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DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA

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Chinese Annals of mathematics,Series B 1996年第2期17卷 199-212页

作者： CHEN CAOYU department of mathematics, Shanghai Normal university, Shanghai 200234, china. SHANGHAI NORMAL UNIV DEPT MATHSHANGHAI 200034PEOPLES R CHINA

Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.

关键词： Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra

A THEOREM ON PLURICANONICAL MAPS OF NONSINGULAR MINIMAL THREEFOLDS OF GENERAL TYPE

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Chinese Annals of mathematics,Series B 1998年第4期19卷 415-420页

作者： CHEN MENG (department of mathematics, TOng n university, Shanghai 200092, china.) Tongji Univ Dept Math Shanghai 200092 Peoples R China

Let X be a complex nonsingular projective threefold of general type. It is shown that the dimension of the image of X through m-canonical maps is at least two for every m 3.

关键词： Minimal model Pluricanonical map Composed of a pencil

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

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Chinese Annals of mathematics,Series B 2003年第2期24卷 249-260页

作者： WANG WENSHENG LIN ZHENGYAN department of mathematics, Zhejiang university, Hangzhou 310028, china. department of mathematics, Hangzhou Teacher’s College, Hangzhou 310012, china. E-mail: wswang@*** department of mathematics, Zhejiang university, Hangzhou 310028, china. Zhejiang Univ Dept Math Hangzhou 310028 Peoples R China Hangzhou Teachers Coll Dept Math Hangzhou 310012 Peoples R China

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of th... 详细信息

关键词： Ornstein-Uhlenbeck processes Stationary Gaussian processes Modulus of continuity Law of the iterated logarithm

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

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Chinese Annals of mathematics,Series B 1996年第2期17卷 227-236页

作者： HAN DEGUANG department of mathematics, Qufa Normal university, Qufu 273165, Shandong, china. QUFA NORMAL UNIV DEPT MATHQUFU 273165SHANDONGPEOPLES R CHINA

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0+ (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.

关键词： Nest algebra Derivation Continuity Linearity Banach space

FUZZY PRETOPOLOGICALSPACES, AN EXTENSIONALTOPOLOGICAL EXTENSION OF FTS

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Chinese Annals of mathematics,Series B 1999年第3期20卷 309-316页

作者： ZHANG DEXUE(department of mathematics, Sichuan university, Chengdu 610064, china.)(Project supported by the National Natural Science Foundation of china.) Sichuan Univ Dept Math Chengdu 610064 Peoples R China

The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topological spaces. Moreover this category contains both the category of pretopological spaces and the category of probabilistic neighbourhood spaces as simultaneously bireflective and bicoreflective full subcategories.

关键词： Fuzzy topological spaces Fuzzy pretopological spaces Extensional topological category

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, Beijing 100871, china. Beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

ADDITIVE FUNCTIONALS AND PERTURBATION OF SEMIGROUP

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Chinese Annals of mathematics,Series B 2001年第4期22卷 503-512页

作者： JIN MENGWEI, YING JIANGANG department of mathematics, Zhejiang university, Hongzhou 310027, china. Email: .jmw@*** department of mathematics, Zhejiang university, Hongzhou 310027, china. Email: jying@*** department of mathematics Zhejiang University Hongzhou 310027 China

The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are di... 详细信息

关键词： Right processes Revuz measures Additive functional

CHAOS FOR MIXING TRANSFORMATIONS

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Chinese Annals of mathematics,Series B 1994年第4期15卷 501-506页

作者： LIAO GONGFU (department of mathematics,Jilin university, Changchun 130023, china.) JILIN UNIV DEPT MATH CHANGCHUN 130023 PEOPLES R CHINA

For a class of mixing transformations of a compact metric space it is proved that each chaoticsubset is'small' but the possibility for any finite subset to display chaotic behavior is 'large'.

关键词： Compact metric space Chaotic subset Mixing transformation Topological mixing map.

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u^k(u)~α

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Chinese Annals of mathematics,Series B 2005年第3期26卷 361-378页

作者： FANGDAOYUAN WANGCHENGBO departmentofmathematics ZhejiangUniversityHangzhou310027China

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H3 and Hs for semilinear wave equations with polynomial nonlinearity in u and (?)u. This ill-posed re... 详细信息

关键词： Semilinear wave equation Low regularity Local well-posedness Ill-posedness