Complete controllability for abstract measure differential systems

In this paper, we investigate the complete controllability for abstract measure differential systems. Firstly, we introduce several new concepts about complete controllability for abstract measure differential systems. Then, on the basis of the Sadovskii fixed‐point theorem, we give sufficient conditions for complete controllability for a class of abstract measure differential systems. The compactness of the semigroup generated by some operator is unnecessary in this paper, and we show that our results, dealing with complete controllability problem for an ordinary differential system in infinite‐dimensional Banach space, are also less conservative than that in the previous literature. Copyright © 2012 John Wiley & Sons, Ltd.     

MC-MLAS: Multi-channel Minimum Latency Aggregation Scheduling in Wireless Sensor Networks

Data aggregation is a key, yet time-consuming functionality in wireless sensor networks (WSNs). Multi-channel design is a promising technique to alleviate interference as a primary reason for long latency of TDMA aggregation scheduling. Indeed, it provides more potential of parallel transmissions over different frequency channels, thus minimizing time latency. In this paper, we focus on designing a multi-channel minimum latency aggregation scheduling protocol, named MC-MLAS, using a new joint approach for tree construction, channel assignment, and transmission scheduling. To our best knowledge, this is the first work in the literature which combines orthogonal channels and partially overlapping channels to consider the total latency involved in data aggregation. Extensive simulations verify the superiority of MC-MLAS in WSNs.     

On stability delay bounds of simple input-delayed linear and non-linear systems: Computational results

This paper deals with the problem of delay size stability analysis of single input-delayed linear and nonlinear systems. Conventional reduction, reduction linked by sliding mode, and linear memoryless control approaches are used for simple input-delayed systems to obtain the stability conditions. Several first order examples are investigated systematically to demonstrate the capabilities and limitations of the advanced stability analysis techniques including Lyapunov-Krasovskii functionals, Newton-Leibniz formula, and a newly addressed Lagrange mean value theorem. Numerical comparative results show the usefulness and effectiveness of the advanced delay size analysis techniques proposed in this paper.     

突变理论在堤防安全综合评价中的应用

堤防工程安全受洪水、地震、堤身土质及堤基结构等多种因素影响,且其作用机理复杂,一旦失事危害巨大.将突变理论引入堤防工程安全评价中,根据突变评价原理,建立了堤防工程安全综合评价指标体系,参照大坝安全评价标准,结合堤防工程特点,建立了堤防工程安全等级划分标准,利用突变评价的归一公式计算了北江大堤石角堤段设计洪水情况的安全评价指标值,根据等级划分标准,从计算结果分析得知该段堤防在设计洪水工况下安全性较高,为堤防工程安全管理提供科学依据.     

知识的属性扰动规律的不等式关系

知识的属性扰动引起知识规律的变化,这些变化的规律称为扰动规律.利用单向S-粗集和单向S-粗集对偶,给出属性扰动的知识规律的上规律.下规律的概念,并对知识规律与属性扰动的知识规律进行了讨论,提出了属性扰动知识规律(上规律,下规律)的不等式定理.     

S-粗集与数据挖掘单位圆特征

给出单向S-粗集(one direction singular rough sets)、单向S-粗集对偶(dual of one direction singular rough sets)的结构。单向S-粗集与单向S-粗集对偶是改进Z.Pawlak粗集得到的,单向S-粗集与单向S-粗集对偶具有动态特性。给出单向S-粗集、单向S-粗集对偶与Z.Pawlak粗集的关系。S-粗集具有三类形式:单向S-粗集、单向S-粗集对偶、双向S-粗集,利用单向S-粗集、单向S-粗集对偶,给出数据内挖掘、数据外挖掘概念,给出数据内挖掘的外同心圆定理、数据外挖掘的内同心圆定理,并给出其应用。S-粗集是粗集理论与应用研究的新分支。     

Spectral preconditioning of Krylov spaces: Combining PLS and PC regression

In regularized regression the vectors that lie in Krylov and eigen subspaces, formed in PLS and PC regressions respectively, provide useful low dimensional approximations for the LS regression coefficient vector. By preconditioning the LS normal equations we provide a framework in which to combine these methods, and so exploit both of their respective advantages. The link between the proposed method to orthogonal signal correction and to cyclic subspace regression is made. The performance of the proposed solution in reducing the dimension of the regression problem, and the shrinkage properties of the resulting coefficient vector, are both examined.     

Automatic Construction and Verification of Isotopy Invariants

We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks. In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach, we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results. This work was previously beyond the capabilities of automated reasoning techniques. The author’s work was supported by EPSRC MathFIT grant GR/S31099.     

A generalization of the Curtis–Hedlund theorem

Let A be a set and let G be a group, and equip A^G with its prodiscrete uniform structure. Let τ:A^G→A^G be a map. We prove that τ is a cellular automaton if and only if τ is uniformly continuous and G-equivariant. We also give an example showing that a continuous and G-equivariant map τ:A^G→A^G may fail to be a cellular automaton when the alphabet set A is infinite.     

Parallel block tridiagonalization of real symmetric matrices

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which frequently results from applications with strong locality properties, a heuristic parallel algorithm is used to transform it into a block tridiagonal matrix such that the eigenvalue errors remain bounded by some prescribed accuracy tolerance. For a dense matrix without any usable structure, orthogonal transformations are used to reduce it to block tridiagonal form using mostly level 3 BLAS operations. Numerical experiments show that block tridiagonal structure obtained from this algorithm directly affects the computational complexity of the parallel block tridiagonal divide-and-conquer eigensolver. Reduction to block tridiagonal form provides significantly lower execution times, as well as memory traffic and communication cost, over the traditional reduction to tridiagonal form for eigensystem computations.