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The Existence of Solutions of Elliptic Equations with Neumann Boundary Condition for Superlinear Problems

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Acta Mathematica Sinica,English Series 2004年第6期20卷 965-976页

作者： chong li Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences

In this paper, we study and discuss the existence of multiple solutions of a class of non–linear elliptic equations with Neumann boundary condition, and obtain at least seven non–trivial solutions in which two are positive, two are negative and three are sign–changing. The study of problem (1.1): is based on the variational methods and critical point theory. We form our conclusion by using the sub–sup solution method, Mountain Pass Theorem in order intervals, Leray–Schauder degree theory and the invariance of decreasing flow.

关键词： Critical point theory Order intervals Decreasing flow

The Study of Minimal Period Estimates for Brake Orbits of Autonomous Subquadratic Hamiltonian Systems

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1645-1658页

作者： chong li Basic Department Beijing Union University

In this paper, we consider the minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems. We prove that if the Hamiltonian function H ∈ C2（R2n,R） is unbounded and not uniformly coercive, there exists at least one nonconstant T-periodic brake orbit （z, T） with minimal period T or T/2 for every number T 〉 0.

关键词： Brake orbits minimal period L-Maslov type index Hamiltonian systems

On Effectiveness of Protocol Creating Maximum Entanglement of Two Charge-Phase Qubits by Cavity Field

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Communications in Theoretical Physics 2007年第5X期48卷 935-942页

作者： li chong Department of Physics Dalian University of Technology Dalian 116024 China Institute of Theoretical Physics The Chinese Academy of Sciences Beijing 100080 China Applied Physics Department Beijing University of Technology Beijing 100022 China

We revisit the protocols to create maximally entangled states between two Josephson junction （33） charge phase qubits coupled to a microwave field in a cavity as a quantum data bus. We analyze a novel mechanism of quantum decoherence due to the adiabatic entanglement between qubits and the data bus, the off-resonance microwave field. We show that even if the variable of the data bus can be adiabatically eliminated, the entanglement between the qubits and data bus remains and can decohere the superposition of two-particle state. Fortunately we can construct a decoherencefree subspace of two-dimension to against this adiabatic decoherence. To carry out the analytic study for this decoherence problem, we develop Frohlich transformation to re-derive the effective Hamiltonian of these systems, which is equivalent to that obtained from the adiabatic elimination approach.

关键词： SQUID quantum entanglement conccurrence decoherence free sub-space

CONVERGENCE OF NEWTON＇S METHOD FOR SYSTEMS OF EQUATIONS WITH CONSTANT RANK DERIVATIVES

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Journal of Computational Mathematics 2007年第6期25卷 705-718页

作者： Xiubin Xu chong li Department of Mathematics Zhejiang Normal University Jinhua 321004 China Department of Mathematics Zhejiang University Hangzhou 310027 China

The convergence properties of Newton＇s method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale＇s point estimate theorems as special cases, are obtained.

关键词： Newton's method Overdetermined system lipschitz condition with L average,Convergence Rank.

Kantorovich’s theorem for Newton’s method on lie groups

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第6期8卷 978-986页

作者： WANG Jin-hua li chong Department of Mathematics Zhejiang University of Technology Hangzhou 310032 China Department of Mathematics Zhejiang University Hangzhou 310027 China

The convergence criterion of Newton’s method to find the zeros of a map f from a lie group to its corresponding lie algebra is established under the assumption that f satisfies the classical lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori.

关键词： Newton's method lie group Kantorovich's theorem lipschitz condition

Rectangle expansion A* pathfinding for grid maps

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Chinese Journal of Aeronautics 2016年第5期29卷 1385-1396页

作者： Zhang An li chong Bi Wenhao School of Aeronautics Northwestern Polytechnical University School of Electronics and Information Northwestern Polytechnical University

Search speed, quality of resulting paths and the cost of pre-processing are the principle evaluation metrics of a pathfinding algorithm. In this paper, a new algorithm for grid-based maps, rectangle expansion A＊（REA＊）, is presented that improves the performance of A＊ significantly. REA＊ explores maps in units of unblocked rectangles. All unnecessary points inside the rectangles are pruned and boundaries of the rectangles （instead of individual points within those boundaries） are used as search nodes. This makes the algorithm plot fewer points and have a much shorter open list than A＊. REA＊ returns jump and grid-optimal path points, but since the line of sight between jump points is protected by the unblocked rectangles, the resulting path of REA＂ is usually better than grid-optimal. The algorithm is entirely online and requires no offline pre-processing. Experimental results for typical benchmark problem sets show that REA＊ can speed up a highly optimized A＊ by an order of magnitude and more while preserving completeness and optimality. This new algorithm is competitive with other highly successful variants of A＊.

关键词： Breaking path symmetries Grid Heuristic algorithms Path search Variant of A*

Two 8-node quadrilateral spline elements by B-net method

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Acta Mechanica Sinica 2012年第6期28卷 1620-1629页

作者： Juan Chen chong-Jun li School of Mathematics and Quantitative Economics Dongbei University of Finance and Economics School of Mathematical Sciences Dalian University of Technology

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

关键词： Spline finite element B-net method Quadri-lateral element - Bivariate spline interpolation The secondorder completeness

Development of quadrilateral spline thin plate elements using the B-net method

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Acta Mechanica Sinica 2013年第4期29卷 567-574页

作者： Juan Chen chong-Jun li School of Mathematics and Quantitative Economics Dongbei University of Finance and Economics School of Mathematical Sciences Dalian University of Technology

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

关键词： Spline finite element ~ Refined quadrilateral el-ement ~ Discrete Kirchhoff plate element ~ Triangular areacoordinates ~ B-net method

Existence of best simultaneous approximations in L_p(S, Σ, X) without the RNP assumption

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Science China Mathematics 2015年第4期58卷 813-820页

作者： LUO XianFa li chong Department of Mathematics China Jiliang University Department of Mathematics Zhejiang University

Let(S, Σ, μ) be a complete positive σ-finite measure space and let X be a Banach space. We consider the simultaneous proximinality problem in Lp(S, Σ, X) for 1 p < +∞. We establish some N-simultaneous proximinali... 详细信息

Let(S, Σ, μ) be a complete positive σ-finite measure space and let X be a Banach space. We consider the simultaneous proximinality problem in Lp(S, Σ, X) for 1 p lish some N-simultaneous proximinality results of Lp(S, Σ0, Y) in Lp(S, Σ, X) without the Radon-Nikody′m property(RNP) assumptions on the space span Y and its dual span Y*, where Σ0is a sub-σ-algebra of Σ and Y a nonempty locally weakly compact closed convex subset of X. In particular, we completely solve one open problem and partially solve another one in Luo et al.(2011).

关键词： measure space the Radon-Nikodym property simultaneous approximation