Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the...Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.展开更多
This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is dis...This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.展开更多
The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are compute...The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz operators.In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.展开更多
Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth m...Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.展开更多
In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each mini...In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.展开更多
The coverage performance is the foundation of information acquisition in distributed sensor networks. The previously proposed coverage work was mostly based on unit disk coverage model or ball coverage model in 2D or ...The coverage performance is the foundation of information acquisition in distributed sensor networks. The previously proposed coverage work was mostly based on unit disk coverage model or ball coverage model in 2D or 3D space, respectively. However, most methods cannot give a homogeneous coverage model for targets with hybrid types. This paper presents a coverage analysis approach for sensor networks based on Clifford algebra and establishes a homogeneous coverage model for sensor networks with hybrid types of targets. The effectiveness of the approach is demonstrated with examples.展开更多
Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L...Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.展开更多
Let V be a vertex operator superalgebra and m, n ∈ 1/2 ?+. We construct an A n (V)-A m (V)-bimodule A n,m (V) which characterizes the action of V from the level m subspace to level n subspace of an admissible V-modul...Let V be a vertex operator superalgebra and m, n ∈ 1/2 ?+. We construct an A n (V)-A m (V)-bimodule A n,m (V) which characterizes the action of V from the level m subspace to level n subspace of an admissible V-module. We also construct the Verma type admissible V-module from an A m (V)-module by using bimodules展开更多
We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules...We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a(not necessarily rigid) braided tensor category of V-modules.We also assume U=ComA(V).Under these conditions,we construct a braid-reversed tensor equivalence τ:u_(A)→v_(A),where u_(A)is the semisimple category of U-modules with simple objects Ui,i∈I,and v_(A)is the category of V-modules whose objects are finite direct sums of Vi.In particular,the V-modules Viare simple and distinct,and v_(A)is a rigid tensor category.As an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p^(-1),p∈Z_(≥2), which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl2-modules.Consequently,the Virasoro vertex operator algebra at central charge 13+6p+6p^(-1)is the PSL_(2)(C)-fixed-point subalgebra of a simple conformal vertex algebra w(-p),analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p^(-1)as the PSL_(2)(C)-fixed-point subalgebra of the triplet algebra W(p).展开更多
In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statisti...In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.展开更多
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's suf...This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.展开更多
Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are ...Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.展开更多
A view in object oriented databases corresponds to virtual schemawith restructured generalization and decomposition hierarchies. Numbers of viewcreation methodologies have been proposed. A major drawback of existing m...A view in object oriented databases corresponds to virtual schemawith restructured generalization and decomposition hierarchies. Numbers of viewcreation methodologies have been proposed. A major drawback of existing method-ologies is that they do not maintain the closure property. That is, the result of aquery does not have the same semantics as embodied in the object oriented datamodel. Therefore, this paper presents a view creation methodology that derives aclass in response to a user's query, integrates derived class in global schema (i.e.,considers the problem of classes moving in class hierarchy) and selects the requiredclasses from global schema to create the view for user's query. Novel idea of viewcreation includes: (a) an object algebra for class derivation and customization (wherethe derived classes in terms of object instances and procedure/methods are studied),(b) maintenance of closure property, and (c) classification algorithm which providesmechanism to deal with the problem of a class moving in a class hierarchy.展开更多
The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in ...The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the g展开更多
基金This work is supported by the National Natural Science Foundation of China (Grant No.10171064)two grants 'Excellent Young Teacher Program' and 'Trans-Century Training Programme Foundation for the Talents' from Ministry of Education of China.
文摘Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
文摘This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.
文摘The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz operators.In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.
基金This research was supported by the National Basic Research Program of China （Grant No. 2007CB209603）, Key Project of the National Natural Science Foundation （Grant No. 40830424）, State Key Laboratory of Geological Processes and Mineral Resources Geo-detection Laboratory of the Ministry of Education for their sponsorship （GPMR 200633, GDL0801）.
文摘Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.
文摘In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.
文摘The coverage performance is the foundation of information acquisition in distributed sensor networks. The previously proposed coverage work was mostly based on unit disk coverage model or ball coverage model in 2D or 3D space, respectively. However, most methods cannot give a homogeneous coverage model for targets with hybrid types. This paper presents a coverage analysis approach for sensor networks based on Clifford algebra and establishes a homogeneous coverage model for sensor networks with hybrid types of targets. The effectiveness of the approach is demonstrated with examples.
文摘Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571119, 10671027)
文摘Let V be a vertex operator superalgebra and m, n ∈ 1/2 ?+. We construct an A n (V)-A m (V)-bimodule A n,m (V) which characterizes the action of V from the level m subspace to level n subspace of an admissible V-module. We also construct the Verma type admissible V-module from an A m (V)-module by using bimodules
文摘We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a(not necessarily rigid) braided tensor category of V-modules.We also assume U=ComA(V).Under these conditions,we construct a braid-reversed tensor equivalence τ:u_(A)→v_(A),where u_(A)is the semisimple category of U-modules with simple objects Ui,i∈I,and v_(A)is the category of V-modules whose objects are finite direct sums of Vi.In particular,the V-modules Viare simple and distinct,and v_(A)is a rigid tensor category.As an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p^(-1),p∈Z_(≥2), which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl2-modules.Consequently,the Virasoro vertex operator algebra at central charge 13+6p+6p^(-1)is the PSL_(2)(C)-fixed-point subalgebra of a simple conformal vertex algebra w(-p),analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p^(-1)as the PSL_(2)(C)-fixed-point subalgebra of the triplet algebra W(p).
文摘In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.
基金supported by the National Natural Science Foundation of China(Grant No.10471025)the Natural Science Foundation of Fujian Province of China(Grant Nos.F0210014&Z0511019).
文摘This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.
文摘Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.
文摘A view in object oriented databases corresponds to virtual schemawith restructured generalization and decomposition hierarchies. Numbers of viewcreation methodologies have been proposed. A major drawback of existing method-ologies is that they do not maintain the closure property. That is, the result of aquery does not have the same semantics as embodied in the object oriented datamodel. Therefore, this paper presents a view creation methodology that derives aclass in response to a user's query, integrates derived class in global schema (i.e.,considers the problem of classes moving in class hierarchy) and selects the requiredclasses from global schema to create the view for user's query. Novel idea of viewcreation includes: (a) an object algebra for class derivation and customization (wherethe derived classes in terms of object instances and procedure/methods are studied),(b) maintenance of closure property, and (c) classification algorithm which providesmechanism to deal with the problem of a class moving in a class hierarchy.
文摘The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the g
