一阶捕食-被捕食系统的单调方法

本文利用单调逼近方法,研究带大小结构的捕食-被捕食系统的初边值问题,得到了系统解的存在唯一性,并且证明了序列是线性收敛的.     

A fuzzy random forest

When individual classifiers are combined appropriately, a statistically significant increase in classification accuracy is usually obtained. Multiple classifier systems are the result of combining several individual classifiers. Following Breiman’s methodology, in this paper a multiple classifier system based on a “forest” of fuzzy decision trees, i.e., a fuzzy random forest, is proposed. This approach combines the robustness of multiple classifier systems, the power of the randomness to increase the diversity of the trees, and the flexibility of fuzzy logic and fuzzy sets for imperfect data management. Various combination methods to obtain the final decision of the multiple classifier system are proposed and compared. Some of them are weighted combination methods which make a weighting of the decisions of the different elements of the multiple classifier system (leaves or trees). A comparative study with several datasets is made to show the efficiency of the proposed multiple classifier system and the various combination methods. The proposed multiple classifier system exhibits a good accuracy classification, comparable to that of the best classifiers when tested with conventional data sets. However, unlike other classifiers, the proposed classifier provides a similar accuracy when tested with imperfect datasets (with missing and fuzzy values) and with datasets with noise.     

一类边界控制半线性抛物型系统的逼近能控性

本文考虑一类Ｄｉｒｉｃｈｌｅｔ型边界控制半线性抛物型系统，应用半群理论和非线性分析的方法，证明了系统解映射的连续性，给出了系统逼近能控的一个充分条件．对于Ｎｅｕｍａｎｎ型边界控制或混合型边界控制的半线性抛物型系统，可以得到类似的结果．     

A construction of unitary linear systems

A construction is made of a unitary linear system whose transfer function is a given power seriesB(z) with operator coefficients such that multiplication byB(z) is an everywhere defined transformation in the space of square summable power series with vector coefficients. A condition is also given for the existence of an observable linear system with such a transfer function. For both constructions properties of the spaces are given which imply essential uniqueness of linear systems with given transfer functions. A canonical conjugate-isometric linear system is uniquely determined by its transfer function whenever the state space is a Pontryagin space.     

A transverse spinning double pendulum

A transverse spinning double pendulum is introduced. This pendulum is of interest as a simple mechanical system with two degrees of freedom with rotation which is autonomous. In addition to having physical origins, the pendulum is constructable for experimental observation. Our main interest in introducing and analyzing this system is that it is the simplest physical system with the codimension two singularity – in the linearization about the trivial solution – associated with coalescence of four zero eigenvalues. It is the dynamics of the nonlinear system in the neighbourhood of this singularity that is of interest. We study this problem using normal form theory. An algorithm for the Cushman–Sanders normal form is constructed and analyzed. A representative model for the truncated normal form is presented. This truncated normal form has seven parameters; it is not integrable in general and it is predicted that the dynamics associated with this model will be quite complex.     

A Simple Criterion for Involutivity

A simple criterion for the involutivity of a system of partialdifferential equations of polynomial type is proved. The criterioninvolves the equations themselves and does not require the systemto be in orthonomic form. It is proved that a system of partialdifferential equations is involutive if it is a differentialGröbner basis with respect to a total degree ordering,and if the compatibility conditions of the symbol equationsof the system consist of equations of degree one. An algorithmfor calculating these compatibility conditions is given.     

方差分析在复杂测量系统能力分析中的应用

测量系统分析是QS9000标准中的核心要素之一,主要用来评估测量系统对工序质量改进的保证程度。传统的测量系统能力分析主要采用极差分析或方差分析研究单台测量仪器组成的二因素交叉型简单测量系统,本文从企业的实际情况出发,采用方差分析法研究包含多台测量仪器的复杂测量系统,基于三因素套析因混合效应实验模型的方差分析和方差估计,提出了这种测量系统能力分析的方法,并给出了应用实例。     

A paired queueing system arising in multimedia synchronization

One of the most important and distinguishing features of multimedia applications is the integration of multiple media streams that have to be presented in a synchronized fashion. In this paper, a queueing system with a special service mechanism arising in multimedia synchronization is considered. The system is characterized by arrival of two types of customers (media streams), and servicing of customers (processing of packets) in pairs with one customer from each type for a pair. The exact transient system size probabilities are obtained as the stationary solutions do not exist for this system and these are illustrated numerically. The density function of the first return to the origin for the queueing system is also obtained.     

A stochastic recirculation system with random access

A model for a stochastic recirculation system with randomly accessed multiple heterogeneous servers, no waiting rooms, and exponentially-distributed service times is provided. In this system the units are assigned to one of the servers upon arrival by random mechanism. Units which find all servers busy recirculate and combine with the incoming arrivals and join those already in the system to initiate the next cycle. The equilibrium behavior of the internal and external stochastic processes of the system is analyzed using a two parameter approximation. A simulation model is also developed and its behavior is compared against the analytical model at the steady state. The model with randomly-accessed servers is compared to a single server model already established in the literature. The performance of the model is then examined for a wide range of parameter values to obtain conclusions about its optimal performances.     

A Riemann solver for RANS

An exact expression for a system of both eigenvalues and right/left eigenvectors of a Jacobian matrix for a convective two-equation differential closure RANS operator split along a curvilinear coordinate is derived. It is shown by examples of numerical modeling of supersonic flows over a flat plate and a compression corner with separation that application of the exact system of eigenvalues and eigenvectors to the Roe approach for approximate solution of the Riemann problem gives rise to an increase in the convergence rate, better stability and higher accuracy of a steady-state solution in comparison with those in the case of an approximate system.     

关于有时滞的反应-扩散耦合系统

The global stability of the steady-state solution to a coupled reaction-diffusion system with time delays is investigated. All factors involved in the system, especially, the permeabilites and diffusion are taken into account, and the relevant results of the papers [1, 2] are thus improved.     

一类具有变时滞的随机logistic种群系统

主要是讨论了一类具有变时滞的随机logi8tic种群系统.首先探讨了系统全局正解的存在性;然后获得了系统弱持久性和灭绝性的充分条件,获得了种群系统弱持续生存与灭绝之间的临界值.     

A SIMPLE EXAMPLE OF A NON-FINITELY BASED SYSTEM OF POLYNOMIAL IDENTITIES

ABSTRACT

A system of polynomial identities is called finitely based if it is equivalent to some finite system of polynomial identities. Every system of polynomial identities in associative algebras over a field of characteristic 0 is finitely based: this is a celebrated result of Kemer. The first non-finitely based systems of polynomial identities in associative algebras over a field of a prime characteristic have been constructed recently by Belov, Grishin and Shchigolev. These systems of identities are relatively complicated. In the present paper we construct a simpler example of such a system and give a simple self-contained proof of the fact that the system is non-finitely based.     

一类基于时滞和年龄分布的种群控制问题

研究一类具有离散时滞和年龄结构的生物种群模型的最优收获策略,其状态方程由一阶偏泛函微分方程描述.运用极值化序列方法和Mazur定理证明了最优控制的存在性,借助非线性泛函分析中的切锥-法锥和共轭系统技巧导出了最优性条件.通过对共轭系统的细致分析,确立了最优控制的唯一性,给出了最优解的特征刻画.     

A Nearly Optimal Inspection Policy

This paper is concerned with an easily computable inspection policy for the detection of the failure of a system. A one-parameter policy is suggested and it is shown that this policy has the property of decreasing (increasing) intervals between successive inspection times if the system has an increasing (decreasing) failure rate. Cost comparisons, using linear cost functions, with a computationally difficult optimal policy which has a minimium expected cost show that the proposed policy compares quite well with the optimal policy.     

A magnet spring model

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north–south pole orientation of the two magnets. The attraction or repelling force induced by the magnets follow an inverse quartic law and thus we are led to a nonlinear model suitable for discussion in a beginning differential equations course. Spring models are common fare in such courses, but usually only linear models with simple sinusoidal forcing are considered. The resultant model is autonomous and thus an energy approach permits a full phase portrait of the resultant motions in the phase plane. These phase portraits show interesting behaviour of the system, reinforcing one's natural physical intuition. The computer algebra system Mathematica is employed here, although almost any other system would suffice. Such a system permits almost effortless calculations and can generate the graphics needed to thoroughly investigate the model.     

A fast algorithm for solving Toeplitz penta-diagonal systems

In this paper a fast algorithm for solving a large system with a symmetric Toeplitz penta-diagonal coefficient matrix is presented. This efficient method is based on the idea of a system perturbation followed by corrections and is competitive with standard methods. The error analysis is also given.     

A new hyperchaotic system and its synchronization

In this paper, a four-dimensional (4D) continuous autonomous hyperchaotic system is introduced and analyzed. This hyperchaotic system is constructed by adding a linear controller to the 3D autonomous chaotic system with a reverse butterfly-shape attractor. Some of its basic dynamical properties, such as Lyapunov exponents, Poincare section, bifurcation diagram and the periodic orbits evolving into chaotic, hyperchaotic dynamical behavior by varying parameter d are studied. Furthermore, the full state hybrid projective synchronization (FSHPS) of new hyperchaotic system with unknown parameters including the unknown coefficients of nonlinear terms is studied by using adaptive control. Numerical simulations are presented to show the effective of the proposed chaos synchronization scheme.     

常数红利边界下的一类马氏风险模型

本文研究了常数红利边界下一类马氏风险模型的红利派发矩,破产前所有红利的分布等相关问题.利用更新方法,给出了该模型破产前红利折现的期望满足的微分-积分方程,得到破产前所有红利的分布.通过构造特殊的初始条件,得到了相关的方程组解,推广了文献[3]的结果.     

A set-valued type inequality system

A set-valued type inequality system is introduced along with two solvability questions composed of existence and perturbation, and main theorems are obtained, which include three necessary and sufficient conditions concerning the existence and a continuity property concerning the perturbation. As applications, two existence criteria with respect to a single-valued type inequality system have also been obtained.