一类Z_p~n到Z_p~m的完美非线性映射

完美非线性映射在原差分攻击中起着重要作用 .对任意素数 p,任意偶数 n,任意正整数m m n2 ,构造了一批 Znp 到 Zmp 的完美非线性映射 .     

一类Znp到Zmp的完美非线性映射

完美非线性映射在原差分攻击中起着重要作用.对任意素数p,任意偶数n,任意正整数m(m≤n/2),构造了一批Znp到Zmp的完美非线性映射.     

随机非线性单调映射

本文讨论随机非线性单调映射的基本性质,得到了关于强制型、扰动型及非强制型随机非线性单调映射的一些重要结果.本文所得结果,改进和推广了近期一些作者的工作.     

与p-Laplace算子方程相关的m增生映射的零点集的构造

许多求非线性系统的均衡解的问题都可以转化为寻找某个m增生映射的零点的问题.将利用非线性增生映射的性质,给出一类与p-Laplace算子方程相关的m增生映射的零点集的构造,其中2N/N+1p+∞且N≥1.     

非线性动力学大范围分析的一种数值方法：单元映射法

本文将非线性动力学问题转化为点映射形式,并以映射的单值连续为条件.将状态空间分割成有限小的单元,用定义在单元上的线性映射逼近原来的非线性映射.映射不动点的大范围分布问题化为线性方程组的求解,继而用迭代法求出不动点的准确位置.用线性映射的变形矩阵可方便地判断不动点的吸引核,从而为描划其吸引域带来了很大便利.本文提出的方法比胞映射法更为简便有效,文后举了例题.     

向量值映射锥鞍点存在定理

本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理.     

Banach空间中α-序压缩映射的不动点定理

在Banach空间中引入了几种压缩映射,证明了一类非线性映射的不动点的存在性,并改进和推广了相应定理.     

对一类非线性Neumann边值问题的研究［英文］

利用H-增生映射的性质,得到一类非线性Neumann边值问题解的存在唯一性的结论.文中所研究的方程是对以往工作的推广.证明方法得到简化.文中列举的一些例子还有助于进一步了解H-增生映射.     

一类非线性强阻尼扰动发展方程的解

研究了在数学、力学中广泛出现的一类三阶非线性强阻尼发展扰动偏微分方程,并求其近似解析解.首先,构造一个泛函同伦映射,将方程的解表示以人工参数的幂级数形式,代入同伦映射,得到一个非线性扰动方程解的逐次迭代关系式,并考虑对应的一个无扰动项情形下的强阻尼发展方程,利用Fourier变换理论,求出其精确解.其次,以得到的精确解为同伦映射迭代式的初始函数,通过非线性扰动方程解的迭代关系式,再用Fourier变换法求解对应的方程.最后,便依次地得到了非线性强阻尼发展扰动偏微分方程的各次近似解析解.用上述方法得到的各次近似解,具有便于求解、精度高等特点.     

T-单调映射及其性质

T-单调映射在变分不等式及非线性互补问题中经常遇到.此映射对应的非线性问题的解具有一些非常好的性质.这些性质在解的存在性证明,数值算法的构造及其收敛性分析中占有重要地位.本文系统讨论T-单调映射的性质,建立T-单调映射与常见的一些映射,如单调映射和Z-映射之间的联系.     

Cn中拟凸映射和星形映射的系数问题

§ 1.　Introduction　　Theconvexfunctionshavebeenextensivelystudiedinonecomplexvariable .Thesefunc tionsareeasilycharacterizedbysimpleanalyticorgeometricconditionsandtherearemanywellknownresultswhichcanhelpusunderstandtheirnature.However,thedifficultiesariseinsev eralcomplexvariables.Imposingtheconditionthatamappingbeconvexmappingturnsouttobeveryrestrictiveandsothefamilyofquasi convexmappingswasintroducedbyROPERKAandSUFFRIDGETJin [1 ].In [2 ]wehaveshown :thefamilyofquasi convexmappings…     

THE GROWTH THEOREM FOR QUASI-CONVEX MAPPINGS IN HILBERT SPACES

In this paper, the authors extend the definition of quasi-convex mappings and obtain the corresponding growth theorem.on the unit ball of a complex Hilbert space X.     

C^n中单位球上的强拟凸映照

若记B^n为C^n中的单位球,本文研究B^n上的强拟凸映强,（1）强拟凸映照与星形映照及凸映照的关系,（2）强拟凸映照的二次项系;（3）单位多圆柱上的强拟凸映照。     

A note on sequence-covering mappings

Summary Let f: X → Y be a mapping. f is called a sequence-covering mapping if in case S is a convergent sequence containing its limit point in Y then there is a compact subset K of X such that f(K) = S. It is shown that each quotient and compact mapping of a metric space is sequence-covering.     

A note on harmonic quasiconformal mappings

In this note we show that a harmonic quasiconformal mapping f=u+iv with respect to the Poincaré metric of the upper half plane onto itself such that v(x,y)=v(y) or u(x,y)=u(x) is a conformal mapping.     

The closure of planar diffeomorphisms in Sobolev spaces

We characterize the (sequentially) weak and strong closure of planar diffeomorphisms in the Sobolev topology and we show that they always coincide. We also provide some sufficient condition for a planar map to be approximable by diffeomorphisms in terms of the connectedness of its counter-images, in the spirit of Young's characterisation of monotone functions. We finally show that the closure of diffeomorphisms in the Sobolev topology is strictly contained in the class INV introduced by Müller and Spector.     

Boundary behaviour of the mappings satisfying generalized inverse modular inequalities

We study the geometric properties of the mappings for which generalized inverse modular inequalities hold. We generalize in this way known theorems from the theory of analytic mappings and the theory of quasiregular mappings, like the theorems of Fatou, M. and F. Riesz, Beurling and Lindelöf and their extensions given for quasiregular mappings by Martio, Rickman and Vuorinen.     

New Subclasses of Biholomorphic Mappings and the Modified Roper-Suffridge Operator

The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B~n in C~n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B~n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.     

关于局部紧度量空间的映象

本文借助于商映射、伪开映射和闭映射建立局部紧度量空间和几类具有某些特定性质mk-系之间的联系，作为推论.得到：双商ss-映射保持局部紧度量空间.