In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existen...By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.展开更多
We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R...We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[X]=W(R)[X]■Z(R[X]),where J(A),N^(*)(A),W(A),Z(A)are the Jacobson radical,upper nilradical,Wedderburn radical,and center of a given ring A,respectively,and A[X]denotes the polynomial ring with a set X of commuting indeterminates over A;we also prove that R is semiprime if and only if the right(left)singular ideal of R is zero.We provide methods to construct C-regular rings which are neither commutative nor von Neumann regular,from any given ring.Moreover,for a C-regular ring R,the following are proved to be equivalent:(i)R is Abelian;(ii)every prime factor ring of R is a duo domain;(ii)R is quasi-duo;and(iv)R/W(R)is reduced.展开更多
Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of(partially) maximai element and equilibrium point are discussed as ap...Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of(partially) maximai element and equilibrium point are discussed as applications of above results.展开更多
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain propertie...In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.展开更多
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co...Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.展开更多
In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching t...In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.展开更多
A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of travel...A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of traveling waves is extended on 2-1 dimension lattice difference equations. As an application, an example is presented to illustrate the main results.展开更多
We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applicat...We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.展开更多
Cognitive radio devices can utilize the licensed channels in an opportunistic manner to solve the spectrum scarcity issue occurring in the unlicensed spectrum.However,these cognitive radio devices(secondary users)are ...Cognitive radio devices can utilize the licensed channels in an opportunistic manner to solve the spectrum scarcity issue occurring in the unlicensed spectrum.However,these cognitive radio devices(secondary users)are greatly affected by the original users(primary users)of licensed channels.Cognitive users have to adjust operation parameters frequently to adapt to the dynamic network environment,which causes extra energy consumption.Energy consumption can be reduced by predicting the future activity of primary users.However,the traditional prediction-based algorithms require large historical data to achieve a satisfying precision accuracy which will consume a lot of time and memory space.Moreover,many of these schemes lack methods to deal with the very busy network environments.In this paper,one semi-supervised learning algorithm,i.e.,tri-training,has been employed to investigate the prediction of primary activity.Based on the prediction results of tri-training,a duty-cycle mechanism and an intermediate node selection approach are proposed to improve the energy efficiency.Simulation results show the effectiveness of the proposed algorithm.展开更多
In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping ...In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping time with finite values and for the general stopping time we prove the result taking limit.We suggest a new approach to generalize the results for the case of constant time horizon to the case of stopping time horizon.展开更多
In this paper, using the notion of subdivision, the authors generalize the definition of cofibration in digital topology and show that this kind of cofibration is injective in the sense of subdivision. Meanwhile, they...In this paper, using the notion of subdivision, the authors generalize the definition of cofibration in digital topology and show that this kind of cofibration is injective in the sense of subdivision. Meanwhile, they give the necessary condition under which a digital map is a cofibration. Furthermore, they consider the Lusternik-Schnirelmann category of digital maps in the sense of subdivision and give several fundamental homotopy properties about it.展开更多
It is proved that for matrices A,B in the n by n upper triangular matrix ring T_(n)(R)over a domain R,if AB is nonzero and central in T_(n)(R)then AB=BA.The n by n full matrix rings over right Noetherian domains are a...It is proved that for matrices A,B in the n by n upper triangular matrix ring T_(n)(R)over a domain R,if AB is nonzero and central in T_(n)(R)then AB=BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties.展开更多
We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solu...We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solution is proved with the help of Browder fixed point theorem.The difference scheme is showed to be unconditionally convergent in Loo norm by constructing an auxiliary Lipschitz continuous function.Based on this result,it is demonstrated that the difference scheme preserves the maximum principle without any restrictions on spatial step size and temporal step size.The numerical experiments also verify the reliability of the method.展开更多
Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(...Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(Z/p,Z/p) in the E_2-term of the ASS and meanwhile p · p is the first periodic element αp.展开更多
Let p be an odd prime and q = 2(p- 1). Up to total degree t - s 〈 max((5p^3 + 6p^2 +6p +4)q- 10,p^4q}, the generators of H^s,t(U(L)), the cohomology of the universal enveloping algebra of a bigraded Lie a...Let p be an odd prime and q = 2(p- 1). Up to total degree t - s 〈 max((5p^3 + 6p^2 +6p +4)q- 10,p^4q}, the generators of H^s,t(U(L)), the cohomology of the universal enveloping algebra of a bigraded Lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.展开更多
Let p be an odd prime. For the Stiefel manifold Wm+k,k = SU(m + k)/SU(m), we obtain an upper bound of its p-primary homotopy exponent in the stable range k ≤ m with k ≤ (p - 1)2 + 1.
In this paper,we determine some nontrivial secondary Adams differentials on the fourth line Ext^(4,*)_A(Z/p,Z/p)of the classical Adams spectral sequence.Specially,among these differentials,two of them are obtained via...In this paper,we determine some nontrivial secondary Adams differentials on the fourth line Ext^(4,*)_A(Z/p,Z/p)of the classical Adams spectral sequence.Specially,among these differentials,two of them are obtained via the matrix Massey products.展开更多
In this paper,the authors introduce a new effective method to compute the generators of the E-term of the May spectral sequence.This helps them to obtain four families of non-trivial product elements in the stable hom...In this paper,the authors introduce a new effective method to compute the generators of the E-term of the May spectral sequence.This helps them to obtain four families of non-trivial product elements in the stable homotopy groups of spheres.展开更多
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
基金supported by Scientific Research Fund of Heilongjiang Provincial Education Department (11544032)the National Natural Science Foundation of China (10571021, 10701020)
文摘By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.
文摘We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[X]=W(R)[X]■Z(R[X]),where J(A),N^(*)(A),W(A),Z(A)are the Jacobson radical,upper nilradical,Wedderburn radical,and center of a given ring A,respectively,and A[X]denotes the polynomial ring with a set X of commuting indeterminates over A;we also prove that R is semiprime if and only if the right(left)singular ideal of R is zero.We provide methods to construct C-regular rings which are neither commutative nor von Neumann regular,from any given ring.Moreover,for a C-regular ring R,the following are proved to be equivalent:(i)R is Abelian;(ii)every prime factor ring of R is a duo domain;(ii)R is quasi-duo;and(iv)R/W(R)is reduced.
基金Supported by the National Natural Science Foundation of China(10361005)
文摘Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of(partially) maximai element and equilibrium point are discussed as applications of above results.
基金Supported by the National Natural Science Foundation of China(11161049)
文摘In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.
基金Project supported by the Natural Science Foundation of Sichuan Province of China(No.2005A132)
文摘Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
文摘In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.
基金Supported by the National Natural Science Foundation of China(Ill61049)
文摘A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of traveling waves is extended on 2-1 dimension lattice difference equations. As an application, an example is presented to illustrate the main results.
基金Supported by the Science Foundation of Education Committee of Jilin Province (20111434])
文摘We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.11761074,61972207,61902041)the Natural Science Foundation of Jilin Province of China(Grant No.2020122336JC)Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project(No.20200301053RQ)and the Project through the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institution.
文摘Cognitive radio devices can utilize the licensed channels in an opportunistic manner to solve the spectrum scarcity issue occurring in the unlicensed spectrum.However,these cognitive radio devices(secondary users)are greatly affected by the original users(primary users)of licensed channels.Cognitive users have to adjust operation parameters frequently to adapt to the dynamic network environment,which causes extra energy consumption.Energy consumption can be reduced by predicting the future activity of primary users.However,the traditional prediction-based algorithms require large historical data to achieve a satisfying precision accuracy which will consume a lot of time and memory space.Moreover,many of these schemes lack methods to deal with the very busy network environments.In this paper,one semi-supervised learning algorithm,i.e.,tri-training,has been employed to investigate the prediction of primary activity.Based on the prediction results of tri-training,a duty-cycle mechanism and an intermediate node selection approach are proposed to improve the energy efficiency.Simulation results show the effectiveness of the proposed algorithm.
文摘In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping time with finite values and for the general stopping time we prove the result taking limit.We suggest a new approach to generalize the results for the case of constant time horizon to the case of stopping time horizon.
基金supported by the National Natural Science Foundation of China (Nos. 12001474,12171165, 12261091)Guangdong Natural Science Foundation (No. 2021A1515010374)
文摘In this paper, using the notion of subdivision, the authors generalize the definition of cofibration in digital topology and show that this kind of cofibration is injective in the sense of subdivision. Meanwhile, they give the necessary condition under which a digital map is a cofibration. Furthermore, they consider the Lusternik-Schnirelmann category of digital maps in the sense of subdivision and give several fundamental homotopy properties about it.
基金The second author was supported by the National Natural Science Foundation of China(11361063)the third author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education of Korea(2016R1D1A1B03931190).
文摘It is proved that for matrices A,B in the n by n upper triangular matrix ring T_(n)(R)over a domain R,if AB is nonzero and central in T_(n)(R)then AB=BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties.
基金This work was supported by National Natural Science Foundation of China(No.11761074)the projection of the Department of Science and Technology of Jilin Province for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project.
文摘We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solution is proved with the help of Browder fixed point theorem.The difference scheme is showed to be unconditionally convergent in Loo norm by constructing an auxiliary Lipschitz continuous function.Based on this result,it is demonstrated that the difference scheme preserves the maximum principle without any restrictions on spatial step size and temporal step size.The numerical experiments also verify the reliability of the method.
基金supported by the National Natural Science Foundation of China(Nos.11761072,11671154)the China Postdoctoral Science Foundation Special Funded Project(No.2015T80909)
文摘Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(Z/p,Z/p) in the E_2-term of the ASS and meanwhile p · p is the first periodic element αp.
基金supported by NSFC(Grant Nos.11671154 and 11761072)General Financial Grant from the China Postdoctoral Science Foundation(Grant No.2017M622721)
文摘Let p be an odd prime and q = 2(p- 1). Up to total degree t - s 〈 max((5p^3 + 6p^2 +6p +4)q- 10,p^4q}, the generators of H^s,t(U(L)), the cohomology of the universal enveloping algebra of a bigraded Lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.
基金Supported by the NSFC(Grant No.11261062)the Special Financial Grant form the China Postdoctoral Science Foundation(Grant No.2015T80909)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20134407110001)
文摘Let p be an odd prime. For the Stiefel manifold Wm+k,k = SU(m + k)/SU(m), we obtain an upper bound of its p-primary homotopy exponent in the stable range k ≤ m with k ≤ (p - 1)2 + 1.
基金Supported by NSFC(Grant Nos.11671154,11761072,12001474 and 11871284)Guangdong Natural Science Foundation(Grant No.2020A1515011008)“13th Five-Year”Science and Technology Project of Jilin Department of Education(Grant No.JJKH20200508KJ)。
文摘In this paper,we determine some nontrivial secondary Adams differentials on the fourth line Ext^(4,*)_A(Z/p,Z/p)of the classical Adams spectral sequence.Specially,among these differentials,two of them are obtained via the matrix Massey products.
基金supported by the National Natural Science Foundation of China(Nos.12001474,12171165)Guangdong Natural Science Foundation(Nos.2020A1515011008,2021A1515010374)the“13th Five-Year”Science and Technology Project of Jilin Department of Education(No.JJKH20200508KJ)
文摘In this paper,the authors introduce a new effective method to compute the generators of the E-term of the May spectral sequence.This helps them to obtain four families of non-trivial product elements in the stable homotopy groups of spheres.