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     

Diffusion instability of a uniform cycle bifurcating from a separatrix loop

We consider the boundary value problem

Reflection and transmission of plasma waves at the interface of crystallites

A linearized problem of the reflection and transmission of a plasma wave at the boundary of a half-space (namely, the plane separating two crystallites) is formulated and analytically solved. The electron distribution function and the electric field inside the half-space of a degenerate plasma are found. The reflection and transmission coefficients are determined as functions of the input parameters of the problem. The longwave limit (i.e., the resonance case when the oscillation frequency of the self-consistent electric field is close to the natural (Langmuir) oscillation frequency) is analyzed.     

Generalization of Ulam stability problem for Euler-Lagrange quadratic mappings

In 1968 S.M. Ulam proposed the problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?” In 1978 P.M. Gruber proposed the Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?” In this paper we solve the generalized Ulam stability problem for non-linear Euler-Lagrange quadratic mappings satisfying approximately a mean equation and an Euler-Lagrange type functional equations in quasi-Banach spaces and p-Banach spaces.