A Class of Simple Modules for Electrical Lie Algebra of Type D5

The simple modules for electrical Lie algebra of type D₅ were investigated. The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules. The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp₄ or Verma module.     

Simple generalized restricted modules for graded Lie algebras of Cartan type

Let %L=X(m:n) (2), X∈{W,S,H,K}% be a simple graded Lie algebra of Cartan type over a field %F% of characteristic p>3. With the aid of Farnsteiner's generalized reduced Verma module, a connection between the simple GR modules and simple graded modules of L is eastablished.     

Implicational lattices and generalization of Stone’s representation theorem

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone's representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.     

Observable Algebra in Field Algebra of G-spin Models

Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observabl ealgebra AH, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that AH is a C^*-algebra. The correspondence between H and AH is strictly monotonic. Finally, a duality between D(H) and A. is given via an irreducible vacuum C^* -representation of F.     

NONLINEAR GENERALIZED HASEMAN BOUNDARY VALUE PROBLEMS FOR FIRST ORDER QUASILINEAR ELLIPTIC SYSTEMS IN THE PLANE

1 Problems and ConditionsA class of the lst order quasilinear elliptic systems in the plane, on the basis of Douglis algebra, can bewritten in the simple form Dw=F(z. w) , here D = / x+ / y+e(a / x+ / y) be the Douglis opearator[1], F be a hypercomplex function.Let be a simple and smooth closed curve in the complex plane C,D~+ be the simple connected domainbounded by and D~-=C- (D~+ ∪ ). Out problem is to find piecewise regular solutions w(z) for Dw=F(z,w) with jump curve in the whole plane that have fixed integer order at infinity and satisfy the condi-tion on ; w~+ (τ) = G_1(τ)w~- (a(τ)) + G_2(τ)w~+ (β(τ)) +g(τ,w+ (τ),w~- (τ)), which be calledthe nonlinear generalized Haseman boundary value problems. By suitable transformations the problem can     

Semantic Cache Replacement Strategy for XML Algebra-Based Query Optimization

Aiming at the fact that traditional cache replacement strategy lacks pertinence to the semantic cache in the process of extensible markup language(XML) algebra query, a replacement strategy based on the semantic cache contribution value is proposed. First, pattern matching rules for XML algebra query and semantic caches are given. Second, the method of calculating the semantic cache contribution value is proposed. In XML documents with four different sizes, the experimental results of time efficiency show that this strategy supports environment of the XML algebra query and it has better time efficiency than both least frequency used(LFU) and least recently used(LRU).     

A representation of sl(2;C) on clifford algebra of even dimension

Under the foundation of Hermitean Clifford setting,we define the fundamental operators for complex Clifford algebra valued functions,obtain some properties of these operators,and discuss a representation of sl(2;C) on Clifford algebra of even dimension.     

Single boson realizations of the deformed angular momentum algebra of Witten’s types

By generalizing the Holstein-Primakoff realization and the Dyson realization of the Lie algebra SU(2),various realizations of the deformed angular momentum algebra Rc0,c1,c2q,s,a five-parameter deformed SU(2) by combining Witten’s two deformation schemes,are investigated in terms of the single boson and the single inversion boson respectively.For each kind,the unitary realization,the non-unitary realization,and their connection by the corresponding similarity transformation are respectively discussed.     

Twisted smash products of multiplier Hopf algebras

In the present paper, we will consider A-bimodule algebra for a regular multiplier Hopf algebra (A,Δ). Using bimodule algebra, we construct the twisted smash product of multiplier Hopf algebras.     

二维布尔运算

In this paper, a mechanismic analysis was made on singular condition of multipoints and multiedges in boolean operation. On the basis of intersection points eigenvalue, the problem of quadruplepoint and multiedges was addressed, and a complete solution for the singular problem on 2D boolean operation was given in a simple way.     

The Engel''''s theorem for braided lie algebras

Throughoutthis paper,let H be a Hopf algebra.Aboutthe propertiesand conceptionsof braided Lie alge-bras,we refer to[1 ].Definition1　Let Abe a finite- dimensional algebra( not necessarily associative) in HHYD.By a braidedderivation of A we mean a HHYD- morphismδ:A→ A satisfying the following rule:δ( ab) =δ( a) b+ (δ(-1 ) .a)δ0 ( b) . ( 1 )　　 Denote by Der H A the setof all braided derivations of A .Now,let L be a braided Lie algebra.Ifx∈ L ,then y|→ [x,y]is an endomorphism …     

Treatment of Dyes Wastewater by a New Kind of Bio - Fluid Bed

A new kind of bio-fluid bed used to treat dyes wastewater is described in detail due to its several special features,such as high removal efficiency,simple struc-ture,shock load resistance,etc.By means of analyzing the experiment data,the results show that the dye wastewater's organic matter is removed greatly after be-ing treated by this new kind of bio-fluid bed.On the other hand,the removal efficiency of chromaticity of the     

The Centralizer on H—Separable Smash Products

Let H be finite dimensinonal Hopf algebra over a field and A an H-module algebra.The H induces an action on the CA#H(A) by adjoint and CA#H(A)^H=Z(A#H)=C,where CA#H(A) denotes the centralizer which algebra A in A#H and Z(A#H)the center of A#H.The aim of this paper is to discuss,the Galois conditions on the centralizer CA#H(A).We prove that CA#H(A)/ZA#H is H^*-Galois if and only if CA#H(A)#H/CA#H(A) is H-separable).Furthermore,if H is a finite dimensional semisimple Hopf algebra and CA#H(A)#H is an Azumaya C-algebra or A#H/A is H-separable,CA#H(A)statisfies the double centralizer property in CA#H(A) H,CA#H(A)?C is separable and there exists a cocommutative left integral t∈∫^1 H,then CA#H(A)/C is H^*-Galois.     

ON LIE ALGEBRAS WITH A CYCLIC NILPOTENT DERIVATION

A derivation of a Lie algebra is said to be cyclic nilpotent, if, as a linear transformation, it is cyclic nilpotent, i. e, its index of nilpotency is equal to the dimension of the algebra. A Lie algebra with such a derivation is called a 2-algebra. In this paper, the structure of s-algebras over an arbitrary field of characteristic zero is investigated.This paper can bs divided into two parts. In the first part, the following two main theorems are proved.     

Influence of polymer solution on the morphology and local structure of NH4ZnPO4powders synthesized by a simple precipitation method at room temperature

NH₄Zn PO₄powders were synthesized using a simple precipitation method at room temperature.The effects of polyvinyl pyrrolidone(PVP),polyvinyl alcohol(PVA),glucose,and hexadecyltrimethylammonium bromide(CTAB)solutions on the morphology and structure of the prepared samples were investigated.The phase composition and morphology of the prepared samples were characterized using X-ray diffraction and scanning electron microscopy,respectively.Depending on the polymer sources,the hexagonal structure prepared using non-surfactant of water completely changed to monoclinic structure when CTAB was added.X-ray absorption near-edge structure(XANES)and X-ray photoelectron spectroscopy(XPS)were performed to study the local structure and surface electronic structure of the prepared samples,confirming that the oxidation states of P and Zn ions are⁵⁺and²⁺,respectively.On the basis of the results of inductively coupled plasma atomic emission spectroscopy(ICP-OES),the NH₄Zn PO₄powders can be classified as a slow-release fertilizer where less than 15%of the ions were released in 24 h.A simple precipitation method using water,PVP,PVA,sucrose,and CTAB as a template can be used to synthesize NH4 Zn PO4 powders.In addition,this method may be extended for the preparation of other oxide materials.     

Yetter-Drinfeld模上的张量代数

The antipode of a Yetter-Drinfeld Hopf algebra is an anti-algebra and anti-coalgebra map is proved. It is also proved that the tensor algebra of Yetter-Drinfeld Hopf module is a Yetter-Drinfeld Hopf algebra.     

A Voronoi-based spatial algebra for spatial relations

Spatial relation between spatial objects is a very important topic for spatial reasoning, query and analysis in geographical information systems (GIS). The most popular models in current use have fundamental deficiencies in theory. In this paper, a generic algebra for spatial relations is presented, in which (i) appropriate operators from set operators (i.e. union, intersection, difference, difference by, symmetric difference, etc.) are utilized to distinguish the spatial relations between neighboring spatial objects; (ii) three types of values are used for the computational results of set operations-content, dimension and number of connected components; and (iii) a spatial object is treated as a whole but the Voronoi region of an object is employed to enhance its interaction with its neighbours. This algebra overcomes the shortcomings of the existing models and it can effectively describe the relations of spatial objects.     

Pairing problem of generators in Kac-Moody algebras

The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra  , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that the subalgebra generated by y and h or y and x β contains the derived algebra g′(A) of g(A) .     

A probabilistic paradigm for handling uncertain objects in GIS by randomized graph algebra

Probability theory faces difficulties when it is applied to describing uncertain objects in geographic information system (GIS). This is mainly due to the fact that an object in GIS is normally described by a series of discrete vertexes. Modeling uncertainty objects should be therefore based on error of the composed vertexes. This type of model is normally complex and relatively difficult to implement because of many unknown factors, such as the number of vertexes of a polygon, error nature of each individual vertex and error correlation among the vertexes. In this paper, a probabilistic paradigm for handling uncertain objects in GIS by randomized graph algebra is presented. The theoretical basis for this paradigm is the randomized graph algebra-a probability theory for graph-which is newly proposed in this study. Classical probability theory is based on numerical algebra and is also an extension of numerical algebra by further defining probability density within a numerical domain. In the same token, this study begins with defining graph algebra as the basis for probability theory for graph. First, we adopt the theory of graph algebra and further refine the theory by defining the modulo operation for graph. As a result, a graph can thereafter be treated as a "number" and operated by "addition", "subtraction" and others. Second, we construct a measure space by generating sigma-algebra and defining measurable function upon it. The measure space becomes a probability space when the measurable function is a probability density function. Third, we propose the probabilistic paradigm for describing and inferring the uncertainty of geometric objects in GIS by applying the developed randomized graph algebra.