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151.
邱春晖 《数学物理学报(B辑英文版)》2003,23(1)
A new Koppelman-Leray-Norguet formula of (p-1,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of (?)-equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals. 相似文献
152.
Tonghai Yang 《Transactions of the American Mathematical Society》2003,355(7):2663-2674
In this paper, we give an explicit formula for the first two terms of the Taylor expansion of a classical Eisenstein series of weight for . Both the first term and the second term have interesting arithmetic interpretations. We apply the result to compute the central derivative of some Hecke -functions.
153.
Ekatherina A. Karatsuba 《BIT Numerical Mathematics》2001,41(4):722-730
The application of the Fast E-function Evaluation (FEE) method to fast calculation of the value of (3) and of some special integrals on the basis of the Ramanujan formula and its generalization is considered.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
154.
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
155.
A. Kohatsu-Higa D. Márquez-Carreras M. Sanz-Solé 《Journal of Theoretical Probability》2001,14(2):427-462
Consider the density of the solution X(t, x) of a stochastic heat equation with small noise at a fixed t[0, T], x[0, 1]. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed. 相似文献
156.
The Hardy operator Ta on a tree is defined by Properties of Ta as a map from Lp() into itselfare established for 1 p . The main result is that, with appropriateassumptions on u and v, the approximation numbers an(Ta) ofTa satisfy for a specified constant p and 1 p < . This extends results of Naimark, Newmanand Solomyak for p = 2. Hitherto, for p 2, (*) was unknowneven when is an interval. Also, upper and lower estimates forthe lq and weak-lq norms of an(Ta) are determined. 2000 MathematicalSubject Classification: 47G10, 47B10. 相似文献
157.
The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses values of linear functionals (integrals over hyperspheres) and is exact for all -harmonic functions, and consequently, for all algebraic polynomials of variables of degree .
158.
Some theoretical aspects of elastic wave modeling with a recently developed spectral element method 总被引:1,自引:0,他引:1
SERIANI Geza 《中国科学G辑(英文版)》2007,50(2):185-207
A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang. 相似文献
159.
160.
A. Chafiq 《Optics Communications》2007,278(1):142-146
In order to avoid the severe axial intensity oscillations which appear when an ideal Mathieu beam is truncated, we propose to modulate it by a flattened multi-Gaussian envelope. The obtained beam, which is referred as flattened Mathieu-Gauss (FTMG) beam, can be expanded into a finite series of Mathieu-Gauss beams with various waists. The propagation study of this beam reveals that the axial intensity is unchanged within a certain propagation distance as for super-Gaussian-Bessel beams or Gori’s flattened Bessel beams. By using Collins formula, we derive closed-form expressions of FTMG beam propagating through a paraxial axisymmetric ABCD optical system. Some numerical calculations and discussions are also given. 相似文献