Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dyn...Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.展开更多
In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra...In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite C^*-algebras.展开更多
We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an ap...We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.展开更多
Let A be a commutative C^* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co(G), the C^*-algebra of all complex continuous functions on G vanishing at...Let A be a commutative C^* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co(G), the C^*-algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the ease of Hopf C^*-algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C^*-algebra are proposed.展开更多
In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some ...In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.展开更多
We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asy...We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.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
The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
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
目的为了提升生成对抗网络汉字风格迁移的图像生成质量,实现汉字智能生成在字库产业中的实际应用,提出了一种基于直观汉字构形学的条件生成对抗网络字体生成优化方法(Optimizationof Conditional Fonts Generation with Chinese Charact...目的为了提升生成对抗网络汉字风格迁移的图像生成质量,实现汉字智能生成在字库产业中的实际应用,提出了一种基于直观汉字构形学的条件生成对抗网络字体生成优化方法(Optimizationof Conditional Fonts Generation with Chinese Character Configuration GANs,C^(3)-GAN)。方法建构了直观汉字构形模组(C^(3)Module),该模组包含了利于条件生成对抗网络进行汉字构形语义特征学习的全特征汉字字符集。C^(3)-GAN在条件生成对抗网络模型下进行字体生成训练,降低了必要训练样本数量,实现对字体生成效果的优化。结果使用C^(3)-GAN生成汉字图像的清晰度更高、字形更准确。在图像相似性定量评估中,使用C^(3)-GAN的实验组相比于其他模型,获得了更高的相似值和更小的误差值。结论使用C^(3)-GAN可以降低必要训练样本数量、提升汉字图像质量。在实际项目中具有一定的应用性和可操作性。展开更多
文摘Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.
文摘In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite C^*-algebras.
基金Supported by National Natural Sciences Foundation of China(Grant Nos.11501357 and 11571008)。
文摘We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.
文摘Let A be a commutative C^* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co(G), the C^*-algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the ease of Hopf C^*-algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C^*-algebra are proposed.
基金jointly supported by the National Natural Science Foundation of China(No.22273093,No.41905018,No.21903080)the Ministry of Science and Technology of China(No.2022YFF0606500)。
基金Supported in part by the National Social Science Foundation of China(19BTJ020)。
文摘In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.
基金Supported by Natural Science Foundation of Jiangsu Province,China (No.BK20171421)。
文摘We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.
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).
基金supported by NSFC (10871192)NSF of Hebei Province (A2010000194)
文摘The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
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.
文摘目的为了提升生成对抗网络汉字风格迁移的图像生成质量,实现汉字智能生成在字库产业中的实际应用,提出了一种基于直观汉字构形学的条件生成对抗网络字体生成优化方法(Optimizationof Conditional Fonts Generation with Chinese Character Configuration GANs,C^(3)-GAN)。方法建构了直观汉字构形模组(C^(3)Module),该模组包含了利于条件生成对抗网络进行汉字构形语义特征学习的全特征汉字字符集。C^(3)-GAN在条件生成对抗网络模型下进行字体生成训练,降低了必要训练样本数量,实现对字体生成效果的优化。结果使用C^(3)-GAN生成汉字图像的清晰度更高、字形更准确。在图像相似性定量评估中,使用C^(3)-GAN的实验组相比于其他模型,获得了更高的相似值和更小的误差值。结论使用C^(3)-GAN可以降低必要训练样本数量、提升汉字图像质量。在实际项目中具有一定的应用性和可操作性。