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51.
M. Bildhauer M. Fuchs V. G. Osmolovskii 《Mathematical Methods in the Applied Sciences》2002,25(4):289-308
We consider the problem of minimizing 0<p<1, h∈?, σ>0, among functions u:?d?Ω→?d, u∣?Ω=0, and measurable characteristic functions χ:Ω→?. Here ?+h, ??, denote quadratic potentials defined on the space of all symmetric d×d matrices, h is the minimum energy of ?+h and ε(u) denotes the symmetric gradient of the displacement field. An equilibrium state û, χ?, of I [·,·,h, σ] is termed one‐phase if χ?≡0 or χ?≡1, two‐phase otherwise. We investigate the way in which the distribution of phases is affected by the choice of the parameters h and σ. Copyright 2002 John Wiley & Sons, Ltd. 相似文献
52.
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
53.
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
54.
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
55.
A general trend of supramolecular chemistry is the building of mesoscopic-oriented nanotubes. When the typical radius of the channel almost fits the mean supramolecular cross-sectional radius, the guest supramolecule is ultraconfined in the channel. In that case, only rotational disorder around the channel axis is allowed. For sufficiently low temperatures, we expect this 2D disorder to be static on the NMR timescale, and it should reflect the local symmetry of the channels. In this article, we show that experiments performed with deuterium single crystal solid-state NMR as a function of rotation around the channel axis may lead to important information concerning the static orientational disorder of the confined supramolecules. Using an inversion method with Tikhonov regularization and a positivity constraint, that also takes into account of the nonideal pulse sequence response, the orientational probability density can be obtained from 1D experiments performed at different angles, even for significant disorder. As a first step, the method is validated on four different theoretical distributions. It is then applied to 2H NMR single crystal experiments performed on an archetype of parallel channels intergrowth compounds: selectively deuterated 1,10-decanedicarboxylic diacids in hydrogenated urea channels. The diacids form one-dimensional infinite hydrogen-bonded chains ultraconfined in urea linear channels. 相似文献
56.
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
57.
We compare the calculation of the two-loop -function in the N=1 supersymmetric electrodynamics regularized via higher derivatives and via dimensional reduction. We show that the renormalized effective action is the same for both regularizations. But in the method of higher derivatives, unlike in the dimensional reduction, the -function defined as the derivative of the renormalized coupling constant with respect to log turns out to be purely one-loop. The anomaly problem therefore does not occur in this regularization, because in the method of higher derivatives, the diagrams with counterterm insertions make a nonzero contribution, which is evaluated exactly in all orders of the perturbation theory. When dimensional reduction is used, this contribution is zero. We argue that this result is a consequence of the mathematical inconsistency of the dimensional reduction method and that just this inconsistency leads to the anomaly problem. 相似文献
58.
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
59.
The technique we propose for solving ill-conditioned linear systems consists of two steps. First we compute the regularized solution on some values of the regularization parameter . Then we use these solutions either to extrapolate at =0 or to estimate the regularized solution with determined by the generalized cross validation or by the L-curve method. 相似文献
60.
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 .