A fuzzy blue sky catastrophe

In this paper, a blue sky catastrophe of limit cycles of a Van der Pol system with fuzzy disturbances is studied by means of the fuzzy generalized cell mapping (FGCM) method. The blue sky catastrophe happens when a fuzzy limit cycle collides with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical value. The fuzzy limit cycle, characterized by its global topology and membership function, suddenly loses stability and disappears into the blue sky after the collision. We illustrate this bifurcation event by considering the Van der Pol system under the multiplicative fuzzy noise. Such a bifurcation is a fuzzy noise-induced effect which cannot be seen in deterministic systems.     

一致L-Lipschitz的渐近拟伪压缩型映象迭代收敛的充要条件

设E是任意的实Banach空间,C是E的非空凸子集(C可以是E的无界子集),T:C→C是→致L-Lipschitz的渐近拟伪压缩型映象,在对参数的一些限制条件下,该文给出了带误差的修改的Ishikawa迭代序列强收敛于T的不动点的充要条件.     

Three limit theorems for vacancy in multivariate coverage problems

Three limit theorems describing asymptotic distribution of vacancy in general multivariate coverage problems are proved, in which nk-dimensional spheres are distributed within a k-dimensional unit cube according to a density f. The first result (a central limit theorem) describes the case where the proportion of vacancy converges to a fixed constant lying between 0 and 1. The last two results treat the case where the proportion of vacancy tends to 1 as n → ∞. Results of this nature have hitherto been available only for restricted k and/or for f equal to the uniform density.     

Asymptotic expansions in functional limit theorems

Asymptotic expansions for a class of functional limit theorems are investigated. It is shown that the expansions in this class fit into a common scheme, defined by a sequence of functions h_n (ε₁,…, ε_n), n ≥ 1, of “weights” (for n observations), which are smooth, symmetric, compatible and have vanishing first derivatives at zero. Then $\text{h}{}_{\mathrm{n}}\text{(n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{,…, n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ admits an asymptotic expansion in powers of $\text{n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$. Applications to quadratic von Mises functionals, the C.L.T. in Banach spaces, and the invariance principle are discussed.     

基于偏爱距离的群体决策

对于群体决策问题,文章引进供选方案间的偏爱距离和偏爱距离映射的概念。在此基础上,建立了序数偏爱下的群体决策公理,即偏爱距离公理。最后,给出一种满足偏爱距离公理的偏爱距离。     

中央火炬设计技术探讨

简要介绍了中央火炬在生产中的作用及其特点,从工艺流程的选择和火炬设计中需注意的事项两方面对中央火炬的设计技术进行了探讨。     

数字化测图技术在城市地形图修测中的应用

随着城市建设的迅速发展,城市地形地貌不断变化,为了适应城市规划和建设要求,现代城市地形图必须不断修测和更新。结合对原有河源市大比例尺地形图进行修测的工程实例,探讨了数字化测图技术用于城市地形图修测时的有关问题。     

Closed mappings onto metric spaces

We investigate the classes of spaces that can be mapped onto a metrizable space by a closed mapping with fibers having a given property $\text{P}$. We give some conditions which assure that such classes are closed under the action of perfect or open and compact mappings. Such a treatment includes the investigation of paracompact p-spaces and M-spaces. We also discuss spaces that can be mapped onto a metacompact Moore space.     

A#H^＊rat为中心单代数的条件

本文用ＭｏｒｉｔａＣｏｎｔｅｘｔ的方法得到域上余ＦｒｏｂｅｎｉｕｓＨｏｐｆ代数Ｈ与Ｈ－余摸代数Ａ的Ｓｍａｓｈ积Ａ＃Ｈ＊ｒａｔ是中心单代数的条件：若Ａ／ＡＣｏＨ是Ｈ－Ｇａｌｏｉｓ扩张，且ＡＣｏＨ是中心单代数，则Ａ＃Ｈ＊ｒａｔ也是中心单代数，特别地，若ＡＣｏＨｋ，则Ａ＃Ｈ＊ｒａｔ是中心单代数，且为ｋ－空间Ａ上线性变换稠密环．作为推论给出Ｈ＃Ｈ＊ｒａｔ是本原中心单代数新的证明．