带阈值的Min—max模糊Hopfield网络的稳定性与容错性分析

本文讨论了带阈值的Ｍｉｎ－ｍａｘ模糊Ｈｏｐｆｉｅｌｄ网络的性质，并研究了该网络的一致稳定性与平衡态的Ｌｙａｐｕｎｏｖ稳定性。给出了一个模糊模式成为该网络吸引子的等价条件。然后在一定的条件下，得到了这个网络吸引子的一个非退化的吸引域，从而我们所建立的模糊神经网络模型具有较强的容错性，最后的例子证实了这一点。     

Structural analysis of a fractional matching problem

Mixed Software Programming refers to a novel software development paradigm resulting from efforts to combine two different programming approaches: Solo Programming and Pair Programming. Solo Programming refers to the traditional practice of assigning a single developer to develop a software module and Pair Programming refers to a relatively new approach where two developers work simultaneously on developing a module. In Mixed Programming, given a set of modules to be developed, a chosen subset of modules may be developed using Solo Programming and the remaining modules using Pair Programming.Motivated by applications in Mixed Software Programming, we consider the following generalization of classical fractional 1-matching problem: Given an undirected simple graph G=(V;E), and a positive number F, find values for x_e,e∈E, satisfying the following:

1.

.

2.

, where δ(i)={e∈E:e=(i,j)},i∈V.

3.

Maximize {2∑_e∈Ex_e−F|{i∈V:∑_e∈δ(i)x_e=1}|}.

We show that this problem is solvable in strongly polynomial time. Our primary focus in this paper is on obtaining the structure of the optimal solution for an arbitrary instance of the problem.     

一个三维Chemostat竞争系统的Hopf分支和周期解

本文研究了一个三维Chemostat竞争系统的解的结构,分析了平衡点的稳定性和当系统的某一微生物物种处于竞争劣势趋于灭绝时另一微生物物种和养料的二维流形上极限环的存在性,以及系统的Hopf分支问题.文中用Friedrich方法得到了系统存在Hopf分支的条件,并判定了周期解的稳定性.     

Structural jump-diffusion model for pricing collateralized debt obligations tranches

This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.     

Stability conditions for a non-linear size-structured model

In this paper we consider a general non-linear size-structured population dynamical model with size- and density-dependent fertility and mortality rates and with size-dependent growth rate. Based on M. Farkas (Appl. Math. Comput. 131 (1) (2002) 107–123) we are able to deduce a characteristic function for a stationary solution of the system in a similar way. Then we establish results about the stability (resp. instability) of the stationary solutions of the system.     

On the identifiability of measurement error in the bifurcating autoregressive model

Huggins and Staudte (1994) considered a mixed linear model for the analysis of cell lineage data and in models for the covariance structure which involved measurement error, it was not immediately clear that the parameters involved were identifiable. Whilst a numerical examination of the Hessian matrix at the estimated parameter values gave some reassurance, this was not theoretically satisfying. Here a matrix formulation of the robust estimating functions of Huggins (1993a, b) as applied in Huggins and Staudte (1994), which include the maximum likelihood estimating functions under the assumption of multivariate normality as a special case, is given along with a direct proof linking identifiability expressed in terms of the estimating functions with the information matrix or its analogue in more general settings. The resulting conditions on the estimating functions may then be checked globally using computer algebra, suggesting a method for establishing identifiability in mixed linear models in general.     

Stability of wavefronts in a variable porosity model

We study the existence and linearized stability of traveling waves to a one-dimensional nonlinear parabolic equation that models the diffusion and convection of a chemical or biological species in a porous domain, where the fraction of volume (porosity) available to the species is a function of its concentration.     

Dynamics of a two-strain vaccination model for polio

A new deterministic model for the transmission dynamics of two strains of polio, the vaccine-derived polio virus (VDPV) and the wild polio virus (WPV), in a population is designed and rigorously analysed. It is shown that Oral Polio Vaccine (OPV) reversion (leading to increased incidences of WPV and VDPV strains), together with the combined effect of vaccinating a fraction of the unvaccinated susceptible and missed susceptible children, could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. Furthermore, the model undergoes competitive exclusion, where the strain with the higher reproduction number (greater than unity) drives the other (with reproduction number less than unity) to extinction. In the absence of OPV reversions (leading to the co-existence of both strains in the population), it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated reproduction number is less than unity. Numerical simulations of the model suggest that the model undergoes the phenomenon of competitive exclusion, where the strain with the higher reproduction number (greater than unity) drives the other to extinction. Furthermore, co-existence of the two strains is feasible if their respective reproduction number are equal or approximately equal (and greater than unity).     

Structural theory and structural formations

This paper introduces a group of articles on structural theory in economics and outlines characteristic methods for structural analysis. A formal theory of ‘structural formations’ is presented and practical automata-theoretic methods for complexity measurement are demonstrated.     

结构优化的并行迭代算法

本文提出一种结构分析和优化平行计算的方法,按结构总势能和结构重量最小化双目标组织算法,改变了完整(或近似完整)的结构分析与优化交替迭代的传统解法,全部计算在单元级进行,不需组装总刚度矩阵和求解系统平衡方程.这种算法具有步骤简单、占内存少、易编程的特点,可用于在微机上作结构优化设计.由于算法的并行性好,它特别适用于并行计算机系统.     

Effect of time-delay on a food chain model

This paper aims to study the effect of discrete time-delay on a tritrophic food chain model with Holling type-II functional responses. Dynamical behaviours such as boundedness, stability, persistence and bifurcation of the model are studied. Our analytical findings are illustrated through computer simulation. Biological implications of our analytical findings are addressed critically.     

On Essential Sets of Fixed Points for Functions

This article studies essential stabilities of fixed points under the dual perturbations of functions and domains using uniform topology. We show that each fixed point for most functions has the ability to resist these dual perturbations. The existence result of minimal essential sets of fixed points is established, and the connectedness of minimal essential sets is proved under some conditions. These generalize some corresponding results in references.     

Identification of the Parameters of a Multivariate Normal Vector by the Distribution of the Maximum

This paper continues the work started by Basu and Ghosh (J. Mult. Anal. (1978), 8, 413–429), by Gilliland and Hannan (J. Amer. Stat. Assoc. (1980), 75, No. 371, 651–654), and then continued on by Mukherjea and Stephens (Prob. Theory and Rel. Fields (1990), 84, 289–296), and Elnaggar and Mukherjea (J. Stat. Planning and Inference (1990), 78, 23–37). Let (X₁, X₂,..., X_n) be a multivariate normal vector with zero means, a common correlation and variances ² ₁, ² ₂,..., ² _n such that the parameters , ² ₁, ² ₂,..., s² _n are unknown, but the distribution of the max{X_i: 1in} (or equivalently, the distribution of the min{X_i: 1in}) is known. The problem is whether the parameters are identifiable and then how to determine the (unknown) parameters in terms of the distribution of the maximum (or its density). Here, we solve this problem for general n. Earlier, this problem was considered only for n3. Identifiability problems in related contexts were considered earlier by numerous authors including: T. W. Anderson and S. G. Ghurye, A. A. Tsiatis, H. A. David, S. M. Berman, A. Nadas, and many others. We also consider here the case where the X_i's have a common covariance instead of a common correlation.     

Bifurcation analysis of a delayed epidemic model

In this paper, Hopf bifurcation for a delayed SIS epidemic model with stage structure and nonlinear incidence rate is investigated. Through theoretical analysis, we show the positive equilibrium stability and the conditions that Hopf bifurcation occurs. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. In addition, we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.     

Analysis of a viral infection model with delayed immune response

It is well known that the immune response plays an important role in eliminating or controlling the disease after human body is infected by virus. In this paper, we investigate the dynamical behavior of a viral infection model with retarded immune response. The effect of time delay on stability of the equilibria of the system has been studied and sufficient condition for local asymptotic stability of the infected equilibrium and global asymptotic stability of the infection-free equilibrium and the immune-exhausted equilibrium are given. By numerical simulating,we observe that the stationary solution becomes unstable at some critical immune response time, while the delay time and birth rate of susceptible host cells increase, and we also discover the occurrence of stable periodic solutions and chaotic dynamical behavior. The results can be used to explain the complexity of the immune state of patients.     

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.     

Structural design and analysis for a sensor-integrated ball bearing

The structural design issues associated with the development of a sensor-integrated ball bearing were investigated. A finite element model was established to analyze the structural integrity of a ball bearing whose outer ring was modified to accommodate a miniaturized load sensor module. The sensor module was designed to monitor dynamic load variations within the bearing, which is an important indicator of a bearings safe operation. This structural integration of “intelligence” is significant in that it bring's automated, on-line, self-diagnosis capability to a dynamic system for which reliable, safe operation is of critical importance. A design tool was developed to evaluate the effect of outer ring modification on the dynamic load-carrying capability of the bearing. The tool also provided quantitative guidelines for the design of load and other types of sensor modules that will be structurally embedded into the outer ring of a conventional bearing for industrial applications.