In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a suf...In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a sufficient condition for lgldim (R1 R2,)≥lgldim R1+lgldimR2, and wgldim (R1 R2) ≥wgldimR1 +wgldimR2展开更多
Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Freml...Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.展开更多
In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a ...In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a random permutation. We now consider a sequence in lp with 1 〈 p 〈 ∞, and a sequence in a Banach lattice X. Instead of normal multiplication, we consider the tensor product of lp and X. We show that in Wittstock injective tensor product, lp iX, and Fremlin projective tensor product, lp FX, the rearrangement inequality still exists.展开更多
In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
Let A and B be nonassociative algebras over a field F.Is every triple derivation of the tensor product algebra A⊗B a derivation if the same holds true for A?We show that the answer is affirmative if B is unital and A^...Let A and B be nonassociative algebras over a field F.Is every triple derivation of the tensor product algebra A⊗B a derivation if the same holds true for A?We show that the answer is affirmative if B is unital and A^(2)has a zero annihilator in A.展开更多
In this paper, the authors first give the properties of the convolutions of Orlicz- Lorentz spaces Aφ1,w and Aφ2,w on the locally compact abelian group. Secondly, the authors obtain the concrete representation as fu...In this paper, the authors first give the properties of the convolutions of Orlicz- Lorentz spaces Aφ1,w and Aφ2,w on the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Aφ1,w and Aφ2,w, and get the space of multipliers from the space Aφ1,w to the space Mφ2.w. Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Aφ,w^p,q.展开更多
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β...We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.展开更多
We treat infinite horizon optimal control problems by solving the associated stationary Bellman equation numerically to compute the value function and an optimal feedback law.The dynamical systems under consideration ...We treat infinite horizon optimal control problems by solving the associated stationary Bellman equation numerically to compute the value function and an optimal feedback law.The dynamical systems under consideration are spatial discretizations of non linear parabolic partial differential equations(PDE),which means that the Bellman equation suffers from the curse of dimensionality.Its non linearity is handled by the Policy Iteration algorithm,where the problem is reduced to a sequence of linear equations,which remain the computational bottleneck due to their high dimensions.We reformulate the linearized Bellman equations via the Koopman operator into an operator equation,that is solved using a minimal residual method.Using the Koopman operator we identify a preconditioner for operator equation,which deems essential in our numerical tests.To overcome computational infeasability we use low rank hierarchical tensor product approximation/tree-based tensor formats,in particular tensor trains(TT tensors)and multi-polynomials,together with high-dimensional quadrature,e.g.Monte-Carlo.By controlling a destabilized version of viscous Burgers and a diffusion equation with unstable reaction term numerical evidence is given.展开更多
A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure...A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure-injective modules is studied.展开更多
We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-modu...We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.展开更多
This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,i...This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.展开更多
We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was pre...We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.展开更多
In this paper, we consider the module-relative-Hochschild homology and cohomology of tensor products of algebras and relate them to those of the factor algebras. Moreover, we show that the tensor product is formally s...In this paper, we consider the module-relative-Hochschild homology and cohomology of tensor products of algebras and relate them to those of the factor algebras. Moreover, we show that the tensor product is formally smooth if and only if one of its factor algebras is formally smooth and the other is separable,展开更多
For any C2-cofinite vertex product and the P（z）-tensor product finite length are proved to exist, which operator superalgebra V, the tensor of any two admissible V-modules of are shown to be isomorphic, and their co...For any C2-cofinite vertex product and the P（z）-tensor product finite length are proved to exist, which operator superalgebra V, the tensor of any two admissible V-modules of are shown to be isomorphic, and their constructions are given explicitly in this paper.展开更多
We unify and generalize several approaches to constructing braid group representa-tions from finite groups,using iterated twisted tensor products.We provide some general characterizations and classification of these r...We unify and generalize several approaches to constructing braid group representa-tions from finite groups,using iterated twisted tensor products.We provide some general characterizations and classification of these representations,focusing on the size of their images,which are typically finite groups.The well-studied Gaussian representations associated with metaplectic modular categories can be understood in this framework,and we give some new examples to illustrate their ubiquity.Our results suggest a relationship between the braiding on the G-gaugings of a pointed modular category C(A,Q)and that of C(A,Q)itself.展开更多
The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. ...The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.展开更多
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzz...The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.展开更多
Slodkowski joint spectrum is similar to Taylor joint spectrum, but it has more important meaning in theory and application. In this paper we characterize Slodkowski joint spectrum and generalize some results about ten...Slodkowski joint spectrum is similar to Taylor joint spectrum, but it has more important meaning in theory and application. In this paper we characterize Slodkowski joint spectrum and generalize some results about tensor product.展开更多
文摘In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a sufficient condition for lgldim (R1 R2,)≥lgldim R1+lgldimR2, and wgldim (R1 R2) ≥wgldimR1 +wgldimR2
文摘Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.
文摘In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a random permutation. We now consider a sequence in lp with 1 〈 p 〈 ∞, and a sequence in a Banach lattice X. Instead of normal multiplication, we consider the tensor product of lp and X. We show that in Wittstock injective tensor product, lp iX, and Fremlin projective tensor product, lp FX, the rearrangement inequality still exists.
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
文摘Let A and B be nonassociative algebras over a field F.Is every triple derivation of the tensor product algebra A⊗B a derivation if the same holds true for A?We show that the answer is affirmative if B is unital and A^(2)has a zero annihilator in A.
基金supported by the National Natural Science Foundation of China(Nos.11401530,11461033,11271330)the Natural Science Foundation of Zhejiang Province(No.LQ13A010018)
文摘In this paper, the authors first give the properties of the convolutions of Orlicz- Lorentz spaces Aφ1,w and Aφ2,w on the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Aφ1,w and Aφ2,w, and get the space of multipliers from the space Aφ1,w to the space Mφ2.w. Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Aφ,w^p,q.
文摘We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
基金support from the Research Training Group“Differential Equation-and Data-driven Models in Life Sciences and Fluid Dynamics:An Interdisciplinary Research Training Group(DAEDALUS)”(GRK 2433)funded by the German Research Foundation(DFG).
文摘We treat infinite horizon optimal control problems by solving the associated stationary Bellman equation numerically to compute the value function and an optimal feedback law.The dynamical systems under consideration are spatial discretizations of non linear parabolic partial differential equations(PDE),which means that the Bellman equation suffers from the curse of dimensionality.Its non linearity is handled by the Policy Iteration algorithm,where the problem is reduced to a sequence of linear equations,which remain the computational bottleneck due to their high dimensions.We reformulate the linearized Bellman equations via the Koopman operator into an operator equation,that is solved using a minimal residual method.Using the Koopman operator we identify a preconditioner for operator equation,which deems essential in our numerical tests.To overcome computational infeasability we use low rank hierarchical tensor product approximation/tree-based tensor formats,in particular tensor trains(TT tensors)and multi-polynomials,together with high-dimensional quadrature,e.g.Monte-Carlo.By controlling a destabilized version of viscous Burgers and a diffusion equation with unstable reaction term numerical evidence is given.
文摘A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure-injective modules is studied.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11471269, 61373140）, the Natural Science Foundation of Fujian Province （2016J01002）, and 2016 Incubation Program for Scientific Research Talent of Distinguished Young of Colledges and Universities in Fujian Province.
文摘We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.
文摘This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.
基金supported by projects MTM 2008-03339 from the Ministerio de Cienica e In,P07-FQM03128FQM0211 from Junta de Andalucía and TEC 2009-13763-C02-02
文摘We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.
文摘In this paper, we consider the module-relative-Hochschild homology and cohomology of tensor products of algebras and relate them to those of the factor algebras. Moreover, we show that the tensor product is formally smooth if and only if one of its factor algebras is formally smooth and the other is separable,
基金Acknowledgements This work was supported by the China Postdoctoral Science Foundation （Grant No. 2013M540709）.
文摘For any C2-cofinite vertex product and the P（z）-tensor product finite length are proved to exist, which operator superalgebra V, the tensor of any two admissible V-modules of are shown to be isomorphic, and their constructions are given explicitly in this paper.
文摘We unify and generalize several approaches to constructing braid group representa-tions from finite groups,using iterated twisted tensor products.We provide some general characterizations and classification of these representations,focusing on the size of their images,which are typically finite groups.The well-studied Gaussian representations associated with metaplectic modular categories can be understood in this framework,and we give some new examples to illustrate their ubiquity.Our results suggest a relationship between the braiding on the G-gaugings of a pointed modular category C(A,Q)and that of C(A,Q)itself.
文摘The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.
基金This work was partially supported by the Natural Science Foundation of China （No. 611 74094） the Tianjin Natural Science Foundation of China （No. 13JCYBJC1 7400） the Program for New Century Excellent Talents in University of China （No. NCET-10-0506）.
文摘The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
文摘Slodkowski joint spectrum is similar to Taylor joint spectrum, but it has more important meaning in theory and application. In this paper we characterize Slodkowski joint spectrum and generalize some results about tensor product.
