The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely met...The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.展开更多
In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the ...In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the question:When is an essential extension of a finitely presented module(an almost finitely presented module)also finitely presented(almost finitely presented)?In Section 2,we study the C-excellent extensions and the finitely presented dimensions.We obtain some results on the homological dimensions of matrix rings and group rings.展开更多
The chaos caused by a strong-mixing preserving transformation is discussed and it is shown that for a topological space X satisfying the second axiom of countability and for an outer measure m on X satisfying the cond...The chaos caused by a strong-mixing preserving transformation is discussed and it is shown that for a topological space X satisfying the second axiom of countability and for an outer measure m on X satisfying the conditions: (i) every non-empty open set of X is m-measurable with positive m-measure; (ii) the restriction of m on Borel σ-algebra B( X) of X is a probability measure, and (iii) for every Y X there exists a Borel set B B(X) such that B Y and m (B)= m (Y), if f : X→X is a strong-mixing measure-preserving transformation of the probability space (X,B(X), m), and if {mi} is a strictly increasing sequence of positive integers, then there exists a subset C X with m (C) = 1, finitely chaotic with respect to the sequence {mi}, i e. for any finite subset A of C and for any map F:A→X there is a subsequence {ri} such that limt→∞fri(a) = F(a) for any a∈A . There are some applications to maps of one dimension展开更多
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity s...In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.展开更多
Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmande...Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.展开更多
In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the...In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the Hormander's condition, and △x =∑j=1^m Xj^2 is a finitely degenera te elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.展开更多
By cognitive radio,the low Earth orbit（LEO） satellites may prefer to operate in the unlicensed spectrum which is open to all the users,and compete for the limited resources with terrestrial cognitive radio networks...By cognitive radio,the low Earth orbit（LEO） satellites may prefer to operate in the unlicensed spectrum which is open to all the users,and compete for the limited resources with terrestrial cognitive radio networks（CRNs）.The competition can be regarded as a game and analyzed with game theory.This particular unlicensed spectrum sharing problem is modeled here,and the special properties of ＂spatially-distinguished-interference＂ and the short period of the interactions between satellites and terrestrial CRNs are explored.Then,the problem is formulated as a ＂partially-blind＂ finitely repeated prisoner＇s dilemma by game theory.Finally,we begin with two promising spectrum sharing schemes,which can be used to enforce the frequency reuse among the remotely located terrestrial CRN players as well as to overcome the observation noise.By analysis and comparison,it is proposed that the novel refreshing-contrite-tit-for-tat（R-CTFT） is the optimal spectrum sharing scheme.Simulation results verify that it can be used to utilize the spectrum most efficiently.展开更多
Arnold difusion for nearly integrable Hamiltonian systems Chong-Qing Cheng&Jinxin Xue Abstract In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈R^(n),n≥3admits...Arnold difusion for nearly integrable Hamiltonian systems Chong-Qing Cheng&Jinxin Xue Abstract In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈R^(n),n≥3admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)(E)provided that E>min h.展开更多
For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and duali...For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.展开更多
In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices...In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.展开更多
In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=（X1,X2,…,Xm） is a system of real smooth vector fields which satisfy the H?rmander’s conditio...In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=（X1,X2,…,Xm） is a system of real smooth vector fields which satisfy the H?rmander’s condition,and △X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.展开更多
Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω（...Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω（S）, where Ω（S）is the Loop category of（S）,and the structure of K<sub>1</sub>S is given.展开更多
Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1（...Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1（r） of R in both real and complex case is proven by the homogeneity of the polynomial germs. It results in the finite determinacy of homogeneous polynomial germs needn＇t be discussed respectively.展开更多
In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of fi...In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of finitely generated nilpotent groups with central associated subgroups are weakly potent.展开更多
The cyclicity of four classes of codimension 3 plnnar polycycles and ensembles containing a saddle-node and two hyperbdic saddles is dealt with. The exnct cyclicity or cyclicity bound of them is obtained by finitely-s...The cyclicity of four classes of codimension 3 plnnar polycycles and ensembles containing a saddle-node and two hyperbdic saddles is dealt with. The exnct cyclicity or cyclicity bound of them is obtained by finitely-smooth normal form theory.展开更多
Let ∧_(0,0)=(A_BMAANB_B)be a Morita ring,where the bimodule homomorphisms φ and ψ are zero.We study the finite presentedness,locally coherence,pure projectivity,pure injectivity,and FP-injectivity of modules over A...Let ∧_(0,0)=(A_BMAANB_B)be a Morita ring,where the bimodule homomorphisms φ and ψ are zero.We study the finite presentedness,locally coherence,pure projectivity,pure injectivity,and FP-injectivity of modules over A_(0,0).Some applications are then given.展开更多
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t...The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.展开更多
In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to character...In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.展开更多
Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax i...Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.展开更多
In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated...In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.展开更多
文摘The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.
基金Supported by the Natural Science Foundation of China
文摘In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the question:When is an essential extension of a finitely presented module(an almost finitely presented module)also finitely presented(almost finitely presented)?In Section 2,we study the C-excellent extensions and the finitely presented dimensions.We obtain some results on the homological dimensions of matrix rings and group rings.
基金Project supported by the National Natural Science Foundation of China.
文摘The chaos caused by a strong-mixing preserving transformation is discussed and it is shown that for a topological space X satisfying the second axiom of countability and for an outer measure m on X satisfying the conditions: (i) every non-empty open set of X is m-measurable with positive m-measure; (ii) the restriction of m on Borel σ-algebra B( X) of X is a probability measure, and (iii) for every Y X there exists a Borel set B B(X) such that B Y and m (B)= m (Y), if f : X→X is a strong-mixing measure-preserving transformation of the probability space (X,B(X), m), and if {mi} is a strictly increasing sequence of positive integers, then there exists a subset C X with m (C) = 1, finitely chaotic with respect to the sequence {mi}, i e. for any finite subset A of C and for any map F:A→X there is a subsequence {ri} such that limt→∞fri(a) = F(a) for any a∈A . There are some applications to maps of one dimension
基金This project is supported by Natural Science Foundation of Sichuan Education Department of China(2003A081)SZD0406
文摘In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.
基金partially supported by the NSFC(11631011,11626251)
文摘Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.
基金Supported by National Natural Science Foundation of China(Grants Nos.11631011 and 11626251)
文摘In this paper, we study the initial-boundary value problem for the semilinear pseudoparabolic equations ut —△xut —△xu =|u|^p-1u, where X =(X1, X2,..., Xm) is a system of real smooth vector fields which satisfy the Hormander's condition, and △x =∑j=1^m Xj^2 is a finitely degenera te elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.
文摘By cognitive radio,the low Earth orbit（LEO） satellites may prefer to operate in the unlicensed spectrum which is open to all the users,and compete for the limited resources with terrestrial cognitive radio networks（CRNs）.The competition can be regarded as a game and analyzed with game theory.This particular unlicensed spectrum sharing problem is modeled here,and the special properties of ＂spatially-distinguished-interference＂ and the short period of the interactions between satellites and terrestrial CRNs are explored.Then,the problem is formulated as a ＂partially-blind＂ finitely repeated prisoner＇s dilemma by game theory.Finally,we begin with two promising spectrum sharing schemes,which can be used to enforce the frequency reuse among the remotely located terrestrial CRN players as well as to overcome the observation noise.By analysis and comparison,it is proposed that the novel refreshing-contrite-tit-for-tat（R-CTFT） is the optimal spectrum sharing scheme.Simulation results verify that it can be used to utilize the spectrum most efficiently.
文摘Arnold difusion for nearly integrable Hamiltonian systems Chong-Qing Cheng&Jinxin Xue Abstract In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈R^(n),n≥3admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)(E)provided that E>min h.
文摘For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.
文摘In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.
基金supported by National Natural Science Foundation of China(11631011 and 11626251)
文摘In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=（X1,X2,…,Xm） is a system of real smooth vector fields which satisfy the H?rmander’s condition,and △X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.
文摘Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω（S）, where Ω（S）is the Loop category of（S）,and the structure of K<sub>1</sub>S is given.
文摘Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1（r） of R in both real and complex case is proven by the homogeneity of the polynomial germs. It results in the finite determinacy of homogeneous polynomial germs needn＇t be discussed respectively.
文摘In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of finitely generated nilpotent groups with central associated subgroups are weakly potent.
文摘The cyclicity of four classes of codimension 3 plnnar polycycles and ensembles containing a saddle-node and two hyperbdic saddles is dealt with. The exnct cyclicity or cyclicity bound of them is obtained by finitely-smooth normal form theory.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11671126,12071120).
文摘Let ∧_(0,0)=(A_BMAANB_B)be a Morita ring,where the bimodule homomorphisms φ and ψ are zero.We study the finite presentedness,locally coherence,pure projectivity,pure injectivity,and FP-injectivity of modules over A_(0,0).Some applications are then given.
文摘The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.
文摘In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.
基金Project supported by the National Natural Science Foundation of China(No.11126346)
文摘Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.
文摘In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
