Multidimensional generalization of the Korous inequality

This paper deals with some qualitative properties of orthogonal polynomials in several variables. The boundedness and relations between two sets of orthonormal polynomials associated with an arbitrary weight function and its extension are investigated. It presents an analogy to Korous' result for general orthogonal polynomials in one variable.     

On the absolute convergence of multiple fourier series

Let f: R ^N → C be a periodic function with period 2π in each variable. We prove suffcient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple Fourier series. This research was started while the first author was a visiting professor at the Department of Mathematics, Texas A&M University, College Station during the fall semester in 2005; and it was also supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192.     

On Riesz transforms and maximal functions in the context of Gaussian Harmonic Analysis

The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type independently of their orders.

     

Resonances in Loewner equations

We prove that given a Herglotz vector field on the unit ball of Cn of the form H(z,t)=(a₁z₁,…,anzn)+O(²|z|) with for all j, its evolution family admits an associated Loewner chain, which is normal if no real resonances occur. Hence the Loewner–Kufarev PDE admits a solution defined for all positive times.     

土壤初始温度及地下水渗流对多供一回中心回水管换热器的影响

为研究地下水渗流对多供一回中心回水管换热器与周围岩土体换热情况的影响,以黄土高原地区实际土壤环境为依托,采用DesignMoldeler软件建立多供一回中心回水管换热器及周围土壤的三维热渗耦合传热模型,利用Meshing软件对模型进行网格划分,并采用Fluent软件对其进行数值模拟.分析岩土体分层条件下,沿埋深方向变化的土壤初始温度、不同地下水渗流方向及间歇运行模式对多供一回中心回水管换热器换热的影响.研究结果表明:分层土壤初始温度不同对不同类型的多供一回中心回水管换热器影响较大,故不可忽略;不同地下水渗流方向对不同类型的多供一回中心回水管换热器影响不同,存在一个最佳渗流方向使得换热效率达到最高;间歇运行模式可提高热泵运行效率,减小埋管的设计长度,从而减少初投资.     

改进遗传算法及其在聚类分析上的应用

本文提出的改进遗传算法通过在选择操作前对种群进行相似性检查来保持群体多样性,解决进化种群早熟问题,提出了与相似率和迭代次数相关的变异概率公式来保持种群多样性和算法收敛性,通过在UCI的WINE和IRIS两组数据集上与c-means算法的聚类实验结果比较,证明了改进遗传算法的有效性．     

多复变广义全纯函数的一个带Haseman位移的非线性边值问题

研究多复变广义全纯函数的一个带Haseman位移的非线性边值问题. 通过定义相关算子并研究它们的性质, 得到了多复变广义全纯函数的Plemelj公式, 并将边值问题转化为积分方程问题, 利用积分方程方法和Schauder不动点原理证明了解的存在性, 得到了解的积分表达式.     

多指标决策优序法在试验评价中的应用

本文利用优序法评价多指标正交设计试验结果,从而求出最佳试验方案,经生产实践验证比较理想。     

激光驱动器能源系统实验平台测控系统的研究

 为了提高激光驱动器能源系统运行的稳定性、可靠性、安全性,研制了一套能源系统实验平台的测控系统。该测控系统采用RS-232串行通讯、多线程程序设计来完成并行处理,具有较强的抗干扰能力,可远距离的进行自动控制、数据采集,并能及时的进行数据处理和分析,显示报表并打印。该项研究的结果为大型激光装置的相关系统设计提供了依据。