En">The Second Cohomology of sl ( m | 1 ) with Coefficients in its Enveloping Algebra is Trivial

Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl ( m | 1 ) m 2, with coefficients in its enveloping algebra is trivial. The obstacles in solving the analogous problem for sl ( 3 | 2 ) are also discussed.     

Noncommutative Cohomology and Electromagnetism on $$\mathbb{C}$$ q [SL2] at Roots of Unity

We compute the noncommutative de Rham cohomology for the finite dimensional q-deformed coordinate ring _q [SL₂] at odd roots of unity and with its standard four-dimensional differential structure. We find that H ⁱ is highly nontrivial compared to case of generic q and has as many modes 1 : 4 : 6 : 4 : 1 as the dimension of the exterior algebra. We solve the spin-0 and Maxwell theory on _q [SL₂], including a complete picture of the self-dual and anti-self dual solutions and of Lorentz and temporal gauge fixing. The system behaves in fact like a noncompact space with self-propagating modes (i.e., in the absence of sources). We also solve with examples of electric and magnetic sources including the biinvariant element H ¹ which we find can be viewed as a source in the local (Minkowski) time-direction (i.e. a uniform electric charge density).     

双参数变形多模玻色算符的代数结构及其应用(Ⅱ)

给出了双参数变形量子代数ＳＵ（２）ｑ，ｓ和ＳＵ（１，１）ｑ，ｓ的多模Ｊｏｒｄａｎ－Ｓｃｈｗｉｎｇｅｒ实现。     

SO（d,d;Z) Transformation Property for Gauge Fluxes and Ramond-Ramond Fields in Noncommutative Geometry

In this paper we study the spinor constructions of gauge fluxes and Ramond-Ramond fields on noncommutative tori T^d up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern-Simons Lagrangian in toroidal compactification as a product of spinors.     

Loop Observables for BF Theories in Any Dimension and the Cohomology of Knots

A generalization of Wilson loop observables for BF theories in any dimension is introduced within the Batalin–Vilkovisky framework. The expectation values of these observables are cohomology classes of the space of imbeddings of a circle. One of the resulting theories discussed in the Letter has only trivalent interactions and, irrespective of the actual dimension, looks like a three-dimensional Chern–Simons theory.     

The Hopf Algebra Structure of GL(1, Hq) and the Isomorphism between SPq(1)and SUq(2)

In this Letter, we introduce the Hopf algebra structure of the quantum quaternionic group GL(1, H₁) and discuss the isomorphism between the quantum symplectic group SP_q(1) and the quantum unitary group SU_q(2).     

利用SU（2）_（q，s）量子代数的两参数变形振子实现讨论SU（2）_（q，s）相干态

利用ＳＵ（２）ｑ，ｓ量子代数的两参数变形振子实现构造出与Ｐｅｒｅｌｏｍｏｖ相干态形式不同的ＳＵ（２）ｑ，ｓ相干态．证明了ＳＵ（２）ｑ，ｓ，量子代数的表示基是正交的，并讨论了它的相干态的归一性和完备性．指出ＳＵ（２）ｑ，ｓ相干态的相干性受参数ｑ，ｓ的影响，它比单参数变形ＳＵ（２）ｑ相干态更具一般性．     

Mathematical structure of the three-dimensional（3D） Ising model

An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a(3+1)-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2) A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/(kBT) of both the hard-core and the Ising models has been proved only for β0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.     

双参数变形量子代数SU（1，1）_（q，s）的Nodvik实现和Holstein—Primakoff实现

给出了双参数变形量子代数ＳＵ（１，１）ｑ，ｓ的Ｎｏｄｖｉｋ实现和Ｈｏｌｓｔｅｉｎ－Ｐｒｉｍａｋｏｆｆ实现，并给出了ＳＵ（１，１）ｑ，ｓ，和双参数变形振子的变形映射。     

Nuclear Algebraic Geometry and SO(10)

In this contribution nuclear representations of the Dirac ring, developed over many years, are shown to be a particular case of a theorem in algebraic geometry which at the same time associates them with a Hodge decomposition of a Kaehler manifold. This yields a shape that in some cases is independent of any appeal to a symmetry group. However, because the nuclear representations are in the infinitesimal ring of SO(4) and the internal space of each representation is in a Kaehler (even Calabi-Yau) manifold K; the group SO(10) = SO(4) × K can give additional information. This paper develops the very fruitful symbiosis between algebra and irreducible representations of SO(10) and covers some aspects of string theory.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

一组新型络合物晶体结构与光学性能的研究

研究了二氯三烯丙基硫脲合镉(ATCC),二氯三烯丙基硫脲合汞(ATMC)和二溴三烯丙基硫脲合镉(ATCB)三种晶体的结构特点.首次报道了ATMC和ATCB晶体的非线性光学系数及倍频性能;文中分析比较了三种晶体的非线性光学性能;讨论了晶体结构与性能的关系,为探索高效非线性光学新材料提供依据.     

The algebra and geometry ofSU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular groupSU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in anSU(3) covariant manner. Thef andd symbols ofSU(3) lead to two ways of ‘multiplying’ two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization ofSU(3) is developed as a generalization of that forSU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.     

Introduction to M(atrix) theory and noncommutative geometry

Noncommutative geometry is based on an idea that an associative algebra can be regarded as “an algebra of functions on a noncommutative space”. The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang–Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was found recently that Yang–Mills theories on noncommutative spaces appear naturally in string/M-theory; the notions and results of noncommutative geometry were applied very successfully to the problems of physics.

In this paper we give a mostly self-contained review of some aspects of M(atrix) theory, of Connes’ noncommutative geometry and of applications of noncommutative geometry to M(atrix) theory. The topics include introduction to BFSS and IKKT matrix models, compactifications on noncommutative tori, a review of basic notions of noncommutative geometry with a detailed discussion of noncommutative tori, Morita equivalence and -duality, an elementary discussion of noncommutative orbifolds, noncommutative solitons and instantons. The review is primarily intended for physicists who would like to learn some basic techniques of noncommutative geometry and how they can be applied in string theory and to mathematicians who would like to learn about some new problems arising in theoretical physics.

The second part of the review (Sections 10–12) devoted to solitons and instantons on noncommutative Euclidean space is almost independent of the first part.     

Y(Fe,M)12化合物的电子结构与磁性(M=Nb,Si)

采用新近发展的全势能线性缀加平面波((L)APW) 局域轨道(lo)和广义梯度近似(GGA)密度泛函方法计算了Y(Fe,M)12化合物(M=Nb,Si)的电子结构,得到了相应的总态密度和局域态密度,并分析了替代原子与替代晶位不同引起态密度的变化。根据计算结果预测的居里温度变化与实验结果基本一致。     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU（2） Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation descr/bing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some ttamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

基于几何标记模型参数反演的作物株形敏感性分析

传统的利用冠层反射光谱和光谱指数进行叶面积指数反演时,株形(利用平均叶倾角ALA等指标来表征)对叶面积指数的反演精度存在较大的影响,使得利用遥感手段进行作物长势监测和肥水调控决策时,株形因素不容忽略,以免造成遥感监测精度不高。研究首先利用模拟作物冠层反射光谱的PROSAIL模型将影响作物冠层光谱的叶面积指数等其他参数保持不变的情况下,分析了ALA对作物冠层反射光谱的影响;并基于半经验的几何光学模型对作物株形对冠层光谱影响的不同波段受到ALA变化的敏感性进行了定量分析,对于研究如何消除株形影响,提高遥感反演作物长势和叶面积指数的精度和提高作物大面积、快速遥感肥水调控决策水平具有重要意义。     

基于核驱动模型参数反演的作物株型遥感识别

传统的单一方向遥感只能得到地面目标一个方向的辐射量,缺乏足够信息来同时推断像元的波谱和空间结构。多角度的反射光谱对于植被结构特征的估算及类型鉴别比垂直光谱具有明显的优越性。将多角度观测数据和核驱动模型结合,构建了基于核参数各向同性核所占比例(f_iso),几何光学核所占比例(f_geo)和体散射核所占比例(f_vol)的植被结构参数敏感指数(SPEI)来进行作物株型的遥感识别,并将SPEI与结构散射指数(SSI)和归一化差异参数指数(NDFI)等对紧凑型品种京411和披散型品种中优9507的实测多角度冠层方向反射率数据进行了核参数的反演,不同指数对作物株型结构表现出的敏感性依次为：SPEI＞SSI＞NDFI。SPEI较以往学者构建的指数对不同株型品种遥感识别具有更好的敏感性,该方法可以在其他作物上拓展应用,具有很好的理论基础和应用前景。