Solutions for the Hyperbolic Dirac Equation on R1, m

In this article the hyperbolic unit ball in R ^m will be identified with the manifold of rays in the future null cone in R ^m+1. By means of the induced Clifford algebra structure there, one can introduce a definition of Dirac operators on sections of homogeneous line bundles. An infinite class of solutions for the resulting hyperbolic Dirac-equation will be constructed, in case of an odd dimension. In order to obtain these solutions a geometrical picture will be used, because each ray in the future cone will be identified with a point on a surface Σ in the future cone. The original Dirac-equation can then be rewritten in terms of the coordinates on this surface, and the resulting equation will be solved by means of Frobenius' method.     

基于KPCA的高校学业预警模型及其应用

针对高校招生规模扩大,学生整体素质下滑,学业完成情况恶化的教育问题,本文从辅导员的工作角度利用核主成分分析(KPCA)建立大学生学业预警创新管理模型,实现动态定性预警与定量预警相结合,对高校科学、及时、有效的开展学业预警工作具有一定的实践指导意义.     

Kernel density in the study of the strong stability of the queueing system

We use kernel density with correction of boundary effects to study the strong stability of the M/M/1 system after perturbation of arrival flow (respectively service times), to evaluate the proximity of G/M/1 (respectively M/G/1) and M/M/1 systems when the distribution G is unknown. Simulation studies are performed to support the results.     

Boundary Values of Cauchy Transforms in Weighted Spaces of Integrable Distributions

Let $ k \in {\shadN} $ , $ w(x) = (1+x^2)^{1/2} $ , $ V^{\prime} _k = w^{k+1} {\cal D}^{\prime} _{L^1} = \{{ \,f \in {\cal S}^{\prime}{:}\; w^{-k-1}f \in {\cal D}^{\prime} _{L^1}}\} $ . For $ f \in V^{\prime} _k $ , let $ C_{\eta ,k\,}f = C_0(\xi \,f) + z^k C_0(\eta \,f/t^k)$ where $ \xi \in {\cal D} $ , $ 0 \leq \xi (x) \leq 1 $ $ \xi (x) = 1 $ in a neighborhood of the origin, $ \eta = 1 - \xi $ , and $ C_0g(z) = \langle g, \fraca {1}{(2i \pi (\cdot - z))} \rangle $ for $ g \in V^{\,\prime} _0 $ , z = x + iy , y p 0 . Using a decomposition of C 0 in terms of Poisson operators, we prove that $ C_{\eta ,k,y} {:}\; f \,\mapsto\, C_{\eta ,k\,}f(\cdot + iy) $ , y p 0 , is a continuous mapping from $ V^{\,\prime} _k $ into $ w^{k+2} {\cal D}_{L^1}$ , where $ {\cal D}_{L^1} = \{ \varphi \in C^\infty {:}\; D^\alpha \varphi \in L^1\ \forall \alpha \in {\shadN} \} $ . Also, it is shown that for $ f \in V^{\,\prime} _k $ , $ C_{\eta ,k\,}f $ admits the following boundary values in the topology of $ V^{\,\prime} _{k+1} : C^+_{\eta ,k\,}f = \lim _{y \to 0+} C_{\eta ,k\,}f(\cdot + iy) = (1/2) (\,f + i S_{\eta ,k\,}f\,); C^-_{\eta ,k\,}f = \lim _{y \to 0-} C_{\eta ,k\,} f(\cdot + iy)= (1/2) (-f + i S_{\eta ,k\,}f ) $ , where $ S_{\eta ,k} $ is the Hilbert transform of index k introduced in a previous article by the first named author. Additional results are established for distributions in subspaces $ G^{\,\prime} _{\eta ,k} = \{ \,f \in V^{\,\prime} _k {:}S_{\eta ,k\,}f \in V^{\,\prime} _k \} $ , $ k \in {\shadN} $ . Algebraic properties are given too, for products of operators C + , C m , S , for suitable indices and topologies.     

Boundary Value Problems for Second－Order Singular Differential Equations on Infinite Intervals

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关于R3上Cusp度量存在性的注记

In this paper, we show that there exists no complete rotationally symmetric cusp metric on R^3. Also we consider the existence of the complete rotationally symmetric cusp metric with other situations.     

Double Solutions of Impulsive Dynamic Boundary Value Problems on a Time Scale

A double fixed-point theorem is applied to obtain the existence of at least two positive solutions of a right focal boundary value problem for a second order impulsive dynamic equation on a time scale.     

Computing an Element in the Lexicographic Kernel of a Game

The lexicographic kernel of a game lexicographically maximizes the surplusses s _ij (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can efficiently compute the surplusses s _ij (x) corresponding to a given allocation x. This approach improves the results in Faigle et al. (in Int J Game Theory 30:79–98, 2001) and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm.We thank the referees for clarifying the presentation of the proof of Proposition 2.1.     

对台湾工农业产品产量的主成分分析

主成分析分析法是一种将多个指标化为少数几个不相关的综合指标 (即主成分 )的多元统计分析方法 .本文通过运用主成分方法对我国台湾地区 1 989 1 996工农业主要指标的原始数据的处理分析 ,表明主成分分析确是在实用中很可行的一种常用的统计方法 .     

基于核函数的混合C均值聚类算法

提出了一种基于核函数的混合C均值聚类算法.首先利用模糊C均值聚类算法和另一种类型的可能性C均值聚类算法的优点,设计出一种混合C均值聚类算法.然而鉴于该算法存在的不足,本文将Mercer核函数引入到该算法中,仿真实验结果证实了该方法的可行性和有效性.     

关于Getz-Jacobson方法的若干讨论

考虑一类右端函数为多项式情形的常微分方程组初值问题的奇异性.先指出Getz-Jacobson所提出的代数方法的某些不足,然后提出一个新的方法,使得更加方便地讨论此类问题解的爆破性质.最后应用这种方法成功地解决了来自化学反应的一个实例.     

我国城市设施水平的主成分分析

本文提出多元统计分析的一种评价方法：通过对全国31个省市自治区的城市设施水平进行主成分分析，就各地区城市设施水平进行统计评价，揭示我国城市的发展质量、城市居民的生活质量，找出各地区在设施建设各方面的优势与不足，为我国今后的城市化道路提供科学的参考依据。     

Some Remarks on Localization in Coalgebras

We analyze the geometry of the Ext-quiver of a coalgebra C in order to study the behavior of simple and injective C-comodules under the action of the functors associated to a localizing subcategory of the category of C-comodules.     

基于主成分分析的湖南竞争力评价研究

介绍了主成分分析方法,提出了运用主成分评价模型必须满足的条件。并且借鉴中国科学院可持续发展研究组构建的可持续发展指标体系,运用主成分分析构建了区域竞争力的综合评价指标,将湖南的经济发展与其他地区比较,并提出相应的策略。     

Optimal Maximum Norm Estimates and Superconvergence for GDM on Two point Boundary Value Problems

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关于随机真度的若干注记

以随机真度为基础,在三值R_0命题逻辑系统中给出了三种不同的近似推理模式并讨论了它们之间的关系,其次利用根的性质得出误差定义的若干推理结果.     

Some Remarks on the Simultaneous Chromatic Number

We present several partial results, variants, and consistency results concerning the following (as yet unsolved) conjecture. If X is a graph on the ground set V with then X has an edge coloring F with colors such that if V is decomposed into parts then there is one in which F assumes all values.Due to some unfortunate misunderstandings, this paper appeared much later than we expected.* Research partially supported by NSF grants DMS-9704477 and DMS-0072560. Research partially supported by Hungarian National Research Grant T 032455.     

Kernel theorems in the setting of mixed nonquasi-analytic classes

Let Ω₁⊂Rr and Ω₂⊂Rs be nonempty and open. We introduce the Beurling-Roumieu spaces D(ω₁,ω₂}(Ω₁×Ω₂), D(M,M^′}(Ω₁×Ω₂) and obtain tensor product representations of them. This leads for instance to kernel theorems of the following type: every continuous linear map from the Beurling space D(ω₁)(Ω₁) (respectively D(M)(Ω₁)) into the strong dual of the Roumieu space D{ω₂}(Ω₂) (respectively D{M^′}(Ω₂)) can be represented by a continuous linear functional on D(ω₁,ω₂}(Ω₁×Ω₂) (respectively D(M,M^′}(Ω₁×Ω₂)).