Architecture Singularity Analysis of 4-U■S/U■U 5-DOF Parallel Mechanism

Architecture singularity of a parallel mechanism with five degrees of freedom (DOF) is analyzed. Such mechanism consists of a movable platform connected to the base by five active limbs. Four of them are identical 6-DOF limbs and the last one has the same DOF as the specified DOF of the movable platform. Based on the kinematics analysis, two categories of architecture singularities for such mechanism are proposed. Then the sufficient condition for each singularity is researched. Results show that the mechanism is singular when it employs each category of the proposed architecture, provided that it satisfies the corresponding sufficient condition. It can be concluded that the proposed two categories of architecture singularities should be avoided with the following dimensional synthesis of such mechanism.     

一类2×2拟线性双曲守恒律组的奇性形成

本文在文[3]的基础上,进一步给出了包含均熵气体动力学方程组在内的一类2×2拟线性双曲守恒律组的奇性形成结果,证明了在“真正大初值”条件下,Lax定理仍然成立。     

宇宙的核式结构模型

根据原子核式结构模型和量子力学理论提出和论述宇宙核式结构的模型,利用宇宙核式结构模型解释了宇宙膨胀现象、哈勃定律、宇宙的产生和演化、奇点等几个重大问题,并进一步说明负(反)质量物质的存在.     

一类具有强奇性的矩阵型偏微分方程的正解的存在性

研究矩阵型强奇异偏微分方程 其中,Ω⊂Rⁿ是有界开集,M（x）是定义在Ω上的实对称矩阵,-p<-1,0 < q < 1,λ>0是参数,f（x）∈L¹（Ω）,f（x）>0 a.e.in Ω。证明,如果存在u₀ ∈H₀¹（Ω）满足∫_Ωf（x）|u₀|^1-pdx <+∞,则对任意的λ>0上述方程都有正H₀¹-解,即慢速解。我们注意到,对于奇异方程,古典解即C²（Ω）∩C（Ω）解不一定是H₀¹（Ω）解。     

挑开人性与社会裂缝的剑客李冯

广西三剑客中,李冯的作品特点最鲜明,最容易命名。其小说明显分为两类：一类是戏仿历史题材,另一类是现实经验题材。两类小说均有鲜明的文体独立性。前者对经典作品中的人物取一种分析与实验的态度,既有解构的游戏意识,也有建构的历史冲动。后者中的人物都有一种不同于世俗的内心激情,这种人物形象的出现,显示出我们赖以生存的社会业已出现的巨大变化。     

一类非线性三阶两点边值问题的三重正解

根据非线性项函数的增长与相应积分方程的特性构造了高度函数,利用高度函数的积分给出了一类非线性三阶两点边值问题解的先验界及三个正解的存在性。     

多输入多输出非线性系统ZG控制方法框架展望

非线性系统的跟踪控制及其奇异点问题求解已在科学和工程领域引起广泛关注。基于作者团队前期主要关于单输入单输出非线性系统跟踪控制的工作,本文进一步提出了面向多输入多输出非线性系统跟踪控制的ZG控制方法的框架与展望。利用该ZG控制方法,可以设计能同时解决多输入多输出非线性系统的跟踪控制问题及可能出现的奇异点问题的ZG控制器。     

A collaborative filtering similarity measure based on singularities

Recommender systems play an important role in reducing the negative impact of information overload on those websites where users have the possibility of voting for their preferences on items. The most normal technique for dealing with the recommendation mechanism is to use collaborative filtering, in which it is essential to discover the most similar users to whom you desire to make recommendations. The hypothesis of this paper is that the results obtained by applying traditional similarities measures can be improved by taking contextual information, drawn from the entire body of users, and using it to calculate the singularity which exists, for each item, in the votes cast by each pair of users that you wish to compare. As such, the greater the measure of singularity result between the votes cast by two given users, the greater the impact this will have on the similarity. The results, tested on the Movielens, Netflix and FilmAffinity databases, corroborate the excellent behaviour of the singularity measure proposed.     

计算一类方程的三阶折叠点

讨论x″ λexp(x/1 μx)=0 x(0)=x(1)=0 (λ,μ为两个实参数)的三阶折叠点问题,并用Matlab画图实现。     

一类三次平面自治系统的异宿环分支

对一类给定的三次多项式系统,寻找该系统的一类特殊代数不变曲线,得到这些代数不变曲线为异宿轨线的条件;并分析该系统的奇点．讨论了闭轨线的存在性问题,得到系统在相平面的单位圆盘叉上的全局结构,从而得出相图随参数变化的情况．