求一类非齐次微分方程特解的待定算子法

给出了求一类非齐次微分方程L(D)y=f(x)特解的待定微分算子解法.即通过求与方程相关的待定微分算子R(D),从而得出非齐次微分方程的特解y=R(D)f(x).     

Some Periodic and Non-Periodic Recursions

 It is well known that the recurrence relations

Recursions for multivariate compound phase variables

We show how to generalize the result given in [Eisele, K.-Th., 2006. Recursions for compound phase distributions. Insurance: Math. Econom. 38, 149-156] to the multivariate case, i.e. we find a Panjer-like recursion principle for the distribution of a multivariate compound phase variable. Recursion formulas and procedures for the bivariate case are given in detail. We give a possible application for agricultural risks and calculate concrete examples via a VB-program.     

Solving Equations Using Models

<正>INVESTIGATE The scale at the right is balanced,and the bag contains a certain number of blocks.1.Suppose you cannot look in the bag.How can you find the number of blocks in the bag?2.In what way is a balanced scale like an equation?3.What does it mean to solve an equation?To solve an cquation using models,you can use these steps.·You can add or subtract the same number of counters from each side of the mat.·You can add or subtract zero from each side of the mat.ACTIVITY Work with a partner.     

Null Space Algorithm and Spanning Trees in Solving Darcy's Equation

A Null Space algorithm is considered to solve the augmented system produced by the mixed finite element approximation of Darcy's Law. The method is based on the combination of a LU factorization technique for sparse matrices with an iterative Krylov solver. The computational efficiency of the method relies on the use of spanning trees to compute the LU factorization without fill-in and on a suitable stopping criterion for the iterative solver. We experimentally investigate its performance on a realistic set of selected application problems.This revised version was published online in October 2005 with corrections to the Cover Date.     

Recursions for the Individual Risk Model

In the actuarial literature,several exact and approximative recursive methods have been proposedfor calculating the distribution of a sum of mutually independent compound Bernoulli distributed randomvariables.In this paper,we give an overview of these methods.We compare their performance with the straight-forward convolution technique by counting the number of dot operations involved in each method.It turns outthat in many practicle situations,the recursive methods outperform the convolution method.     

Recursions for convolutions of discrete uniform distributions revisited

In the present paper we apply the De Pril transform to obtain recursions for convolutions of discrete uniform distributions. Some of the recursions represent improvements and generalisations of recursions presented by Sundt (1988) and seem to be very suitable for application in spread-sheet programs.     

利用Riccati方程求解Burgers方程

应用李群理论中的伸缩变换群,把非线性二阶偏微分方程-Burgers方程转化为非线性非齐次一阶常微分方程-Riccati方程,将Riccati方程转化为Bernoulli方程和齐次线性二阶常微分方程,从而找到了Riccati方程的许多解,最后进一步求出了Burgers方程许多新的解析解.     

一类非齐次树上的非齐次马尔可夫链的若干强极限定理

极限定理一直是国际概率论界研究的中心课题之一.通过构造适当的辅助非负鞅而给出了一类特殊非齐次树上可列状态的非齐次马尔可夫链场的若干强极限定理.     

非齐次树上m重非齐次马氏信源的一个强偏差定理

研究给出了非齐次树上m重非齐次马氏信源的一个强偏差定理.     

非齐次线性方程组的半正解

线性方程组的不带负分量的非零解向量称为半正解.本文给出非齐次线性方程组AX= b (b≠0)的半正解结构,进而得到该类线性方程组有半正解的充分条件和必要条件以及唯一半正解的充要条件.     

单纯形法解装卸工问题

本文提出装卸工问题,对一种特殊情况下的装卸工问题用单纯形方法求得了它的最优解和最优值.     

用龙格-库塔法求解非线性方程组

本文介绍了一种求解非线性方程组的新方法龙格-库塔法。     

Recursions for characteristic numbers of genus one plane curves

Characteristic numbers of families of maps of nodal curves toP ² are defined as intersection of natural divisor classes. (This definition agrees with the usual definition for families of plane curves.) Simple recursions for characteristic numbers of genus one plane curves of all degrees are computed.     

Duality of Non-Homogeneous Central Herz-Morrey-Musielak-Orlicz Spaces

We determine the associate space of non-homogeneous central Herz-Morrey-Musielak-Orlicz space \(\mathcal {H}^{\Phi ,q,\omega }(\textbf {R}^{N})\). We also determine the associate spaces of the space \(\underline {\mathcal {H}}^{\Phi ,q,\omega }(\textbf {R}^{N})\) and its complementary space \(\overline {\mathcal {H}}^{\Phi ,q,\omega }(\textbf {R}^{N})\).     

A Method for Testing Nested Point Null Hypotheses Using Multiple Bayes Factor

As a flexible Bayesian test criterion for nested point null hypotheses, asymmetric and multiple Bayes factors are introduced in the form of a modified Savage-Dickey density ratio. This leads to a simple method for obtaining pairwise comparisons of hypotheses in a statistical experiment with a partition on the parameter space. The method is derived from the fact that in general, the asymmetric Bayes factor can be written as the product of the Savage-Dickey ratio and a correction factor where both terms are easily estimated by means of posterior simulation. Analyses of a censored data problem and a serial correlation problem are illustrated for the method. For these cases, the method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required tests.     

Using a Conic Formulation for Finding Steiner Minimal Trees

We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an ε-optimal solution for this latter problem using an interior-point algorithm.