Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

Fuzzy Model of Regional Economic Competitiveness in GIS Spatial Analysis: Case Study of Gansu, Western China

After more than 20 years of impressive development since the economic reforms in 1978, today western China is facing an increasing development gap between its regions, particularly between urban and rural areas. Using the fuzzy comprehensive evaluation model, this paper aims to demonstrate the evolution of the economic competitiveness levels base on two categories of geographical unity in the province of Gansu located in Northwest China between 2000 and 2004. The results of fuzzy modeling are integrated into GIS spatiotemporal analyses in order to identify the spatial variation of each significant change in terms of the regional economic development. Our research effectively illustrates that there is a particular spatial dynamic of the economic development from region to region. Although the cities have improved very well in their economic competitiveness, the rural areas and minority regions still have a lot of progress to be achieved.     

基于小波的光照补偿及其在人脸识别中的应用

提出了一种基于小波分析的人脸图像光照补偿技术,通过舍弃图像中的低频分量,仅用高频分量进行图像重构,便可较好地消除原始人脸图像中光照的影响.并将该技术应用于特征脸法人脸识别,在Yale库和自建库图像中,实验测得在较大尺度的情况下,图像识别率都有明显提高.     

On the hydrogen etching mechanism in plasma nitriding of metals

Iron alloys and aluminum were nitrogen implanted in a controlled oxygen atmosphere and the role of hydrogen on the surface etching mechanisms studied. The surface composition was analyzed by in situ photoemission electron spectroscopy (XPS). In iron alloys, hydrogen strongly etches oxygen, improving nitrogen retention on the surface. On the other hand, hydrogen removes nitrogen from aluminum surfaces, with a deleterious effect on the nitriding effectiveness. The oxygen removal in iron alloys is associated with the catalytic effect of electrons in d-orbitals and the nitrogen removal in aluminum is associated with a steric effect.     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

Sparse generalized Fourier transforms

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     

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.      

Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.     

On multiple integrals of special form

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.     

影响西安市燃气出租车发展变量的统计分析

燃气汽车规模化发展是解决城市环境污染的一个主要途径.以西安市燃气出租车发展问卷调查结果为依据,利用因子分析法对影响燃气出租车发展的变量进行分类.总结出影响燃气出租车发展的八个重要指标,覆涵了政府、加气站、司机个人等方面.