Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.展开更多
This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).
This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability ...This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.展开更多
Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are considered.It is shown that these equations have solutions on subspaces of the polynomial,...Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are considered.It is shown that these equations have solutions on subspaces of the polynomial,exponential ortrigonometric form defined by linear nth-order ordinary differential equations with constant coefficients for n=4,...,9.Several examples of exact solutions are presented.展开更多
In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the p...In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.展开更多
The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutio...The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutionsof the Z-K equation are obtained.The methods used to solve the Z-K equation can be employed in further work toestablish new solutions for other nonlinear partial differential equations.展开更多
The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships bet...The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.展开更多
A new method for constructing the Wronskian entries is proposed and applied to the differential-difference Kadomtsev-Petviashvilli （DΔKP） equation. The generalized Wronskian solutions to it are obtained, including ...A new method for constructing the Wronskian entries is proposed and applied to the differential-difference Kadomtsev-Petviashvilli （DΔKP） equation. The generalized Wronskian solutions to it are obtained, including rational solutions and Matveev solutions.展开更多
Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixe...Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.展开更多
The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and bounda...The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.展开更多
文摘Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
文摘This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).
文摘This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Northwest University Graduate Innovation and Creativity Funds under Grant No.07YZZ15
文摘Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are considered.It is shown that these equations have solutions on subspaces of the polynomial,exponential ortrigonometric form defined by linear nth-order ordinary differential equations with constant coefficients for n=4,...,9.Several examples of exact solutions are presented.
基金The project supported by National Natural Science Foundation of China under Grant No.10401021
文摘In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.
基金Supported by the National Natural Science Foundation of China under Grant No.10974160
文摘The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutionsof the Z-K equation are obtained.The methods used to solve the Z-K equation can be employed in further work toestablish new solutions for other nonlinear partial differential equations.
文摘The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10371070 and 10671121 .Acknowledgments The authors exPress their thanks to Prof. D.J. Zhang and Dr. J.B. Bi for their good advices.
文摘A new method for constructing the Wronskian entries is proposed and applied to the differential-difference Kadomtsev-Petviashvilli （DΔKP） equation. The generalized Wronskian solutions to it are obtained, including rational solutions and Matveev solutions.
文摘Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.
基金supported in part by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.
