Coding theory and algebraic geometry by Stichtenoth H., Tsfasman M.A. (eds.)

By Stichtenoth H., Tsfasman M.A. (eds.)

The workshop "Algebraic Geometry and Coding conception - three" prepared via the Institute of data Transmission (Moscow), college of Essen, Equipe Arithmetique et Theorie de Tlnformation de C.N.R.S. (Marseille-Luminy), and team d'Etude du Codage de Toulon came about within the Centre overseas de Rencontres Mathematiques> June 17-21,1991.The workshop used to be a continuation of AGCT-1 and AGCT-2 that came about in 1Q87 and 1989, respectively. it's to be through AGCT-4 in 1993, etc., whenever held in C.LR.M.

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Ge, K. -B. Zhang Next we consider Yang-Mills gauge field for reduced Y(SU(2)). tensor wave function (x = {XI,X2,X3,XQ}), * ( I ) = ||iMx)|| (»,j = 1,2,3,4). 19) or [Ja]°f = ui^crySps + v ^ " ) / * * ^ + iaeabc(Sb)a7(Sc)ps. , [ A ^ a / 3 = SMVa/3 + < ^ W ^ < M * ) , AM - A%Ja. , (-id^ix) + g5Al)[Ya)f8 - ig6a{x)Al\Jb, Ja]fs = 0. 26) and i^„ = -[D„DV\ *£„ = 3 ^ - d ^ = F^Ya, + z^afcc^^. e # = "*i 0~ where \I>i and ^ 2 are 2 x 2 wavefunction. 2. 1) where 5 = \ and B = B(£) is magnetic field. The Hamiltonian can easily be diagonalized for any background angular momentum (or spin) K.

7) i=\ Since J —• ^S + J still satisfies Yangian relations, it is natural to appear the term 7S. The interacting Hamiltonian then reads HT(t) = - 7 B ( t ) • S - B(i) • Y. -M. -L. Ge, K. -B. Zhang When Hi = 0, h = 0, it is the usual NMR for spin 1/2. 9) a=±,3;0 where {x±, X3} is the spin triplet and xo singlet. Setting B±(t) = Btit) ± iB2(t) = B i e T i w o t , and B 3 = const. 14) ctt =Him))Noting that Hi is independent of time, we get \$(t))=e-iEt\$(t)). 16) leads to £ 4 - [(Wl - 7B3) 2 + 12B\ + \ti+H-{B\ -u+H-[BfK + Bl)]E2- - 7S3) 2 - 27fl3B12(wo - 7S3) + 7 2 # i ] = 0.

5) Note that since "H is r-invariant, \\n j s si[\\ a Hermitian form. 5) have signature (oo, oo). Now we state a result established in " U 5 . 1. IfH is r-invariant, then A^-H (resp. B^n) is \)n ^ 'n ' self-adjoint (resp skew-adjoint), and 2 1 ^ (resp. VS^n) is t)n (T*X<**F) selfadjoint (resp. skew-adjoint). 1 applies to the operators associated to H = Hc which were considered in section 2. Its implications are discussed in " U 5 and BL °6. 5. The analysis of the hypoelliptic Laplacian Now we briefly describe some results on the analysis of the operator 21?

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