Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

无阻尼单摆运动方程反函数形式的精确解

利用函数进行变换,将单摆的二阶非线性微分方程化为一阶非线性微分方程进行积分求解,再利用三角函数变换,最后求出用Legendre椭圆积分表示的无阻尼单摆运动方程反函数形式的精确解。     

正则长波方程的同宿轨道

在对一类正则长波方程定性分析的基础上,得到了其全局相图.由此推知,此类方程具有渐近值相同的钟状孤波解,并求得了其精确孤立波解,即此正则长波方程的同宿轨道.     

Variance bounds for estimators in autoregressive models with constraints

We consider nonlinear and heteroscedastic autoregressive models whose residuals are martingale increments with conditional distributions that fulfil certain constraints. We treat two classes of constraints: residuals depending on the past through some function of the past observations only, and residuals that are invariant under some finite group of transformations. We determine the efficient influence function for estimators of the autoregressive parameter in such models, calculate variance bounds, discuss information gains, and suggest how to construct efficient estimators. Without constraints, efficient estimators can be given by weighted least squares estimators. With the constraints considered here, efficient estimators are obtained differently, as one-step improvements of some initial estimator, similarly as in autoregressive models with independent increments.     

Some results on renewal equations

In this paper solutions of renewal-type integral equations are studied. It is proved that a recursively spades;efined approximation to the solution has some nice convergence properties. Some simple bounds and other results on the renewal function and the renewal spades;,ensity are obtained.     

On Max-Multiscaling Distributions as Extended Max-Semistable Ones

Abstract

We introduce max-multiscaling distributions as solutions to a functional equation which, in a natural way, extends the one fulfilled by max-semistable distributions. We establish that strictly max-multiscaling distributions are products of at most two max-semistable distributions. Next, we show how to obtain these solutions as limit laws of normalized maximum of suitable independent sequences of random variables when sample size has geometric growth.     

一类n阶非线性微分方程多点边值问题解的存在性

利用Leray-Schauder度理论建立了n阶非线性微分方程y(n)=f(x,y,y′,…,y(n-1)),n≥3,满足多点边界条件yn-1(0)-hyn-2(0)=0,y(i)(ηi)=0,i=0,1,…,n-3,y(n-1)(1)+ky(n-2)(1)=0.的多点边值问题的解存在性的几个充分条件,并给出了应用举例.     

分析电磁散射问题的MGFFT方法

采用多重网格法（ＭＧ）分析电大尺寸物体的电磁散射，这种ＭＧ方法与已有的几种多重矩量法有本质的不同，与其他多层方法相比，它是一种高效率的迭代方法。再利用积分方程的卷积特性引入ＦＦＴ方法快速计算迭代过程中矩阵与矢量的乘积，从而构成ＭＧＦＦＴ新算法，数值结果表明ＭＧＦＦＴ方法具有很高的计算效率，适用于电大尺寸问题的分析。     

弹性力学平面问题的双调和方程的格林函数解法

讨论了弹性力学双调和方程４ Ｕ ＝ ０ 的格林（Ｇｒｅｅｎ） 函数解法     

一类二阶非线性差分方程正解的存在性

主要利用推广的Riccati变换,建立了一类比较广泛的二阶非线性差分方程正解存在的充分和必要条件.