The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from ...The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.展开更多
This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the act...This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system,an algorithm is proposed that is able to exponentially find the Nash equilibrium.Further,the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets.Two examples are used to illustrate the proposed approach.展开更多
We study the Hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and th...We study the Hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and the first gap. This condition is easy to use. Key words linear Cantor set - Hausdorff measure - strong seperated condition CLC number O 174. 12 Foundation item: Supported by the National Natural Science Foundation of China (10171028)Biography: Ma Chao (1975-), male, Ph. D. candidate, research direction: fractal geometry.展开更多
The temporal and spatial distributions of all the 259 M≥6 earthquakes of eastern Chinese mainland (λ≥108° E) and its adjacent area and all the 153 M≥7 earthquakes of western Chinese mainland (λ<108°E...The temporal and spatial distributions of all the 259 M≥6 earthquakes of eastern Chinese mainland (λ≥108° E) and its adjacent area and all the 153 M≥7 earthquakes of western Chinese mainland (λ<108°E) and its adjacent area up to 1991 were analyzed systematically.These earthquakes are called as strong earthquakes and those of the east before and after 1600,and those of the west before and after 1900, are called respectively as former ones and latter ones.Most of these events were divided into 45 sets of which the each relatively concentrated in both time and space and took the form of group.In the grouping form,the probability of occurrence of a strong earthquake higher than the average appeared simultaneously in time and space.The grouping occurrences of the strong earthquakes of Chinese mainland has been determined as a fundamental feature of the seismicity.展开更多
In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence betwe...In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.展开更多
This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a...This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a first countable T_(0) space is sober if and only if it does not contain a∏_(2)^(0)-subspace homeomorphic either to S_(D),the natural number set equipped with the Scott topology,or to S_(1),the natural number set equipped with the cofinite topology,and it does not contain any directed closed subset without maximal elements either.Second,we show that if Y is sober,the function space TOP(X,Y)equipped with the Isbell topology(respectively,Scott topology)may be a non-sober space.Furthermore,we provide a uniform construction to d-spaces and well-filtered spaces via irreducible subset systems introduced in[9];we called this an H-well-filtered space.We obtain that,for a T_(0) space X and an H-well-filtered space Y,the function space TOP(X,Y)equipped with the Isbell topology is H-well-filtered.Going beyond the aforementioned work,we solve several open problems concerning strong d-spaces posed by Xu and Zhao in[11].展开更多
This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is...This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.展开更多
Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers o...Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers of generalηizations of fuzzy graphs have been explored in the literature.Among the others,picture fuzzy graph(PFG)has its own importance.A picture fuzzy graph(PFG)is a pair G=(C,D)defined on a H^(*)=(A,B),where C=(ηC,θ_(C),■_(C))is a picture fuzzy set on A and D=(ηD,θ_(D),■_(D))is a picture fuzzy set over the set B∈A×A such that for any edge mn∈ B with ηD(m,n)≤min(ηC(m),ηC(n)),θD(m,n)≤min(θC(m),θC(n))and ■_(D)(m,n)≥max(■_(C)(m),■_(C)(n)).In this manuscript,we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs.Firstly,we discuss few important characteristics of the Cayley picture fuzzy graphs.We show that Cayley picture fuzzy graphs are vertex transitive and hence regular.Then,we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts.We extensively discuss the term connectivity of the Cayley picture fuzzy graphs.Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed.We also investigate the linkage between these two.Throughout,we provide the extensions of some characηteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs.Finally,we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.展开更多
This note characterizes the set of Fréchet-differentiable points of the projection operator on a polyhedral set and the B-subdifferential of this projection operator at any point.
文摘The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.
基金supported in part by the Research Grants Council of the Hong Kong Special Administration Region under Grant No.14202619in part by the National Natural Science Foundation of China under Grant No.61973260。
文摘This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system,an algorithm is proposed that is able to exponentially find the Nash equilibrium.Further,the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets.Two examples are used to illustrate the proposed approach.
文摘We study the Hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and the first gap. This condition is easy to use. Key words linear Cantor set - Hausdorff measure - strong seperated condition CLC number O 174. 12 Foundation item: Supported by the National Natural Science Foundation of China (10171028)Biography: Ma Chao (1975-), male, Ph. D. candidate, research direction: fractal geometry.
文摘The temporal and spatial distributions of all the 259 M≥6 earthquakes of eastern Chinese mainland (λ≥108° E) and its adjacent area and all the 153 M≥7 earthquakes of western Chinese mainland (λ<108°E) and its adjacent area up to 1991 were analyzed systematically.These earthquakes are called as strong earthquakes and those of the east before and after 1600,and those of the west before and after 1900, are called respectively as former ones and latter ones.Most of these events were divided into 45 sets of which the each relatively concentrated in both time and space and took the form of group.In the grouping form,the probability of occurrence of a strong earthquake higher than the average appeared simultaneously in time and space.The grouping occurrences of the strong earthquakes of Chinese mainland has been determined as a fundamental feature of the seismicity.
文摘In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.
文摘This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a first countable T_(0) space is sober if and only if it does not contain a∏_(2)^(0)-subspace homeomorphic either to S_(D),the natural number set equipped with the Scott topology,or to S_(1),the natural number set equipped with the cofinite topology,and it does not contain any directed closed subset without maximal elements either.Second,we show that if Y is sober,the function space TOP(X,Y)equipped with the Isbell topology(respectively,Scott topology)may be a non-sober space.Furthermore,we provide a uniform construction to d-spaces and well-filtered spaces via irreducible subset systems introduced in[9];we called this an H-well-filtered space.We obtain that,for a T_(0) space X and an H-well-filtered space Y,the function space TOP(X,Y)equipped with the Isbell topology is H-well-filtered.Going beyond the aforementioned work,we solve several open problems concerning strong d-spaces posed by Xu and Zhao in[11].
文摘This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.
文摘Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers of generalηizations of fuzzy graphs have been explored in the literature.Among the others,picture fuzzy graph(PFG)has its own importance.A picture fuzzy graph(PFG)is a pair G=(C,D)defined on a H^(*)=(A,B),where C=(ηC,θ_(C),■_(C))is a picture fuzzy set on A and D=(ηD,θ_(D),■_(D))is a picture fuzzy set over the set B∈A×A such that for any edge mn∈ B with ηD(m,n)≤min(ηC(m),ηC(n)),θD(m,n)≤min(θC(m),θC(n))and ■_(D)(m,n)≥max(■_(C)(m),■_(C)(n)).In this manuscript,we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs.Firstly,we discuss few important characteristics of the Cayley picture fuzzy graphs.We show that Cayley picture fuzzy graphs are vertex transitive and hence regular.Then,we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts.We extensively discuss the term connectivity of the Cayley picture fuzzy graphs.Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed.We also investigate the linkage between these two.Throughout,we provide the extensions of some characηteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs.Finally,we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.
基金supported by the National Natural Science Foundation of China(Nos.12071055,11971089 and 11731013).
文摘This note characterizes the set of Fréchet-differentiable points of the projection operator on a polyhedral set and the B-subdifferential of this projection operator at any point.
