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961.
We briefly describe the theory of root transfer matrices for four-line models with the field in the new indexless form. We
use theoretical and numerical methods to reveal new effects in the theory of singular points and phase transitions. A substantial
part of the results is obtained using a numerical algorithm that drastically (at least exponentially) reduces the computational
complexity of Ising-type models by using the extremely sparse root transfer matrix.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 2, pp. 281–298, November, 2006. 相似文献
962.
A. V. Marshakov 《Theoretical and Mathematical Physics》2006,147(2):583-636
We consider the simplest gauge theories given by one-and two-matrix integrals and concentrate on their stringy and geometric
properties. We recall the general integrable structure behind the matrix integrals and turn to the geometric properties of
planar matrix models, demonstrating that they are universally described in terms of integrable systems directly related to
the theory of complex curves. We study the main ingredients of this geometric picture, suggesting that it can be generalized
beyond one complex dimension, and formulate them in terms of semiclassical integrable systems solved by constructing tau functions
or prepotentials. We discuss the complex curves and tau functions of one-and two-matrix models in detail.
[This article was written at the request of the Editorial Board. It is based on several lectures presented at schools of mathematical
physics and talks at the conference “Complex Geometry and String Theory” and the Polivanov memorial seminar.]
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 163–228, May, 2006. 相似文献
963.
964.
混合互补判断矩阵一致性研究 总被引:3,自引:0,他引:3
给出混合互补判断矩阵一致性的定义和判别加性一致性的方法.定义了核算子、核矩阵,对带有精确数、三角模糊数和梯形模糊数的混合互补判断矩阵给出基于核矩阵的一致性调整方法,调整量可以是精确数也可以是模糊数.最后给出一个应用实例. 相似文献
965.
966.
51.IntroductionLetF=[O,1],foranya,beF,definea b=max{a,b},a*b=min{a,b}.Mn(F)standsforthesetofa1lthenthordermatrixesinF,matrixAinMn(F)iscalledFuzzymatrixA.Letrbeanynon-negativeinteger.lnannthordermatrix,exclusiveofthefirstrow,theelementsofeveryotherrowarethee1ementsoftheprecedingrowthatcirculaterightwardr-co1umns.Thisnthordermatrixisannthorderr-circulantFuzzymatrix(alsocalledgenearLizedcirculantFuzzymatrix)-Wecallrthecircu1antindexofr-circulantFuzzymatrix.Inthebooklistedin[1j,thisisgiven:… 相似文献
967.
关于广义正定矩阵的进一步推广 总被引:3,自引:1,他引:2
受到Johnson、佟文廷、夏长富的启发,进一步推广了广义正定矩阵的定义,并得出了更广义正定矩阵P∈PA+的若干性质. 相似文献
968.
An explicit construction of polynomials over a finite field of odd characteristic, for which the absolute value of trigonometric sums attains the Weil bound, is based on the construction of cyclic matrices of given rank. Dickson polynomials of the second kind play an essential role in the study of such matrices.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 16–25.Original Russian Text Copyright © 2005 by L. A. Bassalygo, V. A. Zinov’ev. 相似文献
969.
Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported. 相似文献
970.
Lattice vibrational properties of uranium pnictides have been studied using breathing shell model (BSM) which includes breathing
motion of electrons of the U-atoms due tof−d hybridization. The phonon dispersion curves of U-pnicitides calculated from the present model agree reasonably well with
the measured data. A comparison has been made between BSM and our results reported earlier obtained from three-body force
rigid ion model to reveal the importance of the short-range electron-phonon interactions in these compounds. We also report,
for the first time, the two phonon density of states and specific heat for these compounds. 相似文献