概率收缩与PN空间的方程

本文引入概率赋范空间(简称PN空间)中概率收缩的概念,借助这个概念,证明了几个PN空间非线性算子方程解的存在唯一性定理,所得结果推广了Altman相应的结果.     

概率收缩偶与非阿基米德Menger概率赋范空间中非线性方程组的解*

本文在非阿基米德Menger概率赋范空间中引入了概率收缩偶的概念,研究了非阿基米德Menger概率赋范空间中具概率收缩偶的非线性方程组的解的存在性与唯一性.发展和改进了引文[1～5]的相应结果.     

强概率收缩对与概率赋范空间中非线性算子方程组的解

在Menger PN空间引入强概率收缩对的概念,并研究了具有强概率收缩对的非线性算子方程组解的存在性和唯一性.这些结果改进和推广了非Archimedean Menger PN空间中相应的结果.     

（Φ,△）型概率收缩与Menger PN—空间中非线性算子方程的解

本文在Ｍｅｎｇｅｒ概率赋范空间中引入了（Φ，△）的型概率收缩的概念，研究了Ｍｅｎｇｅｒ概率赋范空间中具有这类概率收缩的非线性算子方程的解的存在性与唯一性。发展和改进了引文〔１〕、〔４－８〕的相应结果。     

具有随机控制函数的受控分枝过程

本文研究了具有随机控制函数的受控分枝过程的各类概率母函数间的关系.利用对概率母函数求导的方法,获得了过程的期望和方差,推广了该过程概率母函数和矩量的一些基本结果.     

基于校正函数的一类具三角结构的非线性系统的自适应控制

１引言 考虑如下的具有二角结构的作线性系统ＬＰＴＳ（ｌｉｎｅａｒｌｙ　ｐａｒａｍｅｔｅｒｉｚｅｄ ｔｒｉａｎｇｕｌａｒｓｔｒｕｃｔｕｒｅ）．其中ｘ＝（ｘ１,．……ｘｎ）Ｔ０∈Ｒｎ为系统的状态,ｕ∈Ｒ为控制输入,θ∈Ｒｐ为未知常值参数向量,γｉ０及γｉ′,β′（ｘ）β０为已知的光滑非线性函数,γｉ０（０）＝０,γｉ′（０）＝０,β０（０）≠０;（ｉ＝１,…,ｎ）,对这样的系统,Ｄ．Ｓｅｔｏ,Ａ．Ｍ．Ａｎｎａｓｗａｍｙ和Ｊ．Ｂａｉｌｌｉｅｕｌ在［１］中进行了讨论,但是他们对同一参数用了多个估计,使得系…     

带厚尾新息的非线性自回归函数型条件异方差模型的尾概率

研究带厚尾新息的非线性自回归函数型条件异方差(NARFCH)模型的平稳分布的尾概率. 结果表明, NARFCH序列的平稳分布的尾部紧密依赖于其条件方差. 当新息序列呈厚尾分布时, NARFCH序列的平稳分布的尾部会比新息序列的尾部更厚或更薄, 给出了具体的尾概率的增加或减少对条件方差的依赖公式, 并给出了两个具体例子来说明主要结果的应用.     

概率统计与函数的交汇

概率统计与其他相关知识,特别是与函数的交汇应用问题是新课标高考数学的一大创新热点,借助一些特殊函数的基本性质、函数的思想方法等来解决概率统计中的一些应用问题,合理培养学生创新应用与创新意识等,引领并指导数学教学与复习备考.     

广义非线性互补问题的投影收缩法

广义非线性互补问题的投影收缩法孙德锋（中国科学院应用数学研究所）ＡＰＲＯＪＥＣＴＩＯＮＡＮＤＣＯＮＴＲＡＣＴＩＯＮＭＥＴＨＯＤＦＯＲＴＨＥＮＯＮＬＩＮＥＡＲＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＡＮＤＩＴＳＥＸＴＥＮＳＩＯＮＳ￥ＳｕｎＤｅ－ｆｅ...     

Maximally Nonlinear Functions and Bent Functions

We give a construction of bent functions in 2n variables, here n is odd, by using maximally nonlinear functions on GF(2 ⁿ ).     

A Note on Kantorovich's Majorant Method

We prove that in certain function spaces Kantorovich majorants are also majorants for the Hausdorff measure of noncompactness.     

Nonlinear Phase Unwinding of Functions

We study a natural nonlinear analogue of Fourier series. Iterative Blaschke factorization allows one to formally write any holomorphic function F as a series which successively unravels or unwinds the oscillation of the function

$$\begin{aligned} F = a_1 B_1 + a_2 B_1 B_2 + a_3 B_1 B_2 B_3 + \cdots \end{aligned}$$

where \(a_i \in \mathbb {C}\) and \(B_i\) is a Blaschke product. Numerical experiments point towards rapid convergence of the formal series but the actual mechanism by which this is happening has yet to be explained. We derive a family of inequalities and use them to prove convergence for a large number of function spaces: for example, we have convergence in \(L^2\) for functions in the Dirichlet space \(\mathcal {D}\). Furthermore, we present a numerically efficient way to expand a function without explicit calculations of the Blaschke zeroes going back to Guido and Mary Weiss.

     

Majorant estimates for solutions of quadratic difference systems with lag

Systems of differential equations with lag with quadratic right-hand sides are considered. A compact matrix form for representing these systems in the general form is suggested. Upper and lower bounds for solutions of systems of quadratic differential equations with arbitrary lag are obtained by using quadratic Lyapunov functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 542–545, April, 1995.     

单级零点较少的亚纯函数的一个界囿不等式

本文证明了:若.f(z)为复平面上的非线性亚纯函数,满足N1(r,1/f)=S(r,f),则对任何非零复数c,成立T(r,f)<11N(r,f)+11N(r,1/f'-c)+S(r,f).这里N1(r,1/f)表示f(z)的单级零点的计数函数.     

Authentication Schemes from Highly Nonlinear Functions

We construct two families of authentication schemes using highly nonlinear functions on finite fields of characteristic 2. This leads to improvements on an earlier construction by Ding and Niederreiter if one chooses, for instance, an almost bent function as the highly nonlinear function.     

Estimates of The Fourier Widths of the Classes Of Periodic Functions With Given Majorant of the Mixed Modulus of Smoothness

We obtain some order-sharp estimates for the Fourier widths of Nikol'skii–Besov and Lizorkin–Triebel function classes with given majorant of the mixed modulus of smoothness in the Lebesgue space for a few relations between the parameters of the class and the space. The upper bounds follow from estimates of the approximation of functions of these classes by special partial sums of their Fourier series with respect to the multiple system of periodized Meyer wavelets.     

On the Majorant Method for the Cauchy--Kovalevskaya Problem

We present a theory which allows us to justify the existence theorems and derive majorant estimates for solutions of the Cauchy problem for a countable system of partial differential equations. Our results also allow to estimate the maximum existence interval for a solution.     

Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.