The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t...The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.展开更多
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of no...The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...展开更多
In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-comp...In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem展开更多
The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method o...The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...展开更多
Let G be a finite group and k a field of characteristic p】0.In this paper we consider the support variety for the cohomology module Ext<sub>kG</sub><sup>*</sup>（M,N） where M and N are kG-mod...Let G be a finite group and k a field of characteristic p】0.In this paper we consider the support variety for the cohomology module Ext<sub>kG</sub><sup>*</sup>（M,N） where M and N are kG-modules.It is the subvariety of the maximal ideal spectrum of H<sup>*</sup>（G,k） of the annihilator of the cohomology module. For modules in the principal block we show that that the variety is contained in the intersections of the varieties of M and N and the difference between the that intersection and the support variety of the cohomology module is contained in the group theoretic nucleus.For other blocks a new nucleus is defined and a similar theorem is proven.However in the case of modules in a nonprincipal block several new difficulties are highlighted by some examples.展开更多
A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S^(4n-1)→ S^(2n)× S^m as a module and demonstrate that it is not necessarily determined by the map in...A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S^(4n-1)→ S^(2n)× S^m as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality.展开更多
基金the NNSF of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)part by E-Institutes of Shanghai Municipal Education Commission(E03004)
文摘The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
基金Supported by the National Natural Science Foundation of China(40676016 and 10471039)the State Key Program for Basics Research of China(2003CB415101-03 and2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Insitutesof Shanghai Municipal Education Commission(N.E03004)the Natural Science Foudation of Zhejiangnm,China(Y606268)
文摘The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...
文摘In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem
基金Supported by the National Natural Science Foundation of China(40676016 and 10471039)+6 种基金 the State Key Program for Basics Research of China(2003CB415101-03 and2004CB418304) the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221) in part by E-Insitutesof Shanghai Municipal Education Commission(N.E03004) the Natural Science Foudation of Zhejiangnm,China(Y606268)
文摘The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...
基金Partially supported by grants from NSF and EPSRC
文摘Let G be a finite group and k a field of characteristic p】0.In this paper we consider the support variety for the cohomology module Ext<sub>kG</sub><sup>*</sup>（M,N） where M and N are kG-modules.It is the subvariety of the maximal ideal spectrum of H<sup>*</sup>（G,k） of the annihilator of the cohomology module. For modules in the principal block we show that that the variety is contained in the intersections of the varieties of M and N and the difference between the that intersection and the support variety of the cohomology module is contained in the group theoretic nucleus.For other blocks a new nucleus is defined and a similar theorem is proven.However in the case of modules in a nonprincipal block several new difficulties are highlighted by some examples.
基金supported by the National Science and Engineering Research Council of Canada
文摘A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S^(4n-1)→ S^(2n)× S^m as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality.
