无原子布氏代数理论的计算复杂性

研究无原子布氏代数的计算复杂性 .得到了下面的新定理 :定理 1　无原子布氏代数理论Δ具有完全的量词消去法 ,也就是说每一个式子都Δ等价于一个开式子 .定理 2　无原子布氏代数的初等型Γ (x1,… ,xn)是由型内的不含量词的全体开式子所唯一决定 .定理 3　无原子布氏代数的一个长度为 n的语句的判断过程所消耗的 Turing时间和空间都是属于 2 2 cn指数级 .     

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.     

一些包含Lucas数的恒等式

利用第一类Chebyshev多项式的性质以及其与Lucas数的关系得到了关于Lucas数立方的一些恒等式.     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

一个素变数丢番图不等式

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ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

1.IntroductionSince1984,severalchinesemathematicianshaveobtailledmanyresultsboutmatrixoperatornormcondition.umbe.[ll'12'18].Twokindsmatrixconditionnllmbers[9]are:(1)IfAECoxsisnonsingular,thellunlberK.(A)~IIAll.llA--'if.iscalledtheor--normconditionnumberof…     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Number albedo measurements from stratified layers of iron,concrete and aluminium

A layer of stratified combination composed of selected radiation shielding materials acquires better shielding property. Albedo is used in such measurements as an integral measure ofγ-ray scattering. The stratified slabs of alternating heterogeneous layers have been found to have a virtual homogeneous property with a definite effective atomic number. The angular distribution of back-scattered photons as well as the total number albedo values for iron, aluminium and concrete in stratified combination for 662 keV and 1250 keV photons are reported.