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A family of transitive modular Lie superalgebras with depth one

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Science China mathematics 2007年第10期50卷 1451-1466页

作者： Wen-de LIU~(1+) Yong-zheng ZHANG~2 ~1 Department of mathematics,harbin normal university,harbin 150080,China ~2 Department of mathematics,Northeast {4. university,Changchun 130024.China 1. Department of mathematics Harbin Normal University Harbin 150080 China 2. Department of mathematics Northeast Normal University Changchun 130024 China

The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian *** restricted Lie superalgebras are also considered.

关键词： flag, divided power algebra, modular Lie superalgebra, embedding theorem

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2 1. Department of mathematics,Inner Mongolia normal university, Huhhot 010022, China 2. Department of mathematics, {4. Institute of Technology, {4. 150006, China Department of mathematics Inner Mongolia Normal University Huhhot China Department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Study on Green Residential Space Design

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IJLAI Transactions on Science and Engineering

IJLAI Transactions on Science and Engineering 2024年第1期2卷 32-37页

作者： Yu Jiang Shenyang normal university No.253 Huanghe North Street Shenyang 110034China

With the ever-changing nature,green ecology has become an international trend of ***,the green ecological design of residential space has become the main melody of people’s *** always implement the concept of ecological and environmental protection in the design process,attach importance to the ecological effect of residential space,carry out reasonable budget and use of environmentally friendly decorative materials,reduce the waste of materials,save money and save resources at the same time,and protect the *** the same time,people began to put their hopes on the residential space design,which made the green residential space design began to *** the bold exploration and practice of designers,the design of green residential space will be endowed with more distinctive characteristics and unique *** from the concept of green design,this paper explores the method of green space design through typical analysis.

关键词： Green Residential space Haze

Three classes of smooth Banach submanifolds in B(E,F)

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Science China mathematics 2007年第9期50卷 1233-1239页

作者： Ji-pu Ma Tseng Yaun Rong Functional Analysis Research Center,harbin normal university,harbin 150025,China 1. Tseng Yaun Rong Functional Analysis Research Center Harbin Normal University Harbin 150025 China

Let E,F be two Banach spaces, and B(E,F), Ф(E,F), SФ(E,F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result: Let Σ be any one of the following sets: {T ∈ Ф(E,F) : IndexT = const. and dim N(T) = const.}, {T ∈ SФ(E,F) : either dim N(T) = const. < ∞ or codim R(T) = const. < ∞} and {T ∈ R(E,F) : RankT =const.< ∞}. Then Σ is a smooth submanifold of B(E,F) with the tangent space T AΣ = {B ∈ B(E,F) : BN(A) ? R(A)} for any A ∈ Σ. The result is available for the further application to Thom’s famous results on the transversility and the study of the infinite dimensional geometry.

关键词： semi-Fredholm operators smooth submanifold transversility generalized inverse 4.B38 15A29 58A05

A new definition of restricted Lie superalgebras

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Chinese Science Bulletin 2000年第4期45卷 316-321页

作者： WANG Ying & ZHANG Yongzheng1. Department of mathematics, harbin Institute Technology, harbin 150001, China 2. Department of mathematics, Northeast {4. university, Changchun 130024. China Department of mathematics Harbin Institute Technology Harbin China Department of mathematics Northeast Normal University Changchun China

A new definition of restricted Lie superalgebras has been given; some important results on the representation theory of restricted Lie superalgebra have been obtained.

关键词： restricted Lie superalgebra p-mapping p-semilinear mapping α-representation.

Moment bounds for IID sequences under sublinear expectations

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Science China mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2 1Department of mathematics,Qufu normal university,Qufu 273165,China 2school of mathematics,Shandong university,Jinan 250100,China 1. Department of mathematics Qufu Normal University Qufu 273165 China2. School of Mathematics Shandong University Jinan 250100 China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

SPECTRAL AND PSEUDOSPECTRAL APPROXIMATIONS IN TIME FOR PARABOLIC EQUATIONS

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Journal of Computational mathematics 1998年第2期16卷 107-120页

作者： Fa-yong Zhang (Department of mathematics, Heilongjiang university, harbin 150080, China) Heilongjiang Univ Dept Math Harbin 150080 Peoples R China

In this paper, spectral and pseudospectral methods are applied to both time and space variables for parabolic equations. Spectral and pseudospectral schemes are given, and error estimates are obtained for approximate ... 详细信息

关键词： spectral approximation pseudospectral approximation parabolic equation error estimate

On Form Invariance,Lie Symmetry and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

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Communications in Theoretical Physics 2007年第7期48卷 37-42页

作者： ZHAO Shu-Hong LIANG Li-Fuoi school of Civil Engineering,harbin Engineering university,harbin 150001,China2 Engineering College,Northeast Agricultural university,harbin 150030,China school of Civil Engineering Harbin Engineering University Engineering College Northeast Agricultural University

In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noether'sconserved quantity,the new form conserved quantity,and the Hojman's conserved quantity of system are derived ***,an example is given to illustrate the application of the result.

关键词： form invariance Lie symmetry conserved quantity generalized classical mechanics Lagrange’s equation

APPROXIMATION OF SOLUTION OF RELAXED DIFFERENTIAL INCLUSION ON COMPACT SET

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Systems Science and Mathematical Sciences 1996年第4期9卷 289-294页

作者： SONG Wen(Department of mathematics, harbin normal university, harbin 150080, China) 哈尔滨师范大学数学系黑龙江哈尔滨 150080

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关键词： Banach space differential inclusion uniform approximation.