We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, ...We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, f i satisfy 2 f y′ 2 i t =0 =0, we say that F possesses a generalized turning point at t =0. Our goal is to give sufficient conditions for the existence of solution of the problems and to study the asymptotic behavior of the solution when F possesses a generalized turning point at t =0. We mainly discuss regular singular crossings.展开更多
In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism...In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure. Moreover, a weak regular *-product which connects a fundamental weak regular *-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular *-product is in fact a weak regular *-semigroup and any weak regular *-semigroup is constructed in this way.展开更多
Capacity analysis is a fundamental and essential work for evaluating the performance of cognitive wireless mesh network （CWMN） which is considered a promising option for the future network. Power control is an effic...Capacity analysis is a fundamental and essential work for evaluating the performance of cognitive wireless mesh network （CWMN） which is considered a promising option for the future network. Power control is an efficient way to avoid interference and improve capacity of wireless mesh networks. In this paper, a quantitative result of the per-node average throughput capacity of CWMN with power control is deduced for the first time, which is much helpful for understanding the limitations of CWMN. Firstly, under the large-scale channel fading model and protocol interference model, a closed-form expression for the maximum channel capacity of each node with power control is presented, under the constraint that the interference tolerated by the primary users （PUs） does not exceed a threshold. And then, with the deduced channel capacity result, the per-node average throughput capacity of CWMN is derived based on two regular topologies, i.e. square topology and triangle topology. The simulation results indicate that the capacity is effectively improved with power control, and affected by topology, tolerated interference threshold, the number of cognitive users （CUs） and primary users （PUs）.展开更多
文摘We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, f i satisfy 2 f y′ 2 i t =0 =0, we say that F possesses a generalized turning point at t =0. Our goal is to give sufficient conditions for the existence of solution of the problems and to study the asymptotic behavior of the solution when F possesses a generalized turning point at t =0. We mainly discuss regular singular crossings.
基金Subject supported by NNSF of China (60002007)NSF of Guangdong China (011438)
文摘In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure. Moreover, a weak regular *-product which connects a fundamental weak regular *-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular *-product is in fact a weak regular *-semigroup and any weak regular *-semigroup is constructed in this way.
基金supported by the National Science & Technology Major Project of 2011ZX03001-005-02the National Natural Science Foundation of China (61272516, 61272518, 61170275)the China-Canada Project (2010DFA111320)
文摘Capacity analysis is a fundamental and essential work for evaluating the performance of cognitive wireless mesh network （CWMN） which is considered a promising option for the future network. Power control is an efficient way to avoid interference and improve capacity of wireless mesh networks. In this paper, a quantitative result of the per-node average throughput capacity of CWMN with power control is deduced for the first time, which is much helpful for understanding the limitations of CWMN. Firstly, under the large-scale channel fading model and protocol interference model, a closed-form expression for the maximum channel capacity of each node with power control is presented, under the constraint that the interference tolerated by the primary users （PUs） does not exceed a threshold. And then, with the deduced channel capacity result, the per-node average throughput capacity of CWMN is derived based on two regular topologies, i.e. square topology and triangle topology. The simulation results indicate that the capacity is effectively improved with power control, and affected by topology, tolerated interference threshold, the number of cognitive users （CUs） and primary users （PUs）.
