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THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM

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Chinese Annals of mathematics,Series B 2000年第3期21卷 375-380页

作者： FANG XIAOCHUN(department of mathematics, tongji university, shanghai 200092, china) E-mail: xfang@*** department of mathematics Tongji University Shanghai 200092 China

The multiplier bimodule of Hilbert bimodule is introduced in a way similar to [1], and its realization on a quotient of bidual space and Tietze extension theorem are obtained similar to that in C-algebra case. As a re... 详细信息

关键词： Realization on bidual space Multiplier Hilbert bimodule Tietze extension theorem

Uniqueness Theorem of Meromorphic Mappings with Moving Targets

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Chinese Annals of mathematics,Series B 2006年第4期27卷 393-400页

作者： Zhihua CHEN Qiming YAN department of mathematics Tongji University Shanghai 200092 China.

Some uniqueness theorems of meromorphic mappings with moving targets are given under the inclusion relations between the zeros sets of meromorphic mappings.

关键词： Uniqueness theorem Meromorphic mapping Moving hyperplane

Area Comparison, Superharmonic Functions, and Applications

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Acta Mathematica Sinica,English Series 2001年第2期17卷 207-216页

作者： Yi Hu YANG department of Applied mathematics, tongji university, shanghai 200092 P. R. china department of Applied mathematics Tongji University Shanghai 200092 P. R. China

In this paper, we study some geometrical and analytic properties of manifolds with non- negative sectional curvature at, infinity. Then, we apply these results to the study of harmonic maps.

关键词： Area comparison Superharmonic functions Harmonic maps

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 103-114页

作者： FANG XIAOCHUN(department of mathematics, tongji university, shanghai 200029, china.) tongji UNIV DEPT MATHSHANGHAI 200029PEOPLES R CHINA

Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. *** introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.

关键词： C~*-groupoid dynamic system Induced representation Haar system

Rational holomorphic maps from B^2 into B^N with degree 2

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Science china mathematics 2006年第11期49卷 1504-1522页

作者： CHEN Zhihua, Jl Shanyu & XU Dekang department of mathematics, tongji university, shanghai 200092, china department of mathematics, university of Houston, Houston, TX 77204, USA department of mathematics Tongji University Shanghai 200092 China department of mathematics University of Houston Houston TX 77204 United States

Rational proper holomorphic maps from the unit ball in C2 into the unit ball CN with degree 2 are studied. Any such map must be equivalent to one of the four types of maps.

关键词： rational holomorphic maps between balls.

The diophantine equation xy+yz+zx=m

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Chinese Science Bulletin 1999年第12期44卷 1093-1095页

作者： CAI Tianxin and JIAO Rongzhen department of mathematics , Zhejiang university, Hangzhou 310037, china Institute of mathematics , tongji university, shanghai 200092, china department of mathematics Zhejiang University Hangzhou China Institute of mathematics Tongji University Shanghai China

Under the generalized Riemann hypothesis, it is proved that the Diophantine equation xy + yz + zx = m always has a solution except for 18 positive integers m.

关键词： diophantine equation form class group ideal class group generalized Riemann hypothesis.

The truncated Second Main Theorem and uniqueness theorems

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Science china mathematics 2010年第3期53卷 605-616页

作者： CHEN ZhiHua 1 , RU Min 2, & YAN QiMing 1 1 department of mathematics, tongji university, shanghai 200092, china 2 department of mathematics, university of Houston, Houston, TX 77204, USA 1. department of mathematics Tongji University Shanghai 200092 China2. Department of Mathematics University of Houston Houston TX 77204 USA

In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.

关键词： value distribution theory uniqueness theorem meromorphic mappings Fujita’s conjecture

THE INVARIANT CONTINUOUS-TRACE C*-ALGEBRAS BY THE ACTIONS OF COMPACT ABELIAN GROUPS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 489-498页

作者： FANG XIAOCHUN (department of Applied mathematics, Tonaii university, shanghai, 200092, china.) tongji Univ Dept Appl Math Shanghai 200092 Peoples R China

The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra Aα in certain C*-dynamic system (A, G, α) by introducing an α-invariant　continuous trace property. For separable C*-dynamic system (A, G, α) with G compact and　abelian,A liminal, αt ∈ AutCb(A) (A) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains Aα continuousitrace, is obtained.

关键词： Continuous-Trace Action of Group C*-Algebra

AN EMBEDDING THEOREM BETWEEN SPECIAL LINEAR GROUPS OVER ANY FIELDS

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Chinese Annals of mathematics,Series B 1995年第4期16卷 477-486页

作者： ZHA JIANGUO (Departmellt of Applied mathematics, tongji university, shanghai 200092, china.) tongji UNIV DEPT MATH APPLSHANGHAI 200092PEOPLES R CHINA

Abstract homomorphisms between subgroups of algebraic groups were studied in detail by ***, ***.[1] and ***.[2] provided that the images of the homomorphisms are Zariski dense subsets and that the fields over which algebraic groups are defined are infinite. The purpose of this paper is to determine all embedding homomorphisms of SLn(k) into SLn(K) when k and K are any fields of the same characteristic, without assumption of Zariski density and infinitude of fields. The result in this paper generalizes a result of Chen Yu on homomorphisms of two dimensional linear groups[3].

关键词： Classical groups Homomorphisms Field