In this paper,we show that for an Sp(k+1)-invariant metric g on S^(4k+3)(k 1)close to the round metric,the conformally compact Einstein(CCE)manifold(M,g)with(S^(4k+3),[?])as its conformal infinity is unique up to isom...In this paper,we show that for an Sp(k+1)-invariant metric g on S^(4k+3)(k 1)close to the round metric,the conformally compact Einstein(CCE)manifold(M,g)with(S^(4k+3),[?])as its conformal infinity is unique up to isometry.Moreover,by the result in Li et al.(2017),g is the Graham-Lee metric(see Graham and Lee(1991))on the unit ball B_(1)■R^(4k+4).We also give an a priori estimate of the Einstein metric g.As a byproduct of the a priori estimates,based on the estimate and Graham-Lee and Lee's seminal perturbation results(see Graham and Lee(1991)and Lee(2006)),we directly use the continuity method to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity(S^(4k+3),[g])when the metric?is Sp(k+1)-invariant.We also generalize the results to the case of conformal infinity(S^(15),[?])with g a Spin(9)-invariant metric in the appendix.展开更多
A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the unif...A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.展开更多
Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an importa...Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.展开更多
The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as t...The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.展开更多
This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existe...This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11701326)the Fundamental Research Funds of Shandong University(Grant No.2016HW008)the Young Scholars Program of Shandong University(Grant No.2018WLJH85)。
文摘In this paper,we show that for an Sp(k+1)-invariant metric g on S^(4k+3)(k 1)close to the round metric,the conformally compact Einstein(CCE)manifold(M,g)with(S^(4k+3),[?])as its conformal infinity is unique up to isometry.Moreover,by the result in Li et al.(2017),g is the Graham-Lee metric(see Graham and Lee(1991))on the unit ball B_(1)■R^(4k+4).We also give an a priori estimate of the Einstein metric g.As a byproduct of the a priori estimates,based on the estimate and Graham-Lee and Lee's seminal perturbation results(see Graham and Lee(1991)and Lee(2006)),we directly use the continuity method to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity(S^(4k+3),[g])when the metric?is Sp(k+1)-invariant.We also generalize the results to the case of conformal infinity(S^(15),[?])with g a Spin(9)-invariant metric in the appendix.
文摘A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.
文摘Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.
基金The NSF (10801046) of Chinathe Heilongjiang Education Committee Grant(11551362,11551364)the Heilongjiang University Grant(Hdtd2010-14)
文摘The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.
文摘We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.
基金Supported by the NSF of Shandong Province (Y2008A31)
文摘This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.
