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61.
Iterative numerical schemes for solving the electrostatic partial differential equation with variable conductivity, using fast and high-order accurate direct methods for preconditioning, are compared. Two integral method schemes of this type, based on previously suggested splittings of the equation, are proposed, analyzed, and implemented. The schemes are tested for large problems on a square. Particular emphasis is paid to convergence as a function of geometric complexity in the conductivity. Differences in performance of the schemes are predicted and observed in a striking manner.
AMS subject classification (2000) 31A10, 35C15, 65R20.Received May 2004. Accepted September 2004. Communicated by Anders Szepessy.Johan Helsing: This work was supported by the Swedish Science Research Council under contract 621-2001-2799. 相似文献
62.
This paper initiates a general study of the spectrum of two-particle bound states of transfer matrices for a fairly wide class of Gibbs fields at high temperature T. In the present first part of this study, a detailed statement of the problem is given and the existence of a so-called "isolated level" lying at a distance 1/T
2 from the boundary of the continuous spectrum is established for all values of the total quasimomentum of the system. In the concluding part of the paper, we prove that there are no other bound states provided that is far from certain singular values. In the second part, we will consider bound states for close to the singular values. The distance from these states (adjacent levels, in the authors' terminology) to the continuous spectrum is at most of the order of 1/T
4. 相似文献
63.
Patrick?J.?RabierEmail author 《NoDEA : Nonlinear Differential Equations and Applications》2004,11(3):311-333
We give verifiable conditions ensuring that second order quasilinear elliptic equations on
have infinitely many solutions in the Sobolev space
for generic right-hand sides. This amounts to translating in concrete terms the more elusive hypotheses of an abstract theorem. Salient points include the proof that a key denseness property is equivalent to the existence of nontrivial solutions to an auxiliary problem, and an estimate of the size of the set of critical points of nonlinear Schrödinger operators. Conditions for the real-analyticity of Nemytskii operators are also discussed. 相似文献
64.
We investigate quantum mechanical implications of canonically inequivalent Hamilton formulations of the Newtonian dynamics. Generated alternative quantizations, being noncanonical, are consistent with the same equations of motion, i.e., they satisfy E.Wigner's principle of quantization. As illustration we consider a noncanonical one-dimensional harmonic oscillator. 相似文献
65.
We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces H
p
(1<p<). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p=2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol. 相似文献
66.
67.
Daqing Wan 《Journal of the American Mathematical Society》2000,13(4):853-908
In this paper, we prove the rank one case of Dwork's conjecture on the -adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F-crystal. Further explicit information about zeros and poles of the pure slope L-functions are also obtained, including an application to the Gouvêa-Mazur type conjecture in this setting.
68.
In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations
Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions
are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship
between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When
numerical computations are needed for the solution, the method proves to have high precision and fast convergency. 相似文献
69.
所谓的Rice’s方法是估计交错和Df_n=sum from k=0 to n(_k~n)(-1)~kf_k,其中,序列f_n能扩充为一个解析函数f(n).在算法分析的许多问题中,经常导出序列Df_n.在60年代,Knuth在分类交换基 相似文献
70.
The regularized integrodifferential equation for the first kind of Fredholm integral equation with a complex kernel is derived
by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed.
As an application of the method, an inverse problem in the two-demensional wave-making problem of a flat plate is solved numerically,
and a practical approach of choosing optimal regularization parameter is given.
Project supported by the National Natural Science Foundation, of China 相似文献