一个矩阵不等式和Bayes无偏估计（英）

ＡｎＩｎｅｑｕａｌｉｔｙｏｆＭａｔｒｉｘａｎｄＢａｙｅｓＵｎｂｉａｓｅｄＥｓｔｉｍａｔｅｓＺｈａｎｇＹａｏｔｉｎｇ（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，２００４３３）ＡｂｓｔｒａｃｔＴｈｅｉｎｅｑｕａｌｉ...     

GCD和GCUD矩阵行列式的一个不等式（英）

Let S = {x₁, x₂,..., x_n} be a set of distinct positive integers. The n x n matrix (S) whose i, j-entry is the greatest common divisor (x_i, x_j) of x_i and x_j is called the GCD matrix on S. A divisor d of x is said to be a unitary divisor of x if (d, x/d) = 1. The greatest common unitary divisor (GCUD) matrix (S^**) is defined analogously. We show that if S is both GCD-closed and GCUD-closed, then det(S^**) ≥ det(S), where the equality holds if and Only if (S^**) = (S).     

广义相交体的不等式（英文）

1988年,Lutwak首次明确地提出了经典相交体的概念.2005年,Haberl和Ludwig对经典相交体进行了推广,给出了L_p-相交体的概念.最近,汪卫等提出了广义相交体的概念.主要利用L_p-Brunn-Minkowski理论、Hlder积分不等式和Minkowski积分不等式,研究了广义相交体的单调性,并建立了关于径向线性组合和L_p-调和Blaschke组合的Brunn-Minkowski型不等式.     

广义半正定矩阵的一个不等式

在广义半正定矩阵上推广、改进了Ｏｐｐｅｎｈｅｉｍ不等式。     

一个广义Bihari型不等式及其应用

本文对定义于一定有序局部紧空间上的向量值函数建立一个Ｂｉｈａｒｉ型积分不等式，并给出其对于非线性Ｖｏｌｔｅｒｒａ型积分方程的若干应用。     

关于广义对数平均的一个不等式

对于两个正数ａ，ｂ，称Ｓｐ（ａ，ｂ）＝ｂｐ－ａｐｐ（ｂ－ａ）１ｐ－１ａ≠ｂｂａ≠ｂ｛，ｐ≠０，１为广义对数平均（ｓｔｏｌａｒｓｋｙ平均），文［１］指出，当ａ≠ｂ时，Ｓｐ（ａ，ｂ）是ｐ的严格递增函数，因而当ｐ＞２时，对于ａ≠ｂ，有Ｓｐ（ａ，ｂ）＞Ｓ２（...     

关于Erdos序列的一个定理（英）

ＡＴｈｅｏｒｅｍｏｎＥｒｄｏｓＳｅｑｕｅｎｃｅｓＳｈｅｎＺｅｃｈｕｎ（ＥｎｇｉｎｅｅｒｉｎｇＣｏｌｌｅｇｅｏｆＡｎｓｈａｎＩｒｏｎ＆ＳｔｅｅｌＣｏｍｐａｎｙＡｎｓｈａｎ１１４００２）ＡＴｈｅｏｒｅｍｏｎＥｒｄｏｓＳｅｑｕｅｎｃｅｓＳｈｅｎＺｅｃｈｕｎ...     

关于Feller的一个未解决问题（英）

In Feller＇s well-known book, Volume Ⅱ, second edition [1], there is a very interesting problem：No.29 on p.288 with a large Hint, as follows. If a probability distribution F has the property：for some α 〉 0,     

广义回形折线中的一个三角不等式

本文给出广义回形折线中的一个三角不等式，并略述其应用．关于广义回形折线及其内角、环数等概念，请参看拙文［１］，这里沿用而不复述．定理设ｎ边广义回形折线Ａ１Ａ２Ａ３…ＡｎＡ１的各内角∠Ａｉ（ｉ＝１，２，…，ｎ）都是劣角，Ｐ是它的任一同侧点，记θｉ＝∠Ｐ...     

第二类Chebyshev多项式系数的绝对值和的卷积

本文主要的目的是利用广义Fibonacci多项式的生成函数及其偏导数来研究第二类Cheby-shev多项式卷积的计算,并给出—个有趣的计算公式.     

混合广义Jacobi和Chebyshev谱配置法求解时间分数阶对流扩散方程

研究时间Caputo分数阶对流扩散方程的高效高阶数值方法.对于给定的时间分数阶偏微分方程,在时间和空间方向分别采用基于移位广义Jacobi函数为基底和移位Chebyshev多项式运算矩阵的谱配置法进行数值求解.这样得到的数值解可以很好地逼近一类在时间方向非光滑的方程解.最后利用一些数值例子来说明该数值方法的有效性和准确性.     

关于广义变分不等式与广义拟变分不等式

本文在非常一般的框架下,建立了极大极小不等式,广义变分不等式和广义拟变分不等式,证明了解的存在定理,且它们是在非紧集上得到的,从而推广和改进了[3～13]中的相应结果.     

Derivatives of Faber Polynomials and Markov Inequalities

We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erd s. We also prove a new bound for Faber polynomials on piecewise smooth domains.     

A Generalized Markov Sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.     

广义集值拟变分不等式

本文研究了一类广义集值拟变分不等式,得到了这类广义集值拟变分不等式解存在的一个充分条件,并给出了近似解的迭代算法.     

Generalized holomorphic orthogonal function systems over infinite cylinders

In this paper we construct two distinct generalized holomorphic orthogonal function systems over infinite cylinders in . Explicit representation formulae and properties of the obtained basis functions are given. As an application, we present some plot simulations that illustrate the results of this work. Copyright © 2014 John Wiley & Sons, Ltd.     

黎曼流形上关于p-Laplace热方程的Harnack不等式

本文主要讨论Ｒｉｅｍａｎｎ流形上型如：ｄｉｖ（ｕ~ｐ－２ｕ）－ｕ~ｐ－２ｕ－２ｔ＝０（ｐ＞１）的非线性抛物方程（ｐ＞１）,导出其正解的局部Ｈａｒｎａｃｋ不等式,推广了文献［１,２］中的结果．