Statistical estimation of nonlinear regression functions

In order to obtain the first and second moments of a matrix quadratic form under normality assumptions its moment generating function will be derived and then differentiated.

Use is being made of matrix differential calculus as developed by the author     

On Some Applications of a Symbolic Representation of Non Centered Lévy Processes

By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to Lévy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the Kailath-Segall formula in terms of cumulants and we recover simple closed-forms for several families of polynomials with respect to not centered Lévy processes, such as the Hermite polynomials with Brownian motion, Poisson-Charlier polynomials with Poisson processes, actuarial polynomials with Gamma processes, first kind Meixner polynomials with Pascal processes, and Bernoulli, Euler, and Krawtchuk polynomials with suitable random walks.     

一种线性闭环拥塞控制方案的渐近性能分析

分析了一种线性闭环拥塞控制方案的渐近性能；证明了该方案的稳态无振荡特性。利用布朗模型近似背景业务，从理论上探讨了背景业务对实现该方案的系统性能的影响。得出了在背景业务干扰下，该方案中各参数所应作的调整，以达到渐近意义下的系统最佳性能。     

改革农科微积分课程考核方式探讨

考试是测验与评估学生学习效果和教师教学效果的一种基本方式,是教学过程的一个重要环节,它对人才的培养具有深远影响。文章根据在微积分课程教学中推进考核方式改革的实践,分析了在以应试教育为主的考试模式下,考试内容、考试方法等方面存在着的许多弊端;提出了在改革考试方式中“建立考试管理机制、确立以检测能力和素质为主体的考试内容与评分标准、丰富考试方法和形式、使成绩构成多元化、考题类型多样化、增加功能性、改变评分观念、改革记分方式、完善教考分离制度”等建议。     

微积分辩证认识简要

微积分在全部数学的历史中是一个最大创造,微积分发现的全部历史中,展现了辩证思维法的胜利,阿基米德的“穷竭法”,刘徽的“割圆术”,卡瓦列里的不可分量,费马的求切线方法,均是有力的说明。牛顿和莱布尼茨关于建立微积分而作出的杰出贡献,就在于他们分别提出了微积分的基本原理、三个重要概念:流量、流数、瞬和“变量”数学的思想体系。马克思和恩格斯则自觉地运用辩证方法对微积分作了深入探讨。     

THE non-null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix is diagonal

This article deals with the exact non-null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix in a multinormal distribution is diagonal. The exact non-null moments as well as the exact non-null distribution are derived. The distribution is also expressed in computable form with the help of inverse Mellin transform and calculus of residues. The results obtained in this article are useful in studying the power of testing several correlation coefficients simultaneously.     

2n值命题演算的 语义及其在大数据中的应用

本文的目标是建立2n值命题演算(2n-Valued Propositional Calculus,2nP)的语义,为大数据科学奠定逻辑基础.描述了2n值逻辑的真值形式、采用位结构刻画了联结词的功能,并建立了赋值映射;根据多值逻辑的特点,以数据冗余、key-value模型为例,直觉地讨论了2n值逻辑应用于大数据研究的有效性;初步分析了2nP语义与经典命题逻辑语义之间的关系,并展望了2nP在计算机科学、人工智能、信息技术等学科的应用前景.     

A Dynamic Equilibrium Model of International Portfolio Holdings

This paper develops a continuous‐time equilibrium model of a two‐country exchange economy with heterogeneous agents and nontraded goods. Nontraded goods play the role of state variables that shift the marginal utility of traded goods. This affects prices and generates dynamic hedging demands that explain the well documented home bias puzzle in international equity portfolios. When calibrated to both consumption and production data, the model is able to generate significative home bias in equity portfolios. A new methodology, based on Malliavin calculus, is presented to solve for the portfolio policies along the equilibrium path. This methodology allows one to reduce the determination of equilibrium portfolio holdings to the solution of a linear algebraic system, rather than a partial differential equation.