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131.
Zhongxue Lü 《Journal of Mathematical Analysis and Applications》2007,326(2):1452-1457
Some new generalizations of the Hilbert integral inequality by introducing real functions ?(x) and ψ(x). The results of this paper reduce to those of the corresponding inequalities proved by Gao [Mingzhe Gao, On Hilbert's integral inequality, Math. Appl. 11 (3) (1998) 32-35]. Some applications are considered. 相似文献
132.
Djavvat Khadjiev 《Journal of Mathematical Analysis and Applications》2007,326(2):1101-1115
An approach to a definition of an integral, which differs from definitions of Lebesgue and Henstock-Kurzweil integrals, is considered. We use trigonometrical polynomials instead of simple functions. Let V be the space of all complex trigonometrical polynomials without the free term. The definition of a continuous integral on the space V is introduced. All continuous integrals are described in terms of norms on V. The existence of the widest continuous integral is proved, the explicit form of its norm is obtained and it is proved that this norm is equivalent to the Alexiewicz norm. It is shown that the widest continuous integral is wider than the Lebesgue integral. An analog of the fundamental theorem of calculus for the widest continuous integral is given. 相似文献
133.
Desheng Yang 《Journal of Mathematical Analysis and Applications》2007,330(1):550-570
Dynamics for the stochastic Kuramoto-Sivashinsky equation with a nonlocal term is studied. We prove that the stochastic equation has a finite-dimensional random attractor. 相似文献
134.
应用等效原理,通过引入口面上等效磁流将含腔导电目标电磁散射简化为腔内、外两个等效 问题. 腔内问题分段求解并应用级联法获得口面等效导纳矩阵;腔内外的耦合关系应用近似 边界元方法描述并由此获得口面等效磁流;最后,这一具有混合源的腔体内外一体化散射问 题则应用所提出的广义混合场积分方程方法建立电磁模型,并用多层快速多极子方法实现高 效数值求解. 实例计算结果与测试结果具有很好的一致性.
关键词:
含腔目标
电磁散射
混合场积分方程
数值分析 相似文献
135.
136.
We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ0?1. We propose two methods transforming this problem to a finite set of the independent problems of the same type set in an atmosphere with optical thickness much less then τ0. The error estimates are derived. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
137.
This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained. 相似文献
138.
Wengu Chen Yixin Lai 《分析论及其应用》2006,22(2):195-200
Let μ be a Borel measure on Rd which may be non doubling. The only condition that μ must satisfy is μ(Q) ≤ col(Q)n for any cube Q () Rd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1 (μ). 相似文献
139.
In this paper, we prove Lp-boundedness of hyperbolic singular integral operators for kernels satisfying weakened regularity conditions, where 1
相似文献
140.
Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial
differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences.
By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via
a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast.
Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized
matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant
matrix.
By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the
block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method.
A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse
GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are
preserved.
AMS subject classification (2000) 43A30, 65T99, 20B25 相似文献