Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

PURE STATE APPROACH TO $C(X)×_\alpha Z_n$

ＰＵＲＥ ＳＴＡＴＥ ＡＰＰＲＯＡＣＨ ＴＯ Ｃ（ｘ）_αＺ_nＬＩＢＩＮＧＲＥＮ；ＬＩＮＱＩＮＧ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ．Ｐｒｏｊｅｃｔｓｕｐｐｏｒｔｅｄｂｙｔｈ?..     

线性谐振子的计算机代数计算

采用计算机代数方法，通过Mathematica软件计算线性谐振子的波函数，几率密度和几率最大值的位置。计算方法简单、通用，易于推广。     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

On the phase space approach to complexity

We elaborate in some detail on a new phase space approach to complexity, due to Y.-C. Zhang. We show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle. For a 1D signal we find 1/f noise, in accordance with Zhang.     

Poisson单和—类广义Poisson单的刻划

讨论了Ｐｏｉｓｓｏｎ单和一类广义Ｐｏｉｓｓｏｎ单的基本刻划问题。     

教学质量的时齐马尔可夫链评估法

本文研究了教学质量评估中的一种定量分析方法──时齐马尔可夫链评估法．阐明了这种方法的理论依据及其实施程序、并指出它较之其他教学质量评估法更显合理．     

具有非局部边界条件的奇摄动反应扩散问题

本文研究了一类具有非局部边界条件的奇摄动反应扩散初始边值问题．在适当的条件下，利用比较定理讨论了问题解的渐近性态．     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.