ÇÙÐ Ò ½º ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð ¾º Ä Ò Ö Ö Ù Ð Ý Ó ËÝÑ ÒÞ ÔÓÐÝÒÓÑ Ð º Ì ÛÓ¹ÐÓÓÔ ÙÒÖ Ö Ô Û Ö Ö ÖÝ Ñ ¹ ÝÓÒ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ

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1 ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò ÝÒÑ Ò Ò Ö Ð Ö Ò Ó Ò Ö ÀÍ ÖÐ Òµ Ó Ò ÛÓÖ Û Ö Ò ÖÓÛÒ Ö Ú ½ ¼¾º ¾½ Û Åº Ä Ö Ö Ú ½ ¼¾º ¼¼ Û Äº Ñ Ò Ëº Ï ÒÞ ÖÐ Å ÒÞ ½ º¼ º¾¼½

2 ÇÙÐ Ò ½º ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð ¾º Ä Ò Ö Ö Ù Ð Ý Ó ËÝÑ ÒÞ ÔÓÐÝÒÓÑ Ð º Ì ÛÓ¹ÐÓÓÔ ÙÒÖ Ö Ô Û Ö Ö ÖÝ Ñ ¹ ÝÓÒ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ

3 ½º ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð ÅÓ Ú ÓÒ Á Ö Ò Ö Ð Ö ÖÙ Ð ÓÖ ÓÑÔÙ ÓÒ Ó ÝÒÑ Ò Ò Ö Ð ÇÒ Ö ÕÙ ÒÐÝ ÓÑÔÙ Û Ð Ð ÔÓÐÝÐÓ Ö Ñ º º Þ Ü Þ Ä ¾ (Þ) = ¼ Ü ÐÒ(½ Ü Ü Ü Ü ) = ¼ Ü ¼ ½ Ü ÖÑÓÒ ÔÓÐÝÐÓ Ö Ñ º º À( ½, ¼, ¼, ½; Þ) = = Þ ¼ Þ ¼ Ü ½+Ü Ä (Ü ) Ü ½+Ü Ü ¼ Ü Ü Ü ¼ Ü Ü Ü ¼ Ü ½ Ü

4 Ò Ö Ð Ò ÓÒ ÓÖ Ö Ò Ö Ð Ä Ð Ö R ÓÖ Cµ Å ÑÓÓ Ñ Ò ÓÐ ÓÚ Ö γ : [¼, ½] Å ÑÓÓ Ô ÓÒ Å ω ½,..., ω Ò ÑÓÓ Ö Ò Ð ½¹ ÓÖÑ ÓÒ Å γ (ω ) = () ÔÙÐй Ó ω Ó [¼, ½] º Ì Ö Ò Ö Ð Ó ω ½,..., ω Ò ÐÓÒ γ γ ω Ò...ω ½ = Ò( Ò) Ò... ½ ( ½ ) ½. ¼ ½... Ò ½ Ï Ù ÖÑ Ö Ò Ö Ð ÓÖ ¹Ð Ò Ö ÓÑ Ò ÓÒ Ó Ù Ò Ö Ð º

5 Ï Ó Ò Ö Ò Ð Ó ÙÒ ÓÒ Ý ÓÓ Ò Ö Ò Ò Ó ½¹ ÓÖÑ Ωº { } Ω ½ =,, ω ½ ¼, ω ½ ½ Ð Ð ÔÓÐÝÐÓ Ö Ñ Ä Ò(Þ) = γ ω ¼...ω ¼ }{{} Ò ½ Ñ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò ÓÒ Ú Ö Ð Ò ω ½ =... ¾ ¼ ½... Ò ½ Ò ¾ Þ ½ ½ Þ ½ Ä Ò ½,..., Ò Ö (Þ) = ( ½) Ö γ ω ¼...ω ¼ ω ½...ω ¼...ω ¼ }{{}}{{} Ò Ö ½ Ò½ ½ Û Ö γ ÑÓÓ Ô Ò C\{¼, ½} Û Ò ¹ÔÓ Ò Þ ω ½

6 { Ω ÀÝÔ Ò = ½, ½ ½ ½ ½, ¾ ½ ½¾ ½,..., ( Ò } =¾ ) ½ Ò =½ ½ ÈÓ Ò Ö ÃÙÑÑ Ö ½ ¼ Ä ÔÔÓ¹ Ò Ð Ú Ý ½ µ Ô Ð ÓÖ Ò = ¾ ¾ = ½ : ÝÔ ÖÐÓ Ö Ñ { } ½, ½ ½ ½ ½, ½ : ÖÑÓÒ ÔÓÐÝÐÓ Ö Ñ ½+½ Ê Ñ Î ÖÑ Ö Ò ½ µ { } ÓÖ Ò =, ¾ = ½ Þ, = Þ Þ ½ ½, ½ ½ ½ ½, ½ ½+Þ, ½ : ½+Þ ½ ÛÓ¹ Ñ Ò ÓÒ Ð ÖÑÓÒ ÔÓÐÝÐÓ Ö Ñ ÖÑ ÒÒ Ê Ñ ³¼½µ Ç Ö Ð Ó Ö Ò Ö Ð Ù Ò Ô Ý ÝÐÓÓÑ ÖÑÓÒ ÔÓÐÝÐÓ Ö Ñ Ð Ò Ö Ð ÑÐ Ò Ë Ò Ö ³½½µ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ ÓÒ ÖÓÚ ³¼½µ Ï Û Ò Ó ÓÒ ÖÙ Ð ÐÓ ÐÝ Ö Ð Ó ÓÒ ÖÓÚ³ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Û Ô Ö ÙÐ ÖÐÝ ÓÓ ÔÖÓÔ Ö º

7 ÓÖ ÒÝ ÔÓ Ú Ò Ö Ò Û ÓÒ Ö ( ) ½ Ω Ò =,..., Ò, ½ Ò ½ Û Ö ½ Ò Ü ÑÔÐ ÆÓ { } Ω ½ = ½, ½ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ò ÓÒ Ú Ö Ð µ ½ ½ ½ { } Ω ¾ = ½, ¾, ½ ½ ¾ ½ ½, ¾ ¾ ½, ½ ¾+¾ ½ ½¾ ½ Ì Ý ÒÚÓÐÚ ÐÐ ½, ¾,..., Ò. Ì Ý Ö Ó ÝÔ Û = ½.

8 ÖÓÑ Ω Ò Û Û Ò Ó ÓÒ ÖÙ Ö Ò Ö Ð Û Ö ÓÑÓÓÔÝ ÒÚ Ö Òº º ËÑÓÓ Ô γ ½, γ ¾ ÓÒ Å Ö ÓÑÓÓÔ Ö Ò ¹ÔÓ Ò Ó Ò Ò γ ½ Ò ÓÒ ÒÙÓÙ ÐÝ Ö Ò ÓÖÑ ÒÓ γ ¾. º Ò Ö Ò Ö Ð ÐÐ ÓÑÓÓÔÝ ÒÚ Ö Ò ω Ò...ω ½ = ω Ò...ω ½ γ ½ γ ¾ ÓÖ ÓÑÓÓÔ γ ½, γ ¾. Ý Ù Ò Ö Ð Û Ó Ò ÙÒ ÓÒ Ó Ú Ö Ð Ú Ò ÓÒÐÝ Ý Ò ¹ÔÓ Ò Ó Ô º

9 Ï Ò Ò Ö Ò Ö Ð ÓÑÓÓÔÝ ÒÚ Ö Ò ÓÒ Ö Ò ÓÖ ÔÖÓ Ù ω ½... ω Ñ [ω ½... ω Ñ] ÓÚ Ö Q. Ò Ò ÓÔ Ö ÓÖ Ý Ñ Ñ ½ ([ω ½... ω Ñ]) = [ω ½... ω ½ ω ω +½...ω Ñ]+ [ω ½... ω ½ ω ω +½... ω Ñ]. =½ =½ º Q Ð Ò Ö ÓÑ Ò ÓÒ Ó Ò ÓÖ ÔÖÓ Ù Ñ ξ = ½,..., Ð [ω ½... ω Ð ], ½,..., Ð ½,..., Ð Ð=¼ Q ÐÐ Ò Ö Ð ÛÓÖ (ξ) = ¼.

10 ÓÒ Ö Ò Ö ÓÒ Ñ Ô Ñ Ñ ½,..., Ð [ω ½... ω Ð ] ½,..., Ð ω ½...ω Ð Ð=¼ ½,..., Ð Ð=¼ ½,..., γ Ð Ì ÓÖ Ñ Ò ³ µ ÍÒ Ö Ö Ò ÓÒ ÓÒ ÓÒ Ω Ñ Ô Ò ÓÑÓÖÔ Ñ ÖÓÑ Ò Ö Ð ÛÓÖ Ó ÓÑÓÓÔÝ ÒÚ Ö Ò Ö Ò Ö Ð º ÓÒ ÖÙ ÓÒ Ó ÓÙÖ Ð Ó ÓÑÓÓÔÝ ÒÚ Ö Ò ÙÒ ÓÒ ÓÒ ÖÙ Ò Ö Ð ÛÓÖ Ó ½¹ ÓÖÑ Ò Ω Ò. Í Ò ³ ÝÑ ÓÐ Ñ Ô³ºµ Ý Ò Ö ÓÒ Ñ Ô Ó Ò Ó ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð B(Ω Ò).

11 ÈÖÓÔ Ö Ó B(Ω Ò) ÖÓÛÒ ³¼ µ Ì Ý Ö Û Ðй Ò ÙÒ ÓÒ Ó Ò Ú Ö Ð ÓÖÖ ÔÓÒ Ò Ó Ò ¹ÔÓ Ò Ó Ô º ÇÒ ÙÒ ÓÒ ÙÒ ÓÒ Ð Ö Ð ÓÒ ÙÖÒ ÒÓ Ð Ö Ò º Î ³ ÝÑ ÓÐ Ñ Ô³ Û Ú ÓÑÔÓ ÓÒ Ò Ò ÜÔÐ º B(Ω Ò) ÐÓ ÙÒ Ö Ò ÔÖ Ñ Ú º Ä Z Q¹Ú ÓÖ Ô Ó ÑÙÐ ÔÐ Þ Ú ÐÙ º Ì Ð Ñ ¼ Ò ½ Ó ÙÒ ÓÒ Ò B(Ω Ò) Ö Z¹Ð Ò Ö ÓÑ Ò ÓÒ Ó Ð Ñ Ò Ò B(Ω Ò ½ )º

12 ÓÒ ÕÙ Ò Ä { Ò Ú ÓÖ Ô Ó Ö ÓÒ Ð ÙÒ ÓÒ Û ÒÓÑ Ò ÓÖ Ò ½,..., } Ò, ½, ½ Ò. ÓÒ Ö Ò Ö Ð Ó ÝÔ ½ ¼ Ò β Û Ò, β B(Ω Ò). Ï Ò ÓÑÔÙ Ù Ò Ö Ð º Ì Ö ÙÐ Ö Z¹Ð Ò Ö ÓÑ Ò ÓÒ Ó Ð Ñ Ò Ò B(Ω Ò ½ ) ÑÙÐ ÔÐ Ý Ð Ñ Ò Ò Ò ½. ÓÒ Ô Å Ô ÝÒÑ Ò Ò Ö Ð Ó Ò Ö Ð Ó ÝÔ Ò Ú Ð٠Ѻ Ï Ò ÔÓ Ð

13 ¾º Ä Ò Ö Ö Ù Ð Ý Ó ËÝÑ ÒÞ ÔÓÐÝÒÓÑ Ð ÝÒÑ Ò Ò Ö Ð Á (ɛ, Λ ) = Γ(ν Ä /¾) Æ =½ Γ(ν ) Û Ö ν = Æ =½ ν º ËÝÑ ÒÞ ÔÓÐÝÒÓÑ Ð U( ) = F ¼ ( ) = Ü ¼ ( Æ =½ Ü Ü ν ½ Ô ÒÒ Ò Ö Ì Ó / Ì Ô ÒÒ Ò ¾¹ ÓÖ (̽, ̾) F( ) = F ¼ ( )+U( ) Æ Ü Ñ ¾. =½ Ü ) δ ( ½ / (̽, ̾) Æ =½ Ü ) ν (Ä+½) /¾ U Ü (F (Λ )) ν Ä /¾, / (̽, ̾) Õ ¾,

14 Ü ÑÔÐ ½ Î ÙÙÑ Ö Ô Û ν = ¾Ä Ò = : Ü ¼ ( Æ =½ Ü Ü ν ½ ) ( ) Æ ½ δ ½ Ü Ü ÑÔÐ ¾ ËÙÒÖ Ö Ô Û ν = Ä+½ Ò = ¾ : Ü ¼ ( Æ =½ Ü Ü ν ½ ) δ ( ½ =½ =½ U ¾ ) Æ ½ Ü F (Λ )

15 ÙÑ Ò Ò Ö Ð Û Ó Ò Ö Ò Ú Ò Ý ÓÒ ÓÖ Ó Ó ËÝÑ ÒÞ ÔÓÐÝÒÓÑ Ð º ÌÖÝ Ó Ò Ö ÓÙ ÝÒÑ Ò Ô Ö Ñ Ö Ö Ú Ðݺ Ö Ò Ö ÓÒ ÓÚ Ö Ü ÓÒ Ö Ë Ó ÔÓÐÝÒÓÑ Ð Ò ÒÓÑ Ò ÓÖ Ò Ò Ö ÙÑ Ò Ó ÑÙÐ ÔÐ ÔÓÐÝÐÓ º ÐÐ ÔÓÐÝÒÓÑ Ð Ò Ë Ö Ð Ò Ö Ò Ò Ü ÝÒÑ Ò Ô Ö Ñ Ö Ü +½. Å Ô Ò Ö Ð ÓÚ Ö Ü +½ Ó Ò Ò Ö Ð ÓÚ Ö Ò Ó ÓÖÑ Ò Ò Ö ÓÚ Ö Ò. ½ ¼ Ò β Û Ò, β B(Ω Ò) Ì Ð Ò Ö Ö Ù ÓÒ Ð ÓÖ Ñ Ú Ò ÙÔÔ Ö ÓÙÒ ÓÖ Ë º

16 Ä Ò Ö Ö Ù ÓÒ Ð ÓÖ Ñ ÖÓÛÒ ³¼ µ ÁÒÔÙ Ó ÔÓÐÝÒÓÑ Ð Ë ÕÙ Ò Ó ÝÒÑ Ò Ô Ö Ñ Ö Ü Ö ½, ÜÖ ¾,..., ÜÖÒ ÇÙÔÙ ÕÙ Ò Ó Ó ÔÓÐÝÒÓÑ Ð Ë ½, Ë ¾,..., Ë Ò Ë ÓÒ Ò ÔÓÐÝÒÓÑ Ð Û Û ÜÔ Ò Ò Ö Ò Ö Ò Ö Ò ÓÙ Ö Ô Ö Ñ Ö º Á ÐÐ ÔÓÐÝÒÓÑ Ð Ò Ë [Ö ½,..., Ö ] Ö Ð Ò Ö Ò Ü Ö +½, Ò Ü Ò Ö ÓÒ Ò ÓÒ º º Ë Ð Ò ÖÐÝ Ö Ù Ð Ö Ò ÓÖ Ö Ò (Ü Ö ½, ÜÖ ¾,..., ÜÖÒ ) Ù ÓÖ ÐÐ ½ Ò Ú ÖÝ ÔÓÐÝÒÓÑ Ð Ò Ë [Ö ½,..., Ö ] Ð Ò Ö Ò Ü Ö +½. Á ÖÙ ÓÖ {U, F } Û Ý ÝÒÑ Ò Ö Ô Ð Ò ÖÐÝ Ö Ù Ð º

17 ÓÒ Ö Ð ÓÒ Ò ÓÒÖ ÓÒ Ó \ Ö Ô Ó Ò ÖÓÑ Ð Ò Ò // : Ö Ô Ó Ò ÖÓÑ ÓÒÖ Ò Ò Ð ÓÒ Ò ÓÒÖ ÓÒ Ó Ö Ò ÓÑÑÙ º ÓÒ Ö \ // Û Ö, Ö Ó Ò Ó ÒÝ Ù Ö Ô ÐÐ Ñ ÒÓÖ Ó. º G Ó Ö Ô ÐÐ Ñ ÒÓÖ¹ÐÓ ÓÖ G ÐÐ Ñ ÒÓÖ ÐÓÒ Ó G Û Ðк

18 Ä H Ò Ó Ö Ô º Ò G H Ó Ó Ö Ô Û Ó Ñ ÒÓÖ Ó ÒÓ ÐÓÒ Ó H. Ì Ò Ö Ô Ò H Ö ÐÐ ÓÖ Ò Ñ ÒÓÖ Ó G H. Ì G H Ñ ÒÓÖ¹ÐÓ º Ì ÓÖ Ñ ÊÓ Ö ÓÒ Ò Ë ÝÑÓÙÖµ ÒÝ Ñ ÒÓÖ¹ÐÓ Ó Ö Ô Ò Ò Ý Ò Ó ÓÖ Ò Ñ ÒÓÖ º Ü ÑÔÐ Ä G Ó ÐÐ ÔÐ Ò Ö Ö Ô º Ì Ñ ÒÓÖ ÐÓ º Á Ò Ò Ó ÐÐ Ö Ô Û Ú Ò Ö Ã ÒÓÖ Ã, Ñ ÒÓÖº

19 Ì ÓÖ Ñ ÖÓÛÒ ³¼ Ò Ä Ö ³½ µ Ì Ó Ð Ò ÖÐÝ Ö Ù Ð ÝÒÑ Ò Ö Ô Ñ ÒÓÖ¹ÐÓ º Ï ÓÙÐ Ö ÓÖ ÓÖ Ò Ñ ÒÓÖ º Ö Ù Ý Û Åº Ä Ö µ Ä Λ Ó Ñ Ð ÝÒÑ Ò Ö Ô Û ÓÙÖ ÓÒ¹ ÐÐ Ð º ÇÒ¹ ÐÐ ÓÒ ÓÒ Ô ¾ = ¼, = ½,..., µ ÛÓ ÐÓÓÔ Û Ò ÐÐ Ö Ô Ó Ð Ò ÖÐÝ Ö Ù Ð º Ö ÐÓÓÔ Û Ò Ö ÓÖ Ò Ñ ÒÓÖ º ÓÙÖ ÐÓÓÔ Ö ÖÙÒÒ Ò ÓÒ ÓÙÖ ÓÑÔÙ Ö Ò ÓÒ ÖÑ ÓÖ Ò Ö ¹ÐÓÓÔ Ñ ÒÓÖ Ó Öº Þ Ð ÓÒ ÛºÖºº Ð Ò ÖÐÝ Ö Ù Ð Ý ÔÓ Ð Ý ÓÖ Ò Ñ ÒÓÖ º Á Ú Ò ÓÒ ÑÓÖ ÙÐ ÔÖÓ Ð Ñ Ó Û Ö Ô Ú ÐÙ Ó ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Û ÓÒ³º

20 º Ì ÛÓ¹ÐÓÓÔ ÙÒÖ Ö Ô Û Ö Ö ÖÝ Ñ Ñ ½ Ô Ñ ¾ Ñ ÁÒ = ¾ Ñ Ò ÓÒ Û Ó Ò Ò ÝÒÑ Ò Ò Ö Ð ω Ë =¾ () =, σ F Û ω = Ü ½ Ü ¾ Ü + Ü ¾ Ü Ü ½ + Ü Ü ½ Ü ¾ F (, Ñ ¾ ½, Ñ ¾ ¾, Ѿ ) = ܽ Ü ¾ Ü +(Ü ½ Ü ¾ +Ü ¾ Ü +Ü ½ Ü )(Ü ½ Ñ ¾ ½ +Ü ¾Ñ ¾ ¾ +Ü Ñ ¾ ), = Ô¾, σ = { [Ü ½ : Ü ¾ : Ü ] P ¾ Ü ¼, = ½, ¾, } F ÒÓ Ð Ò Ö Ò ÒÝ Ü, Ö Ô ÒÓ Ð Ò ÖÐÝ Ö Ù Ð º

21 ÁÒÓÑÔÐ µ ÓÖÝ Ó ÙÒÖ ÕÙ Ð Ñ ÖÓ ÙÖ Ð Ö Ì Ö ÓÚ ½ µ Ö ÙÐ Û ÝÔ Ö ÓÑ Ö ÙÒ ÓÒ ÖÓÓ È ÚÓÚ ÖÓÚ ¾¼¼¼µ Ù Ó Ý ÖÙÐ Ñ Ò ÖÝ Ô Ö ÜÔÖ Ý ÐÐ Ô Ò Ö Ð Ä ÔÓÖ Ê Ñ ¾¼¼ µ ÓÐÚ Ò ÓÒ ¹ÓÖ Ö Ö Ò Ð ÕÙ ÓÒ Ö ÙÐ Ý Ò Ö Ð ÓÚ Ö ÐÐ Ô Ò Ö Ð Ö Ö ÖÝ Ñ Ö Ò ÙÞ Ñ Ë Ö ½ µ Ö ÙÐ Û Ä ÙÖ ÐÐ ÙÒ ÓÒ Ó ÞÝÞ Ä ÔÓÖ Ê Ñ ½ µ Ý Ñ Ó ÓÙÖ Ö ¹ÓÖ Ö Ö Ò Ð ÕÙ ÓÒ Ò ÒÙÑ Ö Ð ÓÐÙ ÓÒ µ ÖÓÓ Ã ÖÒ Ö È ÚÓÚ ÖÓÚ ¾¼¼ µ Ò Ö Ð Ö ÔÖ Ò ÓÒ ÒÚÓÐÚ Ò Ð ÙÒ ÓÒ Å ÐÐ Ö¹Ë Ï ÒÞ ÖÐ Ý ¾¼½¾µ ÓÒ ÓÒ ¹ÓÖ Ö Ö Ò Ð ÕÙ ÓÒ ÇÙÖ Ó Ð ËÓÐÚ Ò Û Ö Ò Ð ÕÙ ÓÒ Ä ÔÓÖ Ò Ê Ñ ÓÖ ÕÙ Ð Ñ µ Ò Ó Ò Ö ÙÐ ÒÚÓÐÚ Ò ÐÐ Ô Ò Ö Ð

22 Ö ÙÐ ÓÖ Ñ Ò ÓÒ ÒÓÛÒ ÖÓÑ Ö Ò ÙÞ Ñ Ò Ë Ö ½ µ Ë () = ( ( ( ) Γ( )Γ( ¾ ½) Γ( ¾ ) Γ(¾ ¾ )Γ(½ ¾ )Γ( ¾ ½)¾ Γ( ¾) ( (, ¾ ; ¾ ¾, ¾ ¾, ¾ ¾ ; Ѿ ½ + (, ¾ ¾ ; ¾ ¾, ¾, ¾ ¾ ; Ѿ ½, Ѿ ¾, Ѿ, Ѿ ¾, Ѿ )(, ¾ ¾ ; ¾, ¾ ¾, ¾ ¾ ; Ѿ ½, Ѿ ¾, Ѿ Ѿ ½ )( ) Ѿ ¾ ½ ¾ )( + (, ¾ ¾ ; ¾ ¾, ¾ ¾, ¾ ; Ѿ ½, Ѿ ¾, Ѿ Ѿ ( )( +Γ(½ ¾ )¾ (½, ¾ ¾ ; ¾, ¾, ¾ ¾ ; Ѿ ½, Ѿ ¾, Ѿ )( + (½, ¾ ¾ ; ¾, ¾ ¾, ¾ ; Ѿ ½, Ѿ ¾, Ѿ )( + (½, ¾ ¾ ; ¾ ¾, ¾, ¾ ; Ѿ ½, Ѿ ¾, Ѿ Û Ä ÙÖ ÐÐ ÙÒ ÓÒ ) ѽ ¾ Ѿ ¾ ½ ¾ Ñ ¾ ¾ Ѿ ¾ ( ½, ¾ ; ½, ¾, ; Ü ½, Ü ¾, Ü ) = ½=¼ ¾=¼ =¼ Ò ÈÓ ÑÑ Ö ÝÑ ÓÐ ( ) Ò = Γ( +Ò) Γ( ) ) )) ¾ ½ ) ) ¾ ½ ) ѽ ¾ Ѿ ¾ ½ ¾ ¾ ( ½) ½ + ¾ + ( ¾) ½ + ¾ + ( ½) ½ ( ¾) ¾ ( ) Ü ½ ½ Ü ¾ ¾ Ü ½! ¾!! ) ) ¾ ½

23 Í Ò ÙÐ Ö¹ Ö ÙÑ ½ (Ò) = Ò ½ =½, ½½(Ò) = Ò ½ =½ ½( ½) Û Ò ÜÔ Ò Ö ÙÐ Ò = ¾ Ò Ó Ò Ë =¾ () = ½ ½=¼ ¾=¼ =¼ ( ) ( ¾ ½¾! ½! ¾!! Ñ ¾ ½ ) ½ ( Ñ ¾ ¾ ) ( ) ¾ Ñ ¾ (½¾ ½½ ( ½¾ )+ ½ ( ½¾ ) ½ ( ½¾ ) ½ ( ½¾ )( ½ ( ½ )+ ½ ( ¾ )+ ½ ( )) ( ½ ( ½ ) ½ ( ¾ )+ ½ ( ¾ ) ½ ( )+ ( ½ ( ) ½ ( ½ ))+ ( ) ¾(¾ ½ ( ½¾ ) ½ ( ¾ ) ½ ( )) ÐÒ Ñ¾ ½ )+¾(¾ ½ ( ½¾ ) ½ ( ) ½ ( ½ )) ÐÒ Ñ¾ ¾ ( ) +¾(¾ ½ ( ½¾ ) ½ ( ½ ) ½ ( ¾ )) ÐÒ Ñ¾ ( ) ( ( ) ( ( ) ( )) + ÐÒ Ñ¾ ½ ÐÒ Ñ¾ ¾ )+ÐÒ Ñ¾ ¾ ÐÒ Ñ¾ )+ÐÒ Ñ¾ ½ ÐÒ Ñ¾ Ï Ó Ò Ú ¹ ÓÐ Ò ÙѺ Ò Û ÜÔÖ Ò Ö Ð Ý Ö Ò Ö Ð Ò

24 Ë Ö ÖÓÑ ÓÒ ÓÖ Ö Ö Ò Ð ÕÙ ÓÒ (Ô ¼ () ¾ + Ô ½() ) ¾ + Ô ¾() Ë() = Ô () Ô ¼, Ô ½, Ô ¾, Ô Ö ÔÓÐÝÒÓÑ Ð Ò Ó Ö µ Ò Ò Ñ ¾ ½, Ѿ ¾, Ѿ. Ò Þ ÓÖ ÓÐÙ ÓÒ Ë() = ½ ψ ½ ()+ ¾ ψ ¾ ()+ ¼ ½ Ô ( ½ ) Ô ¼ ( ½ )Ï( ½ ) ( ψ ½()ψ ¾ ( ½ )+ψ ¾ ()ψ ½ ( ½ )) Û ÓÐÙ ÓÒ Ó ÓÑÓ Ò ÓÙ ÕÙ ÓÒ ψ ½, ψ ¾ ÓÒ Ò ½, ¾, ÏÖÓÒ ÖÑ Ò Ò Ï() = ψ ½ () ψ ¾() ψ ¾ () ψ ½()

25 Ï Û ÐÐ Ù ÓÑÔÐ ÐÐ Ô Ò Ö Ð Ó Ö Ò Ã( ) = ½ ¼ Ü (½ Ü ¾ )(½ ¾ Ü ¾ ) ÓÑÔÐ ÐÐ Ô Ò Ö Ð Ó ÓÒ Ò ½ ½ ¾ Ü ( ) = ¾ Ü ¼ ½ Ü ¾ ÙÒ ÓÒ (), () Ù () ¾ + () ¾ = ½

26 ÁÒÖÓ Ù ÒÓ ÓÒ Ü ½ = (Ñ ½ Ñ ¾ ) ¾, Ü ¾ = (Ñ ) ¾, Ü = (Ñ + ) ¾, Ü = (Ñ ½ + Ñ ¾ ) ¾ ÓÒ Ö ÙÜ Ð ÖÝ ÐÐ Ô ÙÖÚ Ú Ò Ý ÕÙ ÓÒ Ý ¾ = (Ü Ü ½ )(Ü Ü ¾ )(Ü Ü )(Ü Ü ). Ý Ó ÓÐÓÑÓÖÔ ½¹ ÓÖÑ Ü/Ý ÓÒ Ó Ò Ô Ö Ó Ò Ö Ð () = ψ ½ () = ¾ Ü Ü¾ Ü Ý = ξ() à ( ()), Ü Ü ψ ¾ () = ¾ Ü Ý = ξ() à ( () ) Û ξ() = (Ü Ü ½ )(Ü Ü ¾ ) (Ü Ü¾)(Ü Ü½) (Ü Ü½)(Ü Ü¾), () = (Ü ¾ ܽ)(Ü Ü ) (Ü Ü½)(Ü Ü¾), ()¾ + () ¾ = ½ ψ ½ () Ò ψ ¾ () ÓÐÚ ÓÑÓ Ò ÓÙ Ö Ò Ð ÕÙ ÓÒ ÓÖ Ë().

27 ÙÖ ÖÑÓÖ ÖÓÑ Ò Ö Ò ÓÚ Ö Ü Ü Ý Ì Ô Ö Ó Ñ Ö Ü Ó ÐÐ Ô ÙÖÚ Ò Û Ú Ä Ò Ö Ö Ð ÓÒ Û Ó Ò φ ½ () = (Ã( ()) ( ())) ξ() φ ¾ () = ξ() ( () ) ( ψ½ () ψ ¾ () φ ½ () φ ¾ () ) ψ ½ ()φ ¾ () ψ ¾ ()φ ½ () = π ξ(). Ì Ö ÔÔÖÓÔÖ ÙÒ ÓÒ Ó ÜÔÖ ÙÐÐ ÓÐÙ ÓÒº

28 ÙÐÐ ÓÐÙ ÓÒ ( ) Ë() = ½ Ð ¾ (α ) ψ ½ ()+ ½ π π Û Ö =½ ¼ ½ (η ½ ( ½ ) η ½ ( ½ ) = ψ ¾ ()ψ ½ ( ½ ) ψ ½ ()ψ ¾ ( ½ ) ) ½ ½ ¼ (Ü ¾ Ü ½ )(Ü Ü ) (η ¾( ½ ) η ½ ( ½ )) η ¾ ( ½ ) = ψ ¾ ()φ ½ ( ½ ) ψ ½ ()φ ¾ ( ½ ) Ð Ù Ò ÙÒ ÓÒ Ð ¾ (Ü) = ½ ( Ä ¾ ( Ü ) Ä ( Ü ) ) ( ) ¾ α = ¾ Ö Ò,, δ δ : ÔÓÐÝÒÓÑ Ð Ò Ñ ½, Ñ ¾, Ñ Ó Ö Ò ¾ Ö Ôº = (Ñ ½, Ñ ¾, Ñ ) ÐÒ(Ñ ¾ ½ )+ (Ñ ¾, Ñ, Ñ ½ ) ÐÒ(Ñ ¾ ¾ )+ (Ñ, Ñ ½, Ñ ¾ ) ÐÒ(Ñ ¾ ), ½ (Ñ ½, Ñ ¾, Ñ ) = ¾Ñ ¾ ½ Ѿ ¾ Ѿ, ¼ (Ñ ½, Ñ ¾, Ñ ) = ¾Ñ ½ Ñ ¾ Ñ Ñ¾ ½ Ѿ ¾ Ѿ ½ Ѿ + ¾Ñ¾ ¾ Ѿ

29 ÓÒÐÙ ÓÒ ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð Ö ÓÑÓÓÔÝ ÒÚ Ö Ò Ö Ò Ö Ð Û Ô Ö ÙÐ ÖÐÝ ÓÓ ÔÖÓÔ Ö º Ï Û Ò Ó Ù Ñ Ó Ö Ú ÐÝ Ò Ö ÓÙ ÝÒÑ Ò Ô Ö Ñ Ö º ÌÓ Û Ö ÔÔÖÓ Ò Ù Ö Ö Ö ÓÒ Ó Ð Ò Ö Ö Ù Ð Ý ÓÒ Ö Ô º Ì Ð Ó Ð Ò ÖÐÝ Ö Ù Ð Ö Ô Ñ ÒÓÖ¹ÐÓ º Ì ÐÐÓÛ ÓÖ ÓÒÚ Ò Ò Ð ÓÒ Ý ÓÖ Ò Ñ ÒÓÖ º Ï Ó Ò Ò Û Ö ÙÐ ÓÖ ÙÒÖ Ò Ö Ð Û Ö Ö ÖÝ Ñ º Ì Ö ÙÐ ÓÒ Ò Ò Ö Ð ÓÚ Ö ÐÐ Ô Ò Ö Ð Ò Ò Ù Ð ÙÔ ÖÓÑ Ô Ö Ó Ò Ö Ð Ó Ò ÙÜ Ð Öݵ ÐÐ Ô ÙÖÚ º Ò ÜÔÖ ÓÒ Ò ÖÑ Ó Ö Ò Ö Ð ÛÓÙÐ ÔÖÓ ÐÝ Ö ÕÙ Ö ÙÖ Ö Ü Ò ÓÒ Ó ÔÓÐÝÐÓ Ö Ñ º

30 Û ÐÐ ÒÓÛÒ ÙÒ ÓÒ Ð ÕÙ ÓÒ Ú ¹ ÖÑ¹Ö Ð ÓÒ ( ( ) ½ Ý ½ Ü Ä ¾ ) Ä ¾ ½ ½ ½ ½ +Ä ¾ (ÜÝ) Ä ¾ (Ü) Ä ¾ (Ý) = ½ ¾ ÐÒ¾ (½ Ü)+ ½ ¾ ÐÒ¾ (½ Ý) Ü Ý ÏÖ Ò ÙÒ ÓÒ Ö Ò Ö Ð ÓÒ Ó Ð Ô Ù Ò ψµ Ö Ð ÓÒ ÓÑ Ó Ú ÓÙ ( ) [ ½ Ý Ü Ä ¾ ½ ½ = Ü + Ü ½ Ü Ý ½ Ý Ü ] [ ] [ Ü Ý + Ý Ü Ü ½ ÜÝ ½ Ü Ý Ü ½ Ý Ü + Ü ] ½ Ü Ü ½ Ü ( ) [ ½ Ü Ý Ä ¾ ½ ½ = Ý + Ý ½ Ý Ü ] [ ] [ Ü Ý + Ý Ü Ü + ½ Ü ½ ÜÝ ½ Ü Ý Ý ½ Ý Ý + Ý ] ½ Ý Ý ½ Ý Ý [ Ü Ä ¾ (ÜÝ) = Ü + Ý Ý ] [ ] [ ] Ü Ý + Ý Ü Ü, Ä ¾ (Ü) = ½ ÜÝ Ü Ü Ý, Ä ¾ (Ý) = ½ Ü Ý Ý ½ Ý

31 Á ÔÓÐÝÒÓÑ Ð Ë = { ½,..., Ò} Ö Ð Ò Ö Ò ÝÒÑ Ò Ô Ö Ñ Ö Ü Ö ½, ÓÒ Ö = Ü Ö ½ +, =, = ÜÖ Ü ½ =¼ Ö ½ Ë (Ö ½) = ÖÖ Ù Ð ÓÖ Ó { } ½ Ò, { } ½ Ò, { } Ö ÓÖ ÕÙ Ò (Ü Ö ½, ÜÖ ¾,..., ÜÖÒ ) Ë (Ö ½), Ë (Ö ½, Ö¾),..., Ë (Ö ½,..., Ö Ò) Ò Ö ÓÒ ½ < Ò Ë [Ö ½, Ö¾] = Ë (Ö ½, Ö¾) Ë (Ö ¾, Ö½) Ë [Ö ½, Ö¾,..., Ö ] = ½ Ë [Ö ½,...,ˆÖ,..., Ö ](Ö ), > Ü Ö ½, ÜÖ ¾,..., ÜÖÒ Ë (Ö ½), Ë [Ö ½, Ö¾],..., Ë [Ö ½,..., Ö Ò] º Ë Ð Ò ÖÐÝ Ö Ù Ð Ö Ò ÓÖ Ö Ò (Ü Ö ½, ÜÖ ¾,..., ÜÖÒ ) Ù ÓÖ ÐÐ ½ Ò Ú ÖÝ ÔÓÐÝÒÓÑ Ð Ò Ë [Ö ½,..., Ö ] Ð Ò Ö Ò Ü Ö +½. Á ÖÙ ÓÖ {U, F } Û Ý ÝÒÑ Ò Ö Ô Ð Ò ÖÐÝ Ö Ù Ð º

32

F(jω) = a(jω p 1 )(jω p 2 ) Û Ö p i = b± b 2 4ac. ω c = Y X (jω) = 1. 6R 2 C 2 (jω) 2 +7RCjω+1. 1 (6jωRC+1)(jωRC+1) RC, 1. RC = p 1, p

F(jω) = a(jω p 1 )(jω p 2 ) Û Ö p i = b± b 2 4ac. ω c = Y X (jω) = 1. 6R 2 C 2 (jω) 2 +7RCjω+1. 1 (6jωRC+1)(jωRC+1) RC, 1. RC = p 1, p ÓÖ Ò ÊÄ Ò Ò Û Ò Ò Ö Ý ½¾ Ù Ö ÓÖ ÖÓÑ Ö ÓÒ Ò ÄÈ ÐØ Ö ½¾ ½¾ ½» ½½ ÓÖ Ò ÊÄ Ò Ò Û Ò Ò Ö Ý ¾ Á b 2 < 4ac Û ÒÒÓØ ÓÖ Þ Û Ö Ð Ó ÒØ Ó Û Ð Ú ÕÙ Ö º ËÓÑ Ñ ÐÐ ÕÙ Ö Ö ÓÒ Ò º Ù Ö ÓÖ ½¾ ÓÖ Ù Ö ÕÙ Ö ÓÖ Ò ØÖ Ò Ö ÙÒØ ÓÒ

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