In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf...In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.展开更多
This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolp...This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolpgical group with the axiom (A1).展开更多
In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a ...In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.展开更多
It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0...It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X.展开更多
The purpose of this study was to delve into the aspects of abstract algebra that has a link with topological dynamics in terms of permutation and symmetric groups. This would aid users to appreciate the role it plays ...The purpose of this study was to delve into the aspects of abstract algebra that has a link with topological dynamics in terms of permutation and symmetric groups. This would aid users to appreciate the role it plays in the theory and application of topological dynamics. The usage of matlab programming to carry out the permutations was carried out. The study contributes to the literature by providing candid explanation and usage of data-based evidence documenting the extent to which topological dynamics operates.展开更多
In this paper, we investigate Kazhdan’s relative Property (T) for pairs , where is a topological group and is any subset of . We show that the pair has Property (FH) and every function conditionally of negative type ...In this paper, we investigate Kazhdan’s relative Property (T) for pairs , where is a topological group and is any subset of . We show that the pair has Property (FH) and every function conditionally of negative type on is X-bounded if the pair has relative Property (T). We also prove that has Property (T) whenis a s -compact locally compact group generated by its subgroups and the pair has relative Property (T) for all .展开更多
In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characte...In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.展开更多
In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.
The paper addresses the issue of H_∞ couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control. Both fixed and Markovian switching communication topologies are con...The paper addresses the issue of H_∞ couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control. Both fixed and Markovian switching communication topologies are considered. By employing linear transformations, the closed-loop systems are converted into reduced-order systems and the H_∞ couplegroup consensus issue under consideration is changed into a stochastic H_∞ control problem. New conditions for the mean-square asymptotic stability and H_∞ performance of the reduced-order systems are proposed. On the basis of these conditions, constructive approaches for the design of the output-feedback control protocols are developed for the fixed communication topology and the Markovian switching communication topologies, respectively. Finally, two numerical examples are given to illustrate the applicability of the present design approaches.展开更多
The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for app...The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.展开更多
One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the...One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.展开更多
Li has introduced the concepts of inverse system and direct system for fuzzy topological spaces and studied inverse limits and direct limits on such spaces by presenting the explicit constructions of these limits.In t...Li has introduced the concepts of inverse system and direct system for fuzzy topological spaces and studied inverse limits and direct limits on such spaces by presenting the explicit constructions of these limits.In this paper some important concepts of fuzzy topology,such as,product fuzzy topology,quotient fuzzy topology,fuzzy continuity etc.,are used for further study of inverse limits and direct limits for fuzzy topological spaces.展开更多
New appronches were applied to improve the molecular connectivity indices m^X^τ. The vertex valence is redefined and it was reasonable for hydrogen atom. The distances between vertices were used to propose novel conn...New appronches were applied to improve the molecular connectivity indices m^X^τ. The vertex valence is redefined and it was reasonable for hydrogen atom. The distances between vertices were used to propose novel connectivity topological indexes. The vertices and the distances in a molecular graph were taken into account in this definition. The linear regression was used to develop the structural property models. The results indicate that the novel connectivity topological indexes are useful model parameters for Quantitative Strncture-Property Relationship （ QSPR ） analysis.展开更多
It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F ,where F is a finite group,are studied.In particular,under...It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F ,where F is a finite group,are studied.In particular,under a suitable assumption,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chaotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.展开更多
A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss...A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss in size. Numerical results are given for both the original problem and the reduced problem to make a comparison.展开更多
A Riesz type product as Pn=nЛj=1（1＋awj＋bwj＋1）is studied, where a, b are two real numbers with ｜a｜ ＋ ｜b｜ 〈 1, and {wj} are indepen- dent random variables taking values in （-1, 1} with equal probability. Le...A Riesz type product as Pn=nЛj=1（1＋awj＋bwj＋1）is studied, where a, b are two real numbers with ｜a｜ ＋ ｜b｜ 〈 1, and {wj} are indepen- dent random variables taking values in （-1, 1} with equal probability. Let dw be the normalized Haar measure on the Cantor group Ω = （-1, 1}^N. The sequence of P,~dw 1 probability measures {Pndw/E（Pn） } is showed to converge weakly to a unique continuous measure on/2, and the obtained measure is singular with respect to dw.展开更多
文摘In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
文摘This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolpgical group with the axiom (A1).
基金Supported by the National Natural Science Foundation of China(11201414,11471153)
文摘In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.
文摘It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X.
文摘The purpose of this study was to delve into the aspects of abstract algebra that has a link with topological dynamics in terms of permutation and symmetric groups. This would aid users to appreciate the role it plays in the theory and application of topological dynamics. The usage of matlab programming to carry out the permutations was carried out. The study contributes to the literature by providing candid explanation and usage of data-based evidence documenting the extent to which topological dynamics operates.
文摘In this paper, we investigate Kazhdan’s relative Property (T) for pairs , where is a topological group and is any subset of . We show that the pair has Property (FH) and every function conditionally of negative type on is X-bounded if the pair has relative Property (T). We also prove that has Property (T) whenis a s -compact locally compact group generated by its subgroups and the pair has relative Property (T) for all .
文摘In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.
基金Supported by the National Natural Science Foundation of China (10701032)Natural Science Foundation of Hebei Province (A2008000132)the Doctoral Foundation of Hebei Normal University (L2005B02)
文摘In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503002 and 61573008)
文摘The paper addresses the issue of H_∞ couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control. Both fixed and Markovian switching communication topologies are considered. By employing linear transformations, the closed-loop systems are converted into reduced-order systems and the H_∞ couplegroup consensus issue under consideration is changed into a stochastic H_∞ control problem. New conditions for the mean-square asymptotic stability and H_∞ performance of the reduced-order systems are proposed. On the basis of these conditions, constructive approaches for the design of the output-feedback control protocols are developed for the fixed communication topology and the Markovian switching communication topologies, respectively. Finally, two numerical examples are given to illustrate the applicability of the present design approaches.
文摘The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.
基金the Natural Science Foundation of Anhui Province,China(Grant No.2208085MA11)the National Natural Science Foundation of China(Grants Nos.11974356,12274414,and U1832209)。
文摘One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.
文摘Li has introduced the concepts of inverse system and direct system for fuzzy topological spaces and studied inverse limits and direct limits on such spaces by presenting the explicit constructions of these limits.In this paper some important concepts of fuzzy topology,such as,product fuzzy topology,quotient fuzzy topology,fuzzy continuity etc.,are used for further study of inverse limits and direct limits for fuzzy topological spaces.
基金Funded bythe Natural Science andthe Education Office Founda-tion of Hubei Province(No.2005ABA016 and 2004Q002)
文摘New appronches were applied to improve the molecular connectivity indices m^X^τ. The vertex valence is redefined and it was reasonable for hydrogen atom. The distances between vertices were used to propose novel connectivity topological indexes. The vertices and the distances in a molecular graph were taken into account in this definition. The linear regression was used to develop the structural property models. The results indicate that the novel connectivity topological indexes are useful model parameters for Quantitative Strncture-Property Relationship （ QSPR ） analysis.
文摘It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F ,where F is a finite group,are studied.In particular,under a suitable assumption,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chaotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.
基金Project supported by the National Natural Science Foundation of China (Grant No.10771133)the Research Fundation for the Doctoral Program of Higher Education (Grant No.200802800010)the Key Disciplines of Shanghai Municipality (GrantNo.s30104)
文摘A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss in size. Numerical results are given for both the original problem and the reduced problem to make a comparison.
文摘A Riesz type product as Pn=nЛj=1（1＋awj＋bwj＋1）is studied, where a, b are two real numbers with ｜a｜ ＋ ｜b｜ 〈 1, and {wj} are indepen- dent random variables taking values in （-1, 1} with equal probability. Let dw be the normalized Haar measure on the Cantor group Ω = （-1, 1}^N. The sequence of P,~dw 1 probability measures {Pndw/E（Pn） } is showed to converge weakly to a unique continuous measure on/2, and the obtained measure is singular with respect to dw.
