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61.
An estimate of error in an approximate wave function for a stationary state is put forward that does not require any information about the exact state. The measure is sensitive and direct. Parameters embedded in a trial wave function can be varied to minimize this error as well, leading to a variational principle. Such a scheme works nicely for bound states and the more so for Siegert states, for which the standard energy minimization principle does not apply. Pilot calculations on the anharmonic oscillator system and the radial Stark effect in the hydrogen atom reveal the worth of the endeavor. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 相似文献
62.
We present a method for computing classical Newtonian trajectories that minimize the path length or transit time from reactant
to product. Our approach is based on a generalization of the fast-marching method, which allows us to construct the solution
of the Hamilton-Jacobi equation for the action that optimizes the desired quantity. The resulting “reactive paths” can be
interpreted as reaction coordinates but, unlike more conventional choices, they contain dynamical information about the chemical
system of interest. 相似文献
63.
考虑应变梯度和速度梯度的影响,建立薄板控制微分方程及给出其边值问题的提法,修正了前人给出的薄板角点条件.采用Levy法,给出受分布力作用下简支板的挠度及自由振动频率的解析解.通过与文献中分子动力学数据对比,验证了该文模型的有效性并提出校核材料参数的一种方法.研究结果表明,增大弹性地基和应变梯度参数可以有效提高板的等效刚度,而速度梯度参数则相反.该文提出的板的边值问题为研究薄板在复杂支撑边界及外荷载等条件提供了理论依据.同时,有望为其有限元法、有限差分法和基于能量原理的Galerkin法等数值方法提供理论依据. 相似文献
64.
In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems. 相似文献
65.
Marc Soret 《Annals of Global Analysis and Geometry》1995,13(2):101-116
The main result of this paper is the following maximum principle at infinity:Theorem.Let M
1
and M
2
be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M
1,M
2)=min(dist(M
1,M
2), dist(M
2,M
1)).In case one boundary is empty, e.g. M
1,then dist(M
1,M
2)=dist(M
2,M
1).If both boundaries are empty, then M
1
and M
2
are flat. 相似文献
66.
A. Puhalskii 《Queueing Systems》1995,21(1-2):5-66
We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs. 相似文献
67.
Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution
belongs to the range of the operator (T
*
T)
v
, o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India. 相似文献
68.
F. den Hollander 《Journal of statistical physics》1994,75(5-6):891-918
Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on 2 that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California. 相似文献
69.
Todor Todorov 《Transactions of the American Mathematical Society》1996,348(2):673-689
We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.
70.
Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25. 相似文献