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Connecting orbits among Denjoy minimal sets for monotone twist map

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Science China Mathematics 2003年第2期46卷 159-168页

作者：程伟程崇庆 Department of Mathematics Nanjing University

In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbitsconnecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of theLagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets andthe global minimizer of the Lagrangian action.

关键词： twist map, Denjoy minimal sets, connecting orbits.

Holomorphic map with unipotent Jacobian matrices in C^3

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Science China Mathematics 2002年第2期45卷 147-154页

作者：陈志华陈文革 Department of Mathematics Tongji University Shanghai 200092 China

We prove that the holomorphic unipotent Jacobian conjecture is valid when n = 3.

关键词： Jacobian conjecture, holomorphic unipotent map, analytic variety.

Multi-segment linear gradient optimization strategy based on resolution map in HPLC

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Science China Chemistry 2006年第4期49卷 315-325页

作者： Andreas Seidel-Morgenstern Max-Planck-Institut fr Dynamik Komplexer Technischer Systeme Magdeburg 39106 Germany

Based on the mechanism of chromatographic retention (the relationship between the retention of solute and the mobile phase conditions) and method of resolution map, several methods of optimizing multi-segment linear gradient elution conditions were proposed according to the different separation requirements of various samples. These methods were verified using literature data. Moreover, the advantages and disadvantages of these methods were compared. It was proved that the third method is a fast optimization method which is capable of separating all the components with relatively high resolution.

关键词： optimization, multi-segment, linear gradient, resolution map, liquid chromatography.

A symplectic map and its application to the persistence of lower dimensional invariant tori

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Science China Mathematics 2002年第5期45卷 598-603页

作者：徐君祥尤建功 Department of Applied Mathematics Southeast University Nanjing 210018 China Department of Mathematics Nanjing University Nanjing 210093 China

We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional torus up to (k,w) where ω is the frequency vector of the torus. That means the normal frequencies with a difference (k,w) may be regarded as the same. As an application, we derive a persistence result on lower dimensional tori of nearly integrable Hamiltonian systems when the second Melnikov’s condition is partially violated.

关键词： sympletic map, persistence, invariant tori.

Regularity of harmonic maps with the potential

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Science China Mathematics 2006年第5期49卷 599-610页

作者： CHU Yuming & LIU Xiangao Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China Institute of Mathematics, Fudan University, Shanghai 200433, China Department of Mathematics Huzhou Teachers College Huzhou China Institute of Mathematics Fudan University Shanghai China

The aim of this work is to prove the partial regularity of the harmonic maps with potential. The main difficulty caused by the potential is how to find the equation satisfied by the scaling function. Under the assumption on the potential we can obtain the equation, however, for a general potential, even if it is smooth, the partial regularity is still open.

关键词： harmonic map, partial regularity, potential.

Second variation of harmonic maps between Finsler manifolds

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Science China Mathematics 2004年第1期47卷 39-51页

作者： SHEN Yibing ZHANG Yan Department of Mathematics Zhejiang University Hangzhou 310028 China Department of Mathematics Zhejiang University Hangzhou 310028 China

The first and second variation formulas of the energy functional for a nondegenerate map between Finsler manifolds is derived. As an application, some nonexistence theorems of nonconstant stable harmonic maps from a F... 详细信息

关键词： Finsler manifold, harmonic map, second variation.

Complex geometry and real geometry

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Science China Mathematics 2005年第Z1期48卷 206-216页

作者： YU Yanlin ZHU Lin FENG Xiuhong Department of Mathematics Suzhou UniversitySuzhou215006China Department of MathematicsSuzhou UniversitySuzhou215006China Department of MathematicsSuzhou UniversitySuzhou215006China

There is a well-known way to generalize the Riemann-Roch operator for Kahler manifold to that for Hermitian manifold. In this paper we show a slightly different way to get a generalized Riemann-Roch operator, which is just the Dirac operator. The difference between the two operators is that the latter one enables the so-called Pythagoras equalities.

关键词： spinor, bispinor, Clifford algebra, Jack map, Pythagoras relation

Transformations and non-degenerate maps

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Science China Mathematics 2005年第Z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Graduate School, Chinese Academy of Sciences, Beijing 100080, China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Graduate School Chinese Academy of Sciences Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

Trace maps over M_3(K) associated with the substitutions

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Science China Mathematics 2002年第2期45卷 165-171页

作者：文志雄 Nonlinear Science Center Lab. of Pure Applied Mathematics Wuhan University Wuhan 430072 China

Let K be a field of characteristic zero and M 3(K) the ring of matrices 3×3 over K. In this paper, we establish first the certain identities of traces of some algebras of Min3(K), then we define the trace mapping of 3 × 3 matrices associated with a substitution over a two-letter alphabet on some algebraic variety and study their properties.

关键词： substitution, trace map, PI-algebras.