有限级Dirichlet级数及随机Dirichlet级数

本文研究了全平面上有限级Dirichlet级数的增长性和正规增长性,得到了两个充要条件;证明了有限级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同.     

有限级Dirchlet级数及随机Dirchlet级数

本文研究了全平面上有限级Dirichlet级数的增长性和正规增长性,得到了两个充要条 件;证明了有限级随机Dirichlet级数的增长性几乎必然与其在每条水平直线上的增长性相同．     

一类零级Dirichlet级数的增长性

本文研究了一类零级Dirichlet级数在全平面上的级、下级以及正规增长性.利用Knopp-Kojima的方法,获得了一类零级Dirichlet级数在全平面上的级、下级以及正规增长性的充要条件,推广了平面上零级Dirichlet级数增长性的研究范围.     

平面上零级Dirichlet级数和随机Dirichlet级数的上下级

本文对平面上的零级Dirichlet级数和随机Dirichlet级数的上下级进行了研究.利用Newton多边形,在一定条件下得到了Dirichlet级数和随机Dirichlet级数的上下级与其系数的重要关系.推广了平面上的零级Dirichlet级数和随机Dirichlet级数的增长性的研究范围.     

无限级Dirichlet级数

本文研究了右半平面上无限级的Ｄｉｒｉｃｈｌｅｔ级数及随机Ｄｉｒｉｃｈｌｅｔ级数．这里我们给出一个较宽的系数条件,并证明在一定意义上是最好的;计算无限级Ｄｉｒｉｃｈｌｅｔ级数的精确级;把随机级数的研究引向一般得多的非同分布情况,并得到右半平面上非同分布的无限级随机Ｄｉｒｉｃｈｌｅｔ级数几乎必然（ａ．ｓ．）以虚轴上的每一点为没有有限例外值的Ｂｏｒｅｌ点的结论．     

半平面上无限级Dirichlet级数与随机Dirichlet级数的增长性

研究了半平面上无限级Dirichlet级数及随机Dirichlet级数的增长性,利用熊庆来的型函数及Newton多边形,在较宽的系数条件下给出了几个引理,讨论了半平面上无限级Dirichlet级数关于型函数U(r)的级及下级与系数的关系.得到了相应非同分布的无限级随机Dirichlet级数几乎必然(a.s.)有相同的关系.     

无限级Dirichlet级数的增长性与逼近

文章通过引入β-级的概念讨论了半平面内收敛的无限级Dirichlet级数的增长性.此外,还研究了由Dirichlet多项式逼近β-级Dirichlet级数后的余项,并且得到了余项与增长级的一些关系,以及E_n(f,α)和系数|a_n|之间的等价关系.     

无限级随机Dirichlet级数的值分布

本文研究了右半平面上无限级Dirichlet级数的系数和增长性的关系,给出了一个判定无限级全纯函数Borel点的充分条件,证明了右半平面上ρ(1/σ)级随机Dirichlet级数几乎必然以虚轴上每一点为它的没有有限例外值的ρ(1/σ)级Borel点。     

半平面上零级Dirichlet级数的增长性

本文研究半平面上的零级Dirichlet级数的增长性,定义了半平面上的零级Dirichlet级数的指数级和指数下级,通过用零级Dirichlet级数的系数,得到了其与系数之间的关系.     

全平面上无限级Dirichlet级数的增长性

利用Knopp-Kojima的方法研究在全平面上收敛的无限级Dirichlet级数的增长性,主要是讨论了Dirichlet级数的βU级与下βU级,应用型函数的方法及牛顿多边形,获得了关于βU级增长性的几个定理.     

两类随机控制风险秩序的等价性分析

本文首先对比分析了两类风险秩序:随机控制秩序与对偶随机控制秩序.得到并证明了下述命题:(1)效用自由秩序等价于随机控制秩序;(2)畸变自由秩序等价于对偶随机控制秩序;(3)第一、第二阶随机控制秩序等价于第一、第二阶的对偶随机控制秩序,但对高于三阶的情况由实例说明不一定成立.     

Gompertz分布顺序统计量的一些随机比较

考虑两组相互独立的来自非齐次总体Gompertz分布的样本,给出了最小顺序统计量的反向失效率序、散度序以及凸变换序之间的比较和最大顺序统计量的普通随机序的比较.     

SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS

Some stochastic comparisons of generalized order statistics under the right spread order,the location independent riskier order and the total time transform order are investigated in this paper.The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.     

矩阵的正规化

本文考虑ｎ阶复矩阵可嵌入到ｎ＋１阶的正规矩阵的条件．证明了ｎ＞２阶的复矩阵不一定可嵌入到ｎ＋１阶的正规矩阵,而２阶复矩阵总可嵌入到３阶正规矩阵中．本文还证明了任意ｎ阶复方阵可嵌入到２ｎ阶正规矩阵中     

On different geometric formulations of Lagrangian formalism

We consider two geometric formulations of Lagrangian formalism on fibred manifolds: Krupka's theory of finite order variational sequences, and Vinogradov's infinite order variational sequence associated with the -spectral sequence. On one hand, we show that the direct limit of Krupka's variational bicomplex is a new infinite order variational bicomplex which yields a new infinite order variational sequence. On the other hand, by means of Vinogradov's -spectral sequence, we provide a new finite order variational sequence whose direct limit turns out to be the Vinogradov's infinite order variational sequence. Finally, we provide an equivalence of the two finite order and infinite order variational sequences modulo the space of Euler-Lagrange morphisms.     

Some new results on convolutions of heterogeneous gamma random variables

Convolutions of independent random variables often arise in a natural way in many applied areas. In this paper, we study various stochastic orderings of convolutions of heterogeneous gamma random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [dispersive order, hazard rate order, star order, right spread order, mean residual life order] between convolutions of two heterogeneous gamma sets of variables wherein they have both differing scale parameters and differing shape parameters. The results established in this paper strengthen and generalize those known in the literature.     

向量优化中有效点的存在性

分别在有pre-order的无线性结构的集合和拓扑空间中，给出了有效点的存在性。作为应用，讨论了向量优化问题中解的存在性。最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系。     

Global extrapolation with a parallel splitting method

Extrapolation with a parallel splitting method is discussed. The parallel splitting method reduces a multidimensional problem into independent one-dimensional problems and can improve the convergence order of space variables to an order as high as the regularity of the solution permits. Therefore, in order to match the convergence order of the space variables, a high order method should also be used for the time integration. Second and third order extrapolation methods are used to improve the time convergence and it was found that the higher order extrapolation method can produce a more accurate solution than the lower order extrapolation method, but the convergence order of high order extrapolation may be less than the actual order of the extrapolation. We also try to show a fact that has not been studied in the literature, i.e. when the extrapolation is used, it may decrease the convergence of the space variables. The higher the order of the extrapolation method, the more it decreases the convergence of the space variables. The global extrapolation method also improves the parallel degree of the parallel splitting method. Numerical tests in the paper are done in a domain of a unit circle and a unit square.Supported by the Academy of Finland.     

Necessary and sufficient second order optimality conditions for multiobjective problems with C1 data

In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.     

右半平面上解析的Laplace-Stieltjes变换对数级

本文研究了零级Laplace-Stieltjes变换的增长性问题.利用对数级和对数下级的定义,获得了这类变换具有对数级的特征,即变换的对数级和对数下级与其系数之间的关系,推广了Dirichlet级数的相关结果.