若干周期再生核空间的覆盖数

借助离散Fourier变换给出估计Mercer核矩阵逆矩阵范数上界的一种方法,由此给出了估计周期再生核Hilbert空间覆盖数的上、下界的一般方法.特别, 对两种特殊的周期再生核空间覆盖数的上、下界进行了比较.     

算子代数上的广义正定函数

本文研究定义于基本函数空间Ｄ或Ｓ上取值于ｖｏｎＮｅｕｍａｎｎ代数或Ｃ－－代数中的广义函数．证明了每个从局部紧的交换群到Ｃ－代数的范数连续正定函数可以表示为正向量值测度的富里埃变换．也得到了广义正定函数和平移不变厄米正定双线性泛函的一般表示定理．     

扩张矩阵的一些性质

研究了相关于扩张矩阵A的扩张球和拟范数的一些性质.首先通过具体实例及欧氏范数关于A的上下界估计指出扩张矩阵与经典球及欧氏范数匹配不佳,但欧氏范数相关于A仍能保持全局伸缩性.其次研究了相适应于扩张矩阵的扩张球和拟范数关于伸缩性、凸性、可积性、微分估计及傅里叶变换的一些性质.最后通过欧氏范数与相关于扩张矩阵的拟范数的不等式估计证明了相关于拟范数的两类施瓦茨函数空间和相关于欧氏范数的经典施瓦茨函数空间都是等价的.     

一类奇异积分算子的加权估计

假设A是一个Young函数,MD#为广义sharp极大函数.本文首先引进了LA-Hrmander条件,对于满足LA-Hrmander条件的算子T,得到了与T相关的广义sharp极大函数的估计.然后,再利用该估计得到了算子T的加权Lp范数被Hardy-Littlewood极大函数和与Aˉ相关的极大函数的加权Lp范数所控制(0相似文献   

一些函数空间上带Dini核的Calderón-Zygmund算子的交换子（英文）

本文主要建立了带Dini核的Calderón-Zygmund算子与加权Lipschitz函数生成的交换子在加权Lebesgue空间以及加权广义Morrey空间上的有界性.进一步,给出了带Dini核的奇异积分算子在加权中心Morrey空间上的加权λ-中心BMO估计.     

两类新域上的Bergman核函数的显表达式

在有界对称域上引入两类蛋型域, 得到其上Bergman 核函数的显表达式. 作为辅助工具, 利用著名的Selberg积分, 计算有界对称域上一般范数(generic norm)下复幂积分. 推广了华罗庚的矩阵积分, 得到不可约有界对称域的一个整系数或半整系数特殊多项式.     

用指数型整函数的最佳限制逼近

我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.     

Sobolev空间H~s(R~d)上波包系的框架性质

波包系是通过对有限个函数做伸缩、平移和调制三种运算生成的一种新型函数系,因此传统的小波系和Gabor系都是它的特殊情况.该文首先给出了Sobolev空间H~s(R~d)中一个广义平移函数系成为Bessel点列或框架的充分条件,然后结合波包系是一类特殊的广义平移函数系这一结果,给出了高维Sobolev空间H~s(R~d)上波包系成为框架的一个充分条件.最后,利用矩阵的特征值理论,该文证明了:如果函数g的Fourier变换在某一开球中大于某个正数,那么由它生成的波包系不能成为H~s(R~d)的一个框架.     

四元数矩阵方程AX-YB=C的最佳逼近解

本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．     

混合范数条件下平移不变信号的非均匀平均采样

L~p平移不变子空间中的采样研究通常要求生成函数属于一个不依赖于p的Wiener amalgam空间,此条件因不能控制p而显得太强.本文主要讨论生成函数属于混合范数空间时,非衰减平移不变空间中的非均匀平均采样与重构.生成函数属于混合范数空间的条件弱于Wiener amalgam空间且依赖于参数p.基于混合范数空间中的一些引理,针对两种平均采样泛函建立了采样稳定性,并给出了对应的具有指数收敛的迭代重构算法.     

Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon

Recently, the authors have proposed a new necessary and sufficient condition for turnpike optimality in calculus of variations with singular Euler equation. The method is based on a characterization of the value function and generalizes the well known method based on the Green theorem. Furthermore, it allows the optimality of a competition between several turnpikes to be characterized. For a class of such problems not enjoying the turnpike property, we give an explicit formula for the value function and show how to characterize the optimal solution as the limiting solution of a family of perturbed problems satisfying the turnpike property. The considered problems are scalar with infinite horizon.     

Auxiliary Principle and Iterative Algorithms for Lions-Stampacchia Variational Inequalities

In this paper, we extend the auxiliary principle (Cohen in J. Optim. Theory Appl. 49:325–333, 1988) to study a class of Lions-Stampacchia variational inequalities in Hilbert spaces. Our method consists in approximating, in the subproblems, the nonsmooth convex function by a sequence of piecewise linear and convex functions, as in the bundle method for nonsmooth optimization. This makes the subproblems more tractable. We show the existence of a solution for this Lions-Stampacchia variational inequality and explain how to build a new iterative scheme and a new stopping criterion. This iterative scheme and criterion are different from those commonly used in the special case of nonsmooth optimization. We study also the convergence of iterative sequences generated by the algorithm. This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for the Doctoral Program of Higher Education (20060610005), the National Natural Science Foundation of Sichuan Education Department of China (07ZB068) and the Open Fund (PLN0703) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University).     

奇异线性哈密顿算子自伴扩张的新描述

研究了具有一个奇异端点的线性哈密顿算子的白伴扩张的解析描述.设最小哈密顿算子h的亏指数为(d,d),将Im(h~*y,y)表示为秩为2d的二次型,该文利用二次型的表示矩阵得到了最小哈密顿算子h的自伴扩张域的一种新的完全描述.     

Numerical solution of fuzzy Camassa-Holm equation by using Homotopy analysis methods

In this paper, a fuzzy Camassa-Holm equation is solved by using the  homotopy analysis method (HAM). The approximation solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed method are proved.     

均值混合正态分布统计量的性质

这篇文章基于基因遗传背景,提出了一类均值混合正态分布,它不同于通常所讨论的方差混合正态分布. 作者研究了这类均值混合正态分布统计量的性质,给出了平移变换群下不变量的稳健性,即它与正态分布下该统计量有相同的性质, 并且讨论了其它统计量的分布.     

Continuous functions with impermeable graphs

We construct a Hölder continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We conclude that this function has impermeable graph—one of the key concepts introduced in this paper—and we present further examples of functions both with permeable and impermeable graphs. Moreover, we show that typical (in the sense of Baire category) continuous functions have permeable graphs. The first example function is subsequently used to construct an example of a continuous function on the plane which is intrinsically Lipschitz continuous on the complement of the graph of a Hölder continuous function with impermeable graph, but which is not Lipschitz continuous on the plane. As another main result, we construct a continuous function on the unit interval which coincides in a set of Hausdorff dimension 1 with every function of total variation smaller than 1 which passes through the origin.     

奇异扰动(k, n-k)共轭边值问题的正解

该文通过构造修正函数, 得到了一类奇异扰动(k, n-k)共轭边值问题多个正解的存在性, 其中, 扰动项仅要求是Lebesgue可积的. 最后给出一个例子说明主要结果的应用.     

On the number of \(n\)-dimensional invariant spheres in polynomial vector fields of \(\mathbb{C}^{n+1}\)

We study the polynomial vector fields \(\mathcal{X}= \displaystyle \sum_{i=1}^{n+1} P_i(x_1,\ldots,x_{n+1}) \frac{\partial}{\partial x_i}\) in \(\mathbb{C}^{n+1}\) with \(n\geq 1\) . Let \(m_i\) be the degree of the polynomial \(P_i\). We call \((m_1,\ldots,m_{n+1})\) the degree of \(\mathcal{X}\). For these polynomial vector fields \(\mathcal{X}\) and in function of their degree we provide upper bounds, first for the maximal number of invariant \(n\)-dimensional spheres, and second for the maximal number of \(n\)-dimensional concentric invariant spheres.     

Optimal quality of exceptional points for the Lebesgue density theorem

In spite of the Lebesgue density theorem, there is a positive δ such that, for every non-trivial measurable set S⊂ℝ, there is a point at which both the lower densities of S and of ℝ∖S are at least δ. The problem of determining the supremum of possible values of this δ was studied in a paper of V. I. Kolyada, as well as in some recent papers. We solve this problem in the present work.     

Minimal varieties and quasivarieties of semilattices with one automorphism

We describe all minimal quasivarieties and all minimal varieties of semilattices with one automorphism (considered as algebras with one binary and two unary operations). While working on this paper, the first author was supported by CRDF grant KYM1-2852-BI-07, the second author was supported by the institutional grant MSM0021620839 financed by MSMT, and the third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 48809 and K 60148.