Bansch空间中全纯映射的若干性质

本文将全纯映射的若干性质推广到Ｂａｎａｃｈ空间，并应用这些性质研究有界域中的凸映射与星形映射。     

一类凸模糊映射的注记

本文讨论了一些凸模糊映射与拟凸模糊映射的性质及其在凸模糊优化的应用 .     

仿紧局部cosmic空间的一些性质

给出仿紧局部cosmic空间的一些特征,建立了仿紧局部cosmic空间的几类序列覆盖L映象的特征,证明了闭L映射和商ss映射保持仿紧局部cosmic空间的性质,此外,还给出仿紧局部cosmic空间的一些映射性质。     

一类圆周自映射的伪轨跟踪性质

本研究圈周上的连续自映射，我们得到一类非满映射具有伪轨跟踪性质的充分必要条件。     

若干Banach空间及有界凸域上的凸映射

本文研究了一类Ｂａｎａｃｈ空间上凸映射的性质。找出了一类Ｂａｎａｃｈ空间上单位球上凸映射的特征，并利用这些结果研究了一类有界凸域上的所有凸映射．     

覆盖近似空间的连续与同胚映射

利用一般映射研究了覆盖近似空间的一些性质,并证明了一些结论.接着定义了覆盖空间的粗糙连续映射及粗糙同胚映射.最后在覆盖粗糙连续映射和覆盖粗糙同胚映射的条件下,研究了两个覆盖近似空间的有关性质,进而在某种程度上为覆盖近似空间的分类提供了理论依据.     

Quantale上的双侧核映射

引入Quantale上双侧核映射的概念,研究双侧核映射的若干性质,证明一个核映射是局部核映射当且仅当它是双侧的、幂等的.     

Fuzzy映射与F基数

本文定义了从一个Ｆｕｚｚｙ集到另外一个Ｆｕｚｚｙ集的映射，称之为Ｆｕｚｚｙ映射，它不同于以往人们习惯用的“模糊映射”；给出了Ｆｕｚｚｙ映射的等价条件并研究了Ｆｕｚｚｙ映射的性质；基于这样的Ｆｕｚｚｙ映射定义了Ｆｕｚｚｙ映集的基数简称为Ｆ基数，讨论了它的基本性质；最后说明了Ｆ基数对于连续统假设的影响。     

连续统与集函数Г

本文对集函数Γ的某些性质作了研究。我们给出Γ关于连续映射、单调映射、开映射的映射性质,也给出了集函数Γ可加性、对称性的一些结果。     

多复变数的抛物星形映射

本文给出了抛物星形映射,ρ次的抛物星形映射,抛物形β型螺形映射和ρ次的抛物形β型螺形映射的定义.证明了推广的Rope-Suffridge算子保持这些映射的几何性质不变.     

f-Harmonic maps of doubly warped product manifolds

In this paper, we study f-harmonicity of some special maps from or into a doubly warped product manifold. First we recall some properties of doubly twisted product manifolds. After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M × _μ,λ N can not be proper f-harmonic maps, we use projection maps and product maps to construct nontrivial f-harmonic maps. Thus we obtain some similar results given in [21], such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps. Furthermore, we investigate non-trivial f-harmonicity of the product of two harmonic maps.     

Bi-f-harmonic map equations on singly warped product manifolds

Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps.In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensional manifolds and some special maps from or into a warped product manifold.     

靶流形为球面子流形的调和映射的量子化现象(英文)

本文研究了调和映射和极小子流形的量子化性质.通过运用谱分解方法,获得了靶流形为球面子流形的调和映射的量子化性质,然后将其应用到球面的极小子流形的高斯映射,得到了极小子流形的第二基本形式的量子化性子.     

An application of Newton–Puiseux charts to the Jacobian problem

We study 2-dimensional Jacobian maps using so-called Newton–Puiseux charts. These are multi-valued coordinates near divisors of resolutions of indeterminacies at infinity of the Jacobian map in the source space as well as in the target space. The map expressed in these charts takes a very simple form, which allows us to detect a series of new analytical and topological properties. We prove that the Jacobian Conjecture holds true for maps (f,g) whose topological degree is ≤5, for maps with gcd(degf,degg)≤16 and for maps with. gcd(degf,degg) equal to 2 times a prime.     

THE GAUSS MAP OF TIMELIKE SURFACES IN R_1~n

ＴＨＥＧＡＵＳＳＭＡＰＯＦＴＩＭＥＬＩＫＥＳＵＲＦＡＣＥＳＩＮＲ_１~ｎ￥ＨＯＮＧＪＩＡＮＱＩＡＯＡｂｓｔｒａｃｔ：Ｇａｕｓｓｍａｐｓｏｆｏｒｉｅｎｔｅｄｔｉｍｅｌｉｋｅ２－ｓｕｒｆａｃｅｓｉｎａｒｅｃｈａｒａｃｔｅｒｉｚｅｄ，ａｎｄｉｔｉｓｓｈｏｗｎ...     

Duality theory in multiobjective programming

In this paper, a multiobjective programming problem is considered as that of finding the set of all nondominated solutions with respect to the given domination cone. Two point-to-set maps, the primal map and the dual map, and the vector-valued Lagrangian function are defined, corresponding to the case of a scalar optimization problem. The Lagrange multiplier theorem, the saddle-point theorem, and the duality theorem are derived by using the properties of these maps under adequate convexity assumptions and regularity conditions.     

Stable maps of Polish spaces

We define the notions of stable and transquotient maps and study the relation between these classes of maps. The class of stable maps contains all closed and open maps and their compositions. The transquotient maps preserve the property of being a Polish space, and every stable map between separable metric spaces is transquotient.

In particular, a composition of closed and open maps (the intermediary spaces may not be metric) preserves the property of being a Polish space. This generalizes the results of Sierpinski and Vainstein for open and closed maps.

     

A generalization of Hahn-Banach extension theorem

In this paper, the notion of affinelike set-valued maps is introduced and some properties of these maps are presented. Then a new Hahn-Banach extension theorem with a K-convex set-valued map dominated by an affinelike set-valued map is obtained.