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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

Some Results on the Multiplier Conjecture for the Case n=5n_1

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Acta Mathematica Sinica,English Series 1998年第4期14卷 535-540页

作者： Wan Zhaoze, Department of Mathematics, Peking University, Beijing 100871, China Department of Mathematics Peking University Beijing China

Using the method presented in [1], we obtain some new results which improve on the result of MacFarland’s theorem (see [2]) in this case.

关键词： Difference sets Multiplier CH-equations

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 473-478页

作者： MENG ZAIZHAO(Department of Mathematics, Peking University, Beijing 100871, China) Department of Mathematics Peking University Beijing 100871 China

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2). It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

关键词： Divisor function Multiplicative function Congruence

Neuroimaging studies of self-reflection

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Progress in Natural Science:Materials International 2004年第4期14卷 10-16页

作者： ZHU Ying(Department of Psychology, Peking University, Beijing 100871, China) Dept. of Psychology Peking Univ. Beijing 100871 China

This paper reviews some basic findings and methodological issues in neuroimaging studies of self-referential processing. As a general rule, making judgments about one’s self, inclusive of personality trait adjectives or current mental states (person’ s preferences, norms, aesthetic values and feeling) uniformly generates medial prefrontal activations, regardless of stimulus materials (words or pictures) and modality (visual or auditory). Cingulate activations are also observed in association with most self-referential processing. Methodological issues include treating self-referential processing as either representing one’s own personality traits or representing one’s own current mental states. Finally, self-referential processing could be considered as implement of "I think therefore I am" approach to neuroimaging the self.

关键词： self self-referential processing medial prefrontal cortex cingulate brain image.

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

A　Diference　Scheme　with　Anti－difusion　Terms　to　Improve　the　Computation　of　Contact　Discontinuities　and　the　Study　of　Weak　Discontinuities　in　Compresible　Flow

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Communications in Nonlinear Science and Numerical Simulation 1996年第4期1卷 42-51页

作者： Chunguang XU (College of Mathematical Science ,Peking University, Beijing 100871) College of Mathematical Science Peking University Beijing 100871 USA

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Ａｂｓｔｒａｃｔ：ＴｈｅｉｎｖｅｓｔｉｇａｔｉｏｎｏｆＭａｃｈｒｅｆｌｅｃｔｉｏｎｆｏｒｍｅｄａｆｔｅｒｔｈｅｉｍｐｉｎｇｅｍｅｎｔｏｆａｗｅａｋｐｌａｎｅｓｈｏｃｋｗａｖｅｏｎａｗｅｄｇｅ，ｗｉｔｈｓｈｏｃｋＭａｃｈｎｕｍｂｅｒＭｓｎｅａｒ１，ｉｓｓｔｉｌａｎｏｐｅｎｐｒｏｂｌｅｍ［１２］．Ｉｔ＇ｓｄｉｆｉｃｕｌｔｆｏｒｓｈｏｃｋｔｕｂｅｅｘｐｅｒｉｍｅｎｔｓｗｉｔｈｉｎｔｅｒｆｅｒｏｍｅｔｅｒｔｏｄｅｔｅｃｔｃｏｎｔａｃｔｄｉｓｃｏｎ－ｔｉｎｕｉｔｉｅｓ，ｉｆｉｔｉｓｔｏｏｗｅａｋ；ａｌｓｏｄｉｆｉｃｕｌｔｔｏｃａｔｃｈｗｉｔｈｄｕｅａｃｃｕｒａｃｙｔｈｅｔｒａｎｓｉｔｉｏｎｃｏｎｄｉｔｉｏｎｂｅｔｗｅｅｎＭａｃｈｒｅｆｌｅｃｔｉｏｎａｎｄｒｅｇｕｌａｒｒｅｆｌｅｃｔｉｏｎ．Ｔｈｅｉｎｔｅｒｅｓｔｔｏｔｈｉｓｐｈｅｎｏｍｅｎｏｎｉｓｃｏｎｔｉｎ－ｕｉｎｇ，ｅｓｐｅｃｉａｌｙｆｏｒｗｅａｋｓｈｏｃｋｓ，ｂｅｃａｕｓｅｔｈｅｒｅｗａｓｓｙｓｔｅｍａｔｉｃｄｉｓｃｒｅｐａｎｃｙｂｅｔｗｅｅｎｓｉｍ－ｐｌｉｆｉｅｄｔｈｒｅｅｓｈｏｃｋｔｈｅｏｒｙｏｆｖｏｎＮｅｕｍａｎｎ［８］ａｎｄｓｈｏｃｋｔｕｂｅｒｅｓｕｌｔ

关键词： weak reflection Mach reflection anti-diffusion

Oblique Derivative Problems for Second OrderNonlinear Equations of Mixed Type inMultiply Connected Domains

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 281-284页

作者： Guochun WEN(Department of Mathematics, Peking University, Beijing 100871, China) Department of Mathematics Peking University Beijing 100871 China

1FormulationoftheProblemLetDbeNconnectedboundeddomaininthecomplexplaneCwiththeboundaryNZNOD=WUL,wherer=ZrjEn（00},L=ULi’andrhastheendj=1j=1poiatsal=0 详细信息

1FormulationoftheProblemLetDbeNconnectedboundeddomaininthecomplexplaneCwiththeboundaryNZNOD=WUL,wherer=ZrjEn（00},L=ULi’andrhastheendj=1j=1poiatsal=0

关键词： oblique derivative problems quasinonlinear equations of mixed type mul-tiply connected domains.

REGULARITY OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC EQUATION

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Chinese Annals of Mathematics,Series B 2003年第4期24卷 529-540页

作者： CHEN YEMIN School of Mathematics, Peking University, Beijing 100871, China. School of Mathematics Peking University Beijing 100871 China

In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n... 详细信息

关键词： Regularity Dirichlet problem Degenerate Weighted spaces

On the boundary value problem for harmonic maps of the Poincaré disc

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Chinese Science Bulletin 1997年第24期42卷 2025-2045页

作者： LI ZhongDepartment of Mathematics, Peking University, Beijing 100871, China Department of Mathematics Peking University Beijing China

The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfyingwhere ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with normsIt is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B .

关键词： Harmonic maps quasiconfomial mappings universal Teichmüller spaces.