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Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules

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Science China Chemistry 2009年第11期52卷 1892-1910页

作者： LI Yun ZHAO XueZhuang XU XiuFang SHANG ZhenFeng ZHOU Zhen CAI ZunSheng WANG GuiChang LI RuiFang College of Chemistry Nankai UniversityTianjin 300071China

On the basis of our recent studies on the molecular fuzzy point group symmetry,we further probe into the more complicated planar one-dimensional fuzzy periodic molecules-straight chain conjugate *** for the fuzzy translation transformation,the space transformation of the fuzzy screw rotation and the glide plane will be referred *** addition,other fuzzy point symmetry transformation lain in the space transformation is *** there is a correlation between the fuzzy symmetry characterization caused by the transition of the point symmetry elements and by certain space symmetry *** the molecular orbital,the irreducible * representation component is analyzed besides the membership function of the fuzzy symmetry ***,we inquire into the relativity between some molecular property and the fuzzy symmetry characterization.

关键词： conjugate polyene one-dimensional fuzzy periodic transformation the membership function irreducible representation component

irreducible * representations of Birman-Wenzl algebras

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Science China Mathematics 1995年第11期38卷 1344-1353页

作者：潘峰 Department of Physics Liaoning Normal University Dalian 116022 China (CCAST (World Lab.) Beijing 100080

irreducible * representations of Birman-Wenzl algebras are constructed by using the induced representation and the linear equation method. Self-adjoint representations of Birman-Wenzl algebras Cf (r, q) with f≤4 are pr... 详细信息

关键词： Birman-Wenzl algebra self-adjoint representation irreducible representation.

Biparametric irreducible * representations of Braid Groups

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Science China Mathematics 1994年第11期37卷 1370-1377页

作者：仝殿民朱诚久杨善德 Department of Physics Jilin UniversityChangchun 130023PRCDepartment of PhysicsJilin UniversityChangchun 130023PRCDepartment of PhysicsJilin UniversityChangchun 130023PRC

A series of irreducible * representations of braid group Bn are *** means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are *** the eigenvectors of H(i) as representation bases,the b... 详细信息

关键词： braid group irreducible representation Yang diagram.

Relations of representations of A_∞ and C_∞

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Chinese Science Bulletin 1996年第14期41卷 1155-1159页

作者：姜翠波孟道骥 Department of Mathematics Yantai Teachers University Yantai 264025 China Department of Mathematics Nankai University Tianjin 300071 China

In refs. [1—3] level one highest weight representations of complete infinite rank affine Lie algebra A_∞ were discussed. Since C_∞ is a subalgebra of A_∞, any representation of A_∞ induces a representation of C_... 详细信息

关键词： complete infinite rank affine Lie algebra integrable representation irreducible highest weight representation.

Inhomogeneous Differential Realization, Boson-Fermion Realization of OSP(2,1) Superalgebra and Its representations

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深圳信息职业技术学院学报 2000年第2期 80-85页

作者：陈永清深圳教育学院广东深圳518029

Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are *** new indecomposable and irreducible * representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl *** the finite dimensional irreducible * representation of the OSP(2,1)superalgebra is naturally obtained as special cases.

关键词： Lie superalgebras Inhomogeneous differential realization Boson-fermion realization irreducible representation

Some Remarks on the Non-Abelian Fourier Transform in Crossover Designs in Clinical Trials

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Applied Mathematics 2014年第6期5卷 917-927页

作者： Peter Zizler Department of Mathematics/Physics and Engineering Mount Royal University Calgary Canada

Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concerning G-decorrelated decompositions of functions in l2(G). These G-decorrelated decompositions are obtained using the G-convolution either by the irreducible characters of the group G or by an orthogonal projection onto the matrix entries of the irreducible * representations of the group G. Applications of these G-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William’s 6×3?design with 3 treatments. In our example, the underlying group is the symmetric group S3.

关键词： Non-Abelian Fourier Transform Group Algebra irreducible representation irreducible Character G-Circulant Matrix G-Decorrelated Decomposition Crossover Designs in Clinical Trials

The Matric Expressionsin Pauli-Dirac representation

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International Journal of Mining Science and Technology 1997年第2期18卷 81-83页

作者：张学龙李光惠

In this paper Dirce group is constructed on the basis of algebraic properties of α’s and β’s matrices in Dirac equation. It is then establisbed that the dimensions of the matrices must be four (i. e., 4 × 4 matri... 详细信息

关键词： Hermitian finite group irreducible representation eigenvector

On the classification of compact quantum groups U_θ(2)

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Science China Mathematics 2010年第5期53卷 256-269页

作者： ZHANG XiaoXia Department of Mathematics,Yantai University,Yantai 264005,China

In this paper,we show that the corepresentation of compact group Uθ(2) on the vector space is determined by its infinitesimal generators B0,B2,A0,A1 and A2,where θ is an irrational *** also show that B0 and B2 commute with Aj,j = 0,1,2,so B0,A0,A1 and A2 are sl(2,C) loop *** we exhibit all irreducible * representations of Uθ(2),which are different from those of group U(2),and use above results to give the classification of quantum groups Uθ(2),which is analogous to that of irrational algebra Aθ.At the same time,we also give all the forms of automorphisms on quantum group Uθ(2).

关键词： compact quantum group comultiplication irreducible representation