几个酉不变范数不等式（英文）

利用函数的凸性,得到矩阵酉不变范数的几个不等式.所得不等式改进了一些已有的结果.     

抽象空间缓增分数阶微分方程的吸引性

研究了抽象空间中缓增分数阶微分方程解的吸引性.建立了Cauchy问题存在全局吸引解的充分条件.揭示了缓增分数阶导数求解分数微分方程解的特征.     

多项几何分布（英文）

本文研究了在伯努利试验下的收集问题,利用混料格子点集的理论,推导出了多项几何分布的概率函数.在伯努利试验中,如果假设各种试验结果发生的概率都相等,进一步提出了均匀多项几何分布.我们得到了两类分布的概率函数以及期望与方差,通过模拟验证了这两类分布与正态分布的差异,并由模拟结果建立关于概率与试验次数的多项式回归模型,使用该模型可以有效的简化计算.     

关于2R（w2R）范数的一个注记

证明了自反Banach空间X上的等价w2R范数全体构成一个剩余集;同时证明了X闭子空间上等价的w2R范数均可延拓为X上等价的w2R范数.特别地,当X是可分时,上述w2R范数可替换为2R范数.     

Riesz基,Paley-Wiener类和缓增样条 *

设T ={t_j} j∈Z为实序列 ,使得 {e^it_jξ} j∈Z构成L₂( [-π ,π])的一个Riesz基 .设S₂m(T ,R)∩L₂ (R)是以T ={t_j} j∈Z为非正规节点系的多项式缓增样条函数空间 .证明了S₂m(T ,R)∩L₂ (R)上的Marcinkiewicz Zygmund和Bernstein不等式 .并由此证得渐近关系:E(f,B_{π ,2} ) ₂ =limm_→∞ E(f,S2m(T ,R) ∩L₂ (R) )₂ ,其中B_{π ,2} 表示L₂ (R)中指数≤π的整函数 ,即经典的Paley-Wiener类 .     

威布尔分布或极值分布可靠度置信下限的回归表示

对于定数截尾样本，给出了基于极值分布的位置和尺度参数的最好线性无偏估计（BLUE），获得了威布尔分布的可靠度的点估计和置信限之间的回归模型，从而可由威布 尔可靠度的点估计根据回归方程得到可靠度的置信下限，省去了大量的用表，为实际工作者带来了极大的方便，计算结果表明，回归方程有很高的精度。     

矩阵范数条件数的估计（英文）

本文中,我们获得一类双对角矩阵普范数与Frobenius范数条件数的上、下界估计,所得结果可用于测度线性方程组解的敏度.     

关于ψ（z）f（z）f‘（z）的值分布

本文研究有穷圆内ψ（ｚ）ｆ（ｚ）ｆ＇（ｚ）的值分布，其中ｆ（ｚ）为非常数亚纯函数，ψ（ｚ）为非零亚纯函数，并对平面上这样的函数，若Ｔ（ｒ，ψ）＝Ｓ（ｒ，ｆ），得到Ｔ（ｒ，ｆ）〈９／２Ｎ（ｒ，ｆ）＋１／２Ｎ（ｒ，１／ψｆｆ＇－１）＋Ｓ（ｒ，ｆ）。     

模糊赋范空间的范数结构（英文）

本文研究了模糊赋范空间中的范数结构问题.利用"切片"的方法,通过引入K函数,在更广泛意义下讨论了带连续t-模的模糊范数空间中存在的范数结构,给出了这些范数结构之间的关系.所得结果推广了现有的结论,并为模糊赋范空间的进一步研究提供了一种新的途径.     

A description of smooth vectors of the Weil representation in the geometric realization

We describe the image of the Weil representation of the double covering of the symplectic group in the Schwartz space in the so-called geometric realization, i.e., in holomorphic functions on the symmetric domain called the Siegel upper half-plane.     

Exponential Mixture Representation of Geometric Stable Distributions

We show that every strictly geometric stable (GS) random variable can be represented as a product of an exponentially distributed random variable and an independent random variable with an explicit density and distribution function. An immediate application of the representation is a straightforward simulation method of GS random variables. Our result generalizes previous representations for the special cases of Mittag-Leffler and symmetric Linnik distributions.     

Tempered fractional differential equation: variational approach

In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: (FD) where α∈(1/2,1), λ>0, are the left and right tempered fractional derivatives, is the fractional Sobolev spaces, and . Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd.     

Characterization for Beurling-Björck space and Schwartz space

We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space . The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling-Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.

     

Formal and Tempered Solutions of Regular D-Modules

A new family of sheaves has been recently studied by M. Kashiwara and P. Schapira generalizing to constructible sheaves the notion of moderate and formal cohomology. We prove comparison theorems when we regard these sheaves as solutions of a D-module. These results are natural generalizations of those of Y. Laurent and the author.     

Representation of Infinitely Divisible Distributions on Cones

We investigate infinitely divisible distributions on cones in Fréchet spaces. We show that every infinitely divisible distribution concentrated on a normal cone has the regular Lévy–Khintchine representation if and only if the cone is regular. These results are relevant to the study of multidimensional subordination. Research of J. Rosiński supported by a grant from the National Science Foundation.     

Harish-Chandra's Plancherel theorem for -adic groups

Let be a reductive -adic group. In his paper, ``The Plancherel Formula for Reductive -adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for and sketched a proof of the Plancherel theorem for . One step in the proof, stated as Theorem 11 in Harish-Chandra's paper, has seemed an elusively difficult step for the reader to supply. In this paper we prove the Plancherel theorem, essentially, by proving a special case of Theorem 11. We close by deriving a version of Theorem 11 from the Plancherel theorem.

     

Multiphase Transport in the Space of Stochastic Tempered Distributions

We construct a stochastic distributional theory for multiscale,multiphase transport. Field variables are viewed as stochastictempered distributions on Rⁿ. The field variables are made operationalvia convolution with a deterministic compact distribution whichis a representation of the measurement device. The correlationover scales of a field variable is analysed in a stochasticfunctional setting. Examples of functional transport equations,as represented by spectral measures, are presented