广义Taylor中值函数若干分析性质

文[2-8]对微分中值定理及Taylor定理"中间点"的渐近性质进行了研究,本文在此基础上,给出了"广义Taylor中值函数"的定义,对"广义Taylor中值函数"的分析性质进行了系统的讨论,证明了"广义Taylor中值函数"的单调性、可积性、连续性、可微性等分析性质.     

广义H-空间的理论及其应用*

本文给出了广义H-空间的完备性特征性质和紧性特征性质,同时也研究了这一空间的度量化定理.作为这些理论的应用.我们得到了Menger概率度量空间的完备性特征和紧性特征.给出了该空间的度量化函数的具体形式.     

区域函数的广义导数及其应用

本文以[7]的基本概念为基础,并根据Clarke的广义导数[1],以及Lasotra和Strauss[6]的多值函数f(x)的广义微分D_f(x)的定义.从而建立了区域函数F(x)的广义导数D_F=∪∩{G(x)?B(R),?x∈B(R);G(x)=F_x=F(x)}讨论了区域函数F(x)的广义导数的存在性;建立了区域函数的广义Fréchet导数存在的必要充分条件.     

New Formulas Related to Analytic Number Theory and Their Applications in Statistical Physics

Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to construct a so-called analytic number theory. In statistical physics, we consider parameters such as the volume V, temperature T, and chemical potential μ, which are not integers and are consequently related to analytic number theory. This relation to physical concepts leads us to seek new relations in analytic number theory, and these relations turn out to be useful in statistical physics.     

A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation

We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L _p into L _p^\prime (1<p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies an integral equation related to the generalized Schr?dinger equation. The resulting theorems extend the theory of operator-valued function space integrals substantially and previous theorems about these integrals are generalized by our results.     

A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation

We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L _p into L _p^\prime (1<p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies an integral equation related to the generalized Schr?dinger equation. The resulting theorems extend the theory of operator-valued function space integrals substantially and previous theorems about these integrals are generalized by our results.     

Linear Generalized Analytic Functions

Complex-valued continuous functions are approximated using solutions of complex partial differential equations of Vekua type.     

Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems

Journal of Optimization Theory and Applications - In this paper, we study several interesting basic properties of generalized oriented distance function with respect to co-radiant sets or free...     

On Monodromy of Generalized Analytic Functions

We discuss a number of topics concerned with certain boundary-value problems in the context of generalized analytic functions. Solution of the classical Riemann-Hilbert problem and the linear conjugation problem for analytic functions is described in appropriate function classes and the same scheme is applied to generalized analytic functions and vectors. In particular, we describe solution of the Riemann-Hilbert problem for generalized analytic functions and obtain an explicit analytic presentation of monodromy matrices in the case of generalized analytic vectors. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 15, Theory of Functions, 2004.     

解析算子函数空间上的复合算子理论初步

本文将经典Hardy空间上复合算子的理论、方法应用到解析算子函数空间上,给出了解析算子函数空间的几个基本性质及复合算子的有界性条件.     

单叶解析函数族修正卷积及极值点应用

用线性乘数算子定义了单叶负系数解析函数族J_(λ,μ)~L(α,β),讨论得到其极值点和修正卷积的参变量值,并利用极值点理论对J_(λ,μ)~L(α,β)中有限阶导函数模的界作了精确估计,主要结论可以自然覆盖相关的子类.     

广义Hilbert空间中几何凸函数的几个定理及其应用

研究广义Hilbert空间中几何凸函数的性质,给出一些重要定理,并运用几何凸函数的Jensen不等式建立了三重的双参数Hlder不等式和三重的多参数Minkowski不等式.     

向量优化中广义增广拉格朗日对偶理论及应用

作者介绍了一种基于向量值延拓函数的广义增广拉格朗日函数,建立了基于广义增广拉格朗日函数的集值广义增广拉格朗日对偶映射和相应的对偶问题,得到了相应的强对偶和弱对偶结果,将所获结果应用到约束向量优化问题.该文的结果推广了一些已有的结论.     

Saddle Points Theory of Two Classes of Augmented Lagrangians and Its Applications to Generalized Semi-infinite Programming

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed. This research was supported by the National Natural Science Foundation of P.R. China (Grant No. 10571106 and No. 10701047).     

广义Burger方程的解析解

本文讨论广义Burger方程的解析解,我们证明了:当粘性系数γ(t)=常数或对γ(t)=(3kt k_1)~(-1/3)时,方程满足“有条件的Painlev(?)可积”.并求出了相应的解析解.     

Full Analytic Spectrum of Generalized Jaynes-Cummings Hamiltonians

Theoretical and Mathematical Physics - We develop an analytic formalism using basic quantum mechanics techniques to successfully solve the multiphoton Jaynes–Cummings and the generalized...