图论中若干重要定理的历史注记

考察了图论中若干重要定理的历史背景,这些定理包括图论基本定理,矩阵-树定理,门格尔定理,霍尔定理,柯尼希定理,塔特定理,彼得森定理,库拉托夫斯基定理,布鲁克斯定理和维津定理.     

积分型中值定理的推广及统一表示

通过减弱连续的条件,推广了一类积分型中值定理,在适当的条件下,用一个式子将Lagrange中值定理、Cauchy微分中值定理、积分型Cauchy中值定理、积分中值定理、积分第一中值定理、Lagrange型积分中值定理、Cauchy型积分中值定理及推广的积分第一中值定理这8个中值定理统一起来.     

一个新的Ky Fan匹配定理及其在L-凸度量空间中的应用

建立了转移开覆盖的一个新的Ky Fan型匹配定理．作为应用，获得了Fan-Browder重合定理，不动点定理、极大元定理，相交定理和截口定理．     

播挪运算及其性质

在现有的播挪定义基础上,引入了对偶播挪的概念和任意论域子集族的内并、内交两种新运算,提出了十个定理.它们是：平凡播挪空间定理,最小播挪定理,播挪内运算封闭性定理,播挪任意交定理,播挪上确界定理,播挪运算分配性定理,播挪基判定定理,播挪基闭包定理,播挪基约简定理,播挪基内运算封闭性定理.这些定理对于播挪空间的研究具有一定的理论价值.     

正弦定理、余弦定理、射影定理的关系分析

三角形的正弦定理、余弦定理、射影定理之间有着内在的关系.在正弦定理不涉及外接圆半径的结论的情形下,三个定理是等价的.余弦定理与射影定理与包含外接圆半径的正弦定理等价.     

微积分中值定理间的关系

直观地阐述从微分中值定理到积分中值定理,乃至第二积分中值定理的演绎过程,指出积分中值定理的实质仍是微分中值定理,并在经典积分中值定理的条件下,得到更强的结论。     

一类新的KKM定理及其应用*

本文得到一类新的KKM定理,统一和改进了[2,3,0,7,11]中的结果。作为应用,我们得到了几个匹配定理、重合定理、不动点定理、极大极小不等式定理及截口定理。     

微积分学中中值定理的统一证明

由一个定理的结论,给出Lagrange中值定理,Cauchy中值定理,积分中值定理和Taylor中值定理的统一证明及一个计算待定型极限的方法.     

多项式簇的稳定性分析

本文利用值映射的概念在系数空间里讨论了多项式簇的Hurwitz稳定性的鲁棒性,给出了判别多项式簇是Hurwitz稳定的原象定理,同时应用这个定理证明了边界定理,棱边定理,Харитонов定理和菱形簇定理.     

泛函中的两个对偶定理

本文利用＊隔离定理,证明了Ｍａｚｕｒ定理和凸集的最佳逼近元存在性定理的对偶定理．     

三元函数的重极限与混合极限

本文引入了三元函数的混合极限概念,对三元函数的混合极限与重极限的区别及联系进行了探讨.结论表明,三元函数的混合极限与重极限之间没有必然的蕴含关系,另一方面,在一定条件下二者也存在着联系.     

Derivations of Direct Limits of Lie Superalgebras

We describe the derivations of a direct limit 𝔏 of Lie superalgebras 𝔏ⁱ (i ∈ I) in an 𝔏-module 𝔲 as the inverse limit of the derivations of 𝔏ⁱ's in 𝔲. Using this, in case the first cohomology group of each 𝔏ⁱ with coefficients in 𝔲 is zero, we describe the derivations of 𝔏 in 𝔲 as the inverse limit of 𝔲/𝔲𝔏ⁱ (i ∈ I). This then allows us to compute the derivations of direct limits of finite-dimensional basic classical simple Lie superalgebras.     

On the Limiting Proportion of Types

Consider a system into which units of random type enter at fixed points in time. Suppose each unit is endowed with a lifetime whose distribution is specific to its type, during which it is active (present in the system), and after which it is inactive (deleted from the system). Some unit types may tend to remain active for longer periods than others, and thus the limiting proportion of a given type within the active population may differ from the probability that an entering unit is of that type. The relation between the probabilities of types and the limiting proportion of types is shown to depend on the life distributions in a manner determined by the arrival time sequence.     

On the Continuous Singularity of the Limit Distribution of Products of I.I.D. d×d Stochastic Matrices

This article gives sufficient conditions for the limit distribution of products of i.i.d. d×d random stochastic matrices, d finite and 2, to be continuous singular, when the support of the distribution of the individual random matrices is finite or countably infinite. Proofs are based on applications of the multivariate Central Limit Theorem.     

22号初等元胞自动机的极限语言复杂性

§1Introduction Thetaskofthispaperistosolvetheproblemproposedin[1],i.e.,toexplorethe complexityoflimitset,orequivalently,limitlanguageoftheelementarycellularautomaton ofrule22bythetoolsofformallanguagetheory.Cellularautomata(abbreviatedasCA),asmathematicalmodelsforcomplexnatural systemscontaininglargenumbersofsimpleidenticalcomponentswithlocalinteractions,havebeenwidelyusedinphysical,biological,chemicalandcomputationalsystems[2].Despitetheirsimpleconstruction,someCAcandisplayveryrichandcompl…     

On Kersting's proof of the central limit theorem

By an adaptation of a method originally invented by G. Kersting [1] for the calculation of the limiting distribution of Markovian processes the central limit theorem (CLT) is proven. Only the case of equal variances is considered.     

Some limit analysis in a one-dimensional stationary quantum hydrodynamic model for semiconductors

In this paper, we study the steady-state hydrodynamic equations for isothermal states including the quantum Bohn potential. The one-dimensional equations for the electron current density and the particle density are coupled self-consistently to the Poisson equation for the electric potential. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations. In a bounded interval supplemented by the proper boundary conditions, we investigate the zero-electron-mass limit, the zero-relaxation-time limit, the Debye-length (quasi-neutral) limit, and some combined limits, respectively. For each limit, we show the strong convergence of the sequence of solutions and give the associated convergence rate.     

A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems

In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in ${\mathbb{R}}^2$ and of the discontinuous piecewise differential systems in ${\mathbb{R}}^2$ formed by two linear differential systems separated by a straight line. For this class of discontinuous piecewise differential systems the study of their algebraic and explicit non-algebraic limit cycles just is starting. Here we provide the first explicit non-algebraic limit cycle for the discontinuous piecewise linear differential systems. Additionally we recall seven open questions related with these types of limit cycles.     

The Bott-Borel-Weil Theorem for direct limit groups

We show how highest weight representations of certain infinite dimensional Lie groups can be realized on cohomology spaces of holomorphic vector bundles. This extends the classical Bott-Borel-Weil Theorem for finite-dimensional compact and complex Lie groups. Our approach is geometric in nature, in the spirit of Bott's original generalization of the Borel-Weil Theorem. The groups for which we prove this theorem are strict direct limits of compact Lie groups, or their complexifications. We previously proved that such groups have an analytic structure. Our result applies to most of the familiar examples of direct limits of classical groups. We also introduce new examples involving iterated embeddings of the classical groups and see exactly how our results hold in those cases. One of the technical problems here is that, in general, the limit Lie algebras will have root systems but need not have root spaces, so we need to develop machinery to handle this somewhat delicate situation.

     

Existence and some limits of stationary solutions to a one-dimensional bipolar Euler-Poisson system

In this paper, we study the stationary flow for a one-dimensional isentropic bipolar Euler-Poisson system (hydrodynamic model) for semiconductor devices. This model consists of the continuous equations for the electron and hole densities, and their current densities, coupled the Poisson equation of the electrostatic potential. In a bounded interval supplemented by the proper boundary conditions, we first show the unique existence of stationary solutions of the one-dimensional isentropic hydrodynamic model, based on the Schauder fixed-point principle and the careful energy estimates. Next, we investigate the zero-electron-mass limit, combined zero-electron mass and zero-hole mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit, respectively. We also show the strong convergence of the sequence of solutions and give the associated convergence rates.