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Problems in wavelet analysis of hydrologic series and some suggestions on improvement

Progress in Natural Science:Materials International 2007年第1期17卷 80-86页

作者： WANG Hongrui, YE Letian, LIU Changming, YANG Chi and LIU Peng ( College of Water sciences, beijing normal university, beijing 100875, china Key Laboratory for Water and Sediment sciences, Ministry of Education, beijing 100875, china school of mathematical sciences, Peking university, beijing 100089, china College of Engineering sciences, university of Region, Canada) [a]College of Water sciences Beijing Normal University Beijing China [b]Key Laboratory for Water and Sediment sciences Ministry of Education Beijing China [c]school of mathematical sciences Peking University Beijing China [d]College of Engineering sciences University of Region Canada

Applying the wavelet theory and methods to investigate the hydrologic processes such as precipitation and runoff is a hot field. However, several aspects in research are usually ignored: the effect of admissible condition of wavelet functions and the disturbance of noises for the detection of periods, the effect of the length of a hydrologic time-series on the final result, and the choice between the anomaly and the original time series for wavelet analysis. In this paper, these issues are fully discussed. Precipitation data from Lanzhou Precipitation Station are taken for case study. The result indicates that in the wavelet analysis of hydrologic series, denoise methods should be used to eliminate the influence of noises. The MexHat wavelet function satisfies the admissible condition, which ensures that the periodic properties of hydrologic processes can be well represented by using the MexHat wavelet for decomposition. The affected range of hydro-logic series which should be discarded before analysis is given. It is also suggested that the anomaly series should be used to highlight the actual undulation of the hydrologic series.

关键词： wavelet analysis hydrologic process admissible condition noise period.

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BRILL-NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 531-538页

作者： TAN XIAOJIANGschool of mathematical sciences, Peking university, beijing 100871, china school of mathematical sciences Peking University Beijing 100871 China

Let X be an arbitrary smooth irreducible complex projective curve, E (?)X a rank two vector bundle generated by its sections. The author first represents ?as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H?X, [D1] |D2) is a. collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using / and the Brill-Noether matrix of D1+D2, the author constructs a 2g × d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?) Im{H?X, E) (?) H0(X,[D2]) (?) H0(X, [D2]|D2)} From this and H0(X,E) = H0(X,[D1]) (?)Im{H0(X,E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.

关键词： Brill-Noether matrix Vector bundle Effective divisor

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OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE

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Acta Mathematica Scientia 2008年第3期28卷 604-612页

作者：闻国椿 school of mathematical sciences Peking University

The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.

关键词： Oblique derivative problems nonlinear mixed equations parabolic degeneracy

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SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

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Acta Mathematica Scientia 2007年第3期27卷 663-672页

作者：闻国椿 school of mathematical sciences Peking University

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved.

关键词： Boundary value problems nonlinear elliptic equations parabolic degeneracy

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The lifting scheme of 4-channel orthogonal wavelet transforms

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Progress in Natural Science:Materials International 2006年第1期16卷 100-104页

作者： PENG Lizhong and CHU Xiaoyong (LMAM, school of mathematical sciences, Peking university, beijing 100871, china) [a]Peking Universiy LMAM School of Mathematical Sciences Beijing China

The 4-channel smooth wavelets with linear phase and orthogonality are designed from the 2-channel orthogonal wavelets with high transfer vanishing moments. Reversely, for simple lifting scheme of such 4-channel orthogonal wavelet transforms, a new 2-channel orthogonal wavelet associated with this 4-channel wavelet is constructed. The new 2-channel wavelet has at least the same number of vanishing moments as the associated 4-channel one. Finally, by combining the two such 2-channel wavelet systems, the lifting scheme of 4-channel orthogonal wavelet transform, which has simple structure and is easy to apply, is presented.

关键词： lifting scheme 4-channel orthogonal wavelet 2-channel orthogonal wavelet vanishing moment transfer vanishing moment linear phase.

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Complete solving of explicit evaluation of Gauss sums in the index 2 case

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Science china Mathematics 2010年第9期53卷 2525-2542页

作者： YANG Jing1,2 & XIA LingLi3,1Department of mathematical sciences,Tsinghua university,beijing 100084,china 2Division of mathematical sciences,school of Physical and mathematical sciences,Nanyang Technological university,637371,Singapore 3Basic Courses Department,beijing Union university,beijing 100101,china 1. Department of mathematical sciences Tsinghua University Beijing 100084 China2. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 637371 Nanyang Singapore3. Basic Courses Department Beijing Union University Beijing 100101 China

Let p be a prime number,N be a positive integer such that gcd(N,p) = 1,q = pf where f is the multiplicative order of p modulo *** χ be a primitive multiplicative character of order N over finite field *** paper studies the problem of explicit evaluation of Gauss sums G(χ) in the "index 2 case"(i.e.[(Z/NZ):] = 2).Firstly,the classification of the Gauss sums in the index 2 case is ***,the explicit evaluation of Gauss sums G(χλ)(1 λ N-1) in the index 2 case with order N being general even integer(i.e.N = 2r·N0,where r,N0 are positive integers and N0 3 is odd) is ***,combining with the researches before,the problem of explicit evaluation of Gauss sums in the index 2 case is completely solved.

关键词： Gauss sum Stickelberger’s theorem Stickelberger congruence Davenport-Hasse lifting formula Davenport-Hasse product formula

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Rational points and zeta functions of some curves over finite fields

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Science china Mathematics 2010年第11期53卷 2855-2863页

作者： WANG Long1, & LUO JinQuan2,3 1Department of mathematical sciences, Tsinghua university, beijing 100084, china 2school of mathematical sciences, Yangzhou university, Yangzhou 225002, china 3Division of mathematical sciences, school of Physical and mathematical sciences, Nanyang Technology university, 637371, Singapore 1. Department of mathematical sciences Tsinghua University Beijing 100084 China2. School of Mathematical Sciences Yangzhou University Yangzhou 225002 China3. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technology University Singapore 637371 Singapore

In this paper we study the number of rational points on some curves over finite fields. Moreover, zeta functions of the associated function fields are evaluated explicitly.

关键词： exponential sum rational point rational place zeta function

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RESEARCH　ANNOUNCEMENTS　The　Comparison　Theorem　for　the　Bergman　and　Kobayashi　Metrics　on　a　Class　of　Pseudoconvex　Domains

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数学进展 1996年第3期 277-278页

作者： Yin Weiping(mathematical sciences Research Institute, capital normal university, beijing, 100037)

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＴｈｅＣｏｍｐａｒｉｓｏｎＴｈｅｏｒｅｍｆｏｒｔｈｅＢｅｒｇｍａｎａｎｄＫｏｂａｙａｓｈｉＭｅｔｒｉｃｓｏｎａＣｌａｓｓｏｆＰｓｅｕｄｏｃｏｎｖｅｘＤｏｍａｉｎｓ￥ＹｉｎＷｅ... 详细信息

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＴｈｅＣｏｍｐａｒｉｓｏｎＴｈｅｏｒｅｍｆｏｒｔｈｅＢｅｒｇｍａｎａｎｄＫｏｂａｙａｓｈｉＭｅｔｒｉｃｓｏｎａＣｌａｓｓｏｆＰｓｅｕｄｏｃｏｎｖｅｘＤｏｍａｉｎｓ￥ＹｉｎＷｅｉｐｉｎｇ（Ｍａｔｈｅｍａｔｉｃａ...

关键词： Theorem the Bergman ANNOUNCEMENTS Comparison

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r-matrix and algebraic-geometric symplectic map

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Chinese Science Bulletin 1999年第2期44卷 114-118页

作者： QIAO ZhijunInstitute of Mathematics and school of mathematical sciences, Peking university, beijing 100871, china Institute of Mathematics and school of mathematical sciences Peking University Beijing China

A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution(here, the explicit solution means algebraic-geometric solution expressed by the Riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.

关键词： symplectic map r-matrix algebraic-geometric solution.

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On weak solutions for an image denoising-deblurring model

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 269-281页

作者： HUANG Hai-yang JIA Chun-yan HUAN Zhong-dan school of mathematical sciences,beijing normal university Laboratory of Mathematics and ComplexSystems,Ministry of Education,beijing 100875,china school of mathematical sciences Beijing Normal University Beijing China Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China

A new denoising-deblurring model in image restoration is proposed,in which the regularization term carries out anisotropic diffusion on the edges and isotropic diffusion on the regular *** existence and uniqueness of weak solutions for this model are proved,and the numerical model is also *** with the TV diffusion,this model preferably reduces the staircase appearing in the restored images.

关键词： image restoration deblurring-denoising integro-differential equation weak solution

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