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Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, xuzhou normal university, xuzhou 221116, china department of mathematics, Capital normal university, Beijing 100037, china department of mathematics Xuzhou Normal University Xuzhou 221116 China National Natural Science Foundation of china department of mathematics Capital Normal University Beijing 100037 China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.

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Science china mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & WANG Mingxindepartment of mathematics, Southeast university, Nanjing 210018, china department of mathematics, xuzhou normal university, xuzhou 221116, china department of mathematics Southeast University Nanjing China department of mathematics Xuzhou Normal University Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 1, it is shown that very singular self-similar solutions exist if and only if 1

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

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Science china mathematics 2005年第2期48卷 185-197页

作者： LI Huiling & WANG Mingxin department of mathematics, Southeast university, Nanjing 210018, china department of mathematics, xuzhou normal university, xuzhou 221116, china department of mathematics Southeast University Nanjing China department of mathematics Xuzhou Normal University Xuzhou China

This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.

关键词： parabolic system, localized nonlinear reaction terms, blow-up profiles, boundary layer size.

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science china mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua KONG~(1+) Ming-xin WANG~(2,3) 1 department of Applied mathematics,Dalian university of Technology,Dalian 116024,china 2 department of mathematics,Southeast university,Nanjing 210018,china 3.department of mathematics,xuzhou normal university,xuzhou 221116,china department of Applied mathematics Dalian University of Technology Dalian China department of mathematics Southeast University Nanjing China department of mathematics Xuzhou Normal University Xuzhou China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35K65

THE SECOND EXPONENT SET OF PRIMITIVE DIGRAPHS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 233-236页

作者： MIAO ZHENGKE(department of mathematics, Nanjing university, Nanjing 210093, china.)(department of mathematics, xuzhou normal university, xuzhou 221009, china.) ZHANG KEMIN(department of mathematics, Nanjing university, Nanjing 210093, china.) department of mathematics Nanjing University Nanjing 210093 China department of mathematics Xuzhou Normal University Xuzhou 221009 China

Let D = (V, E) be a primitive digraph. The exponent of D, denoted byγ(D), is the least integer k such that for any u, v∈ V there is a directed walk of length k from u to v. The local exponent of D at a vertex u∈ V, denoted by exp_D (u), is the least integer k such that there is a directed walk of length k from u to v for each v ε V. Let V = {1,2,….,n}. Following [1], the vertices of V are ordered so that exp_D (1) ≤exp_D (2) ≤…≤exp_D(n) =λ(D). Let E_n(i):= {exp_D (i) ∈D PD_n}, where PD_n is the set of all primitive digraphs of order n. It is known that E_n(n) = {γ(D) D∈PD_n} has been completely settled by [7]. In 1998, E_n(1) was characterized by [5]. In this paper, the authors describe E_n(2) for all n≥2.

关键词： Primitive digraph Local exponent Gap

C^MC^N D-computable state

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Science china(Physics,Mechanics & Astronomy) 2008年第9期51卷 1300-1307页

作者： LIU DongDong1,2 & DI YaoMin1 1 School of Physics & Electronic Engineering,xuzhou normal university,xuzhou 221116,china 2 School of mathematics & Physics Science,xuzhou Institute of Technology,xuzhou 221008,china School of Physics & Electronic Engineering Xuzhou Normal University Xuzhou China School of mathematics & Physics Science Xuzhou Institute of Technology Xuzhou China

The notions of D-computable state and D-concurrence are generalized to the CMCN system. A class of D-computable state on CMCN is given and the calculating method of the lower bound of D-concurrence is provided. Th... 详细信息

关键词： quantum entanglement entanglement of formation concurrence D-computable state

Composition Operators Mapping into the E(p,q) Spaces

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Chinese Quarterly Journal of mathematics 2003年第1期18卷 29-34页

作者： LIU Yong-min(department of mathematics, xuzhou normal university, xuzhou 221116, china) departmentofmathematics XuzhouNormulUniversity Xuzhou 221116

Composition operators are used to study the E(p,q) spaces. The boundedness of these operators is also considered. The criteria for these operators to be bounded are given in terms of the Carleson measure.

关键词： bounded operator composition operator Bloch space Carleson measure

Synthesis of some three-qubit gates and their implementation in a three spins system coupled with Ising interaction

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 664-671页

作者： WEI HaiRui, DI YaoMin & WANG Yan School of Physics & Electronic Engineering, xuzhou normal university, xuzhou 221116, china xuzhou normal university School of Physics &amp Electronic Engineering Xuzhou China (GRID:grid.411857.e) (ISNI:***)

The synthesis of the Toffoli gate, Fredkin gate, three-qubit Inversion-on-equality gate and D(α) gate, as well as their implementation in a three spins system coupled with Ising interaction are investigated. The sequences of the control pulse and the drift process to implement these gates are given. It is revealed that the implementation of some three-qubit gates in a circular spin chain is much better than in a linear spin chain, and every two measurements of the quantum computation complexity are not always consistent. It is significant to directly study the implementation of the multi-qubit gates and even more complicated components of quantum information processing without resorting to their synthesis.

关键词： three-qubit gate three spins system Ising interaction the sequences of control pulses and drift processes

RIGIDITY THEOREMS OF CLIFFORD TORUS

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Acta Mathematica Scientia 2010年第3期30卷 890-896页

作者：张运涛 department of mathematics Xuzhou Normal University

In this article, we prove that the Clifford torus S^1（√1-r^2）×^n-1（r） is the only closed hypersurface in the unit sphere S^n＋1（1） with infinite fundamental group, which satisfy r^2≥（n-1）/n,RicM≤C_（H）,and S≤S＋（H）.Moreover, we give a characterization of Clifford torus S^1（√1-r^2）×^n-1（r） with r^2=2n（1＋H^2）^-2（n-1）＋nH^2＋｜H｜√n^2H^2＋4（n-1）.

关键词： Principle curvatual Ricci curvature Clifford torus