Exact solution of the Boltzmann equation in the homogeneous color conductivity problem

An exact solution of the Boltzmann equation for a binary mixture of colored Maxwell molecules is found. The solution corresponds to a nonequilibrium homogeneous steady state created by a nonconservative external force. Explicit expressions for the moments of the distribution function are obtained. By using information theory, an approximate velocity distribution function is constructed, which is exact in the limits of small and large field strengths. Comparison is made between the exact energy flux and the one obtained from the information theory distribution.     

稳定性理论中几个基本定理的推广

本文推广了经典的稳定性,有界性定理及关于渐近稳定的充分条件。去掉了原始定理中,函数的导数在其定义域内常负或定负的要求,并应用于集合稳定性判定.     

复杂应力构件弹性失效疲劳失效新判据——动态静态八面体应力强度理论

本文,在研究现代和经典强度理论的基础之上,提出了一个在复杂应力下弹性失效与疲劳失效的总准则,即动态静态八面体应力强度理论,同时建立了并分析了一个独立的比较完整的理论体系,给出了36种材料广义失效系数,和一点复杂应力的11个状态的计算理论,导出了广义允许强度算子方程.给出了总准则能应用到静态、动态的计算方法,通过8个工程实例的计算,表明该方法有很高的精度,因而笔者建议广泛地应用到工程.     

Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions

Summary A tool for analyzing spatio-temporal complex physical phenomena was recently proposed by the authors, Aubry et al. [5]. This tool consists in decomposing a spatially and temporally evolving signal into orthogonal temporal modes (temporal “structures”) and orthogonal spatial modes (spatial “structures”) which are coupled. This allows the introduction of a temporal configuration space and a spatial one which are related to each other by an isomorphism. In this paper, we show how such a tool can be used to analyze space-time bifurcations, that is, qualitative changes in both space and time as a parameter varies. The Hopf bifurcation and various spatio-temporal symmetry related bifurcations, such as bifurcations to traveling waves, are studied in detail. In particular, it is shown that symmetry-breaking bifurcations can be detected by analyzing the temporal and spatial eigenspaces of the decomposition which then lose their degeneracy, namely their invariance under the symmetry. Furthermore, we show how an extension of the theory to “quasi-symmetries” permits the treatment of nondegenerate signals and leads to an exponentially decreasing law of the energy spectrum. Examples extracted from numerically obtained solutions of the Kuramoto-Sivashinsky equation, a coupled map lattice, and fully developed turbulence are given to illustrate the theory.     

Discriminant versus rough sets approach to vague data analysis

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.     

Some computational methods for systems of nonlinear equations and systems of polynomial equations

This paper gives a brief survey and assessment of computational methods for finding solutions to systems of nonlinear equations and systems of polynomial equations. Starting from methods which converge locally and which find one solution, we progress to methods which are globally convergent and find an a priori determinable number of solutions. We will concentrate on simplicial algorithms and homotopy methods. Enhancements of published methods are included and further developments are discussed.     

A NOTE OF THE SPECTRUM OF HOMOGENEOUS COMPACT OPERATORS

In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.     

THEORY AND APPLICATIONS OF MONOTONE SEMIFLOWS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.