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On the Completeness of eigen and root vector systems for fourth-order operator matrices and their applications

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Chinese Physics B 2011年第10期20卷 8-14页

作者：王华阿拉坦仓黄俊杰 School of Mathematical Sciences Inner Mongolia University College of Sciences Inner Mongolia University of Technology

In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and Completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

关键词： operator matrix eigenvalue problem eigenvector root vector Completeness

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

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Applied Mathematics and Mechanics(English Edition) 2012年第3期33卷 385-398页

作者：王华阿拉坦仓黄俊杰 School of Mathematical Sciences Inner Mongolia University College of Sciences Inner Mongolia University of Technology

This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete Completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the Completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

关键词： upper triangular infinite-dimensional Hamiltonian operator eigenvector root vector multiplicity Completeness

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

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Chinese Physics B 2010年第12期19卷 9-17页

作者：黄俊杰阿拉坦仓王华 School of Mathematical Sciences Inner Mongolia University Department of Mathematics College of ScienceInner Mongolia University of Technology

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of Completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

关键词： off-diagonal operator matrix Completeness double eigenfunction expansion method elasticity theory

Lattice-valued modal propositional logic and its Completeness

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Science China(Information Sciences) 2010年第11期53卷 2230-2239页

作者： SHI HuiXian & WANG GuoJun1 Institute of Mathematics, Shaanxi Normal University, Xi’an 710062, China Institute of Mathematics Shaanxi Normal University Xi’an China

Based on the concept of the complete lattice satisfying the first and second infinite distributive laws, the present paper introduces the semantics of the lattice-valued modal propositional logic. It is pointed out that this semantics generalizes the semantics of both classical modal propositional logic and [0,1]-valued modal propositional logic. The definition of the QMR0-algebra is proposed, and both the Boole-typed latticevalued modal propositional logic system B and the QMR0-typed lattice-valued modal propositional logic system QML* are constructed by use of Boole-algebras and QMR0-algebras, respectively. The main results of the paper are the Completeness theorems of both the system B and QML*.

关键词： latticed-valued modal propositional logic modal model QMR0-algebra validity Completeness

Completeness of the system {z^(λ_n)}in L^2[B,α_0]

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2101-2110页

作者： Ju Hong NING Guan Tie DENG Department of Mathematics Jiangxi Normal University Nanchang 330022 P. R. China School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}（n = 1,2,...） be a sequence of complex numbers satisfying sup ｜ arg（λn）｜〈 α 〈 π/2 and denote by M（∧） = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ（λ∈∧）. Let α0（z） be a weight function defined on B. We obtain a Completeness theorem for the system M（∧） in the Hilbert space L^2 [B, α0].

关键词： Completeness unbounded domain Hilbert space

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中国特色社会主义发展逻辑的整体性指向

中国特色社会主义理论

GLOBAL WEAK SHARP MINIMA AND Completeness OF METRIC SPACE

中国特色社会主义理论 2018年第10期 30-45页

作者：余金成

中国特色社会主义既是马克思主义中国化成果，又是经由改革所诞生的现代社会主义。随着改革深入，中国特色社会主义经历了对社会主义市场经济的探索、定型过程，目前则进入运用、完善的新时代。中国特色社会主义每一环节理论发展，都是... 详细信息

中国特色社会主义既是马克思主义中国化成果，又是经由改革所诞生的现代社会主义。随着改革深入，中国特色社会主义经历了对社会主义市场经济的探索、定型过程，目前则进入运用、完善的新时代。中国特色社会主义每一环节理论发展，都是历史条件重大转折推动实践依序递进的结果，其发展逻辑起始于针对性，展开于渐进性，改革开放40年以及中共十八大以后五年来，中国特色社会主义初步形成了自身的完整性，已经有条件完成对自身的理论阐释和逻辑自洽证明，呈现整体性指向。

关键词：中国特色社会主义改革开放社会主义市场经济发展逻辑整体性 socialism with Chinese characteristics reform and opening up socialist market economy logic of development Completeness

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Acta Mathematica Scientia 2005年第2期25卷 359-366页

作者：黄辉 Department of Mathematics Zhongshan University Guangzhou 510275China Department of MathematicsYunnan UniversityKunming 650091China

A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the Completeness of a metric space is given by the existence of global weak sharp minima.

关键词： Global weak sharp minima Completeness convex function

Research on Petri Net System Parallel Subnet Partitioning Completeness Theory and Algorithm

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Wuhan University Journal of Natural Sciences 2019年第3期24卷 205-217页

作者： LI Wenjing LI Songzhao LU Jianbo School of Logistics Management and Engineering Nanning Normal University Guangxi Higher-Education Key Laboratory of Scientific Computing and Intelligent Information Processing Nanning Normal University College of Computer and Information Engineering Nanning Normal University

In order to solve the parallel algorithm of Petri net system with concurrent function, so as to achieve the parallel control and simulation operation of this system, this paper proposes the function partition Completeness theory and algorithms of Petri net parallelization, thereby providing the theoretical support for the realization of Petri parallel algorithms. Firstly, according to the concurrent characteristics of Petri net model, we analyze the parallelism of Petri net system; then, by giving the solving process of place invariants and the function partitioning of Petri net, we propose the function partitioning conditions and determination theorem of Petri net parallelization, and conduct its theoretical proof and practical verification. On this basis, we conduct the theoretical study and analysis on the situation that Petri net system has several kinds of parallel function partitioning, propose the Completeness theorem of parallelism function partitioning in Petri net system, and verify it. Finally, we give the algorithms, application examples and simulation experiment results of parallel function partitioning of Petri net systems based on place invariant. The theoretical proof and experimental results show that the function partitioning conditions and Completeness theory of Petri net parallelization based on place invariant are correct, and the parallel algorithms under such theoretical basis are also correct and effective.

关键词： Petri net parallelization partitioning conditions Completeness partitioning algorithm

THE Completeness AND A NEW DERIVATION OF THE STROH FORMALISM OF ANISOTROPIC LINEAR ELASTICITY

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Acta Mechanica Sinica 2003年第3期19卷 270-275页

作者：国风林郑泉水 DepartmentofEngineeringMechanics TsinghuaUniversityBeijing100084China

In this paper we present a new,simpler and unified derivation of the Stroh formalism of anisotropic linear elasticity,for both nondegenerate and degenerate cases.It is based on the potential representation and Jordan canonical representation theorems.The Completeness of the Stroh formalism is proved in the derivation process itself.This new approach is also extended to piezoelastic problems.Besides,we show that the eigenvalues of the fundamental elastic matrix in planar anisotropic elasticity are always distinct,except for the case of isotropy.

关键词： Stroh formalism Completeness degenerate cases tetratropy