二元关系的传递性和传递闭包探讨

探讨了二元关系传递性的判定和传递闭包的计算及其教学的有关问题 ,提出了中途点的概念 ,得到传递性在乘幂运算下的不变性 ,以及简化了计算传递闭包的算法 .     

On the Isomorphism of Some Groups with One Defining Relation

Each of the groups in the class under consideration in the paper is presented by one defining relation depending on three integral parameters and is an HNN-extension of some Baumslag—Solitar group. Necessary and sufficient conditions for two groups of this class to be isomorphic and also for two nonisomorphic groups to be homomorphic images of each other are obtained. A consequence of this fact is the negative answer to Question 3.33 in “The Kourovka Notebook.”     

Finite Groups with Only One NonLinear Irreducible Representation

Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.     

一个具有唯一鞍焦点的三维混沌系统分析

讨论了一个具有唯一鞍焦点的多参数三维混沌系统,该系统包含了Sprott提出的一个最简混沌模型.在特定的条件下得到了Hopf分岔的存在性条件;进一步利用规范型理论获得了决定Hopf分岔方向和分支周期解稳定性的公式,同时利用计算机模拟证实本文的理论分析结果.     

二元关系的完全计数

根据二元关系与其矩阵的关系,讨论了满足特殊性质的二元关系的完全计数.特别是以整数分拆的办法得到二元等价关系的完全计数.     

Markov Bases of Binary Graph Models

This paper is concerned with the topological invariant of a graph given by the maximum degree of a Markov basis element for the corresponding graph model for binary contingency tables. We describe a degree four Markov basis for the model when the underlying graph is a cycle and generalize this result to the complete bipartite graph K_2,n. We also give a combinatorial classification of degree two and three Markov basis moves as well as a Buchberger-free algorithm to compute moves of arbitrary given degree. Finally, we compute the algebraic degree of the model when the underlying graph is a forest.AMS Subject Classification: 05C99, 13P10, 62Q05.     

Global Dynamics in Binary Choice Models with Social Influence

A discrete-time dynamical system is proposed to model a class of binary choice games with externalities as those described by Schelling (1973 Schelling , T. C. ( 1973 ). Hockey helmets, concealed weapons, and daylight saving . Journal of Conflict Resolution , 17 ( 3 ), 381 – 428 .[Crossref], [Web of Science ®] , [Google Scholar], 1978 Schelling , T. C. ( 1978 ). Micromotives and Macrobehavior . New York : W. W. Norton . [Google Scholar]). In order to analyze some oscillatory time patterns and problems of equilibrium selection that were not considered in the qualitative analysis given by Schelling, we introduce an explicit adjustment mechanism. We perform a global dynamic analysis that allows us to explain the transition toward nonconnected basins of attraction when several coexisting attractors are present. This gives a formal explanation of some overshooting effects in social systems and of the consequent cyclic behaviors qualitatively described in Schelling (1978 Schelling , T. C. ( 1978 ). Micromotives and Macrobehavior . New York : W. W. Norton . [Google Scholar]). Moreover, we show how the occurrence of a global bifurcation may lead to the explanation of situations of path dependence and the creation of thresholds observed in real life situations of collective choices, leading to extreme forms of irreversible departure from an equilibrium and uncertainty about the long run evolution of the some social systems.     

一个二元丢番图不等式

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单次多水平正交试验中效应的显著性检验

方差分析自试验设计诞生以来一直是用于分析试验中各因子是否显著的统计方法,对于正交试验设计而言其更是唯一的分析方法.然而,当正交表各列放满了被考虑的各个因子及其交互作用并且各条件组合下只能进行一次试验时,方差分析中的误差项将恒等于0,从而方差分析不再能用于对此试验设计的分析.对此,本文针对使用多水平完备正交表的单次正交试验,提出了一种新的统计分析方法.示例表明:本文提出的检验法不仅解决了方差分析无法胜任的问题,而且在表头设计有空白列从而方差分析仍能实施时,其比方差分析具有更大的局部功效.     

Residual Nilpotence of Groups with One Defining Relation

Mathematical Notes - All groups in the family of Baumslag-Solitar groups (i.e., groups of the form G(m,n) = 〈a, b; a?1bma = bn〉, where m and n are nonzero integers) for which...     

On the Relation between Energy-Conserving Low-Order Models and a System of Coupled Generalized Volterra Gyrostats with Nonlinear Feedback

In this paper we first prove the equivalence between the system of coupled Volterra gyrostats and a special class of energy-conserving low-order models. We then extend the definition of the classical Volterra gyrostat to include nonlinear feedback, resulting in a class of generalized Volterra gyrostats. Using this new class of gyrostats as a basic building block, we present an algorithm for converting a general class of energy-conserving low-order models that routinely arise in fluid dynamics, turbulence, and atmospheric sciences into a system of coupled generalized Volterra gyrostats with nonlinear feedback.      

On One of Matérn's Hard-core Point Process Models

By means of time discretization, we approximate evolution variational inequalities by the corresponding elliptic variational inequalities. Using ROTHE'S method (method of lines), an approximate solution is constructed by means of direct variational methods. Existence, uniqueness and regularity of solutions as well as convergence of the approximate solutions are proved.     

On a Pseudorandom Property of Binary Sequences

C. Mauduit and A. Sárközy proposed the use of well-distribution measure and correlation measure as measures of pseudorandomness of finite binary sequences. In this paper we will introduce and study a further measure of pseudorandomness: the symmetry measure. First we will give upper and lower bounds for the symmetry measure. We will also show that there exists a sequence for which each of the well-distribution, correlation and symmetry measures are small. Finally we will compare these measures of pseudorandomness.     

On the Rank of a Binary Form

We describe in the space of binary forms of degree d the strata of forms having a given rank. We also give a simple algorithm for determining the rank of a given form.     

Geometrical and Topological Properties of a Parameterized Binary Relation in Vector Optimization

In real linear spaces, partial orderings are usually generated by ordering cones. In many situations, however, such an ordering cone is too small with respect to the whole space. Therefore, in this paper, we extend the concept of ordering cones to a more general concept. For this purpose, we define a parameterized binary relation, based on a convex cone and a binary function. We investigate some geometrical and topological properties of this relation in detail.     

Null Controllability of Some Reaction-Diffusion Systems with Only One Control Force in Moving Domains

In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The proof is based on Kakutani's fixed point theorem combined with observability estimates for the associated linearized system.