We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig's canonical bases of th...We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.展开更多
In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zy...In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.展开更多
This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W(2, 2) algebra. We show that the q-deformed W(2, 2) algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondenc...This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W(2, 2) algebra. We show that the q-deformed W(2, 2) algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W(2, 2) algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W(2, 2) algebra.展开更多
In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve ...In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.展开更多
In this paper,we give some interesting results concerning the entire function f(z) sharing a small function a CM with its difference operators or shifts.
We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We fu...We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2(Bn,dvα) and g is a square integrable holomorphic function.展开更多
Spectral element method is well known as high-order method, and has potential better parallel feature as compared with low order methods. In this paper, a parallel preconditioned conjugate gradient iterative method is...Spectral element method is well known as high-order method, and has potential better parallel feature as compared with low order methods. In this paper, a parallel preconditioned conjugate gradient iterative method is proposed to solving the spectral element approximation of the Helmholtz equation. The parallel algorithm is shown to have good performance as compared to non parallel cases, especially when the stiffness matrix is not memorized. A series of numerical experiments in one dimensional case is carried out to demonstrate the efficiency of the proposed method.展开更多
This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protoc...This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary Γ:y = g(x, t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.展开更多
The Weyl curvature of a Finsler metric is investigated. This curvature constructed from Riemannain curvature. It is an important projective invariant of Finsler metrics. The author gives the necessary conditions on We...The Weyl curvature of a Finsler metric is investigated. This curvature constructed from Riemannain curvature. It is an important projective invariant of Finsler metrics. The author gives the necessary conditions on Weyl curvature for a Finsler metric to be Randers metric and presents examples of Randers metrics with non-scalar curvature. A global rigidity theorem for compact Finsler manifolds satisfying such conditions is proved. It is showed that for such a Finsler manifold,if Ricci scalar is negative,then Finsler metric is of Randers type.展开更多
An unstructured mesh finite volume discretisation method for simulating diffusion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid c...An unstructured mesh finite volume discretisation method for simulating diffusion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume finite-element method and it retains the local continuity of the flux at the control volume faces. A least squares function recon-struction technique together with a new flux decomposition strategy is used to obtain an accurate flux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it significantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes,and appears independent of the mesh quality.展开更多
A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent mo...A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existingconvexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.展开更多
The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other whi...The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.展开更多
A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This...A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.展开更多
The order of computational complexity of all bounded linear functional approximation problem is determined for the generalized Sobolev class Wp∧(Id), Nikolskii class Hk∞(Id) in the worst (deterministic), stochastic ...The order of computational complexity of all bounded linear functional approximation problem is determined for the generalized Sobolev class Wp∧(Id), Nikolskii class Hk∞(Id) in the worst (deterministic), stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes stochastic and average case setting.展开更多
基金the National Basic Research Program of China under Grant 2013CB338004,Doctoral Program of Higher Education of China under Grant No.20120073120034,National Natural Science Foundation of China under Grants No.61070204,61101108,and National S&T Major Program under Grant No.2011ZX03002-005-01
基金Supported by National Natural Science Foundation of China(Grant Nos.10631060 and 11131008) The author would like to thank Professor George Lusztig and Hiraku Nakajima for many helpful discussions.
文摘We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271209 and 11371056) The author would like to thank Professor Guozhen Lu for suggesting this problem and many helpful discussions, for his constant encouragement and guidance. The author would also like to thank the referees for their time and comments.
文摘In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.
基金Supported by National Natural Science Foundation of China(Grant No.11371222) Natural Science Foundation of Shandong Province(Grant No.ZR2012AM024) China Scholarship Council
基金Supported by China Scholarship Council(Grant No.201206125047) China Postdoctoral Science Foundation Funded Project(Grant No.2012M520715) the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201462)We thank the referees for their time and comments.
文摘This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W(2, 2) algebra. We show that the q-deformed W(2, 2) algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W(2, 2) algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W(2, 2) algebra.
基金supported by Chinese Universities Scientific Fund(Grant No.WK0010000031) supported by National Natural Science Foundation of China(Grant Nos.11231390,11371222,11301511)
文摘In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.
基金Supported by the National Science Foundation of China under Grant No. 11071092 and the Texas Norman Hackerman Advanced Research Program under Grant No. 003599-0001-2009
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1087107611026096)
文摘In this paper,we give some interesting results concerning the entire function f(z) sharing a small function a CM with its difference operators or shifts.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971020)Doctoral Fund of Ministry of Education of China (RFDP)
文摘We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2(Bn,dvα) and g is a square integrable holomorphic function.
基金This work was supported by Natural Science Foundation of Fujian under Grant,教育部优秀青年教师资助计划
文摘Spectral element method is well known as high-order method, and has potential better parallel feature as compared with low order methods. In this paper, a parallel preconditioned conjugate gradient iterative method is proposed to solving the spectral element approximation of the Helmholtz equation. The parallel algorithm is shown to have good performance as compared to non parallel cases, especially when the stiffness matrix is not memorized. A series of numerical experiments in one dimensional case is carried out to demonstrate the efficiency of the proposed method.
文摘This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary Γ:y = g(x, t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.
文摘The Weyl curvature of a Finsler metric is investigated. This curvature constructed from Riemannain curvature. It is an important projective invariant of Finsler metrics. The author gives the necessary conditions on Weyl curvature for a Finsler metric to be Randers metric and presents examples of Randers metrics with non-scalar curvature. A global rigidity theorem for compact Finsler manifolds satisfying such conditions is proved. It is showed that for such a Finsler manifold,if Ricci scalar is negative,then Finsler metric is of Randers type.
文摘An unstructured mesh finite volume discretisation method for simulating diffusion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume finite-element method and it retains the local continuity of the flux at the control volume faces. A least squares function recon-struction technique together with a new flux decomposition strategy is used to obtain an accurate flux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it significantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes,and appears independent of the mesh quality.
文摘A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existingconvexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.
文摘The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.
文摘A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.
文摘The order of computational complexity of all bounded linear functional approximation problem is determined for the generalized Sobolev class Wp∧(Id), Nikolskii class Hk∞(Id) in the worst (deterministic), stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes stochastic and average case setting.