In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strateg...In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.展开更多
We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the...We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.展开更多
The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework...The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework is described.The structure at the macrolevel is discretized by the triangular C^(1) finite elements obeying nonlocal continuum theory,while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable.The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity.The macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent strain.The softening at each material point at the macrolevel is detected by the critical value of the homogenized damage,where homogenization of the damage variable is performed onlywithin softening area.Due to the nonlocal continuumtheory applied,a realistic softening behaviour is demonstrated after the damage initiation,compared to the widely used first-order homogenization approach.All algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark problems.The damage evolution at both microlevel and macrolevel has been demonstrated.展开更多
Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal ...Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.展开更多
针对传统FCM(fuzzy c-means)算法抗噪性差的问题,提出了一种基于一致性分片的模糊c均值聚类算法。为避免额外的空间邻域约束项带来的控制变量设置问题,该算法直接将FCM应用于图像片空间。为减弱空间邻域对图像边缘的模糊,采用基于置信...针对传统FCM(fuzzy c-means)算法抗噪性差的问题,提出了一种基于一致性分片的模糊c均值聚类算法。为避免额外的空间邻域约束项带来的控制变量设置问题,该算法直接将FCM应用于图像片空间。为减弱空间邻域对图像边缘的模糊,采用基于置信区间的局部多项式交叉近似技术(local polynomial approximation and intersection of confidenec intervals,LPA-ICI)构造自适应形状一致性分片。在脑磁共振图像上的实验表明,与传统的FCM算法相比,该算法具有更高的分割精度和运行效率。展开更多
All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as ...All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.展开更多
文摘In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
文摘In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.
基金Supported by the National Natural Science Foundation of China(10371051)
文摘We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
文摘The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework is described.The structure at the macrolevel is discretized by the triangular C^(1) finite elements obeying nonlocal continuum theory,while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable.The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity.The macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent strain.The softening at each material point at the macrolevel is detected by the critical value of the homogenized damage,where homogenization of the damage variable is performed onlywithin softening area.Due to the nonlocal continuumtheory applied,a realistic softening behaviour is demonstrated after the damage initiation,compared to the widely used first-order homogenization approach.All algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark problems.The damage evolution at both microlevel and macrolevel has been demonstrated.
文摘Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.
文摘针对传统FCM(fuzzy c-means)算法抗噪性差的问题,提出了一种基于一致性分片的模糊c均值聚类算法。为避免额外的空间邻域约束项带来的控制变量设置问题,该算法直接将FCM应用于图像片空间。为减弱空间邻域对图像边缘的模糊,采用基于置信区间的局部多项式交叉近似技术(local polynomial approximation and intersection of confidenec intervals,LPA-ICI)构造自适应形状一致性分片。在脑磁共振图像上的实验表明,与传统的FCM算法相比,该算法具有更高的分割精度和运行效率。
基金The author was supported by grant No. 1999-2-102-001-3 from the interdis- ciplinary research program year of the KOSEF.
文摘All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.
