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41.
关于反中心对称矩阵的某些性质探讨 总被引:2,自引:0,他引:2
利用反中心对称矩阵的定义以及翻转矩阵等技巧,给出了反中心对称矩阵的伴随矩阵、特征值及特征向量的一些新结论. 相似文献
42.
Eknath Ghate 《Compositio Mathematica》2002,132(3):243-281
Let f be a primitive Hilbert modular cusp form of arbitrary level and parallel weight k, defined over a totally real number field F. We define a finite set of primes
that depends on the weight and level of f, the field F, and the torsion in the boundary cohomology groups of the Borel–Serre compactification of the underlying Hilbert-Blumenthal variety. We show that, outside
, any prime that divides the algebraic part of the value at s=1 of the adjoint L-function of f is a congruence prime for f. In special cases we identify the boundary primes in terms of expressions of the form
, where is a totally positive unit of F. 相似文献
43.
For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations 相似文献
44.
1.引言19世纪Hamilton提出经典力学的一种基本的方程形式.记P=Mq表示动量,q表示位移,于是动能T=1/2(p,M-1 p),并将总能量H=T+V位能)表示为p,q的函数:于是经典力学的标准形式-Newton形式称为Hamilton正则方程.(1.1)是ZI维相空间或称辛空间中的相变量(PI,...,P。,ql;...,qn)'的一阶微分方程组.其中q-(ql,...;qrt)'是位置向量,dq,、I。。。。。q=i=(ql,...,qh)'是速度向量,dt'"""。'。'。。。l、。。d"q,....、,-,-… 相似文献
45.
Frieder Knüppel 《Geometriae Dedicata》1999,76(3):253-264
Let V be a finite-dimensional vector-space. A linear mapping on V is called simple if V( - 1) is 1-dimensional. Let S be a set of simple bijections on V. We discuss conditions entraining that each element of S is orthogonal (respectively symplectic) under an appropriate symmetric (respectively symplectic) bilinear form on V. 相似文献
46.
Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented.
AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett. 相似文献
47.
By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance. 相似文献
48.
Hui Li 《Proceedings of the American Mathematical Society》2003,131(11):3579-3582
Let be a connected, compact symplectic manifold equipped with a Hamiltonian action. We prove that, as fundamental groups of topological spaces, , where is the symplectic quotient at any value in the image of the moment map .
49.
1. PreliminaryIt is well known that{1] a 8ymPlectic form is invariant along the trajectory of a Hamilto-nian system. Based on this fundamental property, certain techniques have been developed.The purpose of this paper is to extend such an approach to a wider class of dynamic systeIns,namely, genera1ized Hamiltonian systems. Our purpose is to investigate a class of dynaInicsystems, which possess a certain "geometric structure".Deflnition 1.1[1'2]. Let M be a tIlallifo1d. w E fl'(M) is call… 相似文献
50.
A general principle of causal duality for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of quantaloids and quantaloidal morphisms appear naturally within this setting; as in the case of causal duality, they originate from primitive physical reasonings on the lattices of properties of physical systems. Furthermore, an essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of causal duality in operational quantum logic. 相似文献