In this paper,we study the existence of the reflexive,reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P,Q).We derive necessary...In this paper,we study the existence of the reflexive,reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P,Q).We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.展开更多
A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in ...A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently smooth.Numerical results are presented,which confirm the theoretical prediction of the exponential rate of convergence.展开更多
The authors study torsion in the integral cohomology of a certain family of2 n-dimensional orbifolds X with actions of the n-dimensional compact torus. Compact simplicial toric varieties are in our family. For a prime...The authors study torsion in the integral cohomology of a certain family of2 n-dimensional orbifolds X with actions of the n-dimensional compact torus. Compact simplicial toric varieties are in our family. For a prime number p, the authors find a necessary condition for the integral cohomology of X to have no p-torsion. Then it is proved that the necessary condition is sufficient in some cases. The authors also give an example of X which shows that the necessary condition is not sufficient in general.展开更多
In this paper,the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation.The optimal convergent order O(h^(2)+k^(2))is obtained...In this paper,the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation.The optimal convergent order O(h^(2)+k^(2))is obtained for the numerical solution in a discrete L^(2)-norm.A numerical experiment is presented to test the theoretical result.展开更多
We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces.The model is derived through a variational approa...We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces.The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation.This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows(Qian,Wang,and Sheng,J.Fluid Mech.564,333-360(2006)).Physically,the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime.Therefore,the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface.A phase field is employed to model the diffuse interface between two immiscible fluid components,one being the electrolyte and the other a nonconductive fluid,both allowed to slip at solid surfaces.Our model consists of the incompressible Navier-Stokes equation for momentum transport,the Nernst-Planck equation for ion transport,the Cahn-Hilliard phase-field equation for interface motion,and the Poisson equation for electric potential,along with all the necessary boundary conditions.In particular,all the dynamic boundary conditions at solid surfaces,including the generalized Navier boundary condition for slip,are derived together with the equations of motion in the bulk region.Numerical examples in two-dimensional space,which involve overlapped electric double layer fields,have been presented to demonstrate the validity and applicability of the model,and a few salient features of the two-phase immiscible electroosmotic flows at solid surface.The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.展开更多
文摘In this paper,we study the existence of the reflexive,reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P,Q).We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.
基金supported by National Science Foundation of China(11301446,11271145)Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009)+3 种基金the Project of Department of Education of Guangdong Province(2012KJCX0036)China Postdoctoral Science FoundationGrant(2013M531789)Project of Scientific Research Fund ofHunan Provincial Science and Technology Department(2013RS4057)the Research Foundation of Hunan Provincial Education Department(13B116).
文摘A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently smooth.Numerical results are presented,which confirm the theoretical prediction of the exponential rate of convergence.
基金supported by JSPS Grant-in-Aid for Scientific Research(No.25400095)
文摘The authors study torsion in the integral cohomology of a certain family of2 n-dimensional orbifolds X with actions of the n-dimensional compact torus. Compact simplicial toric varieties are in our family. For a prime number p, the authors find a necessary condition for the integral cohomology of X to have no p-torsion. Then it is proved that the necessary condition is sufficient in some cases. The authors also give an example of X which shows that the necessary condition is not sufficient in general.
基金This work is supported by National Natural Science Foundation of China(Grant Nos.11271145 and 11031006)Foundation of Guizhou Science and Technology Department(Grant No.[2011]2098)+1 种基金Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Programof Higher Education(Grant No.20114407110009)the Project of Department of Education of Guangdong Province(Grant No.2012KJCX0036).
文摘In this paper,the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation.The optimal convergent order O(h^(2)+k^(2))is obtained for the numerical solution in a discrete L^(2)-norm.A numerical experiment is presented to test the theoretical result.
基金We would like to thank Professor Chun Liu for helpful discussions and comments on the early stages of thiswork.This publication is based onwork partially supported byAward No.SA-C0040/UK-C0016made by King Abdullah University of Science and Technology(KAUST),and Hong Kong RGC grant No.603510+1 种基金Sihong Shao is also supported by the National Natural Science Foundation of China(No.11101011)and the State Key Laboratory of ASIC&System(Fudan University)under the open project fund No.10KF015.
文摘We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces.The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation.This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows(Qian,Wang,and Sheng,J.Fluid Mech.564,333-360(2006)).Physically,the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime.Therefore,the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface.A phase field is employed to model the diffuse interface between two immiscible fluid components,one being the electrolyte and the other a nonconductive fluid,both allowed to slip at solid surfaces.Our model consists of the incompressible Navier-Stokes equation for momentum transport,the Nernst-Planck equation for ion transport,the Cahn-Hilliard phase-field equation for interface motion,and the Poisson equation for electric potential,along with all the necessary boundary conditions.In particular,all the dynamic boundary conditions at solid surfaces,including the generalized Navier boundary condition for slip,are derived together with the equations of motion in the bulk region.Numerical examples in two-dimensional space,which involve overlapped electric double layer fields,have been presented to demonstrate the validity and applicability of the model,and a few salient features of the two-phase immiscible electroosmotic flows at solid surface.The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.
