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Ritt's theorem and the Heins map in hyperbolic complex manifolds

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Science China Mathematics 2005年第Z1期48卷 238-243页

作者： Marco Abate Filippo Bracci Dipartimento di Matematica Università di Pisa Largo Pontecorvo 556127 PisaItalyDipartimento di Matematica Università di Roma "Tor Vergata"Via della Ricerca Scientifica00133 RomaItaly

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic self-map f: X →X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.

关键词： holomorphic self-map, fixed point, Wolff point, Ritt's theorem, Heins map, Stein manifold.

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 China Department of Mathematics Nanjing University Nanjing 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.

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 China

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

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

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.

Stress emission of helium and argon in coal seams

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Science China Earth Sciences 2003年第6期46卷 547-560页

作者：朱铭周瑞光尹代勋高玉生张福松成彬芳刘强罗信华 InstituteofGeologyandGeophysics ChineseAcademyofSciences NantongMiningBureau TianjinInvestigation DesignandResearchInstituteofWaterResourcesandHydropower

In the Yutianbao Mine, the Nantong Coal Field, Chongqing, a lot of gas samples were measured and analyzed. It has been found in these samples that helium is sensitive to stress concentration, while argon is sensitive to stress release. Compared with the flowing out of gas it-self, the combination of helium and argon can be more suitably used as an indicator to predict gas outburst. In a mining area of this mine, both δ He > 30 and δ Ar maps of δ He, δ Ar and CH4 can provide a guidance for engineering monitoring.

关键词： helium, argon and its isotope, stress emanation, prediction of gas outburst, contour map, engineering geology.

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

Time-like Willmore surfaces in Lorentzian 3-space

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Science China Mathematics 2006年第1期49卷 75-85页

作者： DENG Yanjuan WANG Changping LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P+ 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13.

关键词： Lorentzian 3-space, Willmore surfaces, conformal Gauss map, dual theorem.

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.