交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

基础模糊命题演算系统BL~*的改进系统

基础模糊命题演算系统BL*是一个和基础命题演算系统BL相对独立的命题演算系统。命题演算系统L*是系统BL*的扩张,但不是系统BL的扩张。通过对系统BL*及其它模糊命题演算系统的研究,本文对BL*系统进行了修正,进一步改进了BL*系统中的公理体系。     

拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

分数阶Chen-like系统混沌性态分析及控制

提出了一类Chen-like系统,研究了该系统奇点稳定性、混沌等动力学性态.讨论了Chen-like系中参数与阶数对系统混沌性态的影响,并给出了Chem-like系统出现混沌性态的阶次范围.与分数阶Chen系统相比,系统出现混沌性态的阶次范围增大了.根据分数阶系统稳定性理论及线性反馈控制,对系统进行了混沌控制,得出了混沌系统在平衡点处的稳定性条件.数值模拟验证了理论分析的正确性.     

基于广义反射函数与自治系统等价的非自治系统

自治系统的研究比非自治系统要容易得多,以广义反射函数为前提,给出了等价于自治系统的非自治系统,从而将非自治系统的研究转化为自治系统的研究,并研究了该类系统的周期解及稳定性.     

中介命题演算系统$MP^{M}$的代数系统

MP~M系统是在中介逻辑系统的基础上建立起来的,用于处理数据库中不完全信息的三值逻辑命题演算系统．本文通过在MP~M系统上建立一个代数系统,对MP~M系统进行了代数抽象,讨论了MP~M系统的代数性质．本文还研究了该代数系统的次直积,以及与其它一些代数系统之间的关系．     

多值逻辑系统RDP中的子代数理论

系统RDP是一个带有参数的系统,将参数a赋予不同的值,将会得到不同的多值逻辑系统.本文研究了多值逻辑系统RDP中的子代数理论,讨论了该系统子代数的特征及相关性质,为系统RDP的进一步研究奠定了基础.     

复杂系统的一般数学框架(Ⅰ)

复杂系统的基本和最简单的结构就是网络.根据这一思想,本系列论文拟发展一套处理复杂系统的新数学框架.本文详细论述了系统的概念、一般描述方法:系统=(硬部,软部,环境)和局整关系,包括子系统、元素与系统的关系和系统与系统的关系;给出了系统运算的基本法则;简要论述了系统的软、硬部之间的诱导转化.     

不含混沌真子系统的Li-Yorke混沌

研究了一类Li-Yorke混沌系统,该系统没有真子系统是Li-Yorke混沌的,我们称之为混沌极小系统.本文证明混沌极小系统是拓扑传递的,而且该系统每个非空开集都包含一个不可数混乱集.混沌极小系统不一定是极小的,本文构造了一个这样的反例.特别地,我们考察了线段连续自映射,指出该类系统都不是混沌极小的,线段上混沌极小子系统的存在性和该系统有正熵是等价的.     

一类混沌系统的函数矩阵投影同步

研究了一类混沌系统的函数矩阵投影同步问题,基于函数矩阵方法,利用Lyapunov稳定性理论和极点配置理论,设计了两个连续混沌系统之间的同步方案,同时设计了两个离散混沌系统之间的同步方案,实现了驱动系统与动态系统按给定的函数矩阵投影同步,并给出了证明,通过对Lorenz混沌系统,和Henon系统的数值模拟,表明了该方法的有效性.     

Lower estimates of measure of deviation of polynomials from mathematical expectations

Inequalities that are in a sense reverse to the Carbery–Wright inequality are investigated. Inequalities of this type are proved in the case of a Gaussian measure and a polynomial of arbitrary degree and also in the case of an arbitrary convex measure and a polynomial degree of 2.     

Approximation of a fractional power of an elliptic operator

Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis of an integral representation with a singular integrand. In the present article, new integral representations are proposed for operators with fractional powers. Approximations are based on the classical quadrature formulas. The results of numerical experiments on the accuracy of quadrature formulas are presented. The proposed approximations are used for numerical solving a model two‐dimensional boundary value problem for fractional diffusion.     

Analysis and Implications of Management Uses of Information

It is a prerequisite to a number of management orientated disciplines that a manager's needs for information are defined. An initial stage in being able to adequately define needs is to understand the ways in which information can affect management behaviour. Several ways are suggested in this paper and from these, implications are drawn which are of relevance to designers of information systems.     

Verification of a class of link-level protocols

This paper describes a model of a link-level communication line, and defines a set of operations meant to form the basis of data transfer protocols. Some problems concerning verification of protocols are discussed, and it is shown that all protocols using the given operations as a basis are partially correct. Conditions are given for total correctness.     

Analysis of asymptotic distributions of some profitability characteristics of trade algorithms

The asymptotic behavior of a model sequence of price increments and some probability characteristics of a trade algorithm are investigated. It is proved that characteristics such as the number of buy and sell transactions and the value of total profitability are asymptotically normal for a stationary m-dependent sequence of price increments. Approximate formulas are derived to calculate their mathematical expectations and variances as functions of parameters of the price series and the trade algorithm. Some results of numerical experiments are presented.     

Boundedness of adjoint bases of approximate spectral subspaces and of associated block reduced Resolvents

Block reduced resolvents are often employed in iterative schemes for refining crude approximations of the arithmetic mean of a cluster of eigenvalues and of a basis of the corresponding spectral subspace. We prove that if the bases of approximate spectral subspaces are chosen in such a way that they are bounded and each element of the basis is bounded away from the span of the previously chosen elements, then the corresponding adjoint bases are also bounded. We give an integral representation of the associated block reduced resolvent and show that under such a choice of the bases, the approximate block reduced resolvents are bounded as well. This is crucial in obtaining error estimates for the iterates of several refinement schemes. In the framework of a canonical discretization procedure for finite rank operators, appropriate choices of ises are given for various finite rank approximation methods such as Projection, Sloan, Galerkin, Nyström, Fredholm, Degenerate kernel. If the bases are not chosen appropriately, the error estimates may no longer hold and the iteration scheme may not be numerically stable. Examples are given to illustrate these phenomena     

Comparison of factor spaces of two related populations

A canonical decomposition of two factor spaces obtained from the same variables observed on two populations is considered to obtain statistics of use in the comparison of these spaces. In particular, statistics are derived to test for a common factor space. The asymptotic distributions of these statistics are obtained in a variety of cases using perturbation methods. The methods are applied to a numerical example and results of a simulation are given to indicate the accuracy of the asymptotic results.     

Fuzzy filters of BE-algebras

Characterizations of fuzzy filters in a BE-algebra are established. Conditions for a fuzzy set to be a fuzzy filter are given. For a fuzzy set µ the least fuzzy filter containing µ is constructed. The homomorphic properties of fuzzy filters of a BE-algebra are provided. Finally, characterizations of Noetherian BE-algebras and Artinian BE-algebras via fuzzy filters are obtained.     

Applications of Parameterizations of Oblique Duals of a Frame Sequence

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.