Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.     

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.     

Asymptotic Convergence of Conjugate Gradient Methods for the Partial Symmetric Eigenproblem

Recently an efficient method (DACG) for the partial solution of the symmetric generalized eigenproblem A x = δB x has been developed, based on the conjugate gradient (CG) minimization of the Rayleigh quotient over successive deflated subspaces of decreasing size. The present paper provides a numerical analysis of the asymptotic convergence rate ρ_j of DACG in the calculation of the eigenpair λ_j, u _j, when the scheme is preconditioned with A⁻¹. It is shown that, when the search direction are A-conjugate, ρ_j is well approximated by 4/ξ_j, where ξ_j is the Hessian condition number of a Rayleigh quotient defined in appropriate oblique complements of the space spanned by the leftmost eigenvectors u ₁, u ₂,…, u _j−1 already calculated. It is also shown that 1/ξ_j is equal to the relative separation between the eigenvalue λ_j currently sought and the next higher one λ_j+1 and the next higher one λ_{j + 1}. A modification of DACG (MDACG) is studied, which involves a new set of CG search directions which are made M-conjugate, with M-conjugate, with M-conjugate, with M a matrix approximating the Hessian. By distinction, MDACG has an asymptotic rate of convergence which appears to be inversely proportional to the square root of ξ_j, in complete agreement with the theoretical results known for the CG solution to linear systems. © 1997 by John Wiley & Sons, Ltd.     

任意随机变量序列的一个强极限定理

研究任意随机变量序列的强收敛性.利用鞅差序列级数收敛定理,证明了任意随机序列的一个强极限定理,作为推论,得到了马氏过程、鞅差序列及独立随机变量序列的强大数定律.     

On a generalization of Pólya’s theorem

We consider generalizations of Pólya’s theorem to the case of entire functions taking algebraic values at natural or integer points.     

关于纤维锥的Hilbert系数

Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

关于多重联图的均匀全染色

对一个正常的全染色满足各种颜色所染元素数(点或边)相差不超过1时,称为均匀全染色,其所用最少染色数称为均匀全色数．本文证明了关于多重联图的若干情况下的均匀全色数定理,得到了若干特殊多重联图的均匀全色数．     

平衡规划问题的熵函数方法及其在混合交通流中的应用

将参变极值问题的极大熵函数方法应用到求解平衡规划问题中,通过先验分布信息和Kullback熵概念,给出了平衡规划问题基于Kullback熵表示的熵函数求解方法,并将平衡规划的极大熵函数方法应用于求解混合交通平衡分配问题．