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2 / ISBN /TP 38 8.

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6 . C. C C 5. PASCAL

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13 ... A BX x N Z Q R C N P I I [] N m {,,, Λ, m } {,, Λ, m} {,, Λ, m} P m {} U E A A x X x X A {,,3} B { n n N} C { x x R < x < } Z m

14 {,,}{,} 3 {,,3} {,3, } 4 A {, α,{ }}.. AB B A B A B A A B B A B A A B B A B A A A A B A x B x A A B A B A B B A A B A A B A B B A 3 A A A PA pa P A { B B A} A A A A P A AB A B P A P B P A P B A B A B P A P B P A P B A B 3 P A ΥP B P A Υ B 4 P A Ι P B P A Ι B 5 P A B P A P B Υ{ } 355 A{,}B{,} AB{}PAB{,{ } } P A P B Υ{ } {,{ },{, }}..3 A B Υ Ι ~

15 3 4 A B A B A Υ B A B A B A Ι B A B A B A B A\B B A A B A B B A A B A B A A A ~ A A A A A Υ B { x x Ax B} A Ι B { x x Ax B} A B { x x A x B} A B A B Υ B A A { x x U x A} n n Υ Ai A Υ A i ΥΛ Υ A n n Ι Ai i A Ι A Ι Λ Ι A n J Υ A { x j J, x A } Ι A x j J, x A } j J j j j J j { j John Venn U ABC A Υ A A A Ι A A A Ι B Ι C A Ι B Ι C A Υ B Υ C A Υ B Υ C A Ι B B Ι A A Υ B B Υ A A Ι B Υ C A Ι B Υ A Ι C A Υ B Ι C A Υ B Ι A Υ C A Υ A A Ι U A A Υ U U A Ι A Υ A U A Ι A

16 4 De Morgen A Υ B A Ι B A Ι B A Υ B A Ι A Υ B A A Υ A Ι B A A A 3 ABC A B A Ι B A B B A 3 A A A A A U A A A U 4 A B C A B C 5 A Ι B C A Ι B A Ι C A Υ B C A Υ B A Υ C A{,,3}B{}C{}..4, 5 AB A B A B A B A B { <, > A, B} n A B A B A B B A 4 ABC A B Υ C A B Υ A C A B Ι C A B Ι A C 3 B Υ C A B A Υ C A 4 B Ι C A B A Ι C A 5 A B C A B A C 6 B C A B A C A 7 C A B A C B C C A C B 8 ABCD A B C D A C B D 7 C

17 A A A { A A A, A } α α Aα Ι Aβ, α β Υ A α A α 7 C α A C A { A A A, A } α α α Υ A α α C { Aα Aα A, Aα } A C C A..6 A 5 n+ n n n m + AB A Υ B A + B A Ι B ABC A Υ B Υ C A + B + C A Ι B B Ι C C Ι A + A Ι B Ι C m 6 A, A, Λ, A n n n n Υ Ai Ai Ai Ι Aj + Ai Ι AjΙ Ak + Λ + A Ι A Ι Λ Ι i n i i < j n i < j< k n A n x x 3.5 3

18 6 A Ι A Ι Λ Ι An U n n Υ A i i n U Ai + Ai Ι Aj Ai Ι Aj Ι Ak + Λ + A Ι i i< j n i< j< k n Λ Ι A n A B A B {}{,} 3 4 U A B A B A B A B Υ B A 6 A {} B{{}} PA{,{}} PB{,{{}}}

19 7 7 A B A Ι B A Υ B E A B E E E ABC A B C D A A B B C A C A B B C A C A B B C A C A B B C A C BCD B A{} B{{}}BC C A B{}C{{}} D AB{} C{{}} A B A B B B C A B D A B C 3 P { x x + 4} Q { x x + 6 5x} A P Q B P Q C Q P D Q P C 4 A {{,,3},{4,5},{6,7,8}} A A B{,,3} A C{{ 4,5}} A D A C

20 8 5 A B C { } D { } B 3 6 A { x x x } B { x x 4 <, x Z} C { x y x } D { x x + y 5, xy 6} AAB BAC CCD DCA A 7 A B C D D 8 M x f x }, N { x f x } f x f x { A M Ι N B M Υ N C M N DM N B 9 A {,{ }} A { } P A B { } P A C {{ }} P A D {{ }} P A B A { } BPPA A B B{ } B C{{ }} B D {,{ }} P A D P P P A {{ },{,{ }}} B {,{,{ }},{ }} C {,{,{ }},{{ }},{ }} D {,{,{ }}} C * P B A B C3 D4

21 9.3. M { x x x x Z} N { x x x 3 x Z} M Υ N M Ι N {,3,4,6,8,9,,} { 6,} U {,, Λ,7} A{}B{}C{3 } A Ι B A Ι C A Υ C B Ι C {,5,7 } {,5,7 } {3} 3 A { x x < 3, x Z}, B { x x k, k Z} C {,,3,4,5 } A C A B Ι C 3 B B 4 A C B {,6,7,8} {,3,5} {,,4,6,7,8} 4 I A { x x < 3, x I} B { x xx < } C {,3,5 } A Ι B Υ C B A Υ C 3 C A Ι B A 4 B Ι C A {,,3,5} {,3,5,7,,3,7,9} 5 U {,,3, Λ,} A B C A { x x < 4} B { x x 6x 7 } C { x x < } A B Ι C A Ι B Ι C 3 A Ι B C {,,,3,4,5} {,,,3,4,5} 6 AB A B A {}B {,{,}} A B { } 3 A {} B {,,{ }} 4 A { }, B {,{ }} A A B A B B A B A B

22 C A B A B D A B A B C A C A *7 A {{ x, y},, x, y} A { x, y} A { } {{ x, y}} A A A PA {,{x,y}} {{x,y},x,y} { {x}{y}{ }{{x,y}}{x,y}{x,{x,y}}{y,{x,y}}{,x}{,y} {,{x,y}}{,x,{x,y}}{,y,{x,y}}{,x,y}{x,y,{x,y}}{,x,y,{x,y}}} 8 A {,{ }} PA {,{ },{{ }},{,{ }}} *9 A{{,},{3}}B{{},{},{3}} A Υ B A Ι B PA {{,},{},{},{3}} {3} {,{{,}},{{3}},{{,},{3}}} A { x < x <, x 7n + 3, n Z, x Z} A 5 A A PA 4 Ι { } {,{ }} 3 {,{ }} { } {,{ }} {{ }} *

23 5 A{,,} S {{, },{, }} S {{ },{, },{, }} S {{ },{, }} 6 {{ },{, 3 S 4 {{,, }} S 5 {{ },{ },{ }} S }} A A S S 3 S 4 S 5 S 3 S 4 S * A B A C BC P Υ Q Q P Ι Q P P P Υ Q Q P Ι Q P *3{ } {,{ }} { } {,{ }} 4 A { }, B P P A { } B { } B *5AB A B A B 6 AB PA BPA PB *7 A B B B A A B B A B 8 A { A} P A 9 A B { A Ι B, B A} A Υ B A B A Ι B Υ B A B Ι A Υ B Ι A B Ι U B B A Υ B A B A B {A BB A} A Υ B A Ι B A, B A B Υ B A A Ι B Υ B Ι A A Υ B Ι A Υ B A ΥB A Ι B A Υ B A Ι B A Υ B A Ι B A, B A B B A A B { A Ι B, A B, B A} A Υ B A Ι B A B, B A - AB A Ι B A B B A A Υ B A Ι B A B, B A { A Ι B} A Υ B A B B A

24 A B A B A Ι B B A - A Ι B A Υ B A Ι B A A Υ B A A Ι B A Υ B B A Ι B A Υ B AB A B B A.4 ABC A B, B C A C C { B}, B { A}, A { } {{}} { } {{ }} 3 x { x} {{ x}} 4 { x} { x} {{ x}} 5 A B A B 6 A B A B 7 A A A 8 A B Υ C A B Ι A C 9 A Ι B B A B A { x} Υ x x A x A { x} {{ x}} {x} x A { x} A B A BA A B A BA

25 3 B A B A A Ι B 65 A B A B 7 A A 9 A Ι B B B A x A x { x} A A x x Υ{ x} A x A x A 3 ABCD Z A {,,7,8} B { x x < 5 x Z} C { x x Z x 3x 3 } k D { x x k Z k 6} A Υ B Υ C Υ D A Ι B Ι C Ι 3 B A Υ C 4 A Ι B Υ D D A Υ B Υ C Υ D {x x,,7,8 xk k k <5 x3 3 x k k k6} A Ι B Ι C Ι D {x x,,7,8 xk k k <5 x3 3 x k k k6} 3 B A Υ C {x x B x A C } 4 A Ι B Υ D {x x D x A B } A {,,7,8 } B {,,4,9,6,5,36,49} C {,3,6,9,,5,8,,4,7,3} D {,,4,8,6,3,64} A Υ B Υ C Υ D {,,,3,4,6,7,8,9,,5,6,8,,4,5,7,3,3,36,49,64} A Ι B Ι C Ι D 3 B A Υ C {4,6,5,36,49} 4 A Ι B Υ D {,,,4,8,6,3,64} 4 U {,, Λ,} A {,3,5,7,9,} B {,3,5,7,} C {,3,6,} D {,4,8} A Υ B A Ι C 3 A Υ B Ι C 4 A B 5 C D 6 B D

26 4 A Υ B {,,3,5,7,9,} A Ι C {3} A Υ B Ι C {,5,7,9,} A B {,9 } C D {3,6,} B D {3,4,5,7,8,} 5 A {{ },{,},{,, }}, B {{,},{ }} A Υ B, A Ι B, A B, P A A Υ B {{ },{,},{}} A Ι B {{, }} A B {{ }} P A {,{{ }},{{,},{,}}} {,} {,, } {{ },{,}} 6 A Υ B C Ι A Υ B B A A Υ B C Ι A Υ B B A A Υ B B A A Υ A Ι B A Υ Ι A A Υ B C A Υ B C Ι A A B A Ι B Υ B A A Ι BB A B B A A Ι B A Ι B A A Υ A Ι B A B B A B Ι B Ι A B Ι B Υ A B Ι A 7 A Υ B Ι B A Υ B A Υ B Υ C B Υ C Υ A 3 B A Ι C Υ A Ι B Ι C 4 A Ι B C A Υ B A Υ B Ι B A Υ B B A Υ B A Υ B Υ C B Υ C Υ A A Υ B Υ C Ι B Υ C Υ A A Ι B Υ C Υ B Υ C Ι B Υ C Υ A A Ι B Υ C Υ A A 3 B A Ι C Υ A Ι B Ι C B Ι A Ι C Υ B Ι A Ι C B Ι A Ι C Υ A Ι C B 4 A Ι B C A Υ B A Ι B Ι C Ι A Ι B A Ι B Ι C Υ A Υ B A Ι B Ι C Υ A Ι B Ι A Υ B A Ι B Ι C Υ A Ι B A Ι B

27 5 8 3 { } 4 { } 3 4 { } 9 ABC A BB C A C A BB C A C 3 A BB C A C 4 A BB C A C 5 A BB C A C 6 A BB C A C 7 A BB C A C 8 A BB C A C A{}B{}C{{}} A{}B{{}}CB 3A{}B{,}C{{}} 4A B B C 5A{}B{{},}CB 6A{}B{,}C{B} 7A{}B{,}CB 8A{}B{{},}C{} {, } {,,,{,, }} {, } {,,,{,, }} 3 {, } {,,{{, }}} 4 {, } {,,{{, }}} A C

28 6 3 {, } {,,,{,, }} 3 {, } {,,{{, }}} {,,,{,, }} 4,,,{,,} {,} 4 {,,{{, }}} 3,,{{,}}{,} A {} {{}} 3{,{ }} 4{ } 5{,{},{}} 6 PA{{} } PA{,{{}}} 3PA{,{ },{{ }},{,{ }}} 4PA{,{ }} 5PA{,{ },{{}},{{}},{,{}} {,{}},{{},{}},{,{},{}}} 6PA{ } A { }, B P P A B? B { } B? { } B 3{{ }} B {{ }} B PA{,{ }}B{,{ },{{ }},{,{ }}}, 3 3 A{,{}} { } P A { } P A 3 {{ }} P A 4 {{ }} P A PA{,{},{{}},{,{}}}

29 7 4 A B C A B C A B B A A B C A Ι B C Υ B C Ι A A Ι B Ι C Υ C Ι B Υ B Ι C Υ C Ι B Ι A A Ι B Υ C Ι C Υ B Υ B Ι C Ι A Υ C Ι B Ι A A Ι B Ι C Υ B Ι C Υ B Ι C Ι A Υ C Ι B Ι A A Ι B Ι C Υ A Ι B Ι C Υ B Ι C Ι A Υ C Ι B Ι A ABC A B C A Ι B Ι C Υ A Ι B Ι C Υ B Ι C Ι A Υ C Ι B Ι A A B A B Υ B A B A Υ A B B A 5 ABC A B Υ A C A A B Υ A C 3 A B Ι A C 4 A B A C A B Υ A C A Ι B Υ A Ι C A Ι B Υ C A BΙ C A B Ι C A B Ι C A B Ι C A A B Υ A C A B Ι C B Ι C A 3 A B Ι A C A Ι B Ι A Ι C A Ι B Ι C A BΥC A B Ι A C A B Υ C 3 4 A A A B A B Υ B A A B B A A B B A A B A B A B A B A C *6 A B A B A Ι B A A B B A 3 A B Υ B A A A B A B

30 8 A B A B A B A B B A A B B A A Ι B A B B A A Ι B AB 3 x A x x B x B x B x A B x B A x A B Υ B A A x A x B y B y A y B A A B *7 A BB AB AB x B x A B A Ι B x B x B B A B A A A B *8 A B C A B Υ C A C B A C B C X Y X Ι Y A B C A Ι B Ι C A Ι A B Υ C A Ι B Υ C A Ι A C B A Ι C Ι B A Ι B Ι C B Ι C B Ι C A C B C A Ι C Ι B Ι C A Ι C Ι B Υ C A Ι C Ι B Υ A Ι C Ι C A Ι B Ι C Υ A Ι A B C A B Υ C A C B A C B C B Ι C *9 AB A B C D A C B D < x, y > A B C D x A B y C D x A, x B y C, y D < x, y > A C < x, y > B D < x, y > A C B D A B C D A C B D AB{}C{}D{3}{<,>} A B A Υ B A Υ C A Ι B A Ι C B C B B Ι A Υ B B Ι A Υ C B Ι A Υ B Ι C C Ι A Υ B Ι C C Ι A Υ B C Ι A Υ C C

31 9 ABC U ABC A Ι B Υ C A Ι B Υ C AB A Ι ΥB B 3 A B A Ι Υ B A 4 AB A Ι B A Υ B A Υ Υ Υ 5 ABC B C A B C 6 ABC A B B C A C 4563 A C{} 4 AB 5 A B C {,,3 } Υ 6 A {, } B {,,3 } C { } A Ι B A Ι C B C A Υ B A Υ C B C 3 A Υ B A Ι B A B 4 A B A C B C 5 A B C D A Ι C B Ι D 6 A B C D A D B C 5346 A B{}C{} A{,}B{}C{} 3 A A Υ B A Ι B B B A AB 4 A A B A A C A A B A A C A A B C BC 5 A { } B {, } C {3} D {3,4} 6 C D D C A B A Ι D B Ι C A D B C 4 A B A C x B Υ x A x A Ι B x A B A C x A x A C x A Ι C x C x A x B A x A B A C x A x A C x C

32 B C C B BC 3 ABC A B C A B C A{,,3}BC{}ABC{,3}ABC{,,3} x A B C x A B, x C x A, x B x B C x A B C A B C A B C A B C A Ι B Ι C A Ι B A Ι B Υ C A Ι B Ι C A B C 4 A B A Ι B A Υ B A Ι B A Υ B A Ι B 5 A k A { } { < + / k}, k,, A k Ι A k k A x A, x < + / k, x Ak, k A Ι Ak x Ι A x A x > ε > k k k x > + ε k N x + > + / k + ε > ε [ ] x Ak x A A Ι Ak A Ι Ak 6 C Υ Ι S C S C k S C { } C {,{ }} k 3 C {{ },{ },{, }} 4 C {{ i} i Z} Υ S Ι S S C S C Υ S { } Ι S S C S C 3 Υ S {,} Ι S S C S C k

33 4 Υ S Z Ι S S C S C 7 A B P A Υ P B P A Υ B P A Ι P B P A Ι B 3 P A ΥP B P A Υ B X P A Υ P B X PA X PB X A X B X A Υ B X P A Υ B X P A Ι P B X PA X PB X A X B X A Ι B X P A Ι B P A Ι P B P A Ι B 3 A { }, B {}, A Υ B {,}, P A Υ P B {,{},{}} P A Υ B {,{},{},{,}} 8U A B A Ι B A B A Υ B U 3 A B A B A B x A, x B x A, x B A Ι A B A Ι B A Ι B A ΥB U 3 A B A Ι B A B B 9 A{}B{,}C{,3} A B C B A 3 B A A B A B C { <,, >, <,,3 >, <,, >, <,,3 > } B { <, >, <, >, <, >, <, > } 3 A { <,, > }; B A { <,, >, <,, >, <,, >, <,, > } A B { <, >, <, > } A B { <<, >, <, >>, <<, >, <, >>, <<, >, <, >>, <<, >,, <, >> } 3 A Ι B A Υ B A Ι B A A Υ B B A Ι B A Υ B A A Υ B B

34 < x, y > A Υ B A Ι B x A Υ B y A Ι B x A x B y A y B < x, y > A A < x, y > B B < x, y > A A Υ B B 3 A Υ B C Υ D A C Υ B D A B C D A C B D 3 A B C D A C B D 4 A B C A C B C A{}B{}C{3}D{4} A Υ B {, } C Υ D {3,4} A Υ B C Υ D { <,3 >, <,4 >, <,3 >, <,4 > } A C Υ B D { <,3 >, <,4 > } A{}B{}CD{} A B C D A C B D { <, > } 3AB{}C{}D{3} A B A B C D A C B D { <, > } { <,3 > } { <, > <,3 > } 4 A B C [ A B Υ B A] C [ A B C] Υ [ B A C] [ A C B C] Υ [ B C A C] A C B C 3 3 3,, Λ, p + p 3 ABCD 3 p,, Λ, p + p+ p, Λ, p, p

35 S 3 S ,, Λ, 9 i + + Λ ,, Λ, 7 i Λ A B A Υ B 5 A 85 A Ι B 6 A Υ B A + B A Ι B B A Υ B A + A Ι B AB C A C - B

36 4 A [/5] B [/6]66 C [/8]5 A Ι B [/3]33 A Ι C [/4]5 B Ι C [/4]4 A Ι B Ι C [/]8 A Ι B Ι C U A B C + A Ι B + B Ι C + C Ι A A Ι B Ι C S {,, Λ,999} S 9 S S A 3 B 7 A B A Ι B A Υ B A + B A Ι B A Ι B U A Υ B A Ι B FGR F 6 G 8 R 6 F Ι G 76 F Ι R 48 G Ι R 6 F Ι G Ι R 3 F Υ G Υ R 5

37 5 R G F R G F N Υ Υ Υ Υ + R G F F R R G G F R G F Ι Ι Ι Ι Ι R G F Υ Υ R G F Ι Ι R G F G F Ι Ι Ι R G F Ι Ι R G F R F Ι Ι Ι R G F Ι Ι R G F R G Ι Ι Ι R G F Ι Ι R G F R G F R G F F Ι Ι Ι Ι Ι Ι R G F Ι Ι R G F R G F R G F G Ι Ι Ι Ι Ι Ι R G F Ι Ι R G F R G F R G F R Ι Ι Ι Ι Ι Ι R G F Ι Ι R G F Ι Ι R G F Ι Ι R G F Ι Ι F G R R G F Ι Ι R G F Ι Ι R G F Ι Ι -3

38 6 * ABC C B A C B C A B A C B A C B A Ι Ι Ι Ι Ι Υ Υ C B A U C B A Ι Ι Υ Υ C B C A B A C B A C B A C B A Ι Ι Ι Υ Υ Ι Ι ABC PASCAL 6 COBOL 3 ABC PASCALCCOBOL 58 6 C B A U C B A Ι Ι Υ Υ C B A C B C A B A C B A C B A Ι Ι Ι Ι Ι Υ Υ C B A C B A C B A C B C A B A Υ Υ Ι Ι Ι Ι Ι A B C C B 7 A -5

39 7 C B A B A C B A Ι Ι Ι Ι Ι 3 A C C B B A C B A C B A C B A Ι Ι Ι Ι Ι Ι Ι Ι Ι C B A Ι Ι 3 3

40 ... R A B R A B <, > R R <, > R R A A A R A A R A R : A B R DomR RnR Dom Rn R { x x A, y B, < x, y > R} R { y y B, x A, < x, y > R} Dom R A, Rn R B A m B n A B mn A m A I A A I E A {} { < x, x > x A} { < x, y > x, y A} I A E A A B A {,, Λ, n} B {,, Λ, m} R A B R A B,, Λ, n,, Λ, m i A, j B < i, j > R i j i j R A B, A { x, x, x, x }, B { y, y, } R < x, y >, < x, y, : 3 4 y3 { >

41 9 < x, y3 >, < x3, y3 > } R - x y d x y x 3 y 3 x 4 - A A A B A A < i, j > R i j i j < i, i > R i i R : A A, A {,,, d} R { <, >, <, >, <, >, <, >, <, > } R - R : A B A B A n, B m AB A x, x, Λ, x } B y, y, Λ, y } R n m { n M R r ij n m r ij { m < xi, y j > R rij i,, Λ, n; j,, Λ, m < xi, y j > R MR A B A B R MR..

42 3 R : A B, S : B C R S A C R οs R οs { < x, z > x A, z C, y B < x, y > R, < y, z > S} R : A B R ο I R, I οr R ABCD R ο R οr3 R ο R οr3 B A R : A B, R : B C, R3 : C D 4 3 A R : A A R n R I A { <, > A} R R R n+ R R m n ο R R οr οr n R m+ n n m n mn R R m, n N 4ABCD R : A B, R : B C, R3 : B C, R4 : C D R ο R Υ R3 R οr Υ R οr3 R Υ R3 οr4 R οr4 Υ R3 οr4 R ο R Ι R3 R οr Ι R οr3 R Ι R οr R οr Ι R ο R4 A {,,3 } B {, } C { x, y, z} R { <, >, <, } R { <, x } R { <, x } R Ι R > > 3 > ο R Ι R3 R οr Ι R οr3 { <, x > } R R Ι R3 R οr Ι R οr3 R 3 ο 3 A BR : A B { < y, x > < x, y > R} B A R R ~ R ~ R B A R R R ~ R ABC R : A B, S : B C ~ ~ R ο S S ο R

43 3 3 RS A B R R ~ R R ~ ~ R Υ S R Υ S ~ ~ R Ι S R Ι S ~ ~ R S R S ~ R R ~ ~ ~ S R S R S R S R {,},, A B A B A B ij ij ij ij ij ij M R Υ S M R M S M R Ι S M R M S M R M E A M R E A R M R S M R M S M M R ο S M R M S r n k ik s kj R A

44 3 x A < x, x > R R R x A < x, x > R R R 3 x A, y A < x, y > R < y, x > R R R 4 x A, y A < x, y > R < y, x > R x y R R 5 x A, y A, z A < x, y > R < y, z > R < x, z > R R R R < x, y > R x y < y, x > R R 4 R A R R I A R R Ι I A 3R R R ~ ~ 4R R Ι R 5R R R I A xyz x y y z x z i, j, k {,, Λ, n} rij rjk rik R MR i j r ij

45 33 5 R A R r ii, i,, Λ, n R r ii, i,, Λ, n 3R rij rji, i, j,, Λ, n 4R rij + r ji, i j, i, j,, Λ, n 5R ij rij, i, j,, Λ, n ij MR i j 6 RS A RS R ~, R Υ S, R Ι S, R οs RS R ~, R Υ S, R Ι S, R S 3 RS R ~, R Υ S, R Ι S, R S, R 4 RS R ~, R Ι S, R S 5 RS R ~, R Ι S RS R οs RS R οs RS R Υ S..4 5 R A R A R R R R 3 A R R R rrsrtr R R 7 R A r R R Υ I A

46 34 ~ s R R Υ R Υ 3 t R R R Υ R Υ R i i 3 ΥΛ A A nr A n i n t R Υ R R Υ R ΥΛ Υ R i Wrshll 3 7 M r R M R M I A ~ M s R M R M R i M t R M R i 8 R rrr R srr 3R trr 9 RS A R S r R r S s R s S t R t S RS A r R Υ S r R Υ r S s R Υ S s R Υ s S 3 t R Υ S t R Υ t S 3 38 R A R sr tr R rr tr

47 35 3 R rr R RtsrR R tsrr tsrr srrstrrtrtrr tsr srrstrrtr trrtsr..5 6 A R R R A 7 R A A A R A R [ ] [ ] { x x A, xr} R A A R AR A/ R {[ ] R A} R 3 f x Rx f x f x : X Y, X R X X R X f [ ] f { x A f x f } { f y f y } 3 R A A R A R[ ] [ ] R [ ] R Ι [ ] R 3 Υ [ ] A R A 4 R A AR A A A R R AR R R

48 R A R R A R R A A S S S AS S S R A R A R A{3} C{{}{3} {3}} R R{<> <><33><><><3><3><3><3>} R {{,,3}} C{{3}} R..7 9 A R R R A A A,,,,,, A A,, Hsse 5 A R R R A AR

49 37 A x, y A xy yx A A A A [,] x, y x y y x x, y 5 A B A A x B x x B B B x x x B 3 B B x π π x x B x B x x x B 4 B B x x x B B A B B 5 AB A B B B B B B 3 B B B 4 B B B 5 B B B B 6 B B B B... x π x x

50 X Y X X 3 4 A A A A B, A{,,3}R {<,>} R {<,>,<,>,<,3>} R 3 {<,>,<3,3>}

51 ts R st R t R Ι S t R Ι t S t R ΥS t R Υ t S A{d} d - B{} B B C{}d C C C C - C , -3

52 A {,, Λ,} R { < x, y > x + y, x A, y A} R A B C D B A{} A ρ { <, >, <, >, <, >, <, } > { <, >, <, > B ρ } C ρ { <, >, <, >, <, >, <, } 3 > 4 { <, > D ρ } D 3 R S A A R S R οs B R S R οs C R S R οs D R S R οs A *4 R S A A R S R Ι S B R S R οs C R S R οs

53 4 D R S R Υ S A *5 S{3} -4 S R, R R οr 3 3 R R -4 A B C D C 6 A{345} ρ { < i, j > i < j, i, j A} ~ ρ A B C D D 7 A {,, } R A R { <, >, <, >, <, >, <, > } R A B C D D 8 R S A R Υ S A C B D A 9 R S A A A A R B R C R S D r R S B A R A C B D D * R A R ~ ~ R R Υ R

54 4 A B C D B A 4 A A B4 C5 D7 C C + C + C D R 3 R 4 R 5 A{,,3}{<,>,<,>,<,3>,<3,3>} R 6 A{,,3,4} R{<,><,4><3,3><,3>} rr sr {<,><,><3,3><4,4><,><,4><,3>} {<,><,><,4><4,><3,3><,3><3,>} 7 A 3 A A 3 A 4 A

55 43 5 A R R A R Υ R R Ι R 3 R οr 8 9 R R A R Υ R R Ι R 3 R οr 3R {<>,<>}R {<>,<>} R οr { <, >, <, >, <, >, <, > } R R A R Υ R R Ι R 3 R οr 4 R 4 3 R { <, d >, <, e } R { < d, >, < e, } > R οr { <, >, <, > } 9 R A R R R R >

56 44 R A R R R R 3 A {,,, d, e, f, g A π {{, },{, d, e},{ f, g}} π R 7 *4 R {,, Λ,} 7 [ ] R {,9} 5 R R A R Υ R R Ι R 3 R οr *6 7 A {,, } P A, PA B {,{ },{ },{, },{, }} {}{} {} 8 A {,3,4,5,6,8,,,4} R A A A {,,3,4,5,6,7,8,9,,,} R A B {,4,6} B B B B

57 45 A {,,3,4,5,6,8,,4,36} R A B {,,3,4 B B B B * R A R A A R R ~ 3 4 A{,,3} R 5 A{,,} R{<,><,>} 6 R S A R οs 7 R S A R οs 8 R S A R οs 9 R S A R οs R A tr A{,,}R{<,>,<,>,<,>} R tr A R S A r R Υ S r R Υ r S s R Υ S s R Υ s S t R ΥS t R Υ t S R S A R Υ S A{,,3}R{<,><,><3,3><,><,>}S{<,><,> <3,3><,3><3,>} R S R Υ S {<,><,><3,3> <,><,><,3><3,>} <, > R Υ S <, 3 > R Υ S <, 3 > R Υ S R Υ S 3 R S A R οs R Ι S 4 5 A R R A

58 46.4 N R : N N xry x + y DomR RnR DomR{,,4,6,8,}RnR{5,4,3,,,} S{,,,3} mr n m + n 3 mr n m nmod 3mR 3 n mn 4mR 4 n m+n4 5mR 5 n mx{ m, n} 3 R {<,3>, <,>, <,>, <3,>} R {<,>, <,>, <,>, <3,3>, <,3>, <3,>, <,><,>} R 3 {<,>, <,>, <,>, <,3>, <,>, <,>, <,3>, <,>, <,3>, <3,3>} R 4 {<,>, <,>, <, >, <,3>, <,>, <,>, <,>, <,3>, <,>, <,>,<,>, <3,>, <3,>} R 5 {<,3>, <,3>,<,3>, <3,3>,<3,>,<3,>, <3,>}

59 47 M R M 3 M R 3 4 M 5 M R 5 R R4 3A{,,}9 A R <m,n> mn mn 3mn 4mn 5mnm 6 m + n A 7 m + n 8 m + n 3 9 m mx{n, } {<,>,<,>,<,>,<,>,<,>,<,>} {<,>,<,>,<,>} 3{<,>,<,>,<,>} 4{<,>,<,>,<,>,<,>,<,>} 5{<,>,<,>,<,>,<,><,>} 6{<,>,<,>,<,>,<,>,<,>,<,>} 7{<,>} 8{} 9{<,>,<,>,<,>} 4 R S A{,,3}R{<,><,><,3><3,><3,3>}S{<,> <,3><,><3,3>} R Ι S R Υ S R RS R A A A R Ι S { <, >, < 3,3 > }

60 48 R Υ S { <, >, <, >, <,3 >, <, >, <,3 >, < 3, >, < 3,3 > } R { <,3 >, <, >, <, >, < 3, > } 5Z R Z Z <<,>,<,d>> R d R R Z Z <<,>,<,d>> R + d R, R Υ R, R R, R R d d x y K K R R R x y K K R Υ R x y K K R R x y K K x y K K R R 6 R S R οs R{<x,y> yx-} R{<x,y> yx-4} S{<x,y> yx+3} S{<x,y> yx +3x+} 3R{<x,y> y x } S{<x,y> x y } 4R{<x,y> y x } S{<x,y> yx } R ο S {<x,y> yx-+3} R ο S {<x,y> y x x 4 + } 3 R ο S 4 R ο S {<x,y> xy} {<x,y> y } x 7 A{,,3}B{,,}C{x,y,z} R : A B S : B C R{<,>,<,>, <,>}S{<,y>,<,x>,<,y>,<,z>} R οs RS R οs M R M S M RοS M RοS M R M S

61 49 R S -6 A C x x S R x ο > <, S R z y ο > < > <,,, },,,,, { > < > < > < z y x S R ο 3 M R z y x M S 3 z y x M S Rο R M S M R M S M S R M ο S R M M x y 3 z -6 8{,,3} R R 3 R 7 R R{<,>,<,>,<,>,<,3>,<3,>,<3,3>} R R{<,>,<,3>,<,>,<3,>,<3,3>} R {<,>,<,3>,<,>,<3,>,<3,3>} 3R{<,>,<3,>} R {<,>} 3

62 5 *9 X{,,3,4}R X R{<,>,<3,>,<,3>,<3,3>,<3,>,<4,3>, <4,>,<4,>,<,>} R R 3 R 4 R -7 R R R R M R M R R R R 4 4 R R <, > R R <, > R R < 4, > R, <, 4 > R R <, > R, <, > R <, > R R A{,,3} R R R ~ 3R R Υ R R{<,>,<,>} R{<,>,<,><,3>} 3R{<,>}

63 5 * X R R R R, X R R R R R R R A R A{,,}A R{<,>,<,>,<,>,<,>} R <, > R R S A R Ι S n R 4 R S R οt S οt T οr T οs R Ι S R R Ι S R ο R Ι S R οr R n n n n R Ι S R R Ι S S R Ι S R Ι S 3 R, R S T ~ ~ R R R R ~ ~ R Ι R R Ι R ~ ~ 3 R Υ R R Υ R ~ ~ < t, s > R, < s, t > R R R < s, t > R < t, s > R ~ ~ R R < t, s > R Ι R < s, t > R Ι R ~ ~ < s, t > R < s, t > R < t, s > R < t, s > R ~ ~ ~ ~ < t, s > R Ι R R Ι R R Ι R 3 R R ΥRR R Υ R R ~ R Υ R ~ ~ ~ R R Υ R R ΥR R Υ R R R ~ ~ ~ ~ R ΥR R Υ R R Υ R ~ ~ ~ ~ R ΥR R Υ R R ΥR R Υ R ~ ~ R Υ R R Υ R n Ι S n n n n

64 5 4R A R R Ι ~ R I A I A A ~ ~ R < x, y > R Ι R < x, y > R, < x, y > R ~ < x, y > R, < y, x > R x y R Ι R I A ~ ~ R Ι R E A < x, y > R, < y, x > R < x, y > R, < y, x > R ~ < x, y > R Ι R I x y R A ~ 6 R A R R R ~ ~ R < x, y > R < y, x > R < x, y > R R R ~ ~ R R R R ~ ~ ~ R R < x, y > R R < x, y > R < y, x > R R R S{,,3,4} T{,,} R οr ~ S

65 ~ R οr T 3 R οr ~ ~ R οr M R, ~ M R M R 53 T ~ ~ M R οr M R M R R οr ~ ~ ~ ~ M R οr M R * M R R οr 3 9 rij rjk rik ~ ~ ~ M R οr R οr M R οr r r 3 r 3 R ο R ~ M R M R R R οr ~ ~ R οr R οr ~ <, >, <,3 > R οr ~ <,3 > R οr ~ ~ ~ ~ ~ R ο R R οr R οr R οr ~ ~ R οr M R M R R n 9 R S R n S ~ ~ ~ R R R R ο R R ο R ~ R R ~ n n R R R n * A{,,,d} R { <, >, <, >, <, d > } S { <, d >, <, >, <, d >, <, > } R οs

66 54 M R M R ο S M S M R ο S M R ο S R οs * R S A R Ι S R S A R Ι S r R Ι S R Ι s R Ι S R Ι t R Ι S R Ι S S S R Ι S A R S R I A, S I A R Ι S I A R Ι S ~ ~ ~ ~ R S R R, S S 3d R Ι S R Ι S R Ι S R Ι S R S R R S S R Ι S R Ι S οr R οr R R Ι S S R Ι S R Ι S R Ι S S{,,3,4} S R{<,>,<4,3>,<,>,<,>,<3,>} R R R R R R R R < 4, 3 > R < 3, > R < 4, > R R R {<,>,<4,3>,<,>,<,>,<3,>,<4,>} R R R R {<,><4,3><,><,><3,><4,><3,3>} R R R S

67 55 *3-9 {,,3,4,5,6 } R R R t R { <, >, <,3 >, < 3, >, < 3,3 >, <,3 >, < 4,3 >, < 4,5 >, < 6,5 > } 4{,,,d} R R{<,>,<,>,<,d>,<d,>} R{<,>,<,>,<,>,<,d>,<d,>,<d,d>} tr {<,>,<,>,<,>,<,d>,<,>,<,>,<,>,<,d>,<,>,<,>, <,>,<,d>,<d,>,<d,>,<d,>,<d,d>} tr {<,>,<,>,<,>,<,d>,<,>,<,d>,<d,>,<d,d>} 5{,,,d} R - R d d - - -

68 56 *6 R A T A <, > T <, > R <, > R T R A <, > R <, > R T <, > T T <, > T <, > R<, > R <, > R<, > R <, > T T <, > T <, > T <, > R <, > R <, > R, <, > R R <, > R <, > R <, > R <, > R <, > R <, > R <, > R <, > R <, > T T T A *7S X S I Ι S S x X < x, x > S I Ι S I Ι S < x, x > I < x, x > S S x y *8 R S { < x, y > x, y R, } 3 x, y, z R x x xsxs 3 x y y x x y xsy ysxs x y y z x z x y y z xsyysz + xsz S S R *9 A RS R οs R ο S S οr R οs R ο S R οs ~ ~ ~ ~ R ο S S ο R RS R R, S S R ο S S οr R ο S S οr ~ ~ R ο S S οr R οs R οs R οs 3 R S A RS R οs R ο S S οr

69 57 RS R οs R ο S S οr R R R R ο S S οr RS R ο S R οs ο R οs R ο S οr οr R ο R οs οs R οs R οs R οs R{<,>}S{<,>} R ο S {<,>} S οr R οs S οr RS RS R οs R οs R ο S S οr RS RS R οs RS R ο S S οr R οs RS R ο S S οr R οs R οs 3 R A n R n R n nk R k R nk+ k+ k R R ο R R οr R R οr R R R < x, y > R R < y, y > R < x, y > R οr R R R οr R n R n R *3 N N R R { < x, y > x N, y N, x + y} R R 3 N N f f R x N x + x xrxr < x, y > R x + y y + x < y, x > R R < x, y > R < y, z > R x + y y + z x + z x + y + y + z y < x, z > R R R R [ ] R {,3,5, Λ } [ ] R {,4,6, Λ } x 3 f : N N f x x

70 58 f R *33 A R A R R t R * R οr R + R οr * * * 3 R R tr R + + R t t R tr t t R t R R R + + R + t R * R ο R R ο tr R R ο rt R R ο t R Υ I A i i i + R ο t R Υ R οi A R ο Υ R Υ R Υ R Υ R Υ R R i i i + R ο R R 3 rrtrr * * R tr tr R t tr R tr R R *34 A{,,,3} A i R { < i, j > i, j A, j i + j } S { < i, j > i, j A, i j + } R S R οs i R οs { < i, k > j A j i + j j k + } i R οs { < i, j > j + i + j + } i R ο S { < i, j > j i j } 35 R sr tr R rr tr 3 R rr R R E A s R R E A t R R E A sr tr ~ ~ R R R r R R Υ E R Υ E R Υ E ~ r R rr * A A A +

71 59 tr n n R R t Υ ~ ~ ~ R t R R R R t n n n n n n Υ Υ Υ tr 3 R trr rr trrrr i A i A I R I R t R tr Υ Υ Υ j i j i A R I R Υ Υ R r R I R t I R I R R R tr A A i i A i i j i j i Υ Υ Υ Υ Υ Υ Υ trrrr 36{,,3} R R rr sr 3rsR 4srR 5tsrR R r M R s M 3 R rs M 4 R sr M 5 R tsr M 37 S R R rs R sr R rt R tr 3 R st R ts ~ E R s E R R E R E R E R s R sr A A A A A Υ Υ Υ Υ Υ Υ Υ rsr trr rr R r E R E R t R rt S S Υ Υ 3R{<,>} strsr{<,>,<,>}

72 6 tsrt{<,>,<,>}{<,>,<,>,<,>,<,>} 38 R, R A r R Υ R r R Υ r R R Υ R s R Υ s R R ΥR t R Υ t R s 3 t t R ΥR t R Υ t R r R Υ R R Υ R Υ E A R Υ E A Υ R Υ E A r R Υ r R ~ ~ s R Υ R R Υ R Υ R Υ R R Υ R Υ R Υ R s R Υ s R t R Υ R R ΥR R R R R t R Υ R t R R Υ R t R t R ΥR t R Υ t R 3 t R t t Υ R { <, > }, R { <,3 > } t R Υ t R R Υ R { <, >, <,3 > } t R Υ R { <, >, <,3 >, <,3 } > 39n M n, n A B n P B PAP n A n I n A I n AI n A B P B PAP A P B P P B A 3 A B B C P Q B PAP,, C QBQ C QPAP Q QP A QP QP A C 4R Z mrn m n R R m m m mrm mrn m n n m nrm mrnnrp m n n p m p mrp R [ ] { i, i} R {[ ],[],[], Λ } i R R R R

73 6 4 R A R <, > R <, > R <, > R R R R R <, > R R <, > R <, > R 3R <, > R <, > R <, > R <, > R <, > R 4 R S A A A A R R S 3 R 4 r R S A A R A A{,}R{<,>,<,>} A A R {<,><,>} R S A{,}R{<,><,><,><,>}S{<,> <,>} R S {<,><,>} 3 3 RS 4A{,,3}S{<,><,><3,3><,3><3,>} R A r R S {<,><,><3,3><,><,><,3> <3,>} <, > r R S <,3 > r R S <,3 > r R S 43 A {,,3} {,,3,4 } A R <x,y>r<u,v> x-y u-v R R A R < x, y > A x-y x-y <x,y>r<x,y>r < x, y > A, < u, v > A <x,y>r<u,v> x-y u-v u-v x-y <u,v>r<x,y>r <x,y>r<u,v><u,v>r<p,q> x-y u-v u-v p-q x-y u-v <x,y>r<p,q> R R A

74 6 [, > ] { <, >, <, >, < 3,3 > } < R [, > ] { <, >, <, >, <,3 >, < 3, >, < 3,4 > } < R [,3 > ] { <,3 >, < 3, >, <,4 > } < R [,4 > ] { <,4 > } < R Π {[ <, > ] R,[ <, > ] R,[ <,3 > ] R,[ <,4 > ] R} 44 A{,,,3}A 5 5 X 3 4 A{{,,,3}}, A{{},{,,3}}, A3{{},{,,3}}, A4{{},{,,3}}, A5{{3},{,,}}, A6{{,},{,3}}, A7{{,},{,3}}, A8{{,3},{,}}, A9{{},{},{,3}}, A{{},{},{,3}}, A{{},{3},{,}} A{{},{},{,3}}, A3{{},{3},{,}} A4{{},{3},{,}} A5{{},{},{},{3}} 45X{,,3,4,5,6,7,8,9} X {{,3,6}{,8}{5,7,9}} {{,5,7}{,4,8,9}{3,5,6}} 3{{,4,5,8}{,9}{3,6,7}} 4{{,,7}{3,5}{4,6,8,9}{3,5}} X 4 X 5 3 X 4{3,5} 46 R S A R Ι S, R Υ S A R S R Ι R Ι S, R Υ S A 47 X x, x, x, x, x, } -3 X R { x6 R X R X S, R Υ S

75 63 x x 4 x x 3 x 5-3 R X X {{ x, x, x5},{ x3, x4},{ x, x4}} 48 R R <x,y><z,w> x + y z + w <x,y><z,w> <x,y><z,w><x,y><z,w> <x,y> <z,w> x + y z + w 3 R R {<x,y> <x,y><3,4>} 4 R R {<x,y> <x,y> <3,4>} 35 <3,4> 45 *49 P { x, x, x3, x4, x5} -4 P x x 3 { x, x3, x4} { x3, x4, x5} { x, x, x3} x 4 x 5-4 P x x x 4,x 5 { x, x3, x4} x x 4 x x 4 x, x, } x 3 x x 3 { 3 4 x5 x, x, } x x 4 x x 4 { x3 x

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77 65 A,R R M R R r r ij + ji R R e M R M R d R R S T X R SRT u S, v T, u v R X X F S F u S u u SRS R SRTTRS u S, v T, u v v T, u S, v u S X u Ι u u u u v u u Ι u u u uv S T T S ST R SRTTRW u S, v T, u v v T, w W, v w u S, w W, u w SRW R R

78 ex x 5lu{d,}lu{p,m}lu{w,y,v}gl{,g} d f h e g o m p q k j n r w z x v u y 3-8 h,, o,p,q,r j 3 z u 33 {e,f,g,h}lu{d,}flu{p,m}plu{w,y,v}zgl{,g} 55 S, T, S T < s, t > < s, t > t s t s Z, <,><,><,><,> 56-9 ~

79 A B f A B x A y B < x, y > f f A B f : A B < x, y > f f x y y x f x y f f : A B A f Dom f Im f { f x x Dom f } f Im f f A B A A A f, g : A B A, f g f g f g f : A B x, x A x x f x f x f x, x A f x f x x x f f A B f 3 f f f : A B A A B B f A { f x x A } A f f B { x A f x B } B f

80 68 f : A B A, A A B, B B f A Ι A f A Ι f A A Υ A f A Υ f A A A f A f A f 3 f f f A f f B 4 f B B f B f B 5 A B 6 f B f B f A f A 7 f B Υ B f B Υ f B 8 f B Ι B f B Ι f B R : A B S : B C R οs A C RS R οs A C f : A B g : B C f οg A C f οg x g f x f οg f g f g 3 f : A B g : B C f, g f, g 3 f, g f οg f οg f οg 4 f : A B g : B C f οg f οg f g 3 f οg f g 3 f : A B ~ f : B A B A ~ f f ~ f f f : A B f f x y f y x

81 3 69 ο f I A f ο f I B f 5 f : A B f 6 f : A B f f f f 7 f : A B g : B C f g f οg f οg g ο f AB A B A B A ~ B A B A B A B A B A B A B A B A B 5 A A 8 3 A A [,] S A S SA~S,,

82 A B A B A A A A f οg x g f x f οg x f g x 6 8

83 A {,, } B {, } f : A B A3 B 3 C 3 D3 B A B C D B 3 f, g f οg A B C D C 4 f οg A f B f C g D g C 5 f : Z Z i Z f i imod8 f A B C D A 6Z f Z Z, f x x x f A B C D A 3.3. A{,,}B{,,3}RST A B R{<,><,><,>} S{<,><,>}T{<,><,><,>} A B R T

84 7 A{,,3} f, g, h A A f f f 3 g g 3 g 3 h 3 h h3 g g g 3 A{,,3}RST A R{<,><,3><,>}S{<,> <,><3,3>}T{<,><,3><3,>} A A R ~ ~, S ~, T 4 A{,,,d,e}B{,} A B A B 3 3 A B S5, 5 5 A{,}B{,,} A B 6 6 N f g N N f n n + g n n f ο f n g ο gn f ο gn g ο f n 4 n 4 n + 3 n + n + 7 f A B g B C f οg A C f οg f οg g f 8 N N N Q R 3.4 xry x + y x y x y x y 3 x y 4 x y

85 S{,,3,4,5} S S I S n n f n 6 n g n mx{3, n} h n mx{, n } 3 I S { <, >, <, >, < 3,3 >, < 4,4 >, < 5,5 > } f {<,5>,<,4>,<3,3>,<4,>,<5,>} g {<,3>,<,3>,<3,3>,<4,4>,<5,5>} h {<,>,<,>,<3,>,<4,3>,<5,4>} I s f g h 3-3 I S f g h 3 f : R R f x x S {8} + x f : R R f x S { } 3 f : N N N f n < n, n + > S { <, > } 4 f : N N f n n + S {,3} 5 f : Z N f x x S {, } x 6 f :[,] [,] f x +, S [, ] 4 7 f : R R f x 3 S N 8 f :[, ] R f x S {, } + x 9 f :,, f x S {, } x

86 74 3 S 4 f f S f f f x x R {8} fxx x f x R {} f x log x 3 f n < n, n + > { < n, n + > n N} 4 f n n + {} 5 f x x N {,,} 6 f x x + 3 4, 4 4, 7 f x 3 {3} R 8 f x + x [,] {, } 9 f x x, + 4 f, g, h R R f x x 3 4 4x g x h x x x + h ο g ο f g ο h ο f 3 f ο g οh 4 f ο f 5 g ο g 6 g ο h 7 h ο g h ο g ο f x x + x + 4 g ο h ο f x 4 x + x + 3 f ο g οh x 3 x 4x f ο f x x 4x 4 x 4x 5 g ο g x x

87 g ο h x x + 7 h ο g x 4 x + 4 *5 < A, > A, f { x x A, x } f : A P A f f f x x x f x x, y A f x f y x f x f y x y y x x y f x f x x x f f f 6 P N P N P N N UNION < A, B > A Υ B INTER < A, B > A Ι B SYM < A, B > A B A PN UNION < A, A > A Υ A A INTER < A, A > A Ι A A SYM < A, > A A UNION < N, > UNION <, A > INTER < N, > INTER <, A > SYM < N, N > SYM < A, A >, A N 7 N N f n n + g n mx{, n } f g 3 f g ο I N g ο f I N f n f m n+m+ nm f n N, g n + n, n g gg

88 76 3 f οg x g f x mx{, f x } mx{, x} x I N x f οg I N g ο f f g f g g ο f g ο f 8 f g N N n n f n n g n n n f οg I N g ο f I N f οg n g f n gn n I N n f οg I N f n / n n g ο f n f g n I N n f n / n n g ο f I N 9 R X R [,] f, g X < f, g > S x [,] f x g x S S S x [,] f X fxfx f S f S X x [,] f, g X < f, g > S < g, f > S x [,] f x g x g x f x f xgx S X 3 x [,] f, g, h X < f, g > S < g, h > S x [,] f x g x g x h x f x h x < f, h > S S X S X S f x x, g x x + f g g f f g S X f : A B G : B P A B G { x A f x } f A B G f A B B x A f x G B, B G { x A f x }

89 3 77 G { y A f y } f x f y f x y G G G A {,, } B { x, y, z} f : A B f f x f y G : B P A G x {, } G y { } Gz G f f, g, h N N f n n + g n n h n n n f ο f f ο g 3 g ο f 4 g ο h 5 h ο g 6 f ο g οh f ο f n n + + f ο g n n + 3 g ο f n n + 4 g ο h n 5 h ο g n n n 6 f ο g οh n h g f n h n + f : R R R R f f < x, y > < x + y, x y > f f 3 f 4 f ο f f ο f < x, y >, < x, y > R R f < x, y > f < x, y > x + y x + y < x + y, x y >< x + y, x y > x y x y x x, y y f x p + q / < p, q > R R f < x, y > < p, q > y p q / < p, q > f 3 f f < x, y > x + y x, y

90 78 x + y x y 4 f ο f < x, y > f, < x, y > x+ y, x y < x+ y + x y, x+ y x y >< x, > f ο f < x, y > f y 3 f g {,,3,4} f m mx{,4 m} g m 5 m f g R, R f g R f οrg f g R ο 3 R ~ R ~ R ~ R ~ f M R f M R f ο Rg g f g M Rg M R gο f 3 R ~ R ~ 4 R A A AR f A RI A R A RI A R R R N {{,} {3,4}{5,6}} A AR N R AR A AR 5 X x, x, Λ, x }, Y { y, y, Λ, y } { m n X Y X Y 3 nm 4 nm 5 nm X Y X Y X Y mn P A mn X Y g A

91 3 79 X Y n n m 3 m n Y m m m X Y C m! P n n Λ n m 4 n m m n S m, n n S m, n n! S m, n Stirling S m, S m, S m, n ns m, n + S m, n 5 m n Y X Y m B 6 f : A A, B A A f f B f B n n f f f B B f f B y f f B x f B y B f x y f x y y y B f f B B x B f x f B x f f B B f f B f f B B f f B A{,,3}B{,3} f : A A f f f 3 f B {, } f B {3} f f B {} B {,3} f f B {,,3 } 7 f : X Y g : Y Z f οg g f y Y g z g y Z f οg z Z x X f οg x g f x z g f x y y Y x X f x y f f f X Y y Y y f X g g y z Z f οg z Z x X f x y g y z y y g y g y g f

92 8 8 f : A B A A B B f f f B B f f f A A 5 6 f f B B y B f x f B f x y x f B y f f B f f B B f f B B x A f x f A A A f A B f A B f x B x f f A f f A A x f f A f x f A A x f x f x f x x x A f f A A f f A A 9 f A Υ B f A Υ f B f A Ι B f A Ι f B y f A Υ B x A Υ B f x y x A x B y f x f x f A f x f B y f A Υ f B f A Υ B f A Υ f B y f A Υ f B y f A y f B x A f x y x B f x y x A Υ B f x y y f A Υ B f A Υ B f A Υ f B f A Υ B f A Υ f B y f A Ι B x A Ι B f x y x A x B f x f A f x f B y f A Ι f B f A Ι B f A Ι f B X{,}Y{} f : X Y ff A{} B{} A Ι B f A Ι B f A Ι f B { } f : S T A S f A A f A Ι f A f A Ι A, A, A S f A f A f A A, A A S, A f A A A 3 f S{,}T{} f {<,>,<,>} A { }, A {}

93 3 8 f A Ι f A { } f A Ι A A f A { } { A { } f A f f } f A A f {} { } 3 f A A f : T U f g, h : S T g ο f h ο f g h f g h f : T U g, h : S T g ο f h ο f g h 3 f : A B g, h : B C f f ο g f οh g h s S g ο f s h ο f s f g s f h s f g s h s g h S { } T {, } U {} f x g h g ο f x f g x h ο f x f h x g h 3 f B f A f f ο g f οh g f h f g h g h A B A B A B A,B, ANB N N 3ARB, 4A [, B, 4 f : A B f x x, x A B <,><,><,><,3><,> <3,> x 3 f : A B f x e, x R 4 f : A B f x x +, x [, 4 3 Am,n A, n n + n Am, Am, m> 3 A m, n A[ m, A m, n ] m > n > A,3 A3, A, A, A,

94 8 [, A, ], + 3 [, A, ], A, A A A, A A A, n n + A, A, 3 [, A, ], [, A, ], [, A, ], A, A A A, A A A,3 A A A, n n + 3 A 3, A, [, A3, ], [, A, ], A 3, A A A 3, A A A,3 9, A3, 9

95 n S f : S S S n n S f, f, Λ, f k S, f, f, Λ, f k < S, f, f, Λ, f k > f S n T S,, Λ, n T f,, Λ, n T T f f T f T n A A ο,,, Λ f S f, ο, S * S * S,, S * S * S el er S S e l er el e r S * S e e S * Θ l Θ r S S Θl Θl Θ r Θr Θ l Θ r S * S Θ Θ S * e S * S S e e S

96 84 A A * A x, y A x y x y x y x y A * S * S S * Θ l Θ r Θl Θr Θ Θ S * S * e l e r el er e e S * 3 e S l r * l r * ο 4-4- ο ο ο ο ο ο U A,,, Λ, s V B,,, Λ, s i, i i,, Λ, s k i U A,, + V B,, h : A B, A h h h

97 4 85 h + h h h U h A A h h h h h h U V U A,, + V B,,, +, h U V 3 4 A e B he 5 A Θ B hθ 6 A B h h G * G * G, S H S H S H S S e H S e H H S H S 4-3 { e, }* 4-3 * e * e e e e { e, },*{ e },*{ },* { },*{ e, },* e {} 3 S A S A S i i Λ i n i, i, Λ, i n A, n N i, i, Λ, i n A S S A + A S A A A + S A S G * G

98 86 *,,, G e G e e, G 3 G e, G G * G,* G G,* G Ael G G G M n, m M n, m n m A PERMA A A PERMA 3 A n PERMA n n S S n 3 S S p, p, p, p, p, } 3 { p6 p 3 3 p p 3 3 p p p N p {,,, Λ, p } + p n + p m n + m mod p N, + p p 5 G G n n e e n e n 4 3, * * 4 x y,, n n

99 A,*, A x y A 6 A,* A G n m Z m e n m G G*H G H H,*H,* G G G G G 7 G G 8 G H, H * H H H, H * H 9 H G H G H G G A G { A} A < A > G i i Λ i n i i Λ A Υ A n N < A > G G A A < A > < A >G A G K G S K i n,

100 88 K G S K H G S H K H K S 7 G G <{ }> G G<> G G G G G G G G G G Ael Ael G,* T, ο f G T, G f f ο f f G T G f Im f Im f f G f f G T f f G T f f G T G T G T G ~ T f G,* T, ο Im f T f e G e T f f e G e T G T f f G 3 K { x x G, f x et } K G K f Ker f 4 5 Cyly 6 G, ο H,* G H H,* H G x G H οx { h οx h H} H G x H G x x ο H { x οh h H} x οh G, G, ~ h H h ο οh

101 4 89 H 7 H G G H H eh H He H 3 H H H H H 4 H H H H H H 5 H H H H H H 6, G H H H Ι H 7 H H 8 9 H G x G ϕ H x ϕ H ο ϕ x h οx H G G G / H H GH H G G 3 4 H G H G H G x G x ο H H οx H G H < G H G G H G H G G h H h H G H H 3 G H H f G, ο T, Ker f G x G Ker f K ο x { z z G, f z f x} 3 K G, ο

102 9 G K GK K οx K ο y K ο x ο y GK GK G K γ : G G / K γ x K οx K G GK 4 f G, ο T, K GK f * f G f * * f K ο x f x G G G G 4..8 A A A, Ael A, 3,, A A,, A,, A A A,, A,,, A {} A A A,, A A A {} A A,, 3 A,,

103 4 9 A,, A,, 3,, A, A,, G * 4-4 n 3 n x, y, z G x * y * z x * y * z 8

104 9 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * x*y*zx*y*z * e e e 4-5 e e e * * e e

105 * S{, } S A4 B8 C6 D3 C A {,,3, Λ,} A Ax*ymx{x,y} Bx*ymin{x,y} Cx*yGCDx,y x,y Dx*yLCMx,y x,y D 3 A * B * mx{, } C * + D * B 4 N A * + +3 B * min{, } C * + D * mod 3 C 5 A ο mx{, } B ο C ο D ο D 6* {, },* * * * * A B C D D

106 94 7Q Q** A B C D A 8R *, R, R, A B C D A *9 S, AS{,,3,5} 7 BSQ CSZ DS{,3,4,5,9} D G,* AG{,}* BG{,3,4,5,9}* CGQ* DGQ* D * x,y G, n x n n x A A x y B x y n n+ x n y n x y x C y x y y x n n n n y y D x y x x y x n * B A B C D 3 HK G,ο G,ο B A HK, ο B H Ι K, ο C K H, ο D H K, ο

107 A C B D A *5 Z Z,+? A f x x B f x x C f x x D f x C 6R, R {}, A B C DBC A 7H,*G,* H n G m A n m B m n C n m m n D n m m n A *86 C A B3 C4 D6 9 Z Z C A B C D 3 A { +, Z} B{ n } C { +, Z} D, Z C *+ < S, +, > A S { x x + 3,, Q}

108 96 B S { x x Z x } Υ{ } C S { x x n, n Z} D S { x x n +, n Z} A A C B D C 4.3. * A{,, } 3 9 S P A, Υ, Ι PS Υ PS Ι S S 3 S * S {,, }* 4-6 S * S * * {,, }, ο 5G,* B G B B,* G, B, * B B 6G,* f : G G f x f G Ker f x * ο G {} 7 H{,4,8},+,+ N,+ N {,,, Λ,} + N H 3H 4H H 3 {3,7,} {4,8,}

109 G{,5,7,}G,** 5 G,* N* N *, N * * 3* S S 4* S S 9 5 A, ο,, A ο * A *ο *6 7 S,, S, * 8 S, T { x x S, x x x} T 9 G,*e G * e G,* Ael G, G, G e G e e e e 3 Ael m n 4 G { 3 m, n Z} G, 5 G G H H

110 98 *6 *74 4 *8 HK G H Υ K G 9G,E G f, g E f + g x f x + g x, x G E, G f x x x G f G G * f G H G H 3 4 A, Z A 4.4

111 4 99 * * * * * * * *, * * * A,* A{,,, d }* 4-8 * A A A 4-8 * d d d d d d * d d d d d d * d ; d; ; d * d *3 G * G N, x y min{ x, y} G R, x y x + y 3 G { N} * 4 G { +, Z} *

112 x 5 G x Z * x * y * z x * y + z x + y + z x * y * z x + y + z x G x x x x * * x x G 4 Q * * + Q,* 3Q,, Q * Q,*, Q * e Q e e + e e e A ο ο,, A A, ο

113 4 ο A A,, ο ο ο ο ο ο ο ο ο ο, ο A 6S,* S S ο S y x y x y x,, * * ο, ο S ο S S z y x,, * * * * * * * * * * * * z y x z y x z y x z y x z y x z y x ο ο ο ο ο ο ο, ο S 7S,* S, * * S * S, * * 3 S,, * * * S, * * S * * * * * S, * * * * * * * * * * * * * * * * * * * * * * * * 3 S,, * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *8, A A A x Λ Λ,,,,, 4 3 n x x x x A A i<j j i x x i i j j x x x i j p qi q p i p i q j i q i i q q x x x x x x x x x x

114 p k kp i x kp p kp p p kp x x x x x x x x x x Λ p kp p p kp x kp x kp kp x *9* X X * * * e x, y X * x * y * * x * * y * * x * * y e*xe*y xy N * N Z,+ {} + {} + 3{,} + 4Z + 5{,3} + 6{ 6} Ι {9} + { } N + { } {} 3{,} Z + 4 Z Z + 5 {,3} {,3,4, Λ } { 6} Ι {9} {8} {8,36,54,7, Λ } 8N M 3, 3, , +, 3 4, 8,

115 4 3 3,,, 3 A > G { n Z} P 3 + Q 4 Z 5 n U { z z C, z } n 6 U { z z C, z, n Z } 7 R n n > n N G, ο n + n ο G ο ο ο e ο ο ο ο ο ο e 4 G G n

116 4 G k, Λ Λ k > l l l m ο e ο e m e m e e e > ο m m l *5 G G,, G 3 G k m mk l ο e G {,, Λ, n} G G' {,, Λ, n} G G i j i j G n G G G G k k k y x G *6 G x y xy G G G x e g G x g ge x e x e x g e e x e G 7 G Q Q f, x x +,,, Q G G G G,,, d Q, x Q f, d ο f, x f, x + d x + d + x + d +, d + Q f, d ο f, f, d + G ο G I f, G G, G,,, Q f G, f

117 4 5 f f, ο f f,, + f ο f,, f, f,, f, f, f, G,ο 8A,* A σ σ x * x, x A G { σ A} G A G x A σ οσ x σ σ x x x σ x, A, σ οσ σ G e A σ e x e * x x σ e G Aσ οσ e σ e σ σ e ο σ σ e σ Aσ σ σ οσ σ σ * e σ οσ σ σ * e G 9 G,, G xx x G x x x x, y x y G x y x y G, G * G G u, v, w, x u, v, w, x uw u w vw v w ux u x vx v x uw u w w u w u vx vww u ux vw w u ux vx v w w u ux v ww u u x vx

118 6 G,* x G ο * x *,, G G, ο ο* G G,, G ο ο * x * * x * * x * * x * ο ο x G, ο G ο * οx * x * x x x * x G x * * x G, ο ο x * * x * x * x * * x x x * * x ο x * * x * x * x G, ο 3 Z +,, Z Z,, Z Z Z Z *4 R M { <, >, R, } <,> <,d><,d+> M M <, >, <, d > M,,, d R,, d + R <,> <,d><,d+> M M <, >, <, d >, < e, f > M

119 4 7 <,> <,d> <e,f><,d+> e,f><e,f+d+> <,> <,d> <e,f><,> <e,f+d><e,f+d+> <,> <,d> <e,f><,> <,d> <e,f> <,> M <, > M, <,> <,><, +><,> <,> <,><, +><,> <, > M,<, ><,> <,> <, ><, +><,> <, > <,><, ><,> M, 5 x x x x x f : x x x x 6 7 e e e x x x x x x x e e e e e e 8 S n D {,, Λ, n} S n G S n S n R s, t S n, srt g G, s g tg R S n n 3 S 3 S 3 G R S 3 R s S n G I n G s I n si n srsr s, t srt g G, s g tg g G t g sg S n

120 8 trsr u, v, w S n urvvrw g G, u g vg g G, v g wg u g g wg g g g w g g G g g G urw R R S S 3 6 n p 3 3 p p 3 3 p p p 6 3 S G G p, p } G p, p } G p, p } 3 { { 3, p 4 { p, } p } p, } } { p { 5 p 6 { 3 { 4 x, y S3 xry p x yp y p xp p x yp x y y p xp x y p Rp p 3 Rp 4 p 5 Rp 6 9G,* G H { y y * * y, y G} H,* G H G H x, y H G x y * x * y * x * * y x * * y * x * y * x * y x * y H H e * * e e H x H x * * x x x * x * * x x * * x H x * * x * x H G 3 S 4, ο { f f S4, f 4 4} { f f S4, f } 3 { f f S4, f {, }} 4 { f f S4, f {,}, f {, }}

121 4 9 S f g A, f ο g A 3 G H G x G x H x { x h x h H} G H x H x, x H x h h, x h x x h x x h x x h, H x x h H h h h H x x, h x x h x x H x 3 G H G M { x x G, xhx H} M G x, y M x H x H y H y H y H y H x h h x x H x y y x y H x y x y H y x x H x H x y M M *33 G AB A Υ B G A G B G A G B G A, B B, A A, B A B A Υ B B BG G G A A A A B A Υ B G A G B G *34 H, H, G G H Υ H G H Υ H G H, H G H, H H, H, H Υ H H H H Υ H

122 35 G,* R { <, >, G θ G θ * * θ } R G R x G x e * x * e, G R θ G θ * * θ e G xrxr θ * * θ θ * * θ G θ G θ G RR,, G RR θ G θ * * θ θ G θ * θ * * θ * * θ * θ θ * θ * * θ * θ θ θ,θ G θθ G RR R 36 H G G R R { <, > H} R G R x x e H < x, x > R R <, > R H H H <, > R R <, > R <, > R H H H H <, > R R R 37 G ~ G, x, y G x ~ y x ~ y H { x x G, x ~ e} G e G e H H x H, x ~ e xe ~ xx e ~ x x ~ e x H x, y H, x ~ e, y ~ e x ~ e, y ~ e x ~ y x e ~ x xy e ~ xy xy ~ e xy H H 38 G g G G G gˆ : gˆ x gxg ĝ G G ĝ

123 4 x, y G g ˆ xy g xy g g xg gy g gxg gyg gˆ x gˆ y ĝ x, y G g ˆ x gˆ y gxg gyg xy ĝ y G g ˆ g yg g g yg g y g yg G ĝ ĝ 39 G { f,,, Q} Q x x f x Q H f } G H G {, Q, d ο,, H f, d H f, ο f f H f, d f, d H Q, f H f H, Q,, f, + H G f, H { f, Q}, Q, 4 H G H G G e e HH G H G H e H G *4 G C G C e e e ee C x Λ n n C n n n n Λ x n n nn Λ C 4 H, K G HK G HK KH HK KH HK n n

124 e H e K e ee HK HK x hk, y h k HK h, h H, k k K k, xy hk h h kk h k kk K HKKH h3 H, k3 K k h h3k3 xy h h k hh k HK HK G HK G HKKH x HK HK x HK h H, k K x hk x k h k K, h H x KH HK KH KH KH HKKH 43 G, ο A, ο B, ο AB { ο A, B} AB, ο G, ο G ABBA AB x, y AB, A,, B x y xy A B G xy AB AB, ο G, ο 44 A G A G AA A AA A A A A 45Z+ <> <> 3<{,}> 4<Z> 5<{,3}> 6 < 6 > Ι < 9 > Z 3{,}Z 5{,3}Z {} 4ZZ 66 Ι 98Z 46 H K G G ~ h H, k K, hk ~ G G ] { x x G, x ~ } HK 3 [ ~

125 4 3 [] ~ H [] ~ K [] ~ K Ι H ~ G ee e H, e K ~ ~, G ~ h H, k K, hk h k H K h H, k K ~ ~,, G ~ ~ h H, k K, hk h H, k K, h k h h k k h h k k h h H k k K ~ ~ x G, x [ ] ~ x ~ ~ x h H, k K, x hk x HK [ ] ~ HK 3 [] ~ ~ ~ [ ] ~ [ ] ~ HK HK H He HK H [] ~ H [] ~ e H [] ~ [ ] ~ [ ] ~ K ek HK [] ~ K [] ~ K [] ~ [] ~ h H, k K hk k h K k K k K k h K Ι H K Ι H K Ι H k K, h H kh hk k K [] ~ 47 H G, G 6 H H 3 H 4 H 5HH 6 H Ι H H H H H 3 H h H, h h H 3 4 H h H, h h H h H H 4 5 H h H h x H h H x h hh hh H x H H H x H h H x h h h h h H x H H H HH 5 6 HH H H Ι H 6 H Ι H h, h H h h hh H 48 H G f xh Hx, x G f

126 4 f f G y x, Hy Hx yh xh 3 S G 3 3, 3 3 H 3 3, H 3 3, H 3 3, H 3 3, H H H 49 h Z,Z, n n n h 73 Z,Z, n n h 3Z,, N n Re 5 n m n h 4Z,Z, n n n h h Ker {} h Ker Z 3 h Ker 5Z 4 h Ker {} 5 G f G G f Imf f Ker x f x x f x 3 x x f 4 x x f / 5 x f x 6 x f x+ y x y x f G G ImfR + f Ker {,} xy y x 3 y x y x ImfR + f Ker {, } 4 y x y x ImfG f Ker {} f G 5 y x y x y x y x

127 4 5 5 f G G H G H { x x G, f x H } H G G / H ~ G / H f G G g : G G / H f οg G G / H G / H, ο H g H H f οg HH G G / H ~ G / H 5 G K G H K G / H G / K K / H K G H K H G G G / K K G G / H H K K / H H G / K K / H H G / H H H G / H G / K K / H 53 G H G H{ e }H n n H {e} H H { n n Z +, n H} k min{ n n Z H k +, n H} k H H n l n sk n k s H n sk + l, l < k n k l n k, H H k l k n H k H k k 54Z, Z 5 5Z Z Z 5 Z Υ 5Z + Υ 5Z + Υ 5Z + 3 Υ 5Z + 4 5Z5Z5Z5Z35Z4 5Z 5 *55 G H h H G, h H H H H, G H H h H h H G, h H h H H H h H h h G G h H h h H H H H H H

128 6 *56 H G H n G n H G 3 xhx G ϕ h xhx h H ϕ H xhx xhx H n xhx G n xhx H H G *57 g G, H, K g G / K, g G, GK * K K K,, K ϕ : G / K g G ϕ xk g x, x G, ϕ xk yk ϕ xk ϕ yk xk yk k, k K xk yk g x g x e g x g k g x k g y k g y g k g y ϕ xk ϕ yk ϕ ϕ ϕ ϕ xk ϕ yk g x g y xk yk xk xk xk y y xk g y xk g y g x g k g y g x g k g k e y xk K xk y y xk yk xk yk yk xk xk yk ϕ ϕ K, K G / K 4-9 ϕ K * K ϕ * K g * g g ϕ K ϕ K * d e e d ϕ e d ϕ d e 58 G{,,,d,e}G * 4-9 d d e {e,}* e d e G,* {e,},* e, {e,},** {e,}m M M,M*{,},M*{,},M*d{, e }

129 4 7 G G G / M M G 5, M, G/M 4 G 4-59 G{,,,d,e,f }G * 4- * e d f e e d f <> < > * * < > 3 4 G/<d> 5<d> d f d f e f d e d f d f e f e d e >{, e, } * { *, e *, * }{ f,, d } * { *, * e, * }{ d,, f } 3{ e, },{ e, d }{ e, f } 4 d { e, d } G/< d > G / < d > 6/3 5 d d { d, e }, d * {, }, d * {, f }4 6 X{,,3}x FIX { f f PERM X, f x x} PERMX FIX FIX g : g, g 3, g3 FIX FIX οg 3 FIX οg g οfix 4 PERMXFIX 3 3 FIX, FIX 3 3 f f 3 g FIX FIX ο g { f οg, f οg} 3 3, g οfix, FIX οg g οfix 3 3 4FIX PERMX/FIX PERMX / FIX 6/3

130 8 6 h G G hg 3 K K h h G hg 3 G/K K G / hg /34 K 4 3 G/K G / K / e G 4 G 4 G e G G{e,,,} e, * *64 < G, > x G x x x x x y y x 3 f : G G, f x x G x * x x * x e x x y * x * x * y y * x * x * y e x * y * y * x x * y * y * x e x y y 3 f : G G, f x x x, y G x * e e e 4- e e e x * y x * y f x * f y f x * y f y * x y * x

131 4 9 G *65G* G * *, : x x f G G f f G f y f x f * * * * y x xy f G g g g g f * * * * * * f G y x, * * * * * * * * * * y f x f y x y x y x f f f G 66 H x H H x x H H H T 3 H y z y / y T T 4h T {}, R y y z y h / h H y x, H y x y x + H H H * x x x x x x

132 R x x H R x x H H H 3 T y z y / + R z y y z yx y H y z y, / / + R z y y y x z y y z y H, / / / y z y H H y z y / / T y z y / H 4 T y z y / T y z y / / / / / y y y y y z z y y y h y z y y z y h + / / y z y h y z y h h h f Ker H *67 > < ο A, G > <, B H B A B,,, y f x f y x f A y x f ο H G H B z y x,, f A z y x,, z z f y y f x x f,, f * * * * * z y x f z f y x f z f y f x f z y x ο ο ο * * * * * z y x z f y f x f z y f x f z y x f ο ο ο * A e G B e f e ' * * x x f e x f e f x f e x ο x x e * e B B x e e f x x f x f x f x f x * * ο e x x f * B x f x H f G H G H

133 4 68 g G, + H, G, + H, 69 f g G H ϕ x f x g x, x G ϕ G H H H x, y G ϕ xy f xy g xy f x f y g x g y f x g x f y g y ϕ x ϕ y ϕ G H ϕ G H x, y H f g x, y G g x x, f y y ϕ xy f xy g xy f x f y g x g y f x y x g y ϕ x ϕ y f x g x f y g y f x x y g y f x y x g y f x x y g y y x x y H 7 f G G kerfkh G f f H HK G G e e x HK h H, k K x hk f x f hk f h f k f h e f h f H x f f H HK f f H x f f H f x f H h H f x f h k h x f k f h x f h f x e k K x hk HK f f h HK f f H HK 7 f G H K kerf G f f K x f f f x f f x f f x eh e H H k x K x k K f f K k K f k G f k f f k f k f f K f f f f K 7 G G,G G G G G G Ι G { e } 3 G G, G G <, > <, ><, > < G G, > G ~ G G, < G, > G

134 <, >, <, >, < 3, 3 > G G, > * <, > * <, ><, > * <, >< > < , 3 <, > * <, > * < 3, 3 > < 3, 3 <, > * <, > * < 3, 3 ><, > * <, > * < 3, 3 > > <, > * < e, e >< e, e > * <, ><, > < e, e > < G G, > <, > * <, ><, > * <, >< e, e > < G, > G G, G x G, x ϕ <, > G, G, G,, G G Ι G e ; ϕ G G G ϕ, G,, G ϕ <, ><, > * <, > ϕ ϕ ϕ G G G G ~ G G *73, + C f + g x f x + g x, f ο g x g f x C C, C, ο ο f ο g + h x g + h f x g f x + h f x f οg + f οh x ο f x x, g x x, h x g + h ο f x f g x + h x x + g ο f + h ο f x f g x + f h x x + C *74 S, +, S S S,, S

135 S S, S,, S,,

136 L L xy gl{x,y} lu{x,y} gl inf lu sup {x,y} x y x y x y x y x y x y x y lu{ x, y}, x y gl{ x, y} L, L,, L 3, L 4 L L,,,,, L 3 L,,

137 5 5 L,,, L R xry x y y xry x y x R L 3L x y lu{ x, y } x y gl{ x, y } x y L,, L,, L, L,, x y x y y 3 L,,, L 3, 4, L,,,,, d L d d d 5 L,,, L 3 6 L,,,, L

138 6 P P Q Q P Q L,, T L T T,, L,, 4 L,, S,, h L S x, y L h x y h x h y h x y h x h y h L S h h L,, S,, 7 h L S x, y L x y h x h y [,] L,, x, y, z L x y z x y x z x y z x y x z L,, 6 5-

139 5 7 B E C D 5- B C D B A B B C B D E E E x, y, z L x z x y z x y z,, L 5- L,, L x y L x y, x y y x x x y y x x y x y 5-5- B CDC BD

140 8 8 L,, x x x x x L,,, L,,,,, L B, +,* *,, B + + * * * + * + * + * + * + 3, B * + 4 B * + B, +,* 9 L,,,,, x, y, z L x y y x x y y x x y z x y z x y z x y z 3 x y z x y x z x y z x y x z 4 5 x x x x x x x x x x 6 x x 7 x x 8 x x x x 9 x y x y x y x y x x y x x x y x

141 5 9 L,,,,, B * B, B,, B + + * * * + * + * + * + * + 3 * + 4 B * + B, +,,,, 6 A,,,,, B, Υ, Ι,,ˆ,ˆ ϕ A B, A ϕ ϕ Υ ϕ ϕ ϕ Ι ϕ ϕ ϕ ϕ A,,,, B, Υ, Ι,,ˆ,ˆ ϕ 7 L,,,,, T L,, T,,, L,,,,,, T L,,,,, x L x x u L π u π L, x B x x B

142 3 B x B x x x L,,,,, x B x,, Λ, n i x x Λ n d e x 5-3 Stone L,,,,, S {,, Λ, n} _ L,,,,, P S, Υ, Ι, A n A n

143 {,,,d,}{,,d,e,}{,,,,} d d d d d e d d d d e xz x,y,z x y z x y z x z xz y y x z y N N C A B C D

144 3 * 5-3 A B C D C 5-3 *3 5-4 B A B C D AA{,,,d}{<d,>,<,>,<,>,<d,>,<d,>} BA{,,,d,e}{<,>,<,>,<d,>,<e,>,<e,d>,<e,>} CA{,,,d,e,f,g}{<,>,<d,>,<,>,<,d>,<f,e>,<g,f>} DA{,,3,4}{<,>,<,3>,<,4>,<3,4>} D 5 A N, B Z, C{346} D PA, A{,,} D 6 AB f A B S { f x x P A} P B, A Bf C D D

145 5 33 S B f B 3 S A B C D 5-5 D 8 A B C D D A B C D 5-6 C L, L 3L A B C D C 9 L 3 5 A B C C A P A, PA A B C D A

146 34 3 C A B C D 4A A C B D B A B C D 5-7 C 6S,A S,A A B C D A A B Ce e f d g Df 5-8 B 8A, B, 5-9,, f x f x f x4 f d x8 f

147 5 35 x x x 6 x 4 d 5-9 x 5 x 3 x 8 x 7 A C B D B 9L,S,f L S, L f f A B C D C S Z S A B C D B A{,,} P A, A {, A} B {,{ },{, }, A} C { A,{ },{, }} D {,{ },{, }, A} C An B n C n D4n C 5.3. d L, 5- S {,,, } S {,, d, } S {,, d, } d S, f L, 3 f e f 5- g

148 36 A,, A, 3 4A, A{,,3,4,6,8,,4} A,,, A A, 4 6 K {,,3,4,6,} LCMGCD' LCMGCD x x 7 n A,,, A 3 n L L 5-5-

149 L L *7 8 A P A, 9L,L, A{,,}S 3 P A, S, L, L,,,, L L,,, L, 3 4 A,,, A * 5-3 e f d d d ef d d 3 d

150 38 L L L y x, xy x y L{,,3,4,6,} L{,,3,48,,4} 3L{,,3,4,5,6,7,8,9,} *3 L L,, 4L,,, L L,, 5 > <, L L d,,, d d 3

151 d d d d d d d d 6L,,, L L,,, 7 > <, L L,, L,,

152 4 8L,,, L 4 9 L,L,,,, L 7L,

153 5 4 D D D D9, ; 6 ; 9 3 9; C 45 4 {69}{9}{89}{39} {459}{369}{399}{359} {389}{339}{3459}{59} {559}{589}{539}{5459} {689}{639}{99}{989} {9459}{39}{539}{5459} L, L,, L L {,, Λ, n} Λ n L i i,, Λ, n L Λ L i i,, Λ, n L n