曲面切族芽及其非几何包络面芽的奇点

一族曲面切族芽是一系列正则曲面的运动,这种运动是从一个正则曲面切变到另一个正则曲面.文中给出了在形变意义下稳定的曲面切族芽的分类,并且研究了它们的包络的奇点.     

光滑映射芽的有限决定性(Ⅲ):M-R_k-决定

本文讨论了映射芽的强右等价关系,并得到I决定与M决定的几个估计。     

弱闭T(N)-模中Cp空间的等距映射

刻划了弱闭T(N)-模中Schatten类之间的等距线性满映射.设U、W分别为由左连续序同态N→和N→所确定的弱闭T(N)-模.Φ为U∩Cp到W∩Cp(1≤p<∞,p≠2)上的等距线性映射.若(0)+=(0),H-=H且min{dim(0),dim(0)#,dim(HH～),dim(HH∧)}≥2,则存在到的等距Ui(i=1,2)及酉算子Vi(i=1,2),使得Φ(A)=U1AV1或Φ(A)=V2AU2.     

P_0（X）拓扑空间上由点值映射诱导出的集值映射的一些结果

本文研究了Ｐ０（Ｘ）拓扑空间上由点值映射诱导出的集值映射的性质，并得到一些定理．     

R＋（L）值半连续映射与连续d锥

定义L－fuzzy非负扩充实直线R＋（L）与R＋（L）值半连续映射,证明在一个L－core紧的L－fuzzy拓扑空间（L^x,δ）上的R＋（L）值下半连续映射的全体关于点式序,加法运算与数乘运算的构成一个连续d锥,推广了文献[6]中的结果。     

g－可度量空间的完备逆象

本文的主要目的是建立ｇ－可度量空间的两个映射定理：（１）ｇ－可度量空间是度量空间的商紧映象；（２）ｇ－可度量空间的完备逆象若具有Ｇ＿（δ－）对角线，那么它是ｇ－可度量空间。     

Lauwerier映射的奇怪吸引子的遍历性及其结构

本又考虑Ｌａｕｗｅｒｉｅｒ映射Ｆａ,ｂ（ｘ,ｙ）＝（ｂｘ（１－２ｙ）＋ｙ,ａｙ（１－ｙ））．我们证明对于参数α在一个正测度集合中,对应的映射有非平凡的拓扑可迁的吸引子,其中是某个双曲不动点的不稳定集的闭包．周期点是双曲的且在中稠密,而且中任两个周期点异宿相关（稳定与不稳定集的横截相交）．同时也构造支撑在吸引子上的Ｓｉｎａｌ－Ｂｏｗｅｎ－Ｒｕｅｌｌｅ测度,并研究其性质．     

具误差的三种迭代收敛的等价性

考虑了具误差的Mann迭代,Ishikawa迭代和三重迭代对中间意义下的渐进非扩张映射和强逐次伪压缩映射收敛的等价性.我们的主要结果改善和推广了近期该方向研究所得到的某些成果.     

有限族非扩张映象的公共不动点的具误差和具扰动映射的迭代程序

本文在实一致凸和q-一致光滑Banach空间中研究了一类新的有限族非扩张映象的公共不动点的具误差和具扰动映射的显式迭代程序并且得到了一些收敛性定理.特别地,获得了该显式迭代程序强收敛性的充要条件.本文所得到结果推广了文[1]中的相应结果.     

Notes on Smooth Map Germs

ＮｏｔｅｓｏｎＳｍｏｏｔｈＭａｐＧｅｒｍｓＹｕＬｉ（余立）；ＺｈａｎｇＧｕｏｂｉｎ（张国滨）（ＺｈａｎｊｉａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔｈｅｄｅｔｅｒｍｉｎａｃｙｏｆｒｅａ...     

Contact Finite Determinacy of Relative Map Germs

The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence （or KS,T equivalence） and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, f is finite determined relative to KS,T if and only if there exists a positive integer k, such that M^5（n）ε（S;n）p ∩→ TKs,T（f）.     

光滑映射芽的开折的分级稳定性

光滑映射芽各种稳定性的讨论,一直是奇点理论的一个重要部分． Ｔｈｏｍ Ｒ．［１］在创立突变论时,提出了映射芽的,ｒ－开折的稳定性理论．Ｗａｓｓｅｒｍａｎｎ Ｇ．［２］将之发展为开折的（ｒ,ｓ）稳定理论．本文将他们的结论发展为（ｒ１,ｒ２,…,ｒｄ）稳定性,在任意的分级情况下,得到强稳定性、弱稳定性及无穷小稳定性的等价性,并得到了一些基本结果．     

C^0-Sufficiency, Kuiper-Kuo and Thom Conditions for Non-isolated Singularity

In this paper, a criterion on the C^0-sufficiency for a function germ with non-isolated singularity is obtained analogously to that of Kuiper-Kuo for the case of isolated singularities. Moreover, the Kuiper Kuo condition and the Thom condition for an analytic function germ with non-isolated singularity are proved to be equivalent.     

On the Number of Singularities in Generic Deformations of Map Germs

Let f:Cⁿ, 0C^p, 0 be a K-finite map germ, and let i=(i₁, ...,i_k) be a Boardman symbol such that ⁱ has codimension n in thecorresponding jet space J^k(n, p). When its iterated successorshave codimension larger than n, the paper gives a list of situationsin which the number of ⁱ points that appear in a generic deformationof f can be computed algebraically by means of Jacobian idealsof f. This list can be summarised in the following way: f musthave rank n–i₁ and, in addition, in the case p=6, f mustbe a singularity of type ^i₁,i₂.     

光滑映射芽在A的一个子群下的万有开折(英)

在[1]中,光滑映射芽对于群A的万有开折得到了讨论.本文则定义了A的一个子群,并给出了光滑映射芽的开折对于这个子群为万有的充分必要条件.     

(D6,Z2)-等变分歧问题的识别

利用奇点理论中光滑映射芽的接触等价，研究状态变量和分歧参数均具有对称性的等变分歧问题，给出了状态变量具有D。对称性，分歧参数具有Z2对称性的等变分歧问题的两个识别条件．     

A 14-dimensional Module for the Symplectic Group: Orbits on Vectors

Let 𝔽 be a field, V a 6-dimensional 𝔽-vector space and f a nondegenerate alternating bilinear form on V. We consider a 14-dimensional module for the symplectic group Sp(V, f) ? Sp(6, 𝔽) associated with (V, f), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f) for the fundamental weight λ₃. If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f).     

The Generalized KKM Map and Its Applications to Variational Inequalities

In this paper,applying the concept of generalized KKM map,we study problems ofvariational inequalities.We weaken convexity(concavity)conditions for a functional of two variables■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth-od of acute angle principle about monotone operator as an application of these results.     

Dynamical Behaviors in a Two-dimensional Map

We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto‘s theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.