周期多尺度分析的特征及它的一个应用

在这篇文章里，我们研究了周期多尺度分析的性质，给出了尺度函数序列的一个特征．这个特征能够使我们从一个尺度函数序列得到另一个尺度函数序列．最后，我们给出了主要结果的一个应用．     

一个改进的线性规划预校正算法

本文我们提出了一个改进型线性规划预校正算法，我们的预步和校正步方向与Mizuno－Todd-Ye[4]的方向是不同的．我们的算法的迭代复杂度为，然而在校正步，我们降低对偶间隙一个常数因子．     

阿凡提巧取金环问题的推广

我们都知道，阿凡提是一个聪明机智的传奇人物，在生活中流传着许多阿凡提智慧过人的传奇故事，给我们青少年带来不少启发．其中有这样一个故事：     

快速遴选优胜者

本文给出了一个行之有效的方案来确定某次竞赛的优胜者．首先，假定裁判是理想的（无误差的），我们提出了一个基本模型在几乎最短的时间内确定出前W名．在我们的方案中，用一个矩阵来记录从当前已知的裁判评分中所得到的“当前名次”，并且在一轮之后尽可能多地淘汰试卷．然后，我们考虑现实中的裁判（有误差的），估计了最后选出的W名中包含有非前2W名试卷的概率．进一步，考虑到打分方案中的系统偏差，我们用贝叶斯估计对模型做了改进，使不同裁判的评分有了一定的可比性．为检验模型的可行性，我们做了大量的计算机模拟，模型检验中我们发现，如果适当增加从第一轮中选拔出来的试卷数，将使我们的模型结果更好．我们还通过改变参数P，J，W对模型作了稳定性分析，并且得到了一个经验公式，可以用来预测在一定P，J，W值下评卷的总时间．接下来，我们采用了现实生活中的数据来检验模型，结果相当好当P=50，J=3时，若取W=2，用我们的方案得到了第一名和第三名若取W=3，得出的正是前三名．最后，我们总结出了一个灵活实用的方案，并提出了一些建议在模型推广中，我们还利用经验公式对开支做了预算．     

网上平衡对策与流向对策值的存在性

在一个网络上可以赋以流量，网上每一个孤可以与一个Ｎ人对策的局中人相对应，有了这种对应之后，我们证明了任何一个可加性对策都是流向对策，且证明了如果Ｖ１，Ｖ２是流向对策，则ｍｉｍ｛Ｖ１，Ｖ２｝也是流向对策．在此基础上，我们证明了θ－全平衡对策是流向对策这一主要定理．最后，我们成功地构造了一个很简单的例子说明了此定理的逆命题不成立．这是其它文献［１，２，３，４］中都没有明确指出的结论．关于θ－全平衡对策与流向对策的关系．目前来看我们的结果是较好的结果［９］．     

球面上的几何性质

对于复平面，我们构造一个一一映射，使复平面上的点能够在一个三维球面上被表示，称为复数的球面几何表示．通过这样一个一一映射，我们可将对平面上的复数的研究转移到一个有限的三维空间上去，并在这个新的空间中讨论复数在其上的一些性质及关系．     

用友转型客户经营

在2007年和以往的十年转型基础上，用友怎样继续前行？我们确立的一个基本思路就是在我们商业模式上进行变革和创新，就是要推进一个新的商业模式——客户经营。     

Banach空间中微分包含的生存单调轨道与解的稳定性

我们在无限维空间中研究微分包含的生存W—单调轨道的存在性．基于Zorn引理，我们给出了一个逼近方法，在较弱的条件下得到了一个存在性定理，其特殊情形则包含了已有的生存定理和微分方程理论中的若干结果作为应用，我们首先研究了微分包含生存解的整体存在性，得到了整体生存理．然后我们研究了微分包含解的稳定性，得到一些新的结果．     

基于反Krylov矩阵正交分解的半可分矩阵

在本文中，我们证明了对一个反Krylov矩阵作QR分解后，利用得到的正交矩阵可以将一个具有互异特征值的对称矩阵转化为一个半可分矩阵的形式，这个结果表明了反Krylov矩阵与半可分矩阵之间的联系．另外，我们还证明了这类对称半可分矩阵在QR达代下矩阵结构保持不变性．     

趣味橡皮章的魔力

手工，是我们快乐童年里永远不可或缺的一项内容，它激发着我们极大的想象力和创造力，不需要太长的时间，不需要太大的空间，不需要太多的物品，就把我们带入了一个奇妙世界。今天让我们见识一下自制趣味橡皮章的魔力吧！     

Capability of Crossed Modules of Lie Algebras

In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module.     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

The Siegel norm,the length function and character values of finite groups

In this paper we present some new results on the connection between the Siegel norm, the length function and irreducible character values of finite groups. In addition, we provide algorithms to compute the length of a cyclotomic integer and the set of cyclotomic integers with Siegel norm bounded by a given positive real number.     

On nonlinear Fredholm integral equations with non-differentiable Nemystkii operator

From decomposition method for operators, we consider a Newton-Steffensen iterative scheme for approximating a solution of nonlinear Fredholm integral equations with non-differentiable Nemystkii operator. By means of a convergence study of the iterative scheme applied to this type of nonlinear Fredholm integral equations, we obtain domains of existence and uniqueness of solution for these equations. In addition, we illustrate this study with a numerical experiment.     

The diffeomorphic types of the complements of arrangements in ??3 II

For any arrangement of hyperplanes in ℂℙ³, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the arrangement of hyperplanes. In this paper, we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other. In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected. This generalizes our previous result on hyperplane point arrangements in ℂℙ³. This work was partially supported by NSA grant and NSF grant     

多中心牛顿定理及其应用

本文将论文［１］推广到离散型的多中心泰勒定理。即多中心牛顿定理．从而得到相应的论文［２］．即高阶差分的插值公式，并给出其应用。     

A new theory of regular functions of a quaternionic variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.     

Optimization problems for an energy functional with mass constraint revisited

In this paper we report on a variational problem under a constraint on the mass which is motivated by the torsional rigidity and torsional creep. Following a device by Alt, Caffarelli and Friedman we treat instead a problem without constraint but with a penalty term. We will complete some of the results of [C. Bandle, A. Wagner, Optimization problems for weighted Sobolev constants, Calc. Var. Partial Differential Equations 29 (2007) 481-507] where the existence of a Lipschitz continuous minimizer has been established. In particular we prove qualitative properties of the optimal shape.     

Stabilization of linear distributed control systems with unbounded delay

In this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay. Assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space, we characterize those systems that can be stabilized using a feedback control. As consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control.     

Baskakov-Durrmeyer type operators involving generalized Appell Polynomials

In this paper, we define the Baskakov-Durrmeyer type operators based on generalized Appell polynomials. Here, we establish moment estimates, an estimate via weighted modulus of continuity and a Voronovoskaya type asymptotic result. Further, we study a quantitative-Voronovoskaya-type theorem and Grüss Voronovskaya-type theorem. Lastly, we give the approximation result for functions having derivatives of bounded variation.