The mixed problem for degenerate elliptic equations of second order

The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order.     

Stabilization of transmission coupled wave and Euler–Bernoulli equations on Riemannian manifolds by nonlinear feedbacks

We consider the transmission system of coupling wave equations with Euler–Bernoulli equations on Riemannian manifolds. By introducing nonlinear boundary feedback controls, we establish the exponential and rational energy decay rate for the problem. Our proofs rely on the geometric multiplier method.     

Wavelet-Galerkin method for solving parabolic equations in finite domains

A novel wavelet-Galerkin method tailored to solve parabolic equations in finite domains is presented. The emphasis of the paper is on the development of the discretization formulations that are specific to finite domain parabolic equations with arbitrary boundary conditions based on weak form functionals. The proposed method also deals with the development of algorithms for computing the associated connection coefficients at arbitrary points. Here the Lagrange multiplier method is used to enforce the essential boundary conditions. The numerical results on a two-dimensional transient heat conducting problem are used to validate the proposed wavelet-Galerkin algorithm as an effective numerical method to solve finite domain parabolic equations.     

下料问题的优化模型及其快速算法

结合生产实际中具体的下料问题,本文建立了该类问题的优化模型,并提出下料方式的遴选三准则,即高利用率优先准则,长度优先准则和时间优先准则.运用本文的算法对一维下料的利用率高达99.6%,机器时间4秒.对二维的利用率为98.9%,机器时间约7秒.     

数据稀疏环境下基于用户主题偏好的协同过滤算法

在B2C电子商务中,user-based协同过滤算法是一种重要的推荐方法,但用户共同评价项目数据稀疏影响了user-based协同过滤算法的应用。鉴于此,在考虑用户消费水平的基础上,利用关联规则挖掘形式化描述商品间的替代相似性;利用基于时间的贝叶斯概率描述商品间的关联关系构建商品网络,通过社会网络分析中的成份分析方法对商品网分析,得到面向用户主题偏好的商品间互补性关系,进而利用这两种商品间关系构建用户主题偏好项目集,最后在数据极度稀疏的环境下通过F₁方法和多样性测量方法与传统推荐算法进行对比实验分析,实验结果显示提高了推荐结果的准确性与新颖性。研究用的所有数据均采集于京东商城网站。本文为缓解数据稀疏问题提出了一种新的方法,扩展了整体网分析方法在商品关系分析中的应用,含有理论与实践双重意义。     

GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY "HARMONIC FUNCTIONS

I.IntroductionBecauseofthecouplingcharacteristicbetweenthemechanicaldeformationandthee1ectricaleffect,piezoelectricmaterialshavebeenwidelyusedintransducersandsmartstructures.Moreandmoreattentionshavebeenpaidonsuchmaterials,andgreatadvanceshavebeenmadeinva…     

商人渡河问题的有解性分析

"商人渡河问题"是一个传统的智力游戏问题,常常作为数学模型、数据结构与智能算法分析等学科中很重要的教学与实验案例被引用.其求解算法尚未得到很好的解决,尤其是问题解的存在性等还缺少一般性和明确的结论.对此,将主要从理论上探讨该类问题何时有解的一般性结论,并给出严格的数学证明.同时还将讨论渡船上安全策略的不同选择对问题求解的影响.     

多背包问题的半定松驰算法

The multiple knapsack problem denoted by MKP (B,S,rn,n) can be defined as follows. A set B of n items and a set S of rn knapsacks are given such that each item j has a profit pi and weight wj,and each knapsack i has a capacity Ci. The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks. MKP (B,S,m,n) is strongly NP-Complete and no polynomial time approximation algorithm can have an approximation ratio better than 0.5. In the last ten years,semi-definite programming has been empolyed to solve some combinatorial problems successfully. This paper firstly presents a semi-definite relaxation algorithm (MKPS) for MKP (B,S,rn,n). It is proved that MKPS have a approximation ratio better than 0. 5 for a subclass of MKP (B,S,m,n) with n≤100, m≤5 and max^nj=1{wj}/min^mi=1={Ci}≤2/3.     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题