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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (department of mathematics, capital normal university, beijing 100037, china.) department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

Pairing problem of generators in Kac-Moody algebras

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Chinese Science Bulletin 1998年第22期43卷 1872-1879页

作者： LU Caihui department of mathematics, capital normal university, beijing 100037, china department of mathematics Capital Normal University Beijing China

The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra  , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that th... 详细信息

关键词： generator root system real root vector.

Bergman kernel function on Hua construction of the fourth type

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Progress in Natural Science:Materials International 2007年第8期17卷 893-899页

作者： Yin Weiping~(**) Lin Ping (department of mathematics,capital normal university,beijing 100037,china) [a]department of mathematics Capital Normal University Beijing China

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth *** the Bergman kernel function,under the condition of holomorphie automorphism and the standard complete or- thonormal system of the semi-Reinhardt domain,the infinite series form of the Bergman kernel function is *** applying the prop- erties of polynomial andΓfunctions,various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained,which suggest that many of the previously-reported results are only the special cases of our findings.

关键词： Hua construction Bergman kernel function holomorphic automorphism group

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping mathematics department, Xuzhou normal university, Xuzhou 221116, china mathematics department, capital normal university, beijing 100037, china 1. mathematics department Xuzhou Normal University 221116 Xuzhou China 2. mathematics department Capital Normal University 100037 Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, Xuzhou normal university, Xuzhou 221116, china department of mathematics, capital normal university, beijing 100037, china [a]department of mathematics Xuzhou Normal University Xuzhou China [b]department of mathematics Capital Normal University Beijing China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.

ON THE SYMPLECTIC REDUCTIONS

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Chinese Annals of mathematics,Series B 2002年第3期23卷 425-434页

作者： HE LONGGUANG ZHONG DESHOU LIU BAOKANG: department of mathematics, capital normal university, beijing 100037, china. department of mathematics Capital Normal University Beijing 100037 China

A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.

关键词： Symplectic reduction Symplectic action Poisson action Momentum mapping Stable subgroup

The localization of 1-cohomology of transitive Lie algebroids

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Science china mathematics 2006年第2期49卷 277-288页

作者： CHEN Zhuo & LIU Zhangju department of mathematics, capital normal university, beijing 100037, china School of Mathematical Science, Peking university, beijing 100871, china 1. department of mathematics Capital Normal University Beijing 100037 China 2. School of Mathematical Science Peking University Beijing 100871 China

For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.

关键词： transitive Lie algebroid representation cohomology localization.

NONHOMOGENEOUS HOPF EQUATIONS IN HIGHER DIMENSIONS

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Systems Science and Mathematical Sciences 1999年第2期12卷 115-122页

作者： JIU Quansen(department of mathematics, capital normal university, beijing 100037, china) 首都师范大学数学系北京

The existence and uniqueness of the local classical solution of nonhomogenuous Hopf equations in higher dimensions are proved in this paper. This solution is obtained by vanishing the viscosity term of Burger’s equat... 详细信息

关键词： Existence uniqueness non-strictly hyperbolic equations Hopf equations.

Difference discrete connection and curvature on cubic lattice

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Science china mathematics 2006年第11期49卷 1458-1476页

作者： WU Ke, ZHAO Weizhong & GUO Hanying department of mathematics, capital normal university, beijing 100037, china Institute of Theoretical Physics, Chinese Academy of Sciences, beijing 100080, china 1. department of mathematics Capital Normal University Beijing 100037 China 2. Institute of Theoretical Physics Chinese Academy of Sciences Beijing 100080 China

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.

关键词： discrete connection, discrete curvature, noncommutative calculus, lattice gauge theory, discrete Lax pair.

Lifting Minimal Resolutions over Zariskian Filtered Rings

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Acta Mathematica Sinica,English Series 1997年第4期13卷 513-516页

作者： Wang Zhixi department of mathematics, capital normal university, beijing 100037, china

The correlation between the resolution for a Zariskian filtered ring R and that for its associated graded ring G(R) is discussed in this note. Then we show some examples satisfying the condition of the theorem.

关键词： Zariskian filtered ring Minimal filt--projective resolution Gr-semiperfect ring