随机迭代系统的有界Fatou分支的存在性

本文研究了由m个超越整函数函数f1,f2,···,fm生成的随机迭代系统的Fatou分支的有界性问题.利用复动力系统理论的方法,得到一个Fatou连通分支U分别作为游荡域和非游荡域有界的条件,推广了Zheng的结果,同时也是对Baker的问题在随机迭代系统情形的一个回答.     

POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS

51.IntroductionLetF.beafinitefieldofqele~swithcharederisticp.LetXbeanThdilnensionalalgebraicsetdeadedoverF..ThezetafunctionofX/F.isdennedbywhereXOdenotesthesetofclosedpointsOfX/F.and#X(F.d)denotesthenUInberof.F.d-rationalpointsonX.ItiseasytoseethatZ(X,T)isapowerserieswithintegercoefficients.Dwork'srationalltytheoremIg]showsthatthezetafunctionZ(X,T)isrationalinT.ThuS,therearealgebraicintegerspll'.3Pr,pl,'3basuchthatThereisagoodreasonthatwemoantheabovezetafunctionbythepower(--1)"-…     

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b*(6.7314863965), the only equilibrium state is isotropic and it is stable; when b*< b < 15/2, two anisotropic (prolate) equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state.     

ECONOMIC MODELING OF THE PERSISTENCE OF ANTIMICROBIAL RESISTANCE

Abstract According to the dynamic relationship between antibiotic use and the incidence of multidrug‐resistant bacteria, the effectiveness of antibiotics is characterized as a natural resource exploited by antibiotic use. A major question is whether antibiotic effectiveness should be considered a renewable or an exhaustible resource. This paper presents a model combining epidemiological aspects of the decrease of resistance over time with an economic approach, modeling antimicrobial resistance as a negative externality of antibiotic use. The article concludes that the relative fitness of resistant bacteria is one driving factor for an estimation of the externality. If we, for instance, assume a low degree of relative fitness of resistant bacteria it is shown that resistance decreases fastest directly after antibiotic treatment. Accordingly, cycling of nonidentical drugs improves antibiotic effectiveness because cycling lowers the frequency of use of the individual antibiotic. In this case, antibiotic effectiveness must be characterized as a renewable resource in much the same way as a stock of fish in a lake. In contrast, if we assume a high degree of relative fitness of resistant bacteria, antibiotic effectiveness must be treated as an exhaustible resource because it is declined by every use of antibiotics.     

关于两曲面交线的不变量

本文研究了R3中相交子流形的不变量.利用活动标架法,得出了一个类似的欧拉公式. 即两曲面交线的挠率可以用两曲面的测地挠率、法曲率及两曲面的夹角表示.     

GROUPS OF AUTOMORPHISMS OF CHEVALLEY ALGEBRAS

In the paper we present an extension of Segal theorem on Lie algebra automorphisms of upper triangular nilpotent matrices to the whole class of nilpotent subalgebras generated by positive parts of indecomposable Chevalley algebras.     

算子群的容许子群链

<正> 本文的目的是把作者(1956)最近所得到的一些有关链条件四条件的强果推广到算子群中去.在第一节里的主要结果是定理3,将其用于非结合环即得作者(1956)定理6之推广结果.在§2中讨论算子群的直接乘积的容许子群链,其主要结果为:若诸算子群均各     

二阶代数微分方程亚纯解的增长性估计

本文研究了代数微分方程亚纯解的增长级.运用正规族理论,给出了某类二阶代数微分方程亚纯解的增长级的一个估计,该估计依赖于方程的有理函数系数.推广了2001年廖良文与杨重骏的一个结果.     

混合Weibull分布参数估计的ECM算法

混合威布尔分布是寿命数据分析中一个重要的统计模型.但是利用传统的统计方法,如矩估计、极大似然估计等估计模型的参数比较困难.应用ECM算法详细研究了混合威布尔分布在正常工作条件下,完全数据场合、Ⅰ-型截尾和Ⅱ-截尾场合的参数估计问题.数据模拟表明利用ECM算法来估计混合威布尔分布是一种有效的方法.     

非对称矩阵的病态特征向量的约化

1.引言 关于密集特征值与其病态特征向量之间的内在联系,Varah(1970),Wilkinson(1972及1984)和Kahan(1970)曾经研究过.Varah(1970)最先指出:若矩阵A具有二阶以上的Jordan块,且当A加上一个扰动矩阵(?=A+E)则相似于对角阵时,其相似变换矩阵是病态的(即变换矩阵各列几乎线性相关).Varah对于病态的程度,给予了数     

特征不为 2 的有限域上酉群的极小生成元集

设K=Fq2为含有q2个元素的有限域,q为奇素数的幂,*：a→a*=aq是Fq2的一个二阶自同构．本文用几何方法证明了除K为F32而n=4的情形外,Fq2上的酉群Un（V）可由2个元素生成．     

阵的模数最大的特征根的幅角

<正> 设有元素为实数或复数的方阵(?)多项式(?)做 A 的特征多项式,这里 E 为么阵,λ为未知量,这个多项式的根叫做 A 的特征根.现在采用下面的一些记号.我们用 A~(?)表 A 的共轭转置阵;对于任意正整数 K,令(?)(?)Farnell 和 Gautscui 曾证明:若ω为阵 A 的具有最大模数的特征根,则ω的模数为数列(?)的极限,即     

REPRESENTATIONS OF AFFINE HECKEALGE BRAS OF TYPE G2

Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.     

一个微生物生态模型的周期解

研究一类与厌氧消化过程微生物生态模型有关的微分方程组，在非自治双曲情形扰动下，通过利用重合度的延拓定理，获得了该方程组周期解全局存在性的充分条件．     

EXISTENCE OF GENERALIZED WEAKLY SOLUTIONS OF DIFFERENTIAL EQUATIONS IN PRODUCT SPACES

In this paper, by using Lyapunov function and weak noncompactness conditions, we give an existence theorem of generalized weakly solutions of Cauchy problem of differential equations in product spaces.     

关于抑制物对肿瘤生长直接效果模型的数学分析

本文研究一个用于描述抑制物对肿瘤生长直接作用效果的数学模型,该模型是对Byrne和chaplain相应模型的一个改进.我们分别在c_1=c_2=0和c_1>0,c_2>o但很小两种情况下研究了该模型解的存在性和解在t→∞时的渐近状况,证明了未血管化的肿瘤在某些情况下趋于消失,而在另一些情况下趋于一个休眠态,且抑制物总能减小肿瘤的半径.     

THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS

A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.     

ON MAXIMA OF DUAL FUNCTION OF THE CDT SUBPROBLEM

1. IntroductionConsider the following the CDT problem Pwhere g e n", B E n"'", A E n"'", c E urn, a > 0, (2 0, B is a symmetric matrix notnecessajry positive semi--definde, and throughout this paperg the norm 11' 11 denotes the Euclideannorm. For the conveniellt of our following discussion, let F be the feasible region of the CDTsubproblem,andProblem (1.1)--(1.3) arises in some trust region algorithms for equality constrained optillilzation aiming to conquer the inconsistency between the…     

一类非自治系统的平稳振荡

针对ｎ维非自治系统ｘ＝ｆ（ｔ，ｘ）＋ｇ（ｔ，ｘ）利用矩阵测度的性质，通过建立对线性系统的估计形式，得到了关于这类系统平稳振荡的存在唯一性定理，并给出了定理应用的例子。     

MULTIPLICITY OF POSITIVE SOLUTIONS TO A CLASS OF MULTI-POINT BOUNDARY VALUE PROBLEM

In this paper, an existence criterion of multiple positive solutions to a class of nonlinear multi-point boundary value problem is established by using the Guo-Krasnoselskii's fixed-point theorem. At the same time, an example is also included to testify our conclusion.