The rank one mixed μ problem and ‘kharitonov-type’ analysis

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so-called ‘affine parameter variation’ problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated ‘Kharitonov-type’ results have been proven.     

基于泛布尔代数的结构振动控制机理

本文介绍了泛布尔代数的数学模型、公理体系和化简方法 ;针对高层建筑的特点 ,舍弃寻求被控制对象的精确数学模型 ,提出了“基于泛布尔代数的结构振动控制” ,分析了其的逻辑机理 ,建立了基于泛布尔代数的MR阻尼器的半主动控制算法。应用本文提出的控制方针对 12层的高层结构受控地震反应的模拟仿真 ,结果表明其控制简单、灵活、方便 ,能满足这种结构的控制要求。     

Logical errors in database SQL retrieval queries

SQL is often used to express questions imposed by users. It is well known that this process is not error-free in that it may result in syntactically or semantically incorrect SQL queries. This article is meant to probe deeper into SQL queries that are incorrect, due to delusion errors. A classification of natural language questions will be introduced. The purpose of this classification is two-fold. Firstly, it gives insight into possible errors and enables us to distinguish between types of errors. Secondly, it is a means of determining the influence of measures (for instance, SQL training) that can be taken to reduce the number of aforementioned errors. For discussion, several of these measures will be presented and related to the classification.Abbreviations RA Relational algebra - SQL structured query language     

形态学边缘检测的新算法及其应用

提出了一种基于数学形态学的边缘检测的所算法，该算法具有简便和灵活可编程控制等优点，比原来主算法更国完善，在实际应用中有着很好的前景，并给出了实验结果。     

再论变化电磁场中带电超微粒子的精确量子论

利用创新的SU(1 ,1 )Lie代数理论及SO(3)Lie代数理论 ,得到变化电磁场中带电超微粒子的精确量子论 ,由此进一步明确微观领域中的时空概念     

A stability classification method and its application to pipelined solution of linear recurrences

A new method of classification for numerical stability of parallel algorithms is proposed based on the theoretical foundation of forward error analysis. It partitions the algorithms according to their asymptotic stability—a measure introduced to relate the limiting behavior of the stability to the size of the problem. Using this method, the stability aspect of the pipelined solution technique for first-order and second-order linear recurrences—the core of a tridiagonal linear equation solver—is studied. In particular, it shows that the pipelined solution method of the first-order linear recurrences has the same degree of stability as the commonly used sequential evaluation algorithms. The stability problems of sequential and pipelined solution methods of the second-order linear recurrences are also studied.     

EXTENSION OF THE RELATIONAL DATABASE AND ITS ALGEBRA WITH ROUGH SET TECHNIQUES

This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain. There are several obvious applications for which the rough relational database model can more accurately model an enterprise than does the standard relational model. These include systems involving ambiguous, imprecise, or uncertain data. Retrieval over mismatched domains caused by the merging of one or more applications can be facilitated by the use of indiscernibility, and naive system users can achieve greater recall with the rough relational database. In addition, applications inherently “rough” could be more easily implemented and maintained in the rough relational database.     

THz-TDS signal analysis and substance identification via the conformal split

A terahertz time-domain spectroscopy(THz-TDS)imaging system can obtain high-dimensional signals with substance fingerprint information.By introducing geometric algebra,a novel signal analysis approach to THz-TDS signals is developed based on an optical physical mechanism.Using this approach,signals are represented with vectors in the high-dimensional real vector space.Geometric distribution properties and algebraic relationships of THz-TDS signals are deduced.It is proved that every complex refractive index of substances relates to a unique 2-blade,the vectors corresponding to the samples of the same substance are collinear and belong to the intrinsic 2-blade of the substance.When decomposed through the conformal split with respect to a 2-blade,THz-TDS signals of high dimensionality can be related to vectors in a 2-dimensional subspace.Based on the conformal split properties we deduced,two criteria for substance identification on the basis of THz-TDS signals are proposed.Accordingly,a novel substance identification method via the conformal split is presented.In the method,the 2-blade related to each "known" substance is calculated with two vectors corresponding to THz-TDS signals measured from samples of the substance but with dierent thicknesses.Using the conformal split with respect to those 2-blades,an identified vector corresponding to a THz-TDS signal is linearly related to the vector in a 2-dimensional subspace.The substance of a sample can be identified using criteria on the projected vectors in the subspaces.This method can contribute to accurate classification and identification.Finally,two experiments are presented that show the feasibility and accuracy of this method.     

Matlab在线性代数教学中的应用研究

线性代数是工、管、理科各专业的数学必修课,是学生学习后续专业课的数学工具,同时也是研究生入学必考的科目。把Matlab应用到线性代数的教学中,在课堂上可以吸引同学们的注意力,激发学生学习本门课程的热情,提高教学效果。学生们在后续的专业课学习和工作中可以灵活使用线性代数这门数学工具。笔者结合课堂教学实践,举例说明Matlab在线性代数教学中的作用。     

概念代数在本体合并中的应用

本体合并是本体集成的一种较为有效的方式,是用于解决本体异构以实现本体资源重用和共享的一种方法。引入概念代数以弥补本体的概念深度表达不够、形式化程度低等缺陷。将本体与概念代数结合,提出一种基于概念代数的本体表示方法,其恰好符合领域专家构建本体的意识活动,可以更好地表达和处理知识。概念代数是一种抽象的数学结构,形式化程度较高,并且其概念之间的认知关系更便于进行知识推理。利用概念代数将本体表示为可视化的概念网形式,进而利用概念代数的运算实现概念之间的合并及关联,提出一种基于概念代数的本体合并方法,是对概念代数应用到本体的一种尝试,为本体的处理提供了一个新的视角。