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On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates

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Science china mathematics 2010年第8期53卷 2069-2084页

作者： WANG HaiBing 1,2 & LIU JiJun 1 1 department of mathematics,southeast university,nanjing 210096,china 2 School of mathematics and Computational Science,Hunan university of Science and Technology,Xiangtan 411201,china 1. department of mathematics Southeast University Nanjing 210096 China2. School of Mathematics and Computational Science Hunan University of Science and Technology Xiangtan 411201 China

Consider the determination of Dirichlet-to-Neumann(D-to-N) map from the far-field pattern in inverse scattering problems,which is the key step in some recently developed inversion schemes such as probe ***,this problem is related to the reconstruction of the scattered wave from its far-field *** firstly prove the well-known uniqueness result of the D-to-N map from the far-field pattern using a new scheme based on the mixed reciprocity *** advantage of this new proof scheme is that it provides an efficient algorithm for computing the D-to-N map,avoiding the numerical differentiation for the scattered *** combining with the classical potential theory,a simple and feasible regularizing reconstruction scheme for the D-to-N map is *** the stability estimate for the reconstruction with noisy input data is rigorously analyzed.

关键词： inverse scattering Dirichlet-to-Neumann map regularization mixed reciprocity principle stability

Evolving Objects for Software Engineering

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Wuhan university Journal of Natural Sciences 2001年第Z1期6卷 263-267页

作者： Wang xiao\|ling, Dong yi\|sheng department of Computer Science and Engineering southeast university, nanjing 210018,china department of Computer Science and Engineering southeast university Nanjing 210018 China

This paper is concerned with evolving objects method for software design that can adapt to the changing environments and requirements automatically. We present system architecture with objects library, where there are objects based on domain ontologies. We define some genetic operators for objects, and discuss how to apply these genetic operators on objects to get new objects, which can satisfy new requirements.

关键词： object oriented ontology evolving objects meta object genetic operator mutation operator crossover operator

Variational construction of unbounded orbits in Lagrangian systems

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Science china mathematics 2010年第3期53卷 617-624页

作者： CHENG Chong-Qing 1, & LI Xia 2 1 department of mathematics, nanjing university, nanjing 210093, china 2.department of mathematics, Suzhou university of Science and Technology, Suzhou 215001, china 1. department of mathematics Nanjing University Nanjing 210093 China2. Department of Mathematics Suzhou University of Science and Technology Suzhou 215001 China

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtain... 详细信息

关键词： positive definite Lagrangian variational method unbounded orbit

Integral expressions of Lyapunov exponents for autonomous ordinary differential systems

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Science china mathematics 2009年第1期52卷 195-216页

作者： DAI XiongPing department of mathematics, nanjing university, nanjing 210093, china 1. department of mathematics Nanjing University Nanjing 210093 China

In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ? d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.

关键词： Lyapunov spectrum of differential system multiplicative ergodic theorem C 1-vector field smooth linear skew-product flow lifting of probability 34D08 37C10 60B05 37H15 28D10

Maschke-type theorem and Morita context over weak Hopf algebras

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Science china mathematics 2006年第5期49卷 587-598页

作者： ZHANG Liangyun College of Science, nanjing Agricultural university, nanjing 210095, china department of mathematics, nanjing university, nanjing 210008, china 1. College of Science Nanjing Agricultural University Nanjing 210095 China 2. department of mathematics Nanjing University Nanjing 210008 China

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

关键词： weak Hopf algebra, smash product, Maschke-type theorem, Morita context.

The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras

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Chinese Science Bulletin 1998年第5期43卷 383-385页

作者： JIANG Cuibo 1 and MENG Daoji 2 1.department of mathematics,Yantai Teachers university, Yantai 264025, china 2.department of mathematics,Nankai university,Tianjin 300071, china. department of mathematics Yantai Teachers University Yantai China department of mathematics Nankai University Tianjin China

The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras over the complex field C are given.

关键词： complete Lie algebra Heisenberg algebra nilpotent radical.

THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR 2-D QUASILINEAR WAVEEQUATIONS WITH CUBIC NONLINEARITY

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Chinese Annals of mathematics,Series B 1999年第4期20卷 455-472页

作者： YIN HUICHENG ZHENG QIN(department of mathematics, nanjing university nanjing 210093, china) nanjing Univ Dept Math Nanjing 210093 Peoples R China

For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac[2].

关键词： Lifespan Geometric blowup Nash-M■ser iteration

Measures and dimensions of fractal sets in local fields

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Progress in Natural Science:Materials International 2006年第12期16卷 1260-1268页

作者： QIU Hua** and SU Weiyi(department of mathematics, nanjing university, nanjing 210093, china) [a]department of mathematics Nanjing University Nanjing China

The study of fractal analysis over the local fields as underline spaces is very important since it can motivate new approaches and new ideas, and discover new techniques in the study of fractals. To study fractal sets in a local field K, in this paper, we define several kinds of fractal measures and dimensions of subsets in K. Some typical fractal sets in K are constructed. We also give out the Hausdorff dimensions and measures, Box-counting dimensions and Packing dimensions, and stress that there exist differences between fractal analysis on local fields and Euclidean spaces. Consequently, the theoretical foundation of fractal analysis on local fields is established.

关键词： local field p-series field Hausdorff measure and dimension Boxcounting dimension Packing measure and dimension Cantor type set.

Binomial coefficients,Catalan numbers and Lucas quotients

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Science china mathematics 2010年第9期53卷 2473-2488页

作者： SUN ZhiWei department of mathematics,nanjing university,nanjing 210093,china 1. department of mathematics Nanjing University Nanjing 210093 China

Let p be an odd prime and let a,m ∈ Z with a > 0 and p ︱ *** this paper we determinep ∑k=0 pa-1(2k k=d)/mk mod p2 for d=0,1;for example,where(-) is the Jacobi symbol and {un}n≥0 is the Lucas sequence given by u0 = 0,u1 = 1 and un+1 =(m-2)un-un-1(n = 1,2,3,...).As an application,we determine ∑02 for any integer r,where Ck denotes the Catalan number 2kk /(k + 1).We also pose some related conjectures.

关键词： congruences binomial coefficients Catalan numbers Lucas quotients