行波进位补码加法器的数学分析

加法器对于高性能微处理器和DSP处理器至关重要,而多数加法器是补码加法器,补码加法器的基础是行波进位加法器.目前,行波进位补码加法器的数学基础缺乏严密性与系统性.提出一种不规则补码加法器,其设计思想很简单并且完全不同于常用的补码加法器—变形补码加法器和单符号位加法器.然后对这三种补码加法器的行波进位电路进行了严密、系统、简洁的数学分析.     

可逆测度与拟可逆测度的等价性

本文讨论了一类速度函数的可逆与拟可逆测度间的关系,证明了在[2]的条件下,可逆测度与拟可逆测度是等价的。     

群可逆元的一些刻画

研究了群可逆元的一些性质,给出群可逆元的一些刻画,进一步研究正则元是群可逆元的若干条件.     

幺半群上的斜强可逆环

For a monoid M, we introduce the concept of skew strongly M-reversible rings which is a generalization of strongly M-reversible rings, and investigate their properties. It is shown that if G is a finitely generated Abelian group, then G is torsion-free if and only if there exists a ring R with |R| ≥ 2 such that R is skew strongly G-reversible. Moreover, we prove that if R is a right Ore ring with classical right quotient ring Q, then R is skew strongly M-reversible if and only if Q is skew strongly M-reversible.     

初等变换的关系及可逆矩阵的分解

给出三种初等变换之间的关系 ,指出可逆矩阵可以分解为两种类型的初等矩阵的乘积 .对于行列式为 1的可逆阵 ,我们得出有趣的结果 ,所有这些 ,对于学习线性代数的同学们来说 ,都是很有益的     

坡上矩阵可逆的条件

坡S是一个元素满足条件s 1=1的交换半环．证明了坡S上n×n矩阵A可逆当且仅当∑k=1 n aik=1(i=1,2,…,n)且aikajk=0(i≠j,k=1,2,…,n)．在坡S中可定义补元,得到S上每一个可逆矩阵是一个置换矩阵当且仅当S不包含不同于0和1的有补元．     

可逆模糊自动机

首先提出了可逆模糊自动机的概念,研究了能被可逆模糊自动机接受的语言(简记为F(∑))的一些性质.其次给出了自由群上被可逆模糊自动机接受的模糊子集的概念,详细研究了可逆模糊语言与经典可逆语言的关系.最后,通过引入语法幺半群刻画了F(∑)的代数性质.通过这些性质可以有效的判断一个模糊语言是否能被一个可逆模糊自动机接受.     

一类可逆生化反应模型的定性分析

本研究一类可逆生化反应的数学模型：｛ｄｘｄｔ＝ａ－（ｂ＋１）ｘ＋ｘ＾２ｙ－ｃｘ＾３,ｄｙｄｔ＝ｂｘ－ｘ＾２ｙ＋ｃｘ＾３。应用微分方程定性理论,完整地解决了该系统极限环的存在性、唯一性和不存在性等问题。     

一类可逆生化反应模型的定性分析

本文研究一类可逆生化反应的数学模型 :dxdt=a-( b+1 ) x+x2 y-cx3,dydt=bx-x2 y+cx3.应用微分方程定性理论 ,完整地解决了该系统极限环的存在性、唯一性和不存在性等问题 .     

Reversible hypergroups

Using the properties of the characters of a finite group as a prototype, a new notion of a reversible hypergroupH is introduced which takes account of degrees and multiplicities. Many properties of finite abelian groups have analogues for reversible hypergroups. For example, the hypergroup algebra CH is defined by analogy with a group algebra. Using the representations of this algebra, reversible hypergroups are shown to be in one-to-one correspondence with abstract «character tables» (of which Brauer’s «pseudo groups» are examples). These possess the usual orthogonality relations, whether or not they are character tables of groups. Examples are given of reversible hypergroups which are not isomorphic with the set of characters of any finite group.     

中心零可换环

本文给出了中心零可换环而非中心半交换环的例子,否定地回答了Jung等人在文[Bull.Korean Math.Soc.2015,52(1):247-261]中的一个问题.并证明了如果R是中心约化环,那么对任意正整数n,R[x]/(x~n)是中心对称环.     

Reversible interval homeomorphisms

A characterization of continuously reversible self-mappings of an open interval, that is, compositions of two continuous involutions, is proved.     

基于遗传算法的非规则墙体光伏阵列的设计

提出一种基于遗传算法的非规则墙体上光伏阵列的设计模型.提出适用于非规则墙体上光伏阵列的编解码算法,以及相对应的选择算子、交叉算子、变异算子,利用加权平均的方式对遗传算法中的适应度函数进行定义,实现对光伏阵列的发电量最大化和单位发电成本最小化.最后通过在Matlab环境下仿真,验证了本文算法的有效性.     

Model Design Based on the Systems Approach

It is shown how the (extended) systems approach can be successfully used to design mathematical models in a highly systematic way. The systems approach supports interdisciplinarity in that it encourages participation of non-mathematicians in the model design process. The systems approach also leads to a clear documentation of a model.The basic principle explained in this paper is that indices of a model represent elements of an element set of a system, and that variables and constants of a model represent attributes of the elements. Multi-indexed variables and constants refer to attributes of ‘complex entities’ (from extended systems terminology) which cover the information between the elements.     

一种基于数独的新试验设计

通过研究数独方的构成与设计,建立了一种基于数独的新试验设计,给出了这种设计的数学模型与统计分析。该设计能安排单因素的n个水平,并能在行、列、块3个方向控制变异性。     

基于QFDE的可持续产品设计研究

为了提高可持续产品设计的效率,提出以QFDE(Quality Function Deployment for Environment,面向环境的质量功能展开)为依据的可持续产品设计流程,共有五个阶段.第一阶段将顾客需求展开,建立需求与工程特性矩阵;第二阶段建立工程特性与零件矩阵;基于前两个阶段,分析提高产品可持续性存在的矛盾,运用TRIZ(Theory of Inventive problem solving,发明问题解决理论)提出解决方案;第三阶段计算解决方案对于工程特性的提高率;第四阶段计算顾客需求提高率;第五阶段计算产品零件的可持续性.以净水机为例,验证可持续产品设计流程的有效性.     

The Spectrum of Reversible Minimizers

Poincaré and, later on, Carathéodory, showed that the Floquet multipliers of 1-dimensional periodic curves minimizing the Lagrangian action are real and positive. Even though Carathéodory himself observed that this result loses its validity in the general higherdimensional case, we shall show that it remains true for systems which are reversible in time. In this way, we also generalize a previous result by Offin on the hyperbolicity of nondegenerate symmetric minimizers. Our arguments rely on the higher-dimensional generalizations of the Sturm theory which were developed during the second half of the twentieth century by several authors, including Hartman, Morse or Arnol’d.