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A SIMPLICIAL HOMOTOPY ALGORITHM FOR COMPUTING zero pointS ON POLYTOPES

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Acta Mathematicae Applicatae Sinica 1994年第2期10卷 186-193页

作者：陈开周杨再福梁正礼 Department of Applied Mathematics Xidian University Xi'an China

In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level point to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the *** starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.

关键词： zero point simplicial homotopy algorithm variable dimension algorithm,triangulation, polytope.

A Note on Modified Mann Accretive Iterations for zero points of Operators

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Journal of Mathematical Research and Exposition 2009年第1期29卷 52-56页

作者： WEI Li ZHOU Hai Yan School of Mathematics and Statistics Hebei University of Economics and Business Hebei 050061 China Department of Mathematics Ordnance Engineering College Hebei 050003 China

A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given. The work in this paper is an extension and complement of the corresponding result of Kim T.... 详细信息

关键词： accretive operator zero point strong convergence.

Spatial variation law of vertical derivative zero points for potential field data

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Applied Geophysics 2010年第3期7卷 197-209,292页

作者：王万银张功成梁建设长安大学重磁方法技术研究所长安大学地质工程与测绘学院长安大学西部矿产资源与地质工程教育部重点实验室西安710054 中海石油研究中心北京100027

In this paper we deduce the analytic solutions of the first- and second-order vertical derivative zero points for gravity anomalies in simple regular models with single, double, and multiple edges and analyze their spatial variation. For another simple regular models where it is difficult to obtain the analytic expression of the zero point, we try to use the profile zero points to analyze the spatial variation. The test results show that the spatial variation laws of both first- and second-order vertical derivative zero points are almost the same but the second-order derivative zero point position is closer to the top surface edge of the geological bodies than the first-order vertical derivative and has a relatively high resolution. Moreover, with an increase in buried depth, for a single boundary model, the vertical derivative zero point location tends to move from the top surface edge to the outside of the buried body but finally converges to a fixed value. For a double boundary model, the vertical derivative zero point location tends to migrate from the top surface edge to the outside of the buried body. For multiple boundary models, the vertical derivative zero point location converges from the top surface edge to the outside of the buried body where some zero points coincide and finally vanish. Finally, the effectiveness and reliability of the proposed method is verified using real field data.

关键词： vertical derivative zero point spatial variation law edge location

STABLE AND UNSTABLE STATIONARY TRAJECTORIES

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Applied Mathematics and Mechanics(English Edition) 2005年第1期26卷 52-57页

作者： J.M.Soriano Departamento de Anlisis Matemtico Facultad de MatemticasUniversidad de Sevilla Aptdo.1160 Sevilla 41808 Spain

The stability of stationary trajectories of a particular autonomous system is *** proof of the result is based upon continuation methods.

关键词： autonomous system continuation method trajectory critical point zero point stationary trajectory stable solution asymptotically stable

A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES

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Acta Mathematica Scientia 2007年第3期27卷 535-540页

作者： J.M. Soriano C. Ding Departamento de Andlisis Matemdtico Facultad de Matematicas Universidad de Sevilla Aptdo. 1160 Sevilla 41080 Spain Department of Applied Mathematics Zhejiang University of Technology Hangzhou 310032 China

It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.

关键词： Autonomous system continuation methods trajectory nondegenerate critical point zero point stationary trajectory stable trajectory asymptotically stable Morse inequalities

New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators

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Applied Mathematics(A Journal of Chinese Universities) 2010年第2期25卷 199-208页

作者： WEI Li SU Yong-fu ZHOU Hai-yun School of Mathematics and Statistics Hebei University of Economics and Business Shijiazhuang 050061 China Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Institute of Mathematics and Computer Sciences Hebei Normal University Shijiazhuang 050016 China

In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.

关键词： Strongly relatively nonexpansive mapping maximal monotone operator zero point fixed point,weak convergence.

关于增生算子零点的修正Mann迭代的注(英文)

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Journal of Mathematical Research with Applications 2009年第1期 52-56页

作者：魏利周海云 School of Mathematics and Statistics Hebei University of Economics and Business Department of Mathematics Ordnance Engineering College

A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is *** work in this paper is an extension and complement of the corresponding result of Kim *** Xu H.... 详细信息

关键词： accretive operator zero point strong convergence

FREDHOLM AND COMPACT MAPPINGS SHARING A VALUE

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Applied Mathematics and Mechanics(English Edition) 2001年第6期22卷 682-686页

作者： J.M.Soriano Departmento de Anlisis Matemtico

Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.

关键词： zero point continuation methods C 1 homotopy surjective implicit function theorem compact mapping Fredholm mapping index zero injective diffeomorphism

THE NUMBERS OF JUMP LAYERS OF BOUNDARY VALUE PROBLEMS IN QUASILINEAR DIFFERENTIAL EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 1992年第4期13卷 387-391页

作者：程建华祝清 Mathematics Department Anhui University Hefei

This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed ... 详细信息

关键词： jump layer (free layer transition layer) determinate function zero point shadow approximation