Проекционные операторы и гиперкомплексные числа

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  • 1. ( ) .., .., .. ,

2. 1) ( - ). 2) ( ). 3) . 4) , . 3. . , , . , . 4. , [x, y, z] [x, y, 0]: , , : P2 = P. . 5. ( ), , , , . , . , , ( ). , . 6. 50 : . : (Stewart I. Life's other secret: The new mathematics of the living world. 1999, NewYork: Penguin). 7. , ? , , ; ; ; , . 8. : , , (, , ). . , . , . 9. ( ). - , , . . 10. : , , G, T ( U ). 20 64 - , CAG, ACC, 11. () n-:- 41 (A, C, G, T/U); - 42=16 (AA,AC,AG,.); - 43=64 (AAA,AAC,ACA,) n-, 4n , ( ) [C U; A G](n), (n) ( ) . 12. [C U; A G](n) n = 1, 2, 3. 4 , 16 64 . 13. , , . , : 14. [C U; A G](3), 64 : 15. - 64 32 : ( ). ( 8*8 64!=1089; 1017 ): 16. () () . 17. ?[C U; A G](3) = , . . 18. : +1 -1. , () +1 (1). 19. [C U; A G](3) R8: 1 1 -1 -1 R8 = 1 1 -1 -11 1 -1 -1 1 1 -1 -11 1 1 1 -1 -1 -1 -11 1 1 1 -1 -1 -1 -11 1 -1 -1 1 1 -1 -11 1 -1 -1 1 1 -1 -1-1 -1 -1 -1 1 1 1 1-1 -1 -1 -1 1 1 1 1 20. U ( , .), U- [C U; A G](3) [C T; A G](3) - ( U ). H8. 21. +1 -1. . () +1 ( -1), H8. 22. . , , , , , , . , . . . 23. (8*8)-, - : R8 H8. ? . 24. R8 H8 8 , ( ): R8=s0+s1+s2+s3+s4+s5+s6+s7; H8=u0+u1+u2+u3+u4+u5+u6+u7 25. R8=s0+s1+s2+s3+s4+s5+s6+s7 H8=u0+u1+u2+u3+u4+u5+u6+u7 16 matrices s0, , s7, u0, , u7 , P2 = P. , R8 H8 ; . . 26. . -, , . , () . , . . 27. , s0 s2: 8: (2-0.5*(s0+s2))N = (2-0.5*(s0+s2))N+8 ( N=1, 2, 3, ). 28. Y = (2-0.5*(s0+s2)) 8 X=[x0, x1, x2, x3, x4, x5, x6, x7] X*YN=X*YN+8 8, 0 2 , 0: 29. , ( ) 2- (x0, x2) 8- . , , 2- 8- . 30. , R8 H8 : , 8. 2- 8- . 31. , , : (s0+s1)N = 2N-1*(s0+s1) , , :N ((s0+s6)2) = 4N-1*(s0+s6)2 32. . , , . , (, - ). 33. 34. : , , , . 35. , , ? : , (8*8)- R8 H8 (2N*2N)- : R8 [1 1; 1 1](N) , H8 [1 -1; 1 1](N) ; (N) ; [1 1; 1 1] [1 -1; 1 1] . (2N*2N)- 2N . 2- N 36. (, ), , , . , , , , , ( ). 37. , , , , . 38. , . , . , , , . 39. . . , . .. . . . 40. , , .. , ; , [ , ]. , , , , .. , . 41. , : , ; . , , - , . . . (1956) , . (. ). 42. . , (!) , . . .. [ ]. , , . 43. , ( ). . 44. - ( ). , ? . 45. s0 -s0 s1 s2 s3 s4 s5 s6 s7s1 For R8 : s2 s3 s4 s5 s6 -s7 -u0 u1 u2 u3 u4 u5 u6 u7u0 u1 - For H8 : u2 u3 u4 - u5 u6 u7 - R8 H8. , - . , (2-0.5*(s0+s2))N 8- (x0, x2)- . : 1) ; 2) :=5:3. 46. ( ). 19 ( http://www.ncbi.nlm.nih.gov/Taxonomy/Utils/wprintgc.cgi: 47. , , - [C U; A G] (3) 64 6 19 . , +1 -1, 1- . , 1- [C U; A G](3) 64 19 . : , [, 2013]. 48. The Standard Code: CCC Pro CCA Pro CAC His CAA Gln ACC Thr ACA Thr AAC Asn AAA LysCCU Pro CCG Pro CAU His CAG Gln ACU Thr ACG Thr AAU Asn AAG LysCUC Leu CUA Leu CGC Arg CGA Arg AUC Ile AUA Ile AGC Ser AGA ArgCUU Leu CUG Leu CGU Arg CGG Arg AUU Ile AUG Met AGU Ser AGG ArgUCC Ser UCA Ser UAC Tyr UAA Stop GCC Ala GCA Ala GAC Asp GAA GluUCU Ser UCG Ser UAU Tyr UAG Stop GCU Ala GCG Ala GAU Asp GAG GluUUC Phe UUA Leu UGC Cys UGA Stop GUC Val GUA Val GGC Gly GGA GlyUUU Phe UUG Leu UGU Cys UGG trp GUU Val GUG Val GGU Gly GGG Gly 49. Thraustochytrium Mitochondrial Code: CCC Pro CCA Pro CAC His CAA Gln ACC Thr ACA Thr AAC Asn AAA LysCCU Pro CCG Pro CAU His CAG Gln ACU Thr ACG Thr AAU Asn AAG LysCUC Leu CUA Leu CGC Arg CGA Arg AUC Ile AUA Ile AGC Ser AGA ArgCUU Leu CUG Leu CGU Arg CGG Arg AUU Ile AUG Met AGU Ser AGG ArgUCC Ser UCA Ser UAC Tyr UAA Stop GCC Ala GCA Ala GAC Asp GAA GluUCU Ser UCG Ser UAU Tyr UAG Stop GCU Ala GCG Ala GAU Asp GAG GluUUC Phe UUA Stop UGC Cys UGA Stop GUC Val GUA Val GGC Gly GGA GlyUUU Phe UUG Leu UGU Cys UGG trp GUU Val GUG Val GGU Gly GGG Gly 50. ( )? 51. , +1, . , , , ( +1). , , (, , , ). 52. 16 ( ) (44)- , : 53. , . , , . , . (-, .) , , . , . . 54. : 3-4 2-2 , ( http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mboc4.) 55. 56. 4, h0, h1, h2, h3 h0+h2: e0 e2, . (44)- h0+h2 - ( (0, 2) 4- ). 57. (4*4)- CL=a0*e0+a2*e2. , 0, . CL-1 CL-1*CL =CL*CL-1 = e0. L (44)- . , (22)-: 58. h1+h3 1 3, . , h1+h3 (44)- . CR (4x4)- . CR-1 . 59. (44)- CL CR (.. h0+h1+h2+h3) 4. 4 q0, q1, q2, q3, (q0 ): 60. (88)- 8, (44)- 4 ( ) H4 [1 -1; 1 1] = H8 : 8 8 , ( ) . . 61. , , (88)- , , . (.. , , ) . (.. 8 ) . 62. H4[1 -1; 1 1](N) (N), (1616), (3232),, (2Nx2N), . : - 2N-1 , , - , (2N-2 ); - (2N-3 ) .. ( ). 63. () , . . , . () ., . 64. . 80- .: 65. . , , : 1) ; 2) ; 3) , 4) , . 5) . 66. () ., . . (1965) - () , . , . 67. : : . 68. , , , , . , . 69. : , , , . 64 - : 111110101100011010001000CHYAN 111111TUILIHSUNKANKENKUN111110111101CHEN 111100111011111010111001111000CHYAN 110110111110110110101110100110011110010110001110000TUI 101101111101110101101101100101011101010101001101000LI 100100111100110100101100100100011100010100001100000CHEN 011011111011110011101011100011011011010011001011000HSUN 010010111010110010101010100010011010010010001010000KAN 001001111001110001101001100001011001010001001001000KEN 000000111000110000101000100000011000010000001000000111KUN 70. , , . , . 71. - - (2N*2N)- , 2N . , z=cos450+i*sin450 8: zN=zN+8 8. 72. zN = (a+b*i)N . 2N- , (2N*2N)- , , . 73. . . , , , , , ( ), () . , , 74. . , , . . C () , c , , . 75. , . 76. , , , , . , . , , , , . 77. , , ( ..). . 78. , .. ; , , ( 2002135566/14 2002 .). , .. . .. . 79. : - . .., 2005 . ( http://health-ua.com/articles/1103.html): (), , - 80. , , , . - . , , , : , . , . 81. , , , . - . , , , : , . , . 82. . , . , 10 , , 100 000 , 85 . 0,025 . 83. : 1) , ; 2) , (), 84. : + . 2N- ? 85. , . (), . . , . 86. , 2- . 87. ( http://www.esus.ru/php/content.php?id=1333 ). 88. 89. R4, c0, c1, c2, c3, c0+c2. e0 e2, . (44)- 0+2 - . 90. c1+c3 e1 e3, . (44)- 1+3 - . (44)- , . 91. (44)- (.. c0+c1+c2+c3) R4. R4 r0, r1, r2, r3, (q0 ): 92. (88)- R8, (44)- R4 R4 [1 1; 1 1] = R8 : R8 8 , ( ) . . 93. , , (88)- , , . (.. , , ) . - (.. 8 ) - . 94. R4[1 1; 1 1](N) (N), (1616), (3232),, (2Nx2N), . : - 2N-1 , , - , - (2N-2 ); - - (2N-3 ) .. 95. , . , , . 96. (44)- 4 , (44)- L CR: , , . (44)- , 4- , , : CL*CR CR*CL . 97. V = L+CR, 4- . z = [1 0; 0 1]*a + [0 1; -1 0]*b : 1) V ; 2) V b; 3) V , . 98. V , , ( , ), [1 0; 0 1]S + [0 1; -1 0]G, S G (2x2)-. 99. V : . 100. , (44)- , , (?). () , , . , . (1877 .), . ( .) (2Nx2N)- . 101. (44)- R4, (44)- DL DR: D = DL+DR 4- . 102. D=DL+DR [1 0; 0 1]*a + [0 1; 1 0]*b : 1) D ; 2) D K b; 3) D , . 103. D , , ( ), [1 0; 0 1]S + [0 1; 1 0]G, S G (2x2)-. ( a=b =-d D 0). 104. : 105. (44)- . . (2Nx2N)- . . 1*x0+i1*x1++in*xn :1) 0, 1, ; 2) . , . 106. , , , (. : . . , ., , 1984). , . , . ? , , . 107. (. , 1878 .) 108. , , 4 .. http://petoukhov.com/ : 109. , . , , . . (?) .