaawIcacaGLPaaadaqadaqaaiabes8a0bGaayjkaiaawM caaaGaay5bSlaawIa7aiaadsgacqaHepaDaSqaaiaaicdaaeaacaaI XaaaniabgUIiYdaaaa@5DC3@

lim χ+0 φ( χ ) χ < ( λΒ ) 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabeE8aJjabgkziUkabgUcaRiaaicda aeqaaOWaaSaaaeaacqaHgpGAdaqadaqaaiabeE8aJbGaayjkaiaawM caaaqaaiabeE8aJbaacqGH8aapdaqadaqaaiabeU7aSjabfk5acbGa ayjkaiaawMcaamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@4C86@

λΑ lim χ φ( χ ) χ >1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdWMaeu yKde0aaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiabeE8aJjabgkzi Ukabg6HiLcqabaGcdaWcaaqaaiabeA8aQnaabmaabaGaeq4Xdmgaca GLOaGaayzkaaaabaGaeq4Xdmgaaiabg6da+iaaigdaaaa@49BA@

lim χ φ( χ ) χ ( λ Α ¯ ) 1 +ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabeE8aJjabgkziUkabg6HiLcqabaGc daWcaaqaaiabeA8aQnaabmaabaGaeq4XdmgacaGLOaGaayzkaaaaba Gaeq4XdmgaaiabgwMiZoaabmaabaGaeq4UdWMafuyKdeKbaebaaiaa wIcacaGLPaaadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqGHRaWkcq aH1oqzaaa@4FC6@

lim χ 0 1 χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabeE8aJjabgkziUkaaicdadaahaaad beqaaiabgkHiTaaaaSqabaGcdaWcaaqaaiaaigdaaeaacqaHhpWyaa aaaa@4110@

lim x 0 ( 1 χ + 1 χ 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaWaaWbaaWqa beaacqGHsislaaaaleqaaOWaaeWaaeaadaWcaaqaaiaaigdaaeaacq aHhpWyaaGaey4kaSYaaSaaaeaacaaIXaaabaGaeq4Xdm2aaWbaaSqa beaacaaIYaaaaaaaaOGaayjkaiaawMcaaaaa@4636@

lim x3 1 χ2 χ3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIZaaabeaakmaa laaabaGaaGymaiabgkHiTmaakaaabaGaeq4XdmMaeyOeI0IaaGOmaa WcbeaaaOqaaiabeE8aJjabgkHiTiaaiodaaaaaaa@454F@

lim δx0 φ( χ 0 +δχ)φ( χ 0 ) δχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabes7aKjaadIhacqGHsgIRcaaIWaaa beaakmaalaaabaGaeqOXdOMaaiikaiabeE8aJnaaBaaaleaacaaIWa aabeaakiabgUcaRiabes7aKjabeE8aJjaacMcacqGHsislcqaHgpGA caGGOaGaeq4Xdm2aaSbaaSqaaiaaicdaaeqaaOGaaiykaaqaaiabes 7aKjabeE8aJbaaaaa@5264@

lim β1 β ( γδ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabek7aIjabgkziUkaaigdaaeqaaOWa aSaaaeaacqaHYoGyaeaadaqadaqaaiabeo7aNjabgkHiTiabes7aKb GaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaaaaa@45AF@

 

6.2       Complex

limsup ν ( Ξ ( υ ν ) Ξ ( υ ), υ ν υ )0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaciGGZbGaaiyDaiaacchaaSqaaiabe27aUjab gkziUkabg6HiLcqabaGcdaqadaqaaiqbf65ayzaafaWaaeWaaeaacq aHfpqDdaWgaaWcbaGaeqyVd4gabeaaaOGaayjkaiaawMcaaiabgkHi Tiqbf65ayzaafaWaaeWaaeaacqaHfpqDaiaawIcacaGLPaaacaGGSa GaeqyXdu3aaSbaaSqaaiabe27aUbqabaGccqGHsislcqaHfpqDaiaa wIcacaGLPaaacqGHKjYOcaaIWaaaaa@58B1@

limsup ν | υ ¯ ν | ρ + α φ( υ ν )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaciGGZbGaaiyDaiaacchaaSqaaiabe27aUjab gkziUkabg6HiLcqabaGcdaabdaqaaiqbew8a1zaaraWaaSbaaSqaai abe27aUbqabaaakiaawEa7caGLiWoadaahaaWcbeqaaiabgkHiTiab eg8aYnaaCaaameqabaGaey4kaScaaSGaeqySdegaaOGaeqOXdO2aae WaaeaacqaHfpqDdaWgaaWcbaGaeqyVd4gabeaaaOGaayjkaiaawMca aiabg2da9iabgkHiTiabg6HiLcaa@57F2@

lim Δτ0 λ Δτ 0 1 [ Ξ( τ+Δτ,σ )Ξ( τ,σ ) ]υ( σ )dσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabfs5aejabes8a0jabgkziUkaaicda aeqaaOWaaSaaaeaacqaH7oaBaeaacqqHuoarcqaHepaDaaWaa8qCae aadaWadaqaaiabf65aynaabmaabaGaeqiXdqNaey4kaSIaeuiLdqKa eqiXdqNaaiilaiabeo8aZbGaayjkaiaawMcaaiabgkHiTiabf65ayn aabmaabaGaeqiXdqNaaiilaiabeo8aZbGaayjkaiaawMcaaaGaay5w aiaaw2faaiabew8a1naabmaabaGaeq4WdmhacaGLOaGaayzkaaGaam izaiabeo8aZbWcbaGaaGimaaqaaiaaigdaa0Gaey4kIipaaaa@64DE@

lim ν 0 1 | ( Τ 1 υ ν )( τ ) Τ 1 υ 0 ( τ ) |dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkziUkabg6HiLcqabaGc daWdXbqaamaaemaabaWaaeWaaeaacqqHKoavdaWgaaWcbaGaaGymaa qabaGccqaHfpqDdaWgaaWcbaGaeqyVd4gabeaaaOGaayjkaiaawMca amaabmaabaGaeqiXdqhacaGLOaGaayzkaaGaeyOeI0IaeuiPdq1aaS baaSqaaiaaigdaaeqaaOGaeqyXdu3aaSbaaSqaaiaaicdaaeqaaOWa aeWaaeaacqaHepaDaiaawIcacaGLPaaaaiaawEa7caGLiWoacaWGKb GaeqiXdqhaleaacaaIWaaabaGaaGymaaqdcqGHRiI8aaaa@5C3A@

lim ν φ( τ, υ ν ( τ ), υ ν ( τ ), υ ( τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkziUkabg6HiLcqabaGc cqaHgpGAdaqadaqaaiabes8a0jaacYcacqaHfpqDdaWgaaWcbaGaeq yVd4gabeaakmaabmaabaGaeqiXdqhacaGLOaGaayzkaaGaaiilaiqb ew8a1zaafaWaaSbaaSqaaiabe27aUbqabaGcdaqadaqaaiabes8a0b GaayjkaiaawMcaaiaacYcacuaHfpqDgaGbamaabmaabaGaeqiXdqha caGLOaGaayzkaaaacaGLOaGaayzkaaaaaa@586F@

lim Δτ0 0 1 Ξ( τ+Δτ )Ξ( τ,σ ) Δτ η( σ ) φ( σ,υ( σ ), υ ( σ ), υ ( σ ) )dσ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabgs5aejabes8a0jabgkziUkaaicda aeqaaOWaa8qCaqaabeqaamaalaaabaGaeuONdG1aaeWaaeaacqaHep aDcqGHRaWkcqGHuoarcqaHepaDaiaawIcacaGLPaaacqGHsislcqqH Eoawdaqadaqaaiabes8a0jaacYcacqaHdpWCaiaawIcacaGLPaaaae aacqGHuoarcqaHepaDaaGaeq4TdG2aaeWaaeaacqaHdpWCaiaawIca caGLPaaaaeaacqaHgpGAdaqadaqaaiabeo8aZjaacYcacqaHfpqDda qadaqaaiabeo8aZbGaayjkaiaawMcaaiaacYcacuaHfpqDgaqbamaa bmaabaGaeq4WdmhacaGLOaGaayzkaaGaaiilaiqbew8a1zaagaWaae WaaeaacqaHdpWCaiaawIcacaGLPaaaaiaawIcacaGLPaaacaWGKbGa eq4WdmhaaSqaaiaaicdaaeaacaaIXaaaniabgUIiYdaaaa@751F@

Α= lim ν κ=1 ν φ( δ κ )Δχ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyKdeKaey ypa0ZaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiabe27aUjabgkzi Ukabg6HiLcqabaGcdaaeWbqaaiabeA8aQjaacIcacqaH0oazdaWgaa WcbaGaeqOUdSgabeaakiaacMcacqqHuoarcqaHhpWyaSqaaiabeQ7a Rjabg2da9iaaigdaaeaacqaH9oGBa0GaeyyeIuoaaaa@51B3@

lim χ 0 χ e ψ 2 dψ = π 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiabeE8aJjabgkziUkabg6HiLcqabaGc daWdXaqaaiaadwgadaahaaWcbeqaaiabgkHiTiabeI8a5naaCaaame qabaGaaGOmaaaaaaGccaWGKbGaeqiYdKhaleaacaaIWaaabaGaeq4X dmganiabgUIiYdGccqGH9aqpdaWcaaqaamaakaaabaGaeqiWdahale qaaaGcbaGaaGOmaaaaaaa@4DF4@

 

7.    Matrices

7.1       Simple

( β 1 β 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGabaaabaGaeqOSdi2aaSbaaSqaaiaaigdaaeqaaaGcbaGaeqOS di2aaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaaaa@3CB2@

( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGacaaabaGaeu4Odm1aaSbaaSqaaiaaigdacaGGSaGaaGymaaqa baaakeaacqqHJoWudaWgaaWcbaGaaGymaiaacYcacaaIYaaabeaaaO qaaiabfo6atnaaBaaaleaacaaIYaGaaiilaiaaigdaaeqaaaGcbaGa eu4Odm1aaSbaaSqaaiaaikdacaGGSaGaaGOmaaqabaaaaaGccaGLOa Gaayzkaaaaaa@4714@

( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,2 )= ( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,2 ) 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGacaaabaGaeu4Odm1aaWbaaSqabeaacaaIXaGaaiilaiaaigda aaaakeaacqqHJoWudaahaaWcbeqaaiaaigdacaGGSaGaaGOmaaaaaO qaaiabfo6atnaaCaaaleqabaGaaGOmaiaacYcacaaIXaaaaaGcbaGa eu4Odm1aaWbaaSqabeaacaaIYaGaaiilaiaaikdaaaaaaaGccaGLOa GaayzkaaGaeyypa0ZaaeWaaeaafaqabeGacaaabaGaeu4Odm1aaSba aSqaaiaaigdacaGGSaGaaGymaaqabaaakeaacqqHJoWudaWgaaWcba GaaGymaiaacYcacaaIYaaabeaaaOqaaiabfo6atnaaBaaaleaacaaI YaGaaiilaiaaigdaaeqaaaGcbaGaeu4Odm1aaSbaaSqaaiaaikdaca GGSaGaaGOmaaqabaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacqGH sislcaaIXaaaaaaa@5B10@

( Α Β Β Γ ) 1 =( αα αβ βα ββ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGacaaabaGaeuyKdeeabaGaeuOKdieabaGafuOKdiKbauaaaeaa cqqHtoWraaaacaGLOaGaayzkaaWaaWbaaSqabeaacqGHsislcaaIXa aaaOGaeyypa0ZaaeWaaeaafaqabeGacaaabaGaeqySdeMaeqySdega baGaeqySdeMaeqOSdigabaGaeqOSdiMaeqySdegabaGaeqOSdiMaeq OSdigaaaGaayjkaiaawMcaaaaa@4EA6@

( Υ 1 Υ 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGabaaabaGaeuyPdu1aaSbaaSqaaiaaigdaaeqaaaGcbaGaeuyP du1aaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaaaa@3C80@

( σ 1 2 γ γ σ 2 2 ) Ι ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGacaaabaGaeq4Wdm3aa0baaSqaaiaaigdaaeaacaaIYaaaaaGc baGaeq4SdCgabaGaeq4SdCgabaGaeq4Wdm3aa0baaSqaaiaaikdaae aacaaIYaaaaaaaaOGaayjkaiaawMcaaiabfM5ajnaaBaaaleaacqaH 9oGBaeqaaaaa@4515@

Β 1 =( 1 0 0 0 ) Ι ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOKdi0aaS baaSqaaiaaigdaaeqaaOGaeyypa0ZaaeWaaeaafaqabeGacaaabaGa aGymaaqaaiaaicdaaeaacaaIWaaabaGaaGimaaaaaiaawIcacaGLPa aacqGHxkcXcqqHzoqsdaWgaaWcbaGaeqyVd4gabeaaaaa@432F@

Β 2 =( 0 0 0 1 ) Ι ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOKdi0aaS baaSqaaiaaikdaaeqaaOGaeyypa0ZaaeWaaeaafaqabeGacaaabaGa aGimaaqaaiaaicdaaeaacaaIWaaabaGaaGymaaaaaiaawIcacaGLPa aacqGHxkcXcqqHzoqsdaWgaaWcbaGaeqyVd4gabeaaaaa@4330@

Β 3 =( 0 1 1 0 ) Ι ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOKdi0aaS baaSqaaiaaiodaaeqaaOGaeyypa0ZaaeWaaeaafaqabeGacaaabaGa aGimaaqaaiaaigdaaeaacaaIXaaabaGaaGimaaaaaiaawIcacaGLPa aacqGHxkcXcqqHzoqsdaWgaaWcbaGaeqyVd4gabeaaaaa@4332@

Μ ( Χ 0 0 Χ ) = Ι 2 Μ Χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiNd00aaS baaSqaamaabmaabaqbaeqabiGaaaqaaiabfE6adbqaaiaaicdaaeaa caaIWaaabaGaeu4PdmeaaaGaayjkaiaawMcaaaqabaGccqGH9aqpcq qHzoqsdaWgaaWcbaGaaGOmaaqabaGccqGHxkcXcqqHCoqtdaWgaaWc baGaeu4Pdmeabeaaaaa@462D@

var( vec( Υ _ ^ 1 ) vec( Υ _ ^ 2 ) )=( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,2 ) Ι ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciODaiaacg gacaGGYbWaaeWaaeaafaqabeGabaaabaGaamODaiaadwgacaWGJbWa aeWaaeaacuqHLoqvgaqhgaqcamaaBaaaleaacaaIXaaabeaaaOGaay jkaiaawMcaaaqaaiaadAhacaWGLbGaam4yamaabmaabaGafuyPduLb a0HbaKaadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaaaaaaca GLOaGaayzkaaGaeyypa0ZaaeWaaeaafaqabeGacaaabaGaeu4Odm1a aSbaaSqaaiaaigdacaGGSaGaaGymaaqabaaakeaacqqHJoWudaWgaa WcbaGaaGymaiaacYcacaaIYaaabeaaaOqaaiabfo6atnaaBaaaleaa caaIYaGaaiilaiaaigdaaeqaaaGcbaGaeu4Odm1aaSbaaSqaaiaaik dacaGGSaGaaGOmaaqabaaaaaGccaGLOaGaayzkaaGaey4LIqSaeuyM dK0aaSbaaSqaaiabe27aUbqabaaaaa@5FE9@

Ιν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyMdKKaey 4LIqSaeqyVd4gaaa@3B28@

 

7.2       Complex

( Υ 1 Υ 2 )[ ( Χ 0 0 Χ )( β 1 β 2 ),( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,2 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGabaaabaGaeuyPdu1aaSbaaSqaaiaaigdaaeqaaaGcbaGaeuyP du1aaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaiablYJi6m aadmaabaWaaeWaaeaafaqabeGacaaabaGaeu4PdmeabaGaaGimaaqa aiaaicdaaeaacqqHNoWqaaaacaGLOaGaayzkaaWaaeWaaeaafaqabe GabaaabaGaeqOSdi2aaSbaaSqaaiaaigdaaeqaaaGcbaGaeqOSdi2a aSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaiaacYcadaqada qaauaabeqaciaaaeaacqqHJoWudaWgaaWcbaGaaGymaiaacYcacaaI XaaabeaaaOqaaiabfo6atnaaBaaaleaacaaIXaGaaiilaiaaikdaae qaaaGcbaGaeu4Odm1aaSbaaSqaaiaaikdacaGGSaGaaGymaaqabaaa keaacqqHJoWudaWgaaWcbaGaaGOmaiaacYcacaaIYaaabeaaaaaaki aawIcacaGLPaaaaiaawUfacaGLDbaaaaa@5E20@

( β ^ 1 β ^ 2 )= [ ( Χ 1 0 0 Χ 2 )( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,1 )( Χ 1 0 0 Χ 2 ) ] 1 ×( Χ 1 0 0 Χ 2 )( Σ 1,1 Σ 1,2 Σ 2,1 Σ 2,1 )( Υ 1 Υ 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaqada qaauaabeqaceaaaeaacuaHYoGygaqcamaaBaaaleaacaaIXaaabeaa aOqaaiqbek7aIzaajaWaaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkai aawMcaaiabg2da9maadmaabaWaaeWaaeaafaqabeGacaaabaGafu4P dmKbauaadaWgaaWcbaGaaGymaaqabaaakeaacaaIWaaabaGaaGimaa qaaiqbfE6adzaafaWaaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaa wMcaamaabmaabaqbaeqabiGaaaqaaiabfo6atnaaCaaaleqabaGaaG ymaiaacYcacaaIXaaaaaGcbaGaeu4Odm1aaWbaaSqabeaacaaIXaGa aiilaiaaikdaaaaakeaacqqHJoWudaahaaWcbeqaaiaaikdacaGGSa GaaGymaaaaaOqaaiabfo6atnaaCaaaleqabaGaaGOmaiaacYcacaaI XaaaaaaaaOGaayjkaiaawMcaamaabmaabaqbaeqabiGaaaqaaiabfE 6adnaaBaaaleaacaaIXaaabeaaaOqaaiaaicdaaeaacaaIWaaabaGa eu4Pdm0aaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaaGaay 5waiaaw2faamaaCaaaleqabaGaeyOeI0IaaGymaaaaaOqaaiabgEna 0oaabmaabaqbaeqabiGaaaqaaiqbfE6adzaafaWaaSbaaSqaaiaaig daaeqaaaGcbaGaaGimaaqaaiaaicdaaeaacuqHNoWqgaqbamaaBaaa leaacaaIYaaabeaaaaaakiaawIcacaGLPaaadaqadaqaauaabeqaci aaaeaacqqHJoWudaahaaWcbeqaaiaaigdacaGGSaGaaGymaaaaaOqa aiabfo6atnaaCaaaleqabaGaaGymaiaacYcacaaIYaaaaaGcbaGaeu 4Odm1aaWbaaSqabeaacaaIYaGaaiilaiaaigdaaaaakeaacqqHJoWu daahaaWcbeqaaiaaikdacaGGSaGaaGymaaaaaaaakiaawIcacaGLPa aadaqadaqaauaabeqaceaaaeaacqqHLoqvdaWgaaWcbaGaaGymaaqa baaakeaacqqHLoqvdaWgaaWcbaGaaGOmaaqabaaaaaGccaGLOaGaay zkaaaaaaa@8460@

[ ( Χ 1 0 Σ 2,1 Σ 1,1 1 Χ 1 Χ 2 )( β 1 β 2 ),( Σ 1,1 0 0 Σ 22.1 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada qadaqaauaabeqaciaaaeaacqqHNoWqdaWgaaWcbaGaaGymaaqabaaa keaacaaIWaaabaGaeyOeI0Iaeu4Odm1aaSbaaSqaaiaaikdacaGGSa GaaGymaaqabaGccqqHJoWudaqhaaWcbaGaaGymaiaacYcacaaIXaaa baGaeyOeI0IaaGymaaaakiabfE6adnaaBaaaleaacaaIXaaabeaaaO qaaiabfE6adnaaBaaaleaacaaIYaaabeaaaaaakiaawIcacaGLPaaa daqadaqaauaabeqaceaaaeaacqaHYoGydaWgaaWcbaGaaGymaaqaba aakeaacqaHYoGydaWgaaWcbaGaaGOmaaqabaaaaaGccaGLOaGaayzk aaGaaiilamaabmaabaqbaeqabiGaaaqaaiabfo6atnaaBaaaleaaca aIXaGaaiilaiaaigdaaeqaaaGcbaGaaGimaaqaaiaaicdaaeaacqqH JoWudaWgaaWcbaGaaGOmaiaaikdacaGGUaGaaGymaaqabaaaaaGcca GLOaGaayzkaaaacaGLBbGaayzxaaaaaa@5EC6@

( Ι,0 )( Χ 1 Σ 1,1 Χ 1 Χ 1 Σ 1,2 Χ 2 Χ 2 Σ 2,1 Χ 1 Χ 2 Σ 2,2 Χ 2 )( 0 Ι ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq qHzoqscaGGSaGaaGimaaGaayjkaiaawMcaamaabmaabaqbaeqabiGa aaqaaiqbfE6adzaafaWaaSbaaSqaaiaaigdaaeqaaOGaeu4Odm1aaW baaSqabeaacaaIXaGaaiilaiaaigdaaaGccqqHNoWqdaWgaaWcbaGa aGymaaqabaaakeaacuqHNoWqgaqbamaaBaaaleaacaaIXaaabeaaki abfo6atnaaCaaaleqabaGaaGymaiaacYcacaaIYaaaaOGaeu4Pdm0a aSbaaSqaaiaaikdaaeqaaaGcbaGafu4PdmKbauaadaWgaaWcbaGaaG OmaaqabaGccqqHJoWudaahaaWcbeqaaiaaikdacaGGSaGaaGymaaaa kiabfE6adnaaBaaaleaacaaIXaaabeaaaOqaaiqbfE6adzaafaWaaS baaSqaaiaaikdaaeqaaOGaeu4Odm1aaWbaaSqabeaacaaIYaGaaiil aiaaikdaaaGccqqHNoWqdaWgaaWcbaGaaGOmaaqabaaaaaGccaGLOa GaayzkaaWaaeWaaeaafaqabeGabaaabaGaaGimaaqaaiabfM5ajbaa aiaawIcacaGLPaaaaaa@62B7@

( β ˜ 1 β ˜ 2 ) Ν 2 κ [ ( β 1 β 2 ),( Var( β ˜ 1 ) cov( β ˜ 1 , β ˜ 2 ) cov( β ˜ 2 , β ˜ 1 ) Var( β ˜ 2 ) ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGabaaabaGafqOSdiMbaGaadaWgaaWcbaGaaGymaaqabaaakeaa cuaHYoGygaacamaaBaaaleaacaaIYaaabeaaaaaakiaawIcacaGLPa aacqWI8iIocqqHDoGtdaWgaaWcbaGaaGOmamaaCaaameqabaGaeqOU dSgaaaWcbeaakmaadmaabaWaaeWaaeaafaqabeGabaaabaGaeqOSdi 2aaSbaaSqaaiaaigdaaeqaaaGcbaGaeqOSdi2aaSbaaSqaaiaaikda aeqaaaaaaOGaayjkaiaawMcaaiaacYcadaqadaqaauaabeqaciaaae aacaWGwbGaamyyaiaadkhadaqadaqaaiqbek7aIzaaiaWaaSbaaSqa aiaaigdaaeqaaaGccaGLOaGaayzkaaaabaGaci4yaiaac+gacaGG2b WaaeWaaeaacuaHYoGygaacamaaBaaaleaacaaIXaaabeaakiaacYca cuaHYoGygaacamaaBaaaleaacaaIYaaabeaaaOGaayjkaiaawMcaaa qaaiGacogacaGGVbGaaiODamaabmaabaGafqOSdiMbaGaadaWgaaWc baGaaGOmaaqabaGccaGGSaGafqOSdiMbaGaadaWgaaWcbaGaaGymaa qabaaakiaawIcacaGLPaaaaeaacaWGwbGaamyyaiaadkhadaqadaqa aiqbek7aIzaaiaWaaSbaaSqaaiaaikdaaeqaaaGccaGLOaGaayzkaa aaaaGaayjkaiaawMcaaaGaay5waiaaw2faaaaa@6FAE@

( Υ 1 Υ 2 ) Ν 2ν [ ( Ι 2 Χ )( β 1 β 2 ),( σ 1 2 γ γ σ 2 2 ) Ι ν ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeGabaaabaGaeuyPdu1aaSbaaSqaaiaaigdaaeqaaaGcbaGaeuyP du1aaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaiablYJi6i abf25aonaaBaaaleaacaaIYaGaeqyVd4gabeaakmaadmaabaWaaeWa aeaacqqHzoqsdaWgaaWcbaGaaGOmaaqabaGccqGHxkcXcqqHNoWqai aawIcacaGLPaaadaqadaqaauaabeqaceaaaeaacqaHYoGydaWgaaWc baGaaGymaaqabaaakeaacqaHYoGydaWgaaWcbaGaaGOmaaqabaaaaa GccaGLOaGaayzkaaGaaiilamaabmaabaqbaeqabiGaaaqaaiabeo8a ZnaaDaaaleaacaaIXaaabaGaaGOmaaaaaOqaaiabeo7aNbqaaiabeo 7aNbqaaiabeo8aZnaaDaaaleaacaaIYaaabaGaaGOmaaaaaaaakiaa wIcacaGLPaaacqGHxkcXcqqHzoqsdaWgaaWcbaGaeqyVd4gabeaaaO Gaay5waiaaw2faaaaa@63C6@

( σ 2,0 4 γ 0 2 2 γ 0 σ 2,0 2 γ 0 2 σ 1,0 4 2 γ 0 σ 1,0 2 2 γ 0 σ 2,0 2 2 γ 0 σ 1,0 2 2( σ 1,0 2 , σ 2,0 2 + γ 0 2 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeWadaaabaGaeq4Wdm3aa0baaSqaaiaaikdacaGGSaGaaGimaaqa aiaaisdaaaaakeaacqaHZoWzdaqhaaWcbaGaaGimaaqaaiaaikdaaa aakeaacqGHsislcaaIYaGaeq4SdC2aaSbaaSqaaiaaicdaaeqaaOGa eq4Wdm3aa0baaSqaaiaaikdacaGGSaGaaGimaaqaaiaaikdaaaaake aacqaHZoWzdaqhaaWcbaGaaGimaaqaaiaaikdaaaaakeaacqaHdpWC daqhaaWcbaGaaGymaiaacYcacaaIWaaabaGaaGinaaaaaOqaaiabgk HiTiaaikdacqaHZoWzdaWgaaWcbaGaaGimaaqabaGccqaHdpWCdaqh aaWcbaGaaGymaiaacYcacaaIWaaabaGaaGOmaaaaaOqaaiabgkHiTi aaikdacqaHZoWzdaWgaaWcbaGaaGimaaqabaGccqaHdpWCdaqhaaWc baGaaGOmaiaacYcacaaIWaaabaGaaGOmaaaaaOqaaiabgkHiTiaaik dacqaHZoWzdaWgaaWcbaGaaGimaaqabaGccqaHdpWCdaqhaaWcbaGa aGymaiaacYcacaaIWaaabaGaaGOmaaaaaOqaaiaaikdadaqadaqaai abeo8aZnaaDaaaleaacaaIXaGaaiilaiaaicdaaeaacaaIYaaaaOGa aiilaiabeo8aZnaaDaaaleaacaaIYaGaaiilaiaaicdaaeaacaaIYa aaaOGaey4kaSIaeq4SdC2aa0baaSqaaiaaicdaaeaacaaIYaaaaaGc caGLOaGaayzkaaaaaaGaayjkaiaawMcaaaaa@7D4A@

{ Μ ( Χ 0 0 Χ ) [ ( σ 1,0 2 γ 0 γ 0 σ 2,0 2 ) Ι ν ] Μ ( Χ 0 0 Χ ) } + MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaacq qHCoqtdaWgaaWcbaWaaeWaaeaafaqabeGacaaabaGaeu4PdmeabaGa aGimaaqaaiaaicdaaeaacqqHNoWqaaaacaGLOaGaayzkaaaabeaakm aadmaabaWaaeWaaeaafaqabeGacaaabaGaeq4Wdm3aa0baaSqaaiaa igdacaGGSaGaaGimaaqaaiaaikdaaaaakeaacqaHZoWzdaWgaaWcba GaaGimaaqabaaakeaacqaHZoWzdaWgaaWcbaGaaGimaaqabaaakeaa cqaHdpWCdaqhaaWcbaGaaGOmaiaacYcacaaIWaaabaGaaGOmaaaaaa aakiaawIcacaGLPaaacqGHxkcXcqqHzoqsdaWgaaWcbaGaeqyVd4ga beaaaOGaay5waiaaw2faaiabfY5annaaBaaaleaadaqadaqaauaabe qaciaaaeaacqqHNoWqaeaacaaIWaaabaGaaGimaaqaaiabfE6adbaa aiaawIcacaGLPaaaaeqaaaGccaGL7bGaayzFaaWaaWbaaSqabeaacq GHRaWkaaaaaa@6062@

( η ( Μ Α Σ 0 Μ Α ) + Β 1 ( Μ Α Σ 0 Μ Α ) + η η ( Μ Α Σ 0 Μ Α ) + Β π ( Μ Α Σ 0 Μ Α ) + η ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaqaabe qaaiqbeE7aOzaafaWaaeWaaeaacqqHCoqtdaWgaaWcbaGaeuyKdeea beaakiabfo6atnaaBaaaleaacaaIWaaabeaakiabfY5annaaBaaale aacqqHroqqaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacqGHRaWk aaGccqqHsoGqdaWgaaWcbaGaaGymaaqabaGcdaqadaqaaiabfY5ann aaBaaaleaacqqHroqqaeqaaOGaeu4Odm1aaSbaaSqaaiaaicdaaeqa aOGaeuiNd00aaSbaaSqaaiabfg5abbqabaaakiaawIcacaGLPaaada ahaaWcbeqaaiabgUcaRaaakiabeE7aObqaaiabl6UinbqaaiqbeE7a OzaafaWaaeWaaeaacqqHCoqtdaWgaaWcbaGaeuyKdeeabeaakiabfo 6atnaaBaaaleaacaaIWaaabeaakiabfY5annaaBaaaleaacqqHroqq aeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacqGHRaWkaaGccqqHso GqdaWgaaWcbaGaeqiWdahabeaakmaabmaabaGaeuiNd00aaSbaaSqa aiabfg5abbqabaGccqqHJoWudaWgaaWcbaGaaGimaaqabaGccqqHCo qtdaWgaaWcbaGaeuyKdeeabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaey4kaScaaOGaeq4TdGgaaiaawIcacaGLPaaaaaa@72A6@

Κ=( φ 1 ,, φ ρ( Τ ) )( 1 λ 1 0 0 1 λ ρ( Τ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOMdSKaey ypa0ZaaeWaaeaacqaHgpGAdaWgaaWcbaGaaGymaaqabaGccaGGSaGa eSOjGSKaaiilaiabeA8aQnaaBaaaleaacqaHbpGCdaqadaqaaiabfs 6aubGaayjkaiaawMcaaaqabaaakiaawIcacaGLPaaadaqadaqaauaa beqadmaaaeaadaWcaaqaaiaaigdaaeaadaGcaaqaaiabeU7aSnaaBa aaleaacaaIXaaabeaaaeqaaaaaaOqaaiablAcilbqaaiaaicdaaeaa cqWIUlstaeaacqWIXlYtaeaacqWIUlstaeaacaaIWaaabaGaeS47IW eabaWaaSaaaeaacaaIXaaabaWaaOaaaeaacqaH7oaBdaWgaaWcbaGa eqyWdi3aaeWaaeaacqqHKoavaiaawIcacaGLPaaaaeqaaaqabaaaaa aaaOGaayjkaiaawMcaaaaa@5CF2@

( Σ γ τ(γ) )=( 1 1 1 1 ζ 2 ζ 1 ζ ζ 2 )×( θ σ(θ) σ 2 (θ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa qabeWabaaabaGaeu4OdmfabaGaeq4SdCgabaGaeqiXdqNaaiikaiab eo7aNjaacMcaaaaacaGLOaGaayzkaaGaeyypa0ZaaeWaaeaafaqabe WadaaabaGaaGymaaqaaiaaigdaaeaacaaIXaaabaGaaGymaaqaaiab eA7a6naaCaaaleqabaGaaGOmaaaaaOqaaiabeA7a6bqaaiaaigdaae aacqaH2oGEaeaacqaH2oGEdaahaaWcbeqaaiaaikdaaaaaaaGccaGL OaGaayzkaaGaey41aq7aaeWaaeaafaqabeWabaaabaGaeqiUdehaba Gaeq4WdmNaaiikaiabeI7aXjaacMcaaeaacqaHdpWCdaahaaWcbeqa aiaaikdaaaGccaGGOaGaeqiUdeNaaiykaaaaaiaawIcacaGLPaaaaa a@5EA2@

 

8.    Sets

8.1       Simple

Τ( 0, ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiPdqLaey icI48aaeWaaeaacaaIWaGaaiilaiabg6HiLcGaayjkaiaawMcaaaaa @3D65@

ω=( ω 1 ,, ω ν1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdCNaey ypa0ZaaeWaaeaacqaHjpWDdaWgaaWcbaGaaGymaaqabaGccaGGSaGa eSOjGSKaaiilaiabeM8a3naaBaaaleaacqaH9oGBcqGHsislcaaIXa aabeaaaOGaayjkaiaawMcaaaaa@44F6@

Α =Α×( 0, ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyKde0aaS baaSqaaiabg6HiLcqabaGccqGH9aqpcqqHroqqcqGHxdaTdaqadaqa aiaaicdacaGGSaGaeyOhIukacaGLOaGaayzkaaaaaa@41DF@

Β χ ( 0,; ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOKdi0aaW baaSqabeaacqaHhpWyaaGcdaqadaqaaiaaicdacaGGSaGaeyOhIuQa ai4oaiablkqiJcGaayjkaiaawMcaaaaa@3FC1@

δ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyhHe6aaW baaSqabeaacqaH0oazaaaaaa@3939@

δ\{ 0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdqMaey icI4SaeSyfHuQaaiixamaacmaabaGaaGimaaGaay5Eaiaaw2haaaaa @3E57@

σΩ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey OGIWSaeyOaIyRaeyyQdCfaaa@3CAB@

[ χ κ ,χ ]Κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaacq aHhpWydaWgaaWcbaGaeqOUdSgabeaakiaacYcacqaHhpWyaiaawUfa caGLDbaacqGHckcZcqqHAoWsaaa@415E@

χ Ω ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey icI4SafuyQdCLbaebaaaa@3AD8@

Μ σ ={ Κ,Λ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiNd00aaS baaSqaaiabeo8aZbqabaGccqGH9aqpdaGadaqaaiabfQ5aljaacYca cqqHBoataiaawUhacaGL9baaaaa@4036@

Γ ,α ( Ω×[ 0, ] ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aaW baaSqabeaacqGHEisPcaGGSaGaeqySdegaaOWaaeWaaeaacqGHciIT cqqHPoWvcqGHxdaTdaWadaqaaiaaicdacaGGSaGaeyOhIukacaGLBb GaayzxaaaacaGLOaGaayzkaaaaaa@46B7@

χΩ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey icI4SaeyOaIyRaeuyQdCfaaa@3C26@

{ β σ Κ :σΒ,ΚΜ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaacq aHYoGydaqhaaWcbaGaeq4WdmhabaGaeuOMdSeaaOGaaiOoaiabeo8a ZjabgIGiolabfk5acjaacYcacqqHAoWscqGHiiIZcqqHCoqtaiaawU hacaGL9baaaaa@47BB@

{ Κ Κ ν :ν 0,Ν+1,ΚΜ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaacq qHAoWsdaqhaaWcbaGaeuOMdSeabaGaeqyVd4gaaOGaaiOoaiabe27a UjabgIGiopaaimaabaGaaGimaiaacYcacqqHDoGtcqGHRaWkcaaIXa aacaGLAaJaay5gWaGaaiilaiabfQ5aljabgIGiolabfY5anbGaay5E aiaaw2haaaaa@4C69@

τ 0 [ 0, ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiaaicdaaeqaaOGaeyicI48aamWaaeaacaaIWaGaaiilaiab g6HiLcGaay5waiaaw2faaaaa@3EFD@

υ 0 Λ 2 ( Ω ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaS baaSqaaiaaicdaaeqaaOGaeyicI4Saeu4MdW0aaWbaaSqabeaacaaI YaaaaOWaaeWaaeaacqGHPoWvaiaawIcacaGLPaaaaaa@3FB2@

φ 0 Γ ˙ ( Υ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdO2aaS baaSqaaiaaicdaaeqaaOGaeyicI4Safu4KdCKbaiaadaahaaWcbeqa aiabg6HiLcaakmaabmaabaGaeuyPdu1aaSbaaSqaaiaaicdaaeqaaa GccaGLOaGaayzkaaaaaa@4142@

Η 2 ( ε γ×τ , Ω ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4LdG0aaW baaSqabeaacaaIYaaaaOWaaeWaaeaacqaH1oqzdaahaaWcbeqaaiab gkHiTiabeo7aNjabgEna0kabes8a0baakiaacYcacqqHPoWvdaWgaa WcbaGaeyOhIukabeaaaOGaayjkaiaawMcaaaaa@4613@

Ω ρ :={ χΩ: ρ 2 <| χ |<2ρ,ρ>0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyQdC1aaW baaSqabeaacqaHbpGCaaGccaGG6aGaeyypa0ZaaiWaaeaacqaHhpWy cqGHiiIZcqqHPoWvcaGG6aWaaSaaaeaacqaHbpGCaeaacaaIYaaaai abgYda8maaemaabaGaeq4XdmgacaGLhWUaayjcSdGaeyipaWJaaGOm aiabeg8aYjaacYcacqaHbpGCcqGH+aGpcaaIWaaacaGL7bGaayzFaa aaaa@5313@

Κ={ χ=( χ 1 , χ 2 ) 2 :ρ>0,0<ω< ω 0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOMdSKaey ypa0ZaaiWaaeaacqaHhpWycqGH9aqpdaqadaqaaiabeE8aJnaaBaaa leaacaaIXaaabeaakiaacYcacqaHhpWydaWgaaWcbaGaaGOmaaqaba aakiaawIcacaGLPaaacqGHiiIZcqWIDesOdaahaaWcbeqaaiaaikda aaGccaGG6aGaeqyWdiNaeyOpa4JaaGimaiaacYcacaaIWaGaeyipaW JaeqyYdCNaeyipaWJaeqyYdC3aaSbaaSqaaiaaicdaaeqaaaGccaGL 7bGaayzFaaaaaa@550B@

Α={ τ[ 0,Τ ]:| υ ˙ ( τ ) |1 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyKdeKaey ypa0ZaaiWaaeaacqaHepaDcqGHiiIZdaWadaqaaiaaicdacaGGSaGa euiPdqfacaGLBbGaayzxaaGaaiOoamaaemaabaGafqyXduNbaiaada qadaqaaiabes8a0bGaayjkaiaawMcaaaGaay5bSlaawIa7aiabgwMi ZkaaigdaaiaawUhacaGL9baaaaa@4E38@

η:( 0,1 )[ 0, ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdGMaai OoamaabmaabaGaaGimaiaacYcacaaIXaaacaGLOaGaayzkaaGaeyOK H46aaKGeaeaacaaIWaGaaiilaiabg6HiLcGaay5waiaawMcaaaaa@42AA@

φ:( 0,1 )×( 0, )×( 0, )×( ,0 )[ 0, ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdOMaai OoamaabmaabaGaaGimaiaacYcacaaIXaaacaGLOaGaayzkaaGaey41 aq7aaeWaaeaacaaIWaGaaiilaiabg6HiLcGaayjkaiaawMcaaiabgE na0oaabmaabaGaaGimaiaacYcacqGHEisPaiaawIcacaGLPaaacqGH xdaTdaqadaqaaiabgkHiTiabg6HiLkaacYcacaaIWaaacaGLOaGaay zkaaGaeyOKH46aaKGeaeaacaaIWaGaaiilaiabg6HiLcGaay5waiaa wMcaaaaa@5719@

Γ 2 [ 0,1 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aaW baaSqabeaacaaIYaaaaOWaamWaaeaacaaIWaGaaiilaiaaigdaaiaa wUfacaGLDbaaaaa@3C69@

Κ( ρ )={ υΚ:| υ |<ρ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOMdS0aae WaaeaacqaHbpGCaiaawIcacaGLPaaacqGH9aqpdaGadaqaaiabew8a 1jabgIGiolabfQ5aljaacQdadaabdaqaamaafmaabaGaeqyXduhaca GLjWUaayPcSdaacaGLhWUaayjcSdGaeyipaWJaeqyWdihacaGL7bGa ayzFaaaaaa@4E3A@

χ ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4XdmMaey icI4SaeSyhHe6aaWbaaSqabeaacqaH9oGBaaaaaa@3C87@

α[ 0, π 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey icI48aaKGeaeaacaaIWaGaaiilaiabec8aWnaaCaaaleqabaGaeyOe I0caaOGaeyOeI0IaaGymaaGaay5waiaawMcaaaaa@40E0@

υ Κ( ρ 2 ) ¯ \Κ( ρ 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXduNaey icI48aa0aaaeaacqqHAoWsdaqadaqaaiabeg8aYnaaBaaaleaacaaI YaaabeaaaOGaayjkaiaawMcaaaaacaGGCbGaeuOMdS0aaeWaaeaacq aHbpGCdaWgaaWcbaGaaGymaaqabaaakiaawIcacaGLPaaaaaa@458D@

Κ β ( ρ )={ υ Κ β : υ <ρ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOMdS0aaW baaSqabeaacqaHYoGyaaGcdaqadaqaaiabeg8aYbGaayjkaiaawMca aiabg2da9maacmaabaGaeqyXduNaeyicI4SaeuOMdS0aaWbaaSqabe aacqaHYoGyaaGccaGG6aWaauWaaeaacqaHfpqDaiaawMa7caGLkWoa cqGH8aapcqaHbpGCaiaawUhacaGL9baaaaa@4EC8@

0 Ω 1 Ω ¯ 1 Ω 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGimaiabgI GiolabfM6axnaaBaaaleaacaaIXaaabeaakiabgkOimlqbfM6axzaa raWaaSbaaSqaaiaaigdaaeqaaOGaeyOGIWSaeuyQdC1aaSbaaSqaai aaikdaaeqaaaaa@43B9@

υ * Κ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaW baaSqabeaacaGGQaaaaOGaeyicI4SaeuOMdSeaaa@3B9A@

Γ( 0,σ )0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aae WaaeaacaaIWaGaaiilaiabeo8aZbGaayjkaiaawMcaaiabggMi6kaa icdaaaa@3E98@

Υ 1 ( Χ β1 , Σ 1,1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyPdu1aaS baaSqaaiaaigdaaeqaaOGaeSipIOZaaeWaaeaacqqHNoWqdaWgaaWc baGaeqOSdiMaaGymaaqabaGccaGGSaGaeu4Odm1aaSbaaSqaaiaaig dacaGGSaGaaGymaaqabaaakiaawIcacaGLPaaaaaa@43BC@

( Υ 1 , Υ 2 )= Σ 1,2 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq qHLoqvdaWgaaWcbaGaaGymaaqabaGccaGGSaGaeuyPdu1aaSbaaSqa aiaaikdaaeqaaaGccaGLOaGaayzkaaGaeyypa0Jaeu4Odm1aaSbaaS qaaiaaigdacaGGSaGaaGOmaaqabaGccqGHGjsUcaaIWaaaaa@448B@

Ω ¯ = ΚΜ Κ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuyQdCLbae bacqGH9aqpdaWeqbqaaiqbfQ5alzaaraaaleaacqqHAoWscqGHiiIZ cqqHCoqtaeqaniablQIivbaaaa@4050@

max{ 1,2,3 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacg gacaGG4bWaaiWaaeaacaaIXaGaaiilaiaaikdacaGGSaGaaG4maaGa ay5Eaiaaw2haaaaa@3E90@  

sup{ 1,2,3 }=3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Caiaacw hacaGGWbWaaiWaaeaacaaIXaGaaiilaiaaikdacaGGSaGaaG4maaGa ay5Eaiaaw2haaiabg2da9iaaiodaaaa@4065@

ΑΒ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyKdeKaey OGIWSaeuOKdieaaa@3AB5@

inf{ 1,2,3 }=1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyAaiaac6 gacaGGMbWaaiWaaeaacaaIXaGaaiilaiaaikdacaGGSaGaaG4maaGa ay5Eaiaaw2haaiabg2da9iaaigdaaaa@4048@

α Α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaambuaeaacq qHroqqaSqaaiabeg7aHbqab0GaeSOkIufaaaa@3AAA@

α Α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaebuaeaacq qHroqqaSqaaiabeg7aHbqab0Gaey4dIunaaaa@3B08@

αβ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaeS OkIuLaeqOSdigaaa@3A69@

Α= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyKdeKaey ypa0JaeyybIymaaa@39D6@

αβ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey OkIGSaeqOSdigaaa@3AD7@

cov( β 1 , β 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGG2bWaaeWaaeaacqaHYoGydaWgaaWcbaGaaGymaaqabaGccaGG SaGaeqOSdi2aaSbaaSqaaiaaikdaaeqaaaGccaGLOaGaayzkaaaaaa@402B@

Var( β 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiaadg gacaWGYbWaaeWaaeaacqaHYoGydaWgaaWcbaGaaGymaaqabaaakiaa wIcacaGLPaaaaaa@3CCA@

χΧ:ψΨ:χ=ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyiaIiIaeq 4XdmMaeyicI4Saeu4PdmKaaiOoaiabgoGiKiabeI8a5jabgIGiolab fI6azjaacQdacqaHhpWycqGH9aqpcqaHipqEaaa@4737@

 

8.2       Complex

Γ 0 2 [ 0,1 ]={ υ Γ 2 [ 0,1 ]:υ( 0 )= υ ( 1 )=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4KdC0aa0 baaSqaaiaaicdaaeaacaaIYaaaaOWaamWaaeaacaaIWaGaaiilaiaa igdaaiaawUfacaGLDbaacqGH9aqpdaGadaqaaiabew8a1jabgIGiol abfo5ahnaaCaaaleqabaGaaGOmaaaakmaadmaabaGaaGimaiaacYca caaIXaaacaGLBbGaayzxaaGaaiOoaiabew8a1naabmaabaGaaGimaa GaayjkaiaawMcaaiabg2da9iqbew8a1zaafaWaaeWaaeaacaaIXaaa caGLOaGaayzkaaGaeyypa0JaaGimaaGaay5Eaiaaw2haaaaa@55BC@

max{ 1 5 χ 2 + 1 χ : 1 2 ρτ( 3 τ 2 )χρτ( 2τ ) } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacg gacaGG4bWaaiWaaeaadaWcaaqaaiaaigdaaeaacaaI1aaaaiabeE8a JnaaCaaaleqabaGaaGOmaaaakiabgUcaRmaalaaabaGaaGymaaqaam aakaaabaGaeq4XdmgaleqaaaaakiaacQdadaWcaaqaaiaaigdaaeaa caaIYaaaaiabeg8aYjabes8a0naabmaabaGaaG4maiabgkHiTiabes 8a0naaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaiabgsMiJkab eE8aJjabgsMiJkabeg8aYjabes8a0naabmaabaGaaGOmaiabgkHiTi abes8a0bGaayjkaiaawMcaaaGaay5Eaiaaw2haaaaa@5C0B@

min{ 1 5 χ 2 + 1 χ : 1 2 ρτ( 3 τ 2 )χρτ( 2τ ) } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacM gacaGGUbWaaiWaaeaadaWcaaqaaiaaigdaaeaacaaI1aaaaiabeE8a JnaaCaaaleqabaGaaGOmaaaakiabgUcaRmaalaaabaGaaGymaaqaam aakaaabaGaeq4XdmgaleqaaaaakiaacQdadaWcaaqaaiaaigdaaeaa caaIYaaaaiabeg8aYjabes8a0naabmaabaGaaG4maiabgkHiTiabes 8a0naaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaiabgsMiJkab eE8aJjabgsMiJkabeg8aYjabes8a0naabmaabaGaaGOmaiabgkHiTi abes8a0bGaayjkaiaawMcaaaGaay5Eaiaaw2haaaaa@5C09@

υ τ ξ ={ ξ υ 1 τ ξ ,, ξ υ σ τ ξ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aaS baaSqaaiabes8a0naaCaaameqabaGaeqOVdGhaaaWcbeaakiabg2da 9maacmaabaWaaSaaaeaacqGHciITdaahaaWcbeqaaiabe67a4baaki abew8a1naaBaaaleaacaaIXaaabeaaaOqaaiabgkGi2kabes8a0naa CaaaleqabaGaeqOVdGhaaaaakiaacYcacqWIMaYscaGGSaWaaSaaae aacqGHciITdaahaaWcbeqaaiabe67a4baakiabew8a1naaBaaaleaa cqaHdpWCaeqaaaGcbaGaeyOaIyRaeqiXdq3aaWbaaSqabeaacqaH+o aEaaaaaaGccaGL7bGaayzFaaaaaa@5910@

inf{ β Η β λ ( Ω ) :β Η β λ ( Ω ),β|Γ=υ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyAaiaac6 gacaGGMbWaaiWaaeaadaqbdaqaaiabek7aIbGaayzcSlaawQa7amaa BaaaleaacqqHxoasdaqhaaadbaGaeqOSdigabaGaeq4UdWgaaSWaae WaaeaacqqHPoWvaiaawIcacaGLPaaaaeqaaOGaaiOoaiabek7aIjab gIGiolabfE5ainaaDaaaleaacqaHYoGyaeaacqaH7oaBaaGcdaqada qaaiabfM6axbGaayjkaiaawMcaaiaacYcacqaHYoGydaabbaqaaiab fo5ahbGaay5bSdGaeyypa0JaeqyXduhacaGL7bGaayzFaaaaaa@5C10@

Β δ 0 1,η λ 2 2μ,0 ( ε γτ , Κ ) Β δ 1 ,η λ 2 2μ,0 ( ε γτ , Κ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOKdi0aa0 baaSqaaiabes7aKnaaBaaameaacaaIWaaabeaaliabgkHiTiaaigda caGGSaGaeq4TdGgabaGaeq4UdW2aaSbaaWqaaiaaikdaaeqaaSGaey OeI0IaaGOmaiabeY7aTjaacYcacaaIWaaaaOWaaeWaaeaacqaH1oqz daahaaWcbeqaaiabgkHiTiabeo7aNjabes8a0baakiaacYcacqqHAo WsdaWgaaWcbaGaeyOhIukabeaaaOGaayjkaiaawMcaaiabgkOimlab fk5acnaaDaaaleaacqaH0oazdaWgaaadbaGaaGymaaqabaWccaGGSa Gaeq4TdGgabaGaeq4UdW2aaSbaaWqaaiaaikdaaeqaaSGaeyOeI0Ia aGOmaiabeY7aTjaacYcacaaIWaaaaOWaaeWaaeaacqaH1oqzdaahaa WcbeqaaiabgkHiTiabeo7aNjabes8a0baakiaacYcacqqHAoWsdaWg aaWcbaGaeyOhIukabeaaaOGaayjkaiaawMcaaaaa@6CAA@

υ( ·,τ ) Β μ 2μ ( Κ ) Β β 2μ ( Κ ) Β β+ε 2μ ( Κ ) Η β+ε 2μ ( Κ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXdu3aae WaaeaacqWIpM+zcaGGSaGaeqiXdqhacaGLOaGaayzkaaGaeyicI4Sa euOKdi0aa0baaSqaaiabeY7aTbqaaiaaikdacqaH8oqBaaGcdaqada qaaiabfQ5albGaayjkaiaawMcaaiabgkOimlabfk5acnaaDaaaleaa cqaHYoGyaeaacaaIYaGaeqiVd0gaaOWaaeWaaeaacqqHAoWsaiaawI cacaGLPaaacqGHckcZcqqHsoGqdaqhaaWcbaGaeqOSdiMaey4kaSIa eqyTdugabaGaaGOmaiabeY7aTbaakmaabmaabaGaeuOMdSeacaGLOa GaayzkaaGaeyyyIORaeu4LdG0aa0baaSqaaiabek7aIjabgUcaRiab ew7aLbqaaiaaikdacqaH8oqBaaGcdaqadaqaaiabfQ5albGaayjkai aawMcaaaaa@6D43@

 

9.    Trigonometry

9.1       Simple

tanΑ= sinΑ cosΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaeuyKdeKaeyypa0ZaaSaaaeaaciGGZbGaaiyAaiaac6ga cqqHroqqaeaaciGGJbGaai4BaiaacohacqqHroqqaaaaaa@43A9@

cotΑ= 1 tanΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGG0bGaeuyKdeKaeyypa0ZaaSaaaeaacaaIXaaabaGaciiDaiaa cggacaGGUbGaeuyKdeeaaaaa@402D@

secΑ= 1 cosΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Caiaacw gacaGGJbGaeuyKdeKaeyypa0ZaaSaaaeaacaaIXaaabaGaci4yaiaa c+gacaGGZbGaeuyKdeeaaaaa@4024@

cscΑ= 1 sinΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaaco hacaGGJbGaeuyKdeKaeyypa0ZaaSaaaeaacaaIXaaabaGaci4Caiaa cMgacaGGUbGaeuyKdeeaaaaa@4027@

sec 2 Α tan 2 Α=1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Caiaacw gacaGGJbWaaWbaaSqabeaacaaIYaaaaOGaeuyKdeKaeyOeI0IaciiD aiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaeuyKdeKaeyypa0 JaaGymaaaa@42E5@

tan(Α)=tanΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaaiikaiabgkHiTiabfg5abjaacMcacqGH9aqpcqGHsisl ciGG0bGaaiyyaiaac6gacqqHroqqaaa@4292@

cos(Α)=cosΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaiikaiabgkHiTiabfg5abjaacMcacqGH9aqpciGGJbGa ai4BaiaacohacqqHroqqaaa@41A9@

sin2Α=2sinΑcosΑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbGaaGOmaiabfg5abjabg2da9iaaikdaciGGZbGaaiyAaiaa c6gacqqHroqqciGGJbGaai4BaiaacohacqqHroqqaaa@4518@

cos2Α= cos 2 Α sin 2 Α =12 sin 2 Α=2 cos 2 Α1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaciGGJb Gaai4BaiaacohacaaIYaGaeuyKdeKaeyypa0Jaci4yaiaac+gacaGG ZbWaaWbaaSqabeaacaaIYaaaaOGaeuyKdeKaeyOeI0Iaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaeuyKdeeabaGaeyypa0Ja aGymaiabgkHiTiaaikdaciGGZbGaaiyAaiaac6gadaahaaWcbeqaai aaikdaaaGccqqHroqqcqGH9aqpcaaIYaGaci4yaiaac+gacaGGZbWa aWbaaSqabeaacaaIYaaaaOGaeuyKdeKaeyOeI0IaaGymaaaaaa@5856@

sin3Α=3sinΑ4 sin 3 Α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbGaaG4maiabfg5abjabg2da9iaaiodaciGGZbGaaiyAaiaa c6gacqqHroqqcqGHsislcaaI0aGaci4CaiaacMgacaGGUbWaaWbaaS qabeaacaaIZaaaaOGaeuyKdeeaaa@47BE@

sin 2 Α= 1 2 1 2 cos2Α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaeuyKdeKaeyypa0ZaaSaa aeaacaaIXaaabaGaaGOmaaaacqGHsisldaWcaaqaaiaaigdaaeaaca aIYaaaaiGacogacaGGVbGaai4CaiaaikdacqqHroqqaaa@4512@

sin 4 Α= 3 8 1 2 cos2Α+ 1 8 cos4Α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaI0aaaaOGaeuyKdeKaeyypa0ZaaSaa aeaacaaIZaaabaGaaGioaaaacqGHsisldaWcaaqaaiaaigdaaeaaca aIYaaaaiGacogacaGGVbGaai4CaiaaikdacqqHroqqcqGHRaWkdaWc aaqaaiaaigdaaeaacaaI4aaaaiGacogacaGGVbGaai4Caiaaisdacq qHroqqaaa@4C7C@

cos 5 Α= 5 8 cosΑ+ 5 16 cos3Α+ 1 16 cos5Α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaWbaaSqabeaacaaI1aaaaOGaeuyKdeKaeyypa0ZaaSaa aeaacaaI1aaabaGaaGioaaaaciGGJbGaai4BaiaacohacqqHroqqcq GHRaWkdaWcaaqaaiaaiwdaaeaacaaIXaGaaGOnaaaaciGGJbGaai4B aiaacohacaaIZaGaeuyKdeKaey4kaSYaaSaaaeaacaaIXaaabaGaaG ymaiaaiAdaaaGaci4yaiaac+gacaGGZbGaaGynaiabfg5abbaa@5220@

sinΑ+sinΒ=2sin 1 2 ( Α+Β )cos 1 2 ( ΑΒ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbGaeuyKdeKaey4kaSIaci4CaiaacMgacaGGUbGaeuOKdiKa eyypa0JaaGOmaiGacohacaGGPbGaaiOBamaalaaabaGaaGymaaqaai aaikdaaaWaaeWaaeaacqqHroqqcqGHRaWkcqqHsoGqaiaawIcacaGL PaaaciGGJbGaai4BaiaacohadaWcaaqaaiaaigdaaeaacaaIYaaaam aabmaabaGaeuyKdeKaeyOeI0IaeuOKdieacaGLOaGaayzkaaaaaa@542B@

cos 1 ( χ )=π cos 1 χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaWbaaSqabeaacqGHsislcaaIXaaaaOWaaeWaaeaacqGH sislcqaHhpWyaiaawIcacaGLPaaacqGH9aqpcqaHapaCcqGHsislci GGJbGaai4BaiaacohadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH hpWyaaa@48EF@

cos( χ×ψ )+ tan 2 χ+ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacqaHhpWycqGHxdaTcqaHipqEaiaawIcacaGL PaaacqGHRaWkciGG0bGaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaa GccqaHhpWycqGHRaWkcqaHipqEaaa@48FC@

cos( χ×ψ )+ tan 2 ( χ+ψ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacqaHhpWycqGHxdaTcqaHipqEaiaawIcacaGL PaaacqGHRaWkciGG0bGaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaa GcdaqadaqaaiabeE8aJjabgUcaRiabeI8a5bGaayjkaiaawMcaaaaa @4A85@

cosχ×ψ+ tan 2 χ+ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeq4XdmMaey41aqRaeqiYdKNaey4kaSIaciiDaiaacgga caGGUbWaaWbaaSqabeaacaaIYaaaaOGaeq4XdmMaey4kaSIaeqiYdK haaa@4773@

cosχ×ψ+ tan 2 ( χ+ψ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeq4XdmMaey41aqRaeqiYdKNaey4kaSIaciiDaiaacgga caGGUbWaaWbaaSqabeaacaaIYaaaaOWaaeWaaeaacqaHhpWycqGHRa WkcqaHipqEaiaawIcacaGLPaaaaaa@48FC@

tan ( χ+2×ψ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbWaaeWaaeaacqaHhpWycqGHRaWkcaaIYaGaey41aqRaeqiY dKhacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaaa@4274@

sin 2 (χ+ψ)+cosχ+ ψ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaaiikaiabeE8aJjabgUca RiabeI8a5jaacMcacqGHRaWkciGGJbGaai4BaiaacohacqaHhpWycq GHRaWkcqaHipqEdaahaaWcbeqaaiaaikdaaaaaaa@4887@

cos( xψ )+ tan 2 x+ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaWG4bGaeqiYdKhacaGLOaGaayzkaaGaey4k aSIaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaamiEai abgUcaRiabeI8a5baa@4571@

cos( xψ )+ tan 2 ( χ+y ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaWG4bGaeqiYdKhacaGLOaGaayzkaaGaey4k aSIaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOWaaeWaae aacqaHhpWycqGHRaWkcaWG5baacaGLOaGaayzkaaaaaa@46E4@

cosχy+ tan 2 χ+y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeq4XdmMaamyEaiabgUcaRiGacshacaGGHbGaaiOBamaa CaaaleqabaGaaGOmaaaakiabeE8aJjabgUcaRiaadMhaaaa@43BC@

cosχy+ tan 2 ( x+ψ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeq4XdmMaamyEaiabgUcaRiGacshacaGGHbGaaiOBamaa CaaaleqabaGaaGOmaaaakmaabmaabaGaamiEaiabgUcaRiabeI8a5b GaayjkaiaawMcaaaaa@455B@

cosh 2 χ sinh 2 χ=1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaiiAamaaCaaaleqabaGaaGOmaaaakiabeE8aJjabgkHi TiGacohacaGGPbGaaiOBaiaacIgadaahaaWcbeqaaiaaikdaaaGccq aHhpWycqGH9aqpcaaIXaaaaa@457C@

sin 2 χ+ cos 2 χ=1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaeq4XdmMaey4kaSIaci4y aiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaeq4XdmMaeyypa0 JaaGymaaaa@4399@

sin 1 χsin χ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacqGHsislcaaIXaaaaOGaeq4XdmMaeyiy IKRaci4CaiaacMgacaGGUbGaeq4Xdm2aaWbaaSqabeaacqGHsislca aIXaaaaaaa@4490@

cos( χ+ψ )=cosχcosψsinχsinψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacqaHhpWycqGHRaWkcqaHipqEaiaawIcacaGL PaaacqGH9aqpciGGJbGaai4BaiaacohacqaHhpWycqGHflY1ciGGJb Gaai4BaiaacohacqaHipqEcqGHsislciGGZbGaaiyAaiaac6gacqaH hpWycqGHflY1ciGGZbGaaiyAaiaac6gacqaHipqEaaa@57A1@

cos2χ= cos 2 χ sin 2 χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaGOmaiabgwSixlabeE8aJjabg2da9iGacogacaGGVbGa ai4CamaaCaaaleqabaGaaGOmaaaakiabeE8aJjabgkHiTiGacohaca GGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeE8aJbaa@4A79@

 

9.2       Complex

sinνΑ=sinΑ{ ( 2cosΑ ) ν1 ( ν2 1 ) ( 2cosΑ ) ν3 +( ν3 2 ) ( 2cosΑ ) ν5 } MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbGaeqyVd4MaeuyKdeKaeyypa0Jaci4CaiaacMgacaGGUbGa euyKde0aaiWaaqaabeqaamaabmaabaGaaGOmaiGacogacaGGVbGaai 4Caiabfg5abbGaayjkaiaawMcaamaaCaaaleqabaGaeqyVd4MaeyOe I0IaaGymaaaakiabgkHiTmaabmaaeaqabeaacqaH9oGBcqGHsislca aIYaaabaGaaGymaaaacaGLOaGaayzkaaWaaeWaaeaacaaIYaGaci4y aiaac+gacaGGZbGaeuyKdeeacaGLOaGaayzkaaWaaWbaaSqabeaacq aH9oGBcqGHsislcaaIZaaaaaGcbaGaey4kaSYaaeWaaqaabeqaaiab e27aUjabgkHiTiaaiodaaeaacaaIYaaaaiaawIcacaGLPaaadaqada qaaiaaikdaciGGJbGaai4BaiaacohacqqHroqqaiaawIcacaGLPaaa daahaaWcbeqaaiabe27aUjabgkHiTiaaiwdaaaGccqGHsislcqWIVl ctaaGaay5Eaiaaw2haaaaa@7193@

cosνΑ= 1 2 { ( 2cosΑ ) ν ν 1 ( 2cosΑ ) ν2 + ν 2 ( ν3 1 ) ( 2cosΑ ) ν4 ν 3 ( ν4 2 ) ( 2cosΑ ) ν6 + } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqyVd4MaeuyKdeKaeyypa0ZaaSaaaeaacaaIXaaabaGa aGOmaaaadaGadaabaeqabaWaaeWaaeaacaaIYaGaci4yaiaac+gaca GGZbGaeuyKdeeacaGLOaGaayzkaaWaaWbaaSqabeaacqaH9oGBaaGc cqGHsisldaWcaaqaaiabe27aUbqaaiaaigdaaaWaaeWaaeaacaaIYa Gaci4yaiaac+gacaGGZbGaeuyKdeeacaGLOaGaayzkaaWaaWbaaSqa beaacqaH9oGBcqGHsislcaaIYaaaaOGaey4kaSYaaSaaaeaacqaH9o GBaeaacaaIYaaaamaabmaaeaqabeaacqaH9oGBcqGHsislcaaIZaaa baGaaGymaaaacaGLOaGaayzkaaWaaeWaaeaacaaIYaGaci4yaiaac+ gacaGGZbGaeuyKdeeacaGLOaGaayzkaaWaaWbaaSqabeaacqaH9oGB cqGHsislcaaI0aaaaaGcbaGaeyOeI0YaaSaaaeaacqaH9oGBaeaaca aIZaaaamaabmaaeaqabeaacqaH9oGBcqGHsislcaaI0aaabaGaaGOm aaaacaGLOaGaayzkaaWaaeWaaeaacaaIYaGaci4yaiaac+gacaGGZb GaeuyKdeeacaGLOaGaayzkaaWaaWbaaSqabeaacqaH9oGBcqGHsisl caaI2aaaaOGaey4kaSIaeS47IWeaaiaawUhacaGL9baaaaa@7FB8@

sin 2ν1 Α= ( 1 ) ν1 2 2ν2 { sin( 2ν1 )Α( 2ν1 1 )sin( 2ν3 )Α + ( 1 ) ν1 ( 2ν1 ν1 )sinΑ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaIYaGaeqyVd4MaeyOeI0IaaGymaaaa kiabfg5abjabg2da9maalaaabaWaaeWaaeaacqGHsislcaaIXaaaca GLOaGaayzkaaWaaWbaaSqabeaacqaH9oGBcqGHsislcaaIXaaaaaGc baGaaGOmamaaCaaaleqabaGaaGOmaiabe27aUjabgkHiTiaaikdaaa aaaOWaaiWaaqaabeqaaiGacohacaGGPbGaaiOBamaabmaabaGaaGOm aiabe27aUjabgkHiTiaaigdaaiaawIcacaGLPaaacqqHroqqcqGHsi sldaqadaabaeqabaGaaGOmaiabe27aUjabgkHiTiaaigdaaeaacaaI XaaaaiaawIcacaGLPaaaciGGZbGaaiyAaiaac6gadaqadaqaaiaaik dacqaH9oGBcqGHsislcaaIZaaacaGLOaGaayzkaaGaeuyKdeeabaGa ey4kaSIaeSOjGS0aaeWaaeaacqGHsislcaaIXaaacaGLOaGaayzkaa WaaWbaaSqabeaacqaH9oGBcqGHsislcaaIXaaaaOWaaeWaaqaabeqa aiaaikdacqaH9oGBcqGHsislcaaIXaaabaGaeqyVd4MaeyOeI0IaaG ymaaaacaGLOaGaayzkaaGaci4CaiaacMgacaGGUbGaeuyKdeeaaiaa wUhacaGL9baaaaa@7EC8@

cos 2ν1 Α= 1 2 2ν2 { cos( 2ν1 )Α+( 2ν1 1 )cos( 2ν3 )Α ++( 2ν1 ν1 )cosΑ } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaWbaaSqabeaacaaIYaGaeqyVd4MaeyOeI0IaaGymaaaa kiabfg5abjabg2da9maalaaabaGaaGymaaqaaiaaikdadaahaaWcbe qaaiaaikdacqaH9oGBcqGHsislcaaIYaaaaaaakmaacmaaeaqabeaa ciGGJbGaai4BaiaacohadaqadaqaaiaaikdacqaH9oGBcqGHsislca aIXaaacaGLOaGaayzkaaGaeuyKdeKaey4kaSYaaeWaaqaabeqaaiaa ikdacqaH9oGBcqGHsislcaaIXaaabaGaaGymaaaacaGLOaGaayzkaa Gaci4yaiaac+gacaGGZbWaaeWaaeaacaaIYaGaeqyVd4MaeyOeI0Ia aG4maaGaayjkaiaawMcaaiabfg5abbqaaiabgUcaRiabl+UimjabgU caRmaabmaaeaqabeaacaaIYaGaeqyVd4MaeyOeI0IaaGymaaqaaiab e27aUjabgkHiTiaaigdaaaGaayjkaiaawMcaaiGacogacaGGVbGaai 4Caiabfg5abbaacaGL7bGaayzFaaaaaa@7382@

coshχ= e χ + e χ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaiiAaiabeE8aJjabg2da9maalaaabaGaamyzamaaCaaa leqabaGaeq4XdmgaaOGaey4kaSIaamyzamaaCaaaleqabaGaeyOeI0 Iaeq4XdmgaaaGcbaGaaGOmaaaaaaa@44BE@

 

10.          Mix of Greek & English

( x+ψ+z ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca WG4bGaey4kaSIaeqiYdKNaey4kaSIaamOEaaGaayjkaiaawMcaamaa CaaaleqabaGaaGOmaaaaaaa@3DF7@

( χ+y ) 2 +z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHhpWycqGHRaWkcaWG5baacaGLOaGaayzkaaWaaWbaaSqabeaacaaI YaaaaOGaey4kaSIaamOEaaaa@3DEB@

x+ ( ψ+ζ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgU caRmaabmaabaGaeqiYdKNaey4kaSIaeqOTdOhacaGLOaGaayzkaaWa aWbaaSqabeaacaaIYaaaaaaa@3EB5@

x+ψ+ z 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgU caRiabeI8a5jabgUcaRiaadQhadaahaaWcbeqaaiaaikdaaaaaaa@3C6E@

b c +δε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaada WcaaqaaiaadkgaaeaacaWGJbaaaaWcbeaakiabgUcaRiabes7aKjab gkHiTiabew7aLbaa@3D16@

β c+d ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaada Wcaaqaaiabek7aIbqaaiaadogacqGHRaWkcaWGKbaaaaWcbeaakiab gkHiTiabew7aLbaa@3D14@

β c e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaada Wcaaqaaiabek7aIbqaaiaadogaaaGaeyOeI0IaamyzaaWcbeaaaaa@3A82@

cos( xψ )+ tan 2 x+ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaWG4bGaeqiYdKhacaGLOaGaayzkaaGaey4k aSIaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaamiEai abgUcaRiabeI8a5baa@4571@

cos( xψ )+ tan 2 ( χ+y ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaWG4bGaeqiYdKhacaGLOaGaayzkaaGaey4k aSIaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOWaaeWaae aacqaHhpWycqGHRaWkcaWG5baacaGLOaGaayzkaaaaaa@46E4@

cosχy+ tan 2 χ+y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeq4XdmMaamyEaiabgUcaRiGacshacaGGHbGaaiOBamaa CaaaleqabaGaaGOmaaaakiabeE8aJjabgUcaRiaadMhaaaa@43BC@

cosχy+ tan 2 ( x+ψ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeq4XdmMaamyEaiabgUcaRiGacshacaGGHbGaaiOBamaa CaaaleqabaGaaGOmaaaakmaabmaabaGaamiEaiabgUcaRiabeI8a5b GaayjkaiaawMcaaaaa@455B@

11.          Text and Math

Πολλαπλασιασμ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzahaeaaaaaaaaa8qacaWFmpaaaa@3AC9@ ς πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzahaeaaaaaaaaa8qacaWFnpaaaa@3ACA@ μων

Μαθα ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFVoaaaa@3AAB@ νω να πολλαπλασι ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFSoaaaa@3AA8@ ζω

Μον ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο

Πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο

Δραστηρι ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFmpaaaa@3AC8@ τητα

Να γρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ψετε το γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενο α×( β+γ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey 41aq7aaeWaaeaacqaHYoGycqGHRaWkcqaHZoWzaiaawIcacaGLPaaa aaa@3F60@   σ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A82@ ωνα με την επιμεριστικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ιδι ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τητα και με αν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ λογο τρ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ πο να βρε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ τε την παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ σταση 3× χ 2 ×( 2 χ 3 +6χ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiabgE na0kabeE8aJnaaCaaaleqabaGaaGOmaaaakiabgEna0oaabmaabaGa aGOmaiabeE8aJnaaCaaaleqabaGaaG4maaaakiabgUcaRiaaiAdacq aHhpWyaiaawIcacaGLPaaaaaa@45D5@  

Να γρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ψετε το γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενο ( α+β )×( γ+δ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aHXoqycqGHRaWkcqaHYoGyaiaawIcacaGLPaaacqGHxdaTdaqadaqa aiabeo7aNjabgUcaRiabes7aKbGaayjkaiaawMcaaaaa@4370@   σ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A82@ ωνα με την επιμεριστικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ιδι ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τητα και με αν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ λογο τρ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ πο να βρε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ τε την παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ σταση ( 3 χ 2 ψ+2ψ )×( 2 χ 2 +5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIZaGaeq4Xdm2aaWbaaSqabeaacaaIYaaaaOGaeqiYdKNaey4kaSIa aGOmaiabeI8a5bGaayjkaiaawMcaaiabgEna0oaabmaabaGaaGOmai abeE8aJnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaiwdaaiaawIca caGLPaaaaaa@48C8@  

Μικροπε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFVoaaaa@3AAB@ ραμα

Πολλαπλασιασμ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A89@ ς μονων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A8A@ μου με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8B@ νυμο

Την αλγεβρικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ σταση 3 χ 2 ×( 2 χ 3 +6χ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiabeE 8aJnaaCaaaleqabaGaaGOmaaaakiabgEna0oaabmaabaGaaGOmaiab eE8aJnaaCaaaleqabaGaaG4maaaakiabgUcaRiaaiAdacqaHhpWyai aawIcacaGLPaaaaaa@43BE@   που ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ναι γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενο του μονων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μου 3 χ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiabeE 8aJnaaCaaaleqabaGaaGOmaaaaaaa@3954@   με το πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο 2 χ 3 +6χ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabeE 8aJnaaCaaaleqabaGaaG4maaaakiabgUcaRiaaiAdacqaHhpWyaaa@3CB7@   σ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A82@ ωνα με την επιμεριστικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ιδι ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τητα μπορο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ με να την γρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ψουμε

3 χ 2 ×( 2 χ 3 +6χ )=3 χ 2 ×2 χ 3 +3 χ 2 ×6χ=6 χ 5 +18 χ 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiabeE 8aJnaaCaaaleqabaGaaGOmaaaakiabgEna0oaabmaabaGaaGOmaiab eE8aJnaaCaaaleqabaGaaG4maaaakiabgUcaRiaaiAdacqaHhpWyai aawIcacaGLPaaacqGH9aqpcaaIZaGaeq4Xdm2aaWbaaSqabeaacaaI YaaaaOGaey41aqRaaGOmaiabeE8aJnaaCaaaleqabaGaaG4maaaaki abgUcaRiaaiodacqaHhpWydaahaaWcbeqaaiaaikdaaaGccqGHxdaT caaI2aGaeq4XdmMaeyypa0JaaGOnaiabeE8aJnaaCaaaleqabaGaaG ynaaaakiabgUcaRiaaigdacaaI4aGaeq4Xdm2aaWbaaSqabeaacaaI Zaaaaaaa@5FF3@  

Διαπιστ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νουμε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τι για να πολλαπλασι ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ σουμε μον ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο, πολλαπλασι ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ζουμε το μον ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο με κ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ θε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ ρο του πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μου και προσθ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ τουμε τα γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενα που προκ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ πτουν.

Πολλαπλασιασμ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A89@ ς πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A8A@ μου με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8B@ νυμο και πρ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A89@ σθεση-α φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A83@ α ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6C@ ρεση πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbbKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A8A@ μων

Την αλγεβρικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ σταση ( 3 χ 2 ψ+2ψ )×( 2 χ 2 +5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIZaGaeq4Xdm2aaWbaaSqabeaacaaIYaaaaOGaeqiYdKNaey4kaSIa aGOmaiabeI8a5bGaayjkaiaawMcaaiabgEna0oaabmaabaGaaGOmai abeE8aJnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaiwdaaiaawIca caGLPaaaaaa@48C8@  που ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ναι γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενο του πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μου 3 χ 2 ψ+2ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiabeE 8aJnaaCaaaleqabaGaaGOmaaaakiabeI8a5jabgUcaRiaaikdacqaH ipqEaaa@3E98@   με το πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο 2 χ 2 +5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabeE 8aJnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaiwdaaaa@3AFE@   , σ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A82@ ωνα με την επιμεριστικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ιδι ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τητα μπορο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ με να τη γρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ψουμε

( 3 χ 2 ψ+2ψ )×( 2 χ 2 +5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIZaGaeq4Xdm2aaWbaaSqabeaacaaIYaaaaOGaeqiYdKNaey4kaSIa aGOmaiabeI8a5bGaayjkaiaawMcaaiabgEna0oaabmaabaGaaGOmai abeE8aJnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaiwdaaiaawIca caGLPaaaaaa@48C8@   =3 χ 2 ψ×2 χ 2 +3 χ 2 ψ×5+2ψ×2 χ 2 +2ψ×5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4maiabeE8aJnaaCaaaleqabaGaaGOmaaaakiabeI8a5jabgEna0kaa ikdacqaHhpWydaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaIZaGaeq 4Xdm2aaWbaaSqabeaacaaIYaaaaOGaeqiYdKNaey41aqRaaGynaiab gUcaRiaaikdacqaHipqEcqGHxdaTcaaIYaGaeq4Xdm2aaWbaaSqabe aacaaIYaaaaOGaey4kaSIaaGOmaiabeI8a5jabgEna0kaaiwdaaaa@59C7@  

=6 χ 4 ψ+15 χ 2 ψ+4 χ 2 ψ+10ψ=6 χ 4 ψ+19 χ 2 ψ+10ψ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG OnaiabeE8aJnaaCaaaleqabaGaaGinaaaakiabeI8a5jabgUcaRiaa igdacaaI1aGaeq4Xdm2aaWbaaSqabeaacaaIYaaaaOGaeqiYdKNaey 4kaSIaaGinaiabeE8aJnaaCaaaleqabaGaaGOmaaaakiabeI8a5jab gUcaRiaaigdacaaIWaGaeqiYdKNaeyypa0JaaGOnaiabeE8aJnaaCa aaleqabaGaaGinaaaakiabeI8a5jabgUcaRiaaigdacaaI5aGaeq4X dm2aaWbaaSqabeaacaaIYaaaaOGaeqiYdKNaey4kaSIaaGymaiaaic dacqaHipqEaaa@5E85@  

Διαπιστ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νουμε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τι για να πολλαπλασι ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ σουμε πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο  με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο, πολλαπλασι ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ζουμε κ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ θε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ ρο του εν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ ς πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μου με κ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ θε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ ρο του ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ λλου  πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μου και προσθ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ τουμε τα γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενα που προκ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ πτουν.

Ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmoaaaa@3A48@ ταν κ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ νουμε πολλαπλασιασμ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μονων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μου με πολυ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ νυμο ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@  δ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ο πολυων ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μων, λ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ με ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ τι αναπτ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ σσουμε τα γιν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFmpaaaa@3A88@ μενα αυτ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ και το αποτ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ λεσμα ονομ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ζεται αν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ πτυγμα του γινομ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ νου.

Τριγωνομετρικο ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFVoaaaa@3AAB@ αριθμο ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFVoaaaa@3AAB@ της γων ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzahaeaaaaaaaaa8qacaWFVoaaaa@3AAB@ ας 2α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabeg 7aHbaa@3852@  

 

Οι τ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ποι που εκ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A82@ ρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ζουν τους τριγωνομετρικο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ς αριθμο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ς αυτ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ς της γων ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ας ως συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ ρτηση των τριγωνομετρικ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ ν αριθμ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ ν της γων ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ας α, ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ναι ειδικ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ ς περιπτ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFopaaaa@3A8A@ σεις των τ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ πων της προηγο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μενης παραγρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFgpaaaa@3A82@ ου. Συγκεκριμ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ να, αν στους τ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ πους του  sin( α+β ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaeWaaeaacqaHXoqycqGHRaWkcqaHYoGyaiaawIcacaGL Paaaaaa@3E7A@   , του cos( α+β ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacqaHXoqycqGHRaWkcqaHYoGyaiaawIcacaGL Paaaaaa@3E75@   και της tan( α+β ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbWaaeWaaeaacqaHXoqycqGHRaWkcqaHYoGyaiaawIcacaGL Paaaaaa@3E73@   αντικαταστ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ σουμε το β με το α, έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ χουμε

sin( 2α )=sin( α+α )=sin( α )×cos( α )+cos( α )×sin( α )=2×sin( α )×cos( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyyp a0Jaci4CaiaacMgacaGGUbWaaeWaaeaacqaHXoqycqGHRaWkcqaHXo qyaiaawIcacaGLPaaacqGH9aqpciGGZbGaaiyAaiaac6gadaqadaqa aiabeg7aHbGaayjkaiaawMcaaiabgEna0kGacogacaGGVbGaai4Cam aabmaabaGaeqySdegacaGLOaGaayzkaaGaey4kaSIaci4yaiaac+ga caGGZbWaaeWaaeaacqaHXoqyaiaawIcacaGLPaaacqGHxdaTciGGZb GaaiyAaiaac6gadaqadaqaaiabeg7aHbGaayjkaiaawMcaaiabg2da 9iaaikdacqGHxdaTciGGZbGaaiyAaiaac6gadaqadaqaaiabeg7aHb GaayjkaiaawMcaaiabgEna0kGacogacaGGVbGaai4CamaabmaabaGa amyyaaGaayjkaiaawMcaaaaa@7578@  Επομ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ νως:           sin( 2α )=2×sin( α )×cos( α ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyyp a0JaaGOmaiabgEna0kGacohacaGGPbGaaiOBamaabmaabaGaeqySde gacaGLOaGaayzkaaGaey41aqRaci4yaiaac+gacaGGZbWaaeWaaeaa cqaHXoqyaiaawIcacaGLPaaaaaa@4E9E@

cos( 2α )=cos( α+α )=cos( α )×cos( α )sin( α )×sin( α )= cos 2 α sin 2 α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyyp a0Jaci4yaiaac+gacaGGZbWaaeWaaeaacqaHXoqycqGHRaWkcqaHXo qyaiaawIcacaGLPaaacqGH9aqpciGGJbGaai4Baiaacohadaqadaqa aiabeg7aHbGaayjkaiaawMcaaiabgEna0kGacogacaGGVbGaai4Cam aabmaabaGaeqySdegacaGLOaGaayzkaaGaeyOeI0Iaci4CaiaacMga caGGUbWaaeWaaeaacqaHXoqyaiaawIcacaGLPaaacqGHxdaTciGGZb GaaiyAaiaac6gadaqadaqaaiabeg7aHbGaayjkaiaawMcaaiabg2da 9iGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeg7aHj abgkHiTiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiab eg7aHbaa@7109@                       = cos 2 α(1 cos 2 α)=2 cos 2 α1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaci 4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaeqySdeMaeyOe I0IaaiikaiaaigdacqGHsislciGGJbGaai4BaiaacohadaahaaWcbe qaaiaaikdaaaGccqaHXoqycaGGPaGaeyypa0JaaGOmaiGacogacaGG VbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeg7aHjabgkHiTiaaig daaaa@4E84@  

=(1 sin 2 α) sin 2 α=12 sin 2 α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaai ikaiaaigdacqGHsislciGGZbGaaiyAaiaac6gadaahaaWcbeqaaiaa ikdaaaGccqaHXoqycaGGPaGaeyOeI0Iaci4CaiaacMgacaGGUbWaaW baaSqabeaacaaIYaaaaOGaeqySdeMaeyypa0JaaGymaiabgkHiTiaa ikdaciGGZbGaaiyAaiaac6gadaahaaWcbeqaaiaaikdaaaGccqaHXo qyaaa@4E93@  

Επ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ σης: cos( 2α )= cos 2 α sin 2 α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyyp a0Jaci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaeqySde MaeyOeI0Iaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGa eqySdegaaa@4970@  

Επομ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ νως:  cos( 2α )= cos 2 α sin 2 α=2 cos 2 α1=12 sin 2 α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyyp a0Jaci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaeqySde MaeyOeI0Iaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGa eqySdeMaeyypa0JaaGOmaiGacogacaGGVbGaai4CamaaCaaaleqaba GaaGOmaaaakiabeg7aHjabgkHiTiaaigdacqGH9aqpcaaIXaGaeyOe I0IaaGOmaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaaki abeg7aHbaa@5B13@  

tan(2α)= tanα+tanα 1tanαtanα = 2tanα 1 tan 2 α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaaiikaiaaikdacqaHXoqycaGGPaGaeyypa0ZaaSaaaeaa ciGG0bGaaiyyaiaac6gacqaHXoqycqGHRaWkciGG0bGaaiyyaiaac6 gacqaHXoqyaeaacaaIXaGaeyOeI0IaciiDaiaacggacaGGUbGaeqyS deMaciiDaiaacggacaGGUbGaeqySdegaaiabg2da9maalaaabaGaaG OmaiGacshacaGGHbGaaiOBaiabeg7aHbqaaiaaigdacqGHsislciGG 0bGaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaaGccqaHXoqyaaaaaa@5F29@   , επομ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ νως tan(2α)= 2tanα 1 tan 2 α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaaiikaiaaikdacqaHXoqycaGGPaGaeyypa0ZaaSaaaeaa caaIYaGaciiDaiaacggacaGGUbGaeqySdegabaGaaGymaiabgkHiTi GacshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeg7aHbaa aaa@49C9@  

cos(2α)=2 cos 2 α11+cos( 2α )=2 cos 2 α cos 2 α= 1+cos2α 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaiikaiaaikdacqaHXoqycaGGPaGaeyypa0JaaGOmaiGa cogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeg7aHjabgk HiTiaaigdacqGHuhY2caaIXaGaey4kaSIaci4yaiaac+gacaGGZbWa aeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyypa0JaaGOmai GacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeg7aHjab gsDiBlGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeg 7aHjabg2da9maalaaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4C aiaaikdacqaHXoqyaeaacaaIYaaaaaaa@6782@  

cos( 2α )=12 sin 2 α2 sin 2 α=1cos(2α)si n 2 α= 1cos( 2α ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaeWaaeaacaaIYaGaeqySdegacaGLOaGaayzkaaGaeyyp a0JaaGymaiabgkHiTiaaikdaciGGZbGaaiyAaiaac6gadaahaaWcbe qaaiaaikdaaaGccqaHXoqycqGHuhY2caaIYaGaci4CaiaacMgacaGG UbWaaWbaaSqabeaacaaIYaaaaOGaeqySdeMaeyypa0JaaGymaiabgk HiTiGacogacaGGVbGaai4CaiaacIcacaaIYaGaeqySdeMaaiykaiab gsDiBlaacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeg 7aHjabg2da9maalaaabaGaaGymaiabgkHiTiGacogacaGGVbGaai4C amaabmaabaGaaGOmaiabeg7aHbGaayjkaiaawMcaaaqaaiaaikdaaa aaaa@692E@  

tan 2 α= sin 2 α cos 2 α = 1cos(2α) 2 1+cos( 2α ) 2 = 1cos(2α) 1+cos(2α) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaeqySdeMaeyypa0ZaaSaa aeaaciGGZbGaaiyAaiaac6gadaahaaWcbeqaaiaaikdaaaGccqaHXo qyaeaaciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaikdaaaGccqaH XoqyaaGaeyypa0ZaaSaaaeaadaWcaaqaaiaaigdacqGHsislciGGJb Gaai4BaiaacohacaGGOaGaaGOmaiabeg7aHjaacMcaaeaacaaIYaaa aaqaamaalaaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4Camaabm aabaGaaGOmaiabeg7aHbGaayjkaiaawMcaaaqaaiaaikdaaaaaaiab g2da9maalaaabaGaaGymaiabgkHiTiGacogacaGGVbGaai4CaiaacI cacaaIYaGaeqySdeMaaiykaaqaaiaaigdacqGHRaWkciGGJbGaai4B aiaacohacaGGOaGaaGOmaiabeg7aHjaacMcaaaaaaa@6BD9@  

Με τη βο ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ θεια των παραπ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ νω τ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ πων μπορο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ με να υπολογ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ σουμε τους τριγωνομετρικο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ς αριθμο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ς του μισο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ μιας γων ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ας , αν γνωρ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ζουμε τους τριγωνομετρικο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ς αριθμο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFnpaaaa@3A89@ ς της γων ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ας αυτ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ς. Για παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFSoaaaa@3A68@ δειγμα οι τριγωνομετρικο ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ αριθμο ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ της γων ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ας 22.5°= 45° 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiaaik dacaGGUaGaaGynaiabgclaWkabg2da9maalaaabaGaaGinaiaaiwda cqGHWcaSaeaacaaIYaaaaaaa@4007@   υπολογ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFVoaaaa@3A6B@ ζονται ως εξ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFUoaaaa@3A6A@ ς:

sin 2 ( 22.5° )= 1cos( 45° ) 2 = 1 2 2 2 = 2 2 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM gacaGGUbWaaWbaaSqabeaacaaIYaaaaOWaaeWaaeaacaaIYaGaaGOm aiaac6cacaaI1aGaeyiSaalacaGLOaGaayzkaaGaeyypa0ZaaSaaae aacaaIXaGaeyOeI0Iaci4yaiaac+gacaGGZbWaaeWaaeaacaaI0aGa aGynaiabgclaWcGaayjkaiaawMcaaaqaaiaaikdaaaGaeyypa0ZaaS aaaeaacaaIXaGaeyOeI0YaaSaaaeaadaGcaaqaaiaaikdaaSqabaaa keaacaaIYaaaaaqaaiaaikdaaaGaeyypa0ZaaSaaaeaacaaIYaGaey OeI0YaaOaaaeaacaaIYaaaleqaaaGcbaGaaGOmaaaaaaa@54E2@   sin( 22.5° )= 2 2 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taci 4CaiaacMgacaGGUbWaaeWaaeaacaaIYaGaaGOmaiaac6cacaaI1aGa eyiSaalacaGLOaGaayzkaaGaeyypa0ZaaSaaaeaadaGcaaqaaiaaik dacqGHsisldaGcaaqaaiaaikdaaSqabaaabeaaaOqaaiaaikdaaaaa aa@45F6@  

cos 2 (22.5°)= 1+cos( 45° ) 2 = 1+ 2 2 2 = 2+ 2 2 cos(22.5°)= 2+ 2 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaaiikaiaaikdacaaIYaGa aiOlaiaaiwdacqGHWcaScaGGPaGaeyypa0ZaaSaaaeaacaaIXaGaey 4kaSIaci4yaiaac+gacaGGZbWaaeWaaeaacaaI0aGaaGynaiabgcla WcGaayjkaiaawMcaaaqaaiaaikdaaaGaeyypa0ZaaSaaaeaacaaIXa Gaey4kaSYaaSaaaeaadaGcaaqaaiaaikdaaSqabaaakeaacaaIYaaa aaqaaiaaikdaaaGaeyypa0ZaaSaaaeaacaaIYaGaey4kaSYaaOaaae aacaaIYaaaleqaaaGcbaGaaGOmaaaacqGHshI3ciGGJbGaai4Baiaa cohacaGGOaGaaGOmaiaaikdacaGGUaGaaGynaiabgclaWkaacMcacq GH9aqpdaWcaaqaamaakaaabaGaaGOmaiabgUcaRmaakaaabaGaaGOm aaWcbeaaaeqaaaGcbaGaaGOmaaaaaaa@644B@  

Επομ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaruWqHXwAIjxAaG qbaKqzagaeaaaaaaaaa8qacaWFToaaaa@3A69@ νως: tan(22.5°)= 2 2 2+ 2 = 2 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaaiikaiaaikdacaaIYaGaaiOlaiaaiwdacqGHWcaScaGG PaGaeyypa0ZaaSaaaeaadaGcaaqaaiaaikdacqGHsisldaGcaaqaai aaikdaaSqabaaabeaaaOqaamaakaaabaGaaGOmaiabgUcaRmaakaaa baGaaGOmaaWcbeaaaeqaaaaakiabg2da9maakaaabaGaaGOmaaWcbe aakiabgkHiTiaaigdaaaa@48C4@   και cot(22.5°)= 2+ 2 2 2 = 2 +1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGG0bGaaiikaiaaikdacaaIYaGaaiOlaiaaiwdacqGHWcaScaGG PaGaeyypa0ZaaSaaaeaadaGcaaqaaiaaikdacqGHRaWkdaGcaaqaai aaikdaaSqabaaabeaaaOqaamaakaaabaGaaGOmaiabgkHiTmaakaaa baGaaGOmaaWcbeaaaeqaaaaakiabg2da9maakaaabaGaaGOmaaWcbe aakiabgUcaRiaaigdaaaa@48BC@  

 

Εκτ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa83Rdaaa@37DB@ μηση ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8hRdaaa@37D8@ γνωστων συναρτ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8NRdaaa@37DA@ σεων πυκν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8hZdaaa@37F8@ τητας πιθαν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8hZdaaa@37F8@ τητας και      εκτ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa83Rdaaa@37DB@ μηση παραμ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8xRdaaa@37D9@ τρων με τη μ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8xRdaaa@37D9@ θοδο μ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8xRdaaa@37D9@ γιστης πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8NXdaaa@37F2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugWbabaaa aaaaaapeGaa8hRdaaa@37D8@ νειας

 

Ας θεωρ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ σουμε έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ να πρ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ βλημα Μ κλ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ σεων, με διαν ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ σματα χαρακτηριστικ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NZdaaa@37BA@ ν κατανεμημ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ να σ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ μ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ωνα με τις p(χ| ω ι ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaacI cacqaHhpWydaabbaqaaiabeM8a3naaBaaaleaacqaH5oqAaeqaaOGa aiykaaGaay5bSdaaaa@3F42@  , για i απ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ 1 ως Μ. Υποθ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ τουμε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τι αυτ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ ς οι συναρτ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ σεις πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νειας δ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ νονται σε παραμετρικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ μορ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ και ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τι οι αντ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ στοιχες παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ μετροι σχηματ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ζουν διαν ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ σματα θ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUde3aaS baaSqaaiaadMgaaeqaaaaa@38C7@  που ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ γνωστα. Προκειμ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ νου να δε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ξουμε την εξ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση των συναρτ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ σεων πυκν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τητας πιθαν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τητας απ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τα διαν ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ σματα αυτ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ γρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ουμε p(χ| ω ι ;θ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaacI cacqaHhpWydaabbaqaaiabeM8a3naaBaaaleaacqaH5oqAaeqaaOGa ai4oaiabeI7aXjaacMcaaiaawEa7aaaa@41B7@  . Ο στ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ χος μας ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι να εκτιμ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ σουμε τις ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ γνωστες παραμ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ τρους χρησιμοποι ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NZdaaa@37BA@ ντας έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ να σ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ νολο απ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ διαθ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ σιμα διαν ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ σματα χαρακτηριστικ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NZdaaa@37BA@ ν απ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ κ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ θε κλ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ση.

Ας υποθ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ σουμε ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τι χ 1 ,, χ Ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiaaigdaaeqaaOGaaiilaiablAciljaacYcacqaHhpWydaWg aaWcbaGaeuyNd4eabeaaaaa@3E7D@  ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι τυχα ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ α δε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ γματα που προ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ κυψαν απ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τη συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση πυκν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τητας πιθαν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τητας. Σχηματ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ζουμε την απ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ κοινο ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση πυκν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τητας πιθαν ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ τητας p(Χ;θ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaacI cacqqHNoWqcaGG7aGaeqiUdeNaaiykaaaa@3C32@ . Υποθ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ τωντας στατιστικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ ανεξαρτησ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ α μεταξ ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ των δειγμ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ των , έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ χουμε

p(Χ;θ)=p( χ 1 , χ 2 ,, χ Ν ;θ)= κ=1 Ν p( χ κ ;θ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaacI cacqqHNoWqcaGG7aGaeqiUdeNaaiykaiabg2da9iaacchacaGGOaGa eq4Xdm2aaSbaaSqaaiaaigdaaeqaaOGaaiilaiabeE8aJnaaBaaale aacaaIYaaabeaakiaacYcacqWIMaYscaGGSaGaeq4Xdm2aaSbaaSqa aiabf25aobqabaGccaGG7aGaeqiUdeNaaiykaiabg2da9maarahaba GaamiCaiaacIcacqaHhpWydaWgaaWcbaGaeqOUdSgabeaakiaacUda cqaH4oqCcaGGPaaaleaacqaH6oWAcqGH9aqpcaaIXaaabaGaeuyNd4 eaniabg+Givdaaaa@5E68@  

Αυτ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι μια συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση του θ και ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι γνωστ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ ως συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νειας του θ ως προς Χ. Η μ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ θοδος μ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ γιστης πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νειας εκτιμ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ το θ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NZdaaa@37BA@ στε η συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νειας να λαμβ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νει την μ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ γιστη τιμ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ της, δηλαδ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@

θ ML =arg max θ κ=1 Ν p( χ κ ;θ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUde3aaS baaSqaaiaad2eacaWGmbaabeaakiabg2da9iGacggacaGGYbGaai4z aiGac2gacaGGHbGaaiiEamaaBaaaleaacqaH4oqCaeqaaOWaaebCae aacaWGWbGaaiikaiabeE8aJnaaBaaaleaacqaH6oWAaeqaaOGaai4o aiabeI7aXjaacMcaaSqaaiabeQ7aRjabg2da9iaaigdaaeaacqqHDo Gta0Gaey4dIunaaaa@5193@  

Μια αναγκαστικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ συνθ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ κη που πρ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ πει να πληρε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ αυτ ό MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hZdaaa@37B8@ το θ ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι να ε ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ναι μ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ γιστο, ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρα να μηδεν ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ζει την παρ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ γωγο της συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτησης πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νειας ως προς θ, δηλαδ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ :

κ=1 Ν p( χ κ ;θ) θ =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITdaqeWbqaaiaadchacaGGOaGaeq4Xdm2aaSbaaSqaaiabeQ7a RbqabaGccaGG7aGaeqiUdeNaaiykaaWcbaGaeqOUdSMaeyypa0JaaG ymaaqaaiabf25aobqdcqGHpis1aaGcbaGaeyOaIyRaeqiUdehaaiab g2da9iaaicdaaaa@4BD2@  

Εξαιτ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ας της γνησ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ως α ύ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xZdaaa@37B9@ ξουσας μονοτον ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ας της λογαριθμικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ ς συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτησης, ορ ί MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa83Rdaaa@379B@ ζουμε τη λογαριθμικ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ συν ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ ρτηση πιθανο φ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NXdaaa@37B2@ ά MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8hRdaaa@3798@ νειας ως:

L(θ)=ln κ=1 Ν p( χ κ ;θ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaiaacI cacqaH4oqCcaGGPaGaeyypa0JaciiBaiaac6gadaqeWbqaaiaadcha caGGOaGaeq4Xdm2aaSbaaSqaaiabeQ7aRbqabaGccaGG7aGaeqiUde NaaiykaaWcbaGaeqOUdSMaeyypa0JaaGymaaqaaiabf25aobqdcqGH pis1aaaa@4C40@  

Επομ έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ νως τ ώ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NZdaaa@37BA@ ρα έ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8xRdaaa@3799@ χουμε το εξ ή MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhD YfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaajugGbabaaa aaaaaapeGaa8NRdaaa@379A@ ς:

L(θ) θ = κ=1 Ν lnp( χ κ ;θ) θ = κ=1 Ν 1 p( χ κ ;θ) × p( χ κ ;θ) θ =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITcaWGmbGaaiikaiabeI7aXjaacMcaaeaacqGHciITcqaH4oqC aaGaeyypa0ZaaabCaeaadaWcaaqaaiabgkGi2kGacYgacaGGUbGaam iCaiaacIcacqaHhpWydaWgaaWcbaGaeqOUdSgabeaakiaacUdacqaH 4oqCcaGGPaaabaGaeyOaIyRaeqiUdehaaaWcbaGaeqOUdSMaeyypa0 JaaGymaaqaaiabf25aobqdcqGHris5aOGaeyypa0ZaaabCaeaadaWc aaqaaiaaigdaaeaacaWGWbGaaiikaiabeE8aJnaaBaaaleaacqaH6o WAaeqaaOGaai4oaiabeI7aXjaacMcaaaGaey41aq7aaSaaaeaacqGH ciITcaWGWbGaaiikaiabeE8aJnaaBaaaleaacqaH6oWAaeqaaOGaai 4oaiabeI7aXjaacMcaaeaacqGHciITcqaH4oqCaaaaleaacqaH6oWA cqGH9aqpcaaIXaaabaGaeuyNd4eaniabggHiLdGccqGH9aqpcaaIWa aaaa@77B5@