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A spectral interpretation for the explicit formula in the theory of prime numbers

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Science China Mathematics 2010年第3期53卷 791-812页

作者： LI Xian-Jin Department of Mathematics, Brigham Young University, Provo, Utah 84602, usa 1. Department of Mathematics Brigham Young University Provo Utah 84602 USA

A spectral interpretation for the poles and zeros of the L-function of algebraic number fields is given by Meyer. As Meyer works with Schwartz spaces which are not Hilbert spaces, the information on the location of zeros of the L-function is lost. In 1999, A. Connes gave a spectral interpretation for the critical zeros the Riemann zeta function. He works with Hilbert spaces. In this paper, we show that a variant of Connes’ trace formula is essentially equal to the explicit formula of A. Weil.

关键词： explicit formula fourier analysis Riemann hypothesis trace formula

ECOLOGICAL CONSEQUENCES OFSOIL EROSION AND SEDIMENTATION

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International Journal of Sediment Research 1999年第2期14卷 355-361页

作者： Grace S. BRUSH (Johns Hopkins University , Baltimore, Maryland, usa)

Sediment erosion and siltation in waterways can have ecological consequences as disastrous economically as those related to transport and flooding of adjacent lands. The impact of sediment erosion and deposition on human societies is recorded in many historical documents. The paleoecological record also provides evidence of the long-term effects of siltation. Sedimentation rates in the Chesapeake Bay estuary, in mid-Atlantic usa, have doubled and quadrupled over the last 200 to 300 years with the initiation and intensification of agriculture. The result has been filling in of many estuarine tributaries and the transformation of the estuary from a benthic to a planktonic ecosystem. This change took place as light became limiting in the water column and benthic plants could no longer photosynthesize, resulting in a proliferation of planktonic algae. Planktonic algal growth was also fueled by fertilizers attached to eroded soil particles. leading ultimately to eutrophication within the water column and anoxia of the bottom waters.

关键词： Sedimentation Civilizations Land use Sediment cores

On interpolation for Hormander’s algebras

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Science China Mathematics 2010年第3期53卷 763-770页

作者： LI Bao Qin Department of Mathematics, Florida International University, Miami, FL 33199, usa 1. Department of Mathematics Florida International University Miami FL 33199 USA

We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating... 详细信息

关键词： weight pseudoconvex set Hrmander’s algebra interpolating variety plurisubharmonic function holomorphic function entire function

Prolog to the Section on Radar System Engineering

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Journal of Systems Engineering and Electronics 1995年第1期6卷 46-47页

作者： Hill, R. T. Radar consultant, usa November, 1994, Beijing Radar consultant USA November 1994 Beijing

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关键词： Prolog to the Section on Radar System Engineering

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The New Methodology

Wuhan University Journal of Natural Sciences 2001年第Z1期6卷 12-24页

作者： Martin Fowler 651 W Washington Blvd,Suite 500,Chicago,IL 60661, usa Chicago USA

In the past few years there's been a rapidly growing interest in “lightweight” methodologies. Alternatively characterized as an antidote to bureaucracy or a license to hack they've stirred up interest all over the software landscape. In this essay I explore the reasons for lightweight methods, focusing not so much on their weight but on their adaptive nature and their people first orientation. I also give a summary and references to the processes in this school and consider the factors that should influence your choice of whether to go down this newly trodden path.

关键词： lightweight method people\|first orietation

OPTIMAL COARSE GRID SIZE IN DOMAIN DECOMPOSITION

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Journal of Computational Mathematics 1994年第4期12卷 291-297页

作者： Tony Chan Jian-Ping Shao(Department of Mathematics, University of Califoruia, Los Angeles, usa) UNIV CALIF LOS ANGELES DEPT MATHLOS ANGELESCA 90024

In most domain decomposition (DD) methods, a coarse grid solve is employed to provide the global coupling required to produce an optimal method. The total cost of a method can depend sensitively on the choice of the coaxse grid size H. In this paper, we give a simple analysis of this phenomenon for a model elliptic problem and a variant of Smith's vertex space domain decomposition method [11, 3]. We derive the optimal value Hopt which asymptotically minimises the total cost of method (number of floating point operations in the sequential case and execution time in the parallel case), for subdomain solvers with different complekities. Using the value of Hopt, we derive the overall complexity of the DD method, which can be significantly lower than that of the subdomain solver

关键词： UCLA OPTIMAL COARSE GRID SIZE IN DOMAIN DECOMPOSITION CAM

PDE-BASED MEDIAL AXIS EXTRACTION AND SHAPE MANIPULATION OF ARBITRARY MESHES

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Journal of Systems Science & Complexity 2008年第4期21卷 609-625页

作者： Haixia DU Terry YOO Hong QIN Sterne Kessler Goldstein & Fox P.L.L.C. Washington 20005 USA. National Library of Medicine National Institutes of Health Bethesda 20894 USA. Computer Science Department Stony Brook University Stony Brook NY 11794 USA.

Shape skeletonization （i.e., medial axis extraction） is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper, the authors expand the use of diffusion equations combined with distance field information to approximate medial axes of arbitrary 3D differential properties. It offers an alternative solids represented by polygonal meshes based on their but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, this system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, the proposed model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated mesh objects.

关键词： Diffusion Equation Medial Axis Extraction PDE techniques Polygonal Meshes Shape Manipulation.

Classification of rational holomorphic maps from B^2 into B^N with degree 2

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Science China Mathematics 2009年第12期52卷 2647-2667页

作者： JI ShanYu 1 & ZHANG Yuan 2 1 Department of Mathematics, University of Houston, Houston, TX 77204, usa 2 Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, usa 1. Department of Mathematics University of Houston Houston TX 77204 USA 2. Department of Mathematics Rutgers University New Brunswick NJ 08903 USA

Rational proper holomorphic maps from the unit ball in C 2 into the unit ball C N with degree 2 are classified, up to automorphisms of balls.

关键词： rational holomorphic maps between balls classification maps with degree 2

A FINITE DIFFERENCE SCHEME FOR THE GENERALIZED NONLINEAR SCHRDINGER EQUATION WITH VARIABLE COEFFICIENTS

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Journal of Computational Mathematics 2000年第2期18卷 123-132页

作者： Wei-zhong Dai Raja Nassar (Mathematics and Statistics, College of Engineering and Science, Louisiana Tech University, Ruston, LA 71272, usa) Louisiana Tech University 美国 Ruston 71272

A finite difference scheme for the generalized nonlinear Schr dinger equation with variable coefficients is developed. The scheme is shown to satisfy two conservation laws. Numerical results show that the scheme is a... 详细信息

关键词： Finite difference scheme Schrdinger equation Discrete energy method.