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Some new results on planar harmonic mappings

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science china mathematics 2010年第3期53卷 597-604页

作者： CHEN HuaiHui Department of mathematics, nanjing normal university, nanjing 210097, china 1. Department of mathematics Nanjing Normal University Nanjing 210097 China

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

关键词： harmonic mapping Landau theorem Bloch constant Schwarz-Pick lemma quasi-regularity

A relative local variational principle for topological pressure

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science china mathematics 2010年第6期53卷 1491-1506页

作者： MA XianFeng1,CHEN ErCai2,3,& ZHANG AiHua2,4 1Department of mathematics,East china university of science and Technology,Shanghai 200237,china 2school of mathematics and computer science,nanjing normal university.nanjing 210097,china 3Center of Nonlinear science,nanjing university.nanjing 210093,china 4College of mathematics and Physics,nanjing university of Posts and Telecommunications,nanjing 210046,china 1. Department of mathematics East China University of Science and Technology Shanghai 200237 China2. School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China3. Center of Nonlinear Science Nanjing University Nanjing 210093 China4. College of Mathematics and Physics Nanjing University of Posts and Telecommunications Nanjing 210046 China

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle

On the variational principle for the topological pressure for certain non-compact sets

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science china mathematics 2010年第4期53卷 1117-1128页

作者： PEI Yu 1 & CHEN ErCai 1,2,1 Department of mathematics,nanjing normal university.nanjing 210097,china 2 Center for Nonlinear science,nanjing university.nanjing 210093,china 1. Department of mathematics Nanjing Normal University Nanjing 210097 China2. Center for Nonlinear Science Nanjing University Nanjing 210093 China

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous *** assume that the dynamical system satisfies g-almost product property and the uniform separation *** compute the topological pressure of saturated sets under these two *** the uniform separation property does not hold,we compute the topological pressure of the set of generic *** give an application of these results to multifractal analysis and finally get a conditional variational principle.

关键词： uniform separation property g-almost product property topological pressure of non-compact sets variational principle BS-dinmension

Basin filling algorithm for the circular packing problem with equilibrium behavioral constraints

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science china(Information sciences) 2010年第5期53卷 885-895页

作者： LIU JingFa1& LI Gang2 1school of computer and Software, nanjing university of Information science & Technology, nanjing 210044, china 2school of mathematics and Physics, nanjing university of Information science & Technology, nanjing 210044, china 1. school of computer and Software Nanjing University of Information Science & Technology Nanjing 210044 China2. School of Mathematics and Physics Nanjing University of Information Science & Technology Nanjing 210044 China

With the background of the satellite module layout design, the circular packing problem with equilibrium behavioral constraints is a layout optimization problem and NP-hard problem in math. For lack of a powerful optimization method, this problem is hard to solve. The energy landscape paving (ELP) method is a class of stochastic global optimization algorithms based on the Monte Carlo sampling. Based on the quasiphysical strategy and the penalty function method, the problem is converted into an unconstrained optimization problem. Here by combining the improved ELP method, the gradient method based on local search and the heuristic configuration update mechanism, a new global search algorithm, basin filling algorithm, is put forward. The numerical results show that the proposed algorithm is effective to solving the circular packing problem with equilibrium behavioral constraints, and is easy to be popularized to other layout optimization problems.

关键词： equilibrium behavioral constraints packing problem layout optimization

Concatenating construction of the multisymplectic schemes for 2+1-dimensional sine-Gordon equation

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science china mathematics 2004年第1期47卷 18-30页

作者： WANG Yushun, WANG Bin & QIN MengzhaoLASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 100029, china school of mathematics and computer science, nanjing normal university, nanjing 210097, china school of mathematics and System science, Chinese Academy of sciences, Beijing 100080, china 1. LASG Institute of Atmospheric Physics Chinese Academy of Sciences 100029 Beijing China 2. school of mathematics and computer science Nanjing Normal University 210097 Nanjing China 3. school of mathematics and System science Chinese Academy of Sciences 100080 Beijing China

In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.

关键词： 2+l-climensional sine-Gordon equation multisymplectic scheme concatenating method solitons

Regular n-simplices in R^n with vertices in Z^(n)

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science china mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN HourongDepartment of mathematics, nanjing normal university, nanjing 210097, china (email: jgxia@***) Department of mathematics, nanjing university, nanjing 210093, china Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

HAJOS' CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS

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Journal of Systems science & Complexity 2002年第3期15卷 295-298页

作者： XU Baogang (school of mathematics and computer science, nanjing normal university, nanjing 210097, china) school of mathematics and computer science Nanjing Normal University Nanjing 210097

Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits. In this paper, we propose a new conjecture which is equivalent to Hajos' conjecture, and show that to prove Hajos' conjecture, it is sufficient to prove this new conjecture for 3-connected graphs. Furthermore, a special 3-cut is considered also.

关键词： Circuit decomposition connectivity eulerian graph.

Completely regular paracompact reflection of locales

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science china mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang Department of mathematics, nanjing normal university, nanjing 210097, china Department of mathematics, Sichuan university, Chengdu 610064, china Department of mathematics Nanjing Normal University Nanjing 210097 China Department of mathematics Sichuan University Chengdu 610064 China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

The Alternating-Direction Schemes and Numerical Analysis for the Three-dimensional Seawater Intrusion Simulation

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 389-404页

作者： Zhi-yue ZhangLASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 100029, china & school of mathematics and computer science, nanjing normal university, nanjing 210097, china LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China school of mathematics and computer science Nanjing Normal University Nanjing China

Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristic of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H1 norm are derived for the error in the approximate solution.

关键词： Three-dimensional seawater intrusion characteristic finite element alternating-direction optimal order estimate in H^1