广义凸集的支撑函数

本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。     

幂函数的一些密码学性质

二元域上n数组空间上的非线性置换在分组码，杂凑函数与流密码等密码学领域中有重要应用.域GF（2n）上的幂函数提供了二元域上n数组空间上的一类非线性置换．本文着重研究幂函数的强完全性、完全性与非线性度等密码学性质．作为结果，本文证明了幂函数具有完全性；证明了具有强完全性的函数必有较高的拓扑非线性度；木文找到一类具有强完全性的幂函数；周时也定出了幂函数的代数非线性度．     

扰动周期KdV方程的小波基分析

本文利用样条小波基构造近似惯性流形来研究扰动周期ＫｄＶ方程的长期动力学行为·     

关于布尔函数的二次逼近

本文首先利用矩阵形式引入了二阶ｗａｌｓｈ谱的概念并讨论了其性质，其次引入了二次ｂｅｎｔ函数的概念，同时论述了二次ｂｅｎｔ函数的密码学意义。     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

几乎齐次函数的刻划定理

给出了几乎齐次函数的一个新的刻划定理，这一刻划是齐次函数欧拉定理的拓广。     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Urn模型的B网及其应用

Urn模型的离散概率分布被用于构造逼近格式,具有Bernstein多项式的许多特性。本文用B网技术对Urn模型概率分布给出新的解释,指出了Urn模型B网的诸多性质,导出分布函数曲线的导数公式,构造了Urn分布的对偶基及与此相关的拟插值算子。     

On generalized gradients

In this paper we present a concept of the construction of generalized gradients by considering a development of directional derivatives into spherical harmonics. This leads to a derivation system as a system of generalized partial derivatives. Necessary conditions for local extrema for a broad class of not necessarily differentiable function can be given and a characterization of points of differentiability can be proved by using generalized gradients.     

Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.