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。     

对波动方程初边值问题边界条件齐次化函数的一个注解

基于传统的齐次化边界条件方法,采用傅里叶级数法讨论了波动方程初边值问题第一类非齐次边界条件齐次化函数问题,分析表明:对同一定解问题,在不同齐次化函数下的解在适定意义下是等价的.     

关于二元分式线性齐次复合函数的积分

通过把二重积分转化成曲线积分,得到二元分式线性齐次复合函数积分的两个定理及其若干推论,并构造一些比较典型的用一般方法难以计算的例子说明结论的应用.     

齐次函数的一个仿射球定理

本文研究了相关齐次函数的仿射球定理.利用Hopf极大值原理,对任意给定的带凹性条件的初等对称曲率问题,获得了此类仿射球定理.特别地,这也给出了Deicke齐次函数定理的一个新证明.     

准齐次核的Hardy-Hilbert型级数不等式

定义了一类准齐次函数, 将齐次函数进行了推广. 讨论了具有准齐次核的Hardy-Hilbert型级数不等式, 并在一定条件下研究了最佳常数因子.     

椭圆重复齐次化问题W_0~(1,p)空间的收敛性

该文研究了形如-div(A(x/ε,x/ε~2)▽u_ε)=f(x)的椭圆重复齐次化问题解的收敛性,得到了Dirichlet边界条件下解在W_0~(1,p)空间的收敛率.证明所用的技巧是基于得到算子格林函数的估计.     

一道2016年全国大学生数学竞赛试题的注记

对2016年全国大学生数学竞赛的一道试题做出了推广.     

齐次生产函数条件下长期成本函数的确定方法

文章研究一般性齐次生产函数条件下长期成本函数的确定方法，证明了长期成本函数是关于产量的幂函数，并指出了长期边际成本函数和长期平均成本函数之间的特殊关系。     

根据齐次函数模型的无约束极小化方法（Ⅱ）直交分解校正法

矩阵分解的校正技术是数值线性代数中最有效的工具之一。作者根据基于齐次函数模型的无约束最优化方法的特点,提出的了这种类型的最优化算法的改进形式——修改的Bartels-Golub方法,即直交分解校正法。文章给出了详细算法。若干数值试验表明所提出的算法是稳定的和有效的。     

关于方程f“＋Af=F（z）的复振荡

本文讨论了当Ａ（ｚ）为多项式，Ｆ（ｚ）为具有无穷多个零点的整函数时，微分方程：ｆ＂＋Ａ（ｚ）ｆ＝Ｆ（ｚ）的解ｆ（ｚ）的复振荡的性质。     

拓扑向量空间中实齐性连续函数的延拓定理

得到如下结果,在有限维具To公理的拓扑向量空间中,其内任意不含原点的有界闭集上定义的齐性连续函数均可延拓为全空间上的齐性连续函数。     

On methods for converting exhausters of positively homogeneous functions

In the paper we develop a method for converting a (not necessarily uniformly bounded) upper (lower) primal exhauster of a continuous positively homogeneous function to a lower (upper) primal exhauster of the same function. The method is based on representation of a continuous positively homogeneous function as a pointwise supremum (infimum) of an one-parameter monotone family of Lipschitz continuous positively homogeneous functions that is of independent interest.     

V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.     

Hilbert空间上凸函数的上、下指数的共轭性质

本文引入Ｈｉｌｂｅｒｔ空间上非负凸函数具有一般性的上下指数的概念，得到相互共轭凸函数的上下指数的共轭性质，也讨论了由内积范数导出的正ｐ（ｐ＞１）次齐次函数与正ｑ（ｑ＞１，１ｐ＋１ｑ＝１）之间的关系     

The convolution and multiplication of one‐dimensional associated homogeneous distributions

The set of associated homogeneous distributions (AHDs) with support in R is an important subset of the tempered distributions because it contains the majority of the (one‐dimensional) distributions typically encountered in physics applications (including the δ distribution). In a previous work of the author, a convolution and multiplication product for AHDs on R was defined and fully investigated. The aim of this paper is to give an easy introduction to these new distributional products. The constructed algebras are internal to Schwartz’ theory of distributions and, when one restricts to AHDs, provide a simple alternative for any of the larger generalized function algebras, currently used in non‐linear models. Our approach belongs to the same class as certain methods of renormalization, used in quantum field theory, and are known in the distributional literature as multi‐valued methods. Products of AHDs on R, based on this definition, are generally multi‐valued only at critical degrees of homogeneity. Unlike other definitions proposed in this class, the multi‐valuedness of our products is canonical in the sense that it involves at most one arbitrary constant. A selection of results of (one‐dimensional) distributional convolution and multiplication products are given, with some of them justifying certain distributional products used in quantum field theory. Copyright © 2012 John Wiley & Sons, Ltd.     

Composition of fractional Orlicz maximal operators and A 1-weights on spaces of homogeneous type

For a Young function θ with 0 ≤α 〈 1, let Mα,θ be the fractional Orlicz maximal operator defined in the context of the spaces of homogeneous type （X, d, μ） by Mα,θf（x） = supx∈（B）α ｜｜f｜｜θ,B, where ｜｜f｜｜θ,B is the mean Luxemburg norm of f on a ball B. When α= 0 we simply denote it by Me. In this paper we prove that if Ф and ψare two Young functions, there exists a third Young function θ such that the composition Mα,ψ o MФ is pointwise equivalent to Mα,θ. As a consequence we prove that for some Young functions θ, if Mα,θf 〈∞a.e. and δ ∈（0,1） then （Mα,θf）δ is an A1-weight.     

Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex

In this paper we study a method for global optimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. Some properties of the auxiliary subproblem are studied and a special algorithm for its solution is proposed. A cutting angle method based on this algorithm allows one to find an approximate solution of some problems of global optimization with 50 variables. Results of numerical experiments are discussed.     

Convolution product formula for associated homogeneous distributions on R

The set of Associated Homogeneous Distributions (AHDs) on R, ??′(R), consists of distributional analogues of power‐log functions with domain in R. This set contains the majority of the (one‐dimensional) distributions typically encountered in physics applications. In earlier work of the author it was shown that ??′(R) admits a closed convolution structure, provided that critical convolution products are defined by a functional extension process. In this paper, the general convolution product formula is derived. Convolution of AHDs on R is found to be associative, except for critical triple products. Critical products are shown to be non‐associative in a minimal and interesting way. Copyright © 2010 John Wiley & Sons, Ltd.     

Multiplication product formula for associated homogeneous distributions on R

The set of associated homogeneous distributions (AHDs) on R, ??^′(R), consists of the distributional analogues of power‐log functions with domain in R. This set contains the majority of the (one‐dimensional) distributions one typically encounters in physics applications. The recent work done by the author showed that the set ??^′(R) admits a closed convolution structure (??^′(R), *). By combining this structure with the generalized convolution theorem, a distributional multiplication product was defined, resulting in also a closed multiplication structure (??^′(R), .). In this paper, the general multiplication product formula for this structure is derived. Multiplication of AHDs on R is associative, except for critical triple products. These critical products are shown to be non‐associative in a simple and interesting way. The non‐associativity is necessary and sufficient to circumvent Schwartz's impossibility theorem on the multiplication of distributions. Copyright © 2011 John Wiley & Sons, Ltd.