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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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灵光独耀:沈宗灵与中国法理学

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中国法律评论 2024年第4期 149-154页

作者： peking university Law school 北京大学法学院

在其诸多弟子的追忆中,沈宗灵先生一生专心治学、淡泊名利,由此常常对世事保持一种有意的疏离。“灵光独耀,迥脱根尘”,或许便是这位法理学大家的灵魂写照。壹“经国济民”:沈宗灵的早年岁月1923年2月24日,沈宗灵出生于浙江杭州的一个... 详细信息

在其诸多弟子的追忆中,沈宗灵先生一生专心治学、淡泊名利,由此常常对世事保持一种有意的疏离。“灵光独耀,迥脱根尘”,或许便是这位法理学大家的灵魂写照。壹“经国济民”:沈宗灵的早年岁月1923年2月24日,沈宗灵出生于浙江杭州的一个商人家庭,后随家人迁居上海。

关键词：沈宗灵淡泊名利法理学浙江杭州灵光

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INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

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Journal of Computational Mathematics 2000年第6期18卷 657-672页

作者： Lung-an Ying (school of mathematical sciences, peking university, beijing 100871, china) 北京大学北京 100871

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

关键词： Helmholtz equation exterior problem infinite element method

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On Riemann-Finsler geometry

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Chinese Science Bulletin 1998年第6期43卷 447-450页

作者： MO Xiaohuan school of mathematical sciences, peking university, beijing 100871, china school of mathematical sciences Peking University Beijing China

The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.

关键词： Finsler space Chern connection Hilbert form Minkowski potential projective sphere bundle.

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Hausdorff dimension of Julia set of a polynomial with a Siegel disk

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Science china Mathematics 2006年第9期49卷 1284-1296页

作者： SHEN Liang LMAM, school of mathematical sciences, peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let f(z) = e2πiθz(1+z/d)d,θ∈R\Q be a polynomial. Ifθis an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension o... 详细信息

关键词： Hausdorff dimension Siegel disk porous set

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Uniqueness and local stability for the inverse scattering problem of determining the cavity

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Science china Mathematics 2005年第8期48卷 1113-1123页

作者： FENG Lixin & MA Fuming LMAM, school of mathematical sciences, peking university, beijing 100871, china school of mathematical sciences, Heilongjiang university, Harbin 150080, china school of mathematical sciences, Jilin university, Changchun 130012, china 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China 2. school of mathematical sciences Heilongjiang University 150080 Harbin China 3. school of mathematical sciences Jilin University 130012 Changchun China

Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by Maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2-dimensional TM (transverse magnetic) polarization are proved in this paper.

关键词： uniqueness, stability, Maxwell's equations, inverse scattering problem.

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A quantitative program for Hadwiger's covering conjecture

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Science china Mathematics 2010年第9期53卷 2551-2560页

作者： ZONG Chuanming school of mathematical sciences,peking university,beijing 100871,china 1. school of mathematical sciences Peking University Beijing 100871 China

In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its *** to now,this conjecture is still open for all n *** 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller *** to now,this conjecture is open for 4 n *** this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.

关键词： convex body Hadwiger’s conjecture Banach-Mazur metric β-net Borsuk’s conjecture

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Wavelets associated with Hankel transform and their Weyl transforms

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Science china Mathematics 2004年第3期47卷 393-400页

作者： PENG Lizhong MA Ruiqin LMAM, school of mathematical sciences, peking university, beijing 100871, china 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China

The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne... 详细信息

关键词： Bessel function, Hankel transform, wavelets, Weyltransform, boundedness, compactness.

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On multiply of sections of line bundles on compact Riemann surfaces

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Science china Mathematics 2008年第4期51卷 721-727页

作者： TAN XiaoJiang LMAM and school of mathematical sciences peking university beijing 100871 china 1. LMAM and school of mathematical sciences Peking University Beijing 100871 China

In this paper,we give some conditions on the surjective of multiply maps H^0(R,L)×H^0(R,K)→H^0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle.

关键词： compact Riemann surfaces line bundles 14E20 14F24

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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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