贝卡的历险日记

担心着．担心着．北风来了,冰雪的脚步近了。一切都像没睡醒的样子．昏昏然紧闭着喉。山冷冻起来了．水凉起来了太阳在地平线下躲起来了．海豹偷偷地从水里钻出来．傻傻的．胖胖的．海洋里．浮冰上．瞧去．一大片一大片满是的．坐着．漂着．打两个滚．踢几块．水．赛几趟泳．捉几回迷藏。     

同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

近程空中目标航路研究

本文在等加速俯冲飞行假定下．分析了近程空中目标航路的特点，并据此提出了目标航路模型．经过投影变换，把目标航路模型转化为二次函数．从而使目标航路的滤波及预报问题得到简化．采用进推最小二乘(RLS)原理．给出了目标航路的在线滤波器及预报器．最后．对本文方法进行了仿真．并对仿真结果进行了分析．     

完全分配格上的点式拟一致结构与p．q．度量

在完全分配格上建立了点式拟一致结构理论．讨论了诱导拓扑分子格中闭包，局部基，连续等性质．证明了每个拓扑分子格皆可点式拟一致化．另外借助纯距离函数与真正的远域映射族给出了［８］中ｐ．ｑ．度量的等价定义与刻画，得到了点式拟一致分子格的ｐ．ｑ．度量化定理．     

三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

局部对称流形中具常平均曲率的完备超曲面

本文研究了局部对称流形中具常平均曲率的完备超曲面，得到了这种超曲面的一个特征定理，推广了H．Alencar和M．do Carmo以及N．X．Shui和G．Q．Wu的结果。     

数学基础课是通向数学主流的门户

2007年．作者翻译T．Needham所写的《可视的复分析》（Visual Complex Analysis．Oxford Univ．Press．2006）一书．以为这是一本很好的教本．值得许多同志花一点时间读一下．译后有一些感想．因此写了一篇较长的译后记．主要思想即认为数学基础课是通向数学主流的门户．译本将由人民邮电出版社出版．现在征得出版社的同意,将这篇译后记发表于此．在发表时又作了一点补充．补写的文字放在方括号内．     

D.C.隶属函数模糊集及其应用(Ⅱ)--D.C.隶属函数模糊集的万能逼近性

本文是D．C．隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D．C．隶属函数模糊集，建立了D．C．隶属函数模糊集对模糊集的万有逼近性。探讨了D．C．隶属函数模糊集与模糊数之间的关系，给出了用D．C．隶属函数模糊集逼近模糊数的e-Cellina逼近形式，得到模糊数与D．C．函数之间的一个对应算子，指出了用模糊数表示D．C．函数的问题。     

货币政策从紧企业六招应对

企业界的人士都知道．货币政策从紧的提法已经多年没听说过了。早在1997年之前．为了抑制通货膨胀．我国曾采用过适度从紧的货币政策，后来为了应对亚洲金融危机．刺激经济增长．实际上是加大了货币供应量．因而就再也没提过适度从紧的货币政策了。这次刚闭幕的中央经济工作会议提出了从紧的货币政策．人们都非常重视．把它看成货币政策的一个转折点。     

A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.     

浮体与自由面交线附近流场的奇异性

本文研究了浮体与自由面交线附近势流流场的奇异性。结果表明,线性时域解在交线附近的奇异特征是d2lnd.线性频域解在交线附近的奇异特征也是d2lnd,但若采用无穷大频率自由面条件φ=0,交线附近流场的奇异特征是d1nd,这里的d表示交线上的点与场点的距离。     

Dual simplex method for GUB problems

The dual simplex method for generalized upper bound (GUB) problems is presented. One of the major operations in the dual simplex method is to update the elements of therth row, wherer is the index for the leaving basic variable. Those updated elements are used for the ratio test to determine the entering basic variabble. A very simple formula for therth row update for the dual simplex method for a GUB problem is derived, which is similar to the formula for the standard linear program. This derivation is based on the change key operation, which is to exchange the key column and its counterpart in the nonkey section. The change key operation is possible because of a theorem that guarantees the existence of such a counterpart.     

SU(1,1)对称量子系统时间最优控制

基于李群分解,讨论了控制不受限情况下SU(1,1)对称量子控制系统的时间最优控制问题.针对系统控制哈密顿项为椭圆型和抛物型这两种情形,分别给出了实现任意演化矩阵所需要的最短时间.针对系统控制哈密顿项为双曲型情形,给出了实现任意演化矩阵所需要最短时间的一个上界.     

Central intertwining lifting,maximum entropy and their permanence

The central intertwining lifting is used to establish a maximum principle for the commutant lifting theorem. This maximum principle is used to prove that the central intertwining lifting is also a maximal entropy solution for the commutant lifting theorem, when T is a unilateral shift of finite multiplicity. The maximum principle is based on the residual spaces for intertwining liftings, and is motivated by Robinson's minimum energy delay principle for outer functions. A permanence property for the central intertwining lifting is also given.     

直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

RC_Link: Genetic linkage analysis using Bayesian networks

Genetic linkage analysis is a statistical method for mapping genes onto chromosomes, and is useful for detecting and predicting diseases. One of its current limitations is the computational complexity of the problems of interest. This research presents methods for mapping genetic linkage problems as Bayesian networks and then addresses novel techniques for making the problems more tractable. The result is a new tool for solving these problems called RC_Link, which in many cases is orders of magnitude faster than existing tools.     

The Schwarz problem for analytic functions in torus-related domains

The Cauchy kernel is one of the two significant tools for solving the Riemann boundary value problem for analytic functions. For poly-domains, the Cauchy kernel is modified in such a way that it corresponds to a certain symmetry of the boundary values of holomorphic functions in poly-domains. This symmetry is lost if the classical counterpart of the one-dimensional form of the Cauchy kernel is applied. It is also decisive for the establishment of connection between the Riemann–Hilbert problem and the Riemann problem. Thus, not only the Schwarz problem for holomorphic functions in poly-domains is solved, but also the basis is established for solving some other problems. The boundary values of functions, holomorphic in poly-domains, are classified in the Wiener algebra. The general integral representation formulas for these functions, the solvability conditions and the solutions of the corresponding Schwarz problems are given explicitly. A necessary and sufficient condition for the boundary values of a holomorphic function for arbitrary poly-domains is given. At the end, well-posed formulations of the torus-related problems are considered.     

马氏环境中可数马氏链的Poisson极限率

研究了马氏环境中的可数马氏链,主要证明了过程于小柱集上的回返次数是渐近地服从Poisson分布。为此,引入熵函数h,首先给出了马氏环境中马氏链的Shannon-Mc Millan-Breiman定理,还给出了一个非马氏过程Posson逼近的例子。当环境过程退化为一常数序列时,便得到可数马氏链的Poisson极限定理。这是有限马氏链Pitskel相应结果的拓广。     

整数规划中割平面法的研究

割平面法是求解整数规划问题常用方法之一.用割平面法求解整数规划的基本思路是:先用单纯形表格方法去求解不考虑整数约束条件的松弛问题的最优解,如果获得的最优解的值都是整数,即为所求,运算停止.如果所得最优解不完全是整数,即松弛问题最优解中存在某个基变量为非整数值时,就从最优表中提取出关于这个基变量的约束等式,再从这个约束式出发构造一个割平面方程加入最优表中,再求出新的最优解,这样不断重复的构造割平面方程,直到找到整数解为止.主要研究以下四个关键点:一是研究从最优表中提取出的、关于基变量的约束等式出发,通过将式中的系数进行整数和非负真分数的分解,从而得到一个小于等于0的另外一个不等式的推导过程;二是总结出从小于等于0的那个约束不等式出发构造割平面方程的四种方法;三是分析构造割平面方程的这四种方法相互之间的区别和联系;四是探讨割平面法的几何意义.通过对这四个方面的分析和研究,对割平面法进行透彻的剖析,使读者能够全面把握割平面法.