In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.
In this letter, we shall show how to construct constrained Bell-type inequality for a generaltwo-party system, and violating this inequality is equivalent to being inseparable. For 2 (×) 2 system, the maximum vio...In this letter, we shall show how to construct constrained Bell-type inequality for a generaltwo-party system, and violating this inequality is equivalent to being inseparable. For 2 (×) 2 system, the maximum violation is 3,while for 3 (×) 3 system, the largest violation is 11/3.展开更多
The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for t...The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.展开更多
The singularly perturbed nonlinear problem where y,f, A, B are n-dimensional vectors is considered. Under the appropriate assump- tions the authors prove that there exists a solution y(x, ) and the estimation of y(x,...The singularly perturbed nonlinear problem where y,f, A, B are n-dimensional vectors is considered. Under the appropriate assump- tions the authors prove that there exists a solution y(x, ) and the estimation of y(x,) is obtained using the method of differential inequalities.展开更多
we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(-1/2,1/2;1;1- xc) and F(-1/2- δ,1/2 + δ;1;1- xd) on(0,1) for given 0 < c 5d/6 < ∞ andδ∈(-1/2,1/2),and find the la...we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(-1/2,1/2;1;1- xc) and F(-1/2- δ,1/2 + δ;1;1- xd) on(0,1) for given 0 < c 5d/6 < ∞ andδ∈(-1/2,1/2),and find the largest value δ1 = δ1(c,d) such that inequality F(-1/2,1/2;1;1- xc) <F(-1/2- δ,1/2 + δ;1;1- xd) holds for all x ∈(0,1). Besides,we also consider the Gaussian hypergeometric functions F(a- 1- δ,1- a + δ;1;1- x3) and F(a- 1,1- a;1;1- x2) for given a ∈ [1/29,1) and δ∈(a- 1,a),and obtain the analogous results.展开更多
This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensio...This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.展开更多
This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variati...This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem(i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality' solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.展开更多
This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorr...This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result.By computing the geometric error directly without accumulating the approximation error and chord error,the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.展开更多
文摘In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
文摘A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.
文摘In this letter, we shall show how to construct constrained Bell-type inequality for a generaltwo-party system, and violating this inequality is equivalent to being inseparable. For 2 (×) 2 system, the maximum violation is 3,while for 3 (×) 3 system, the largest violation is 11/3.
基金the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,Chinathe Dawn Program Foundationin Shanghai
文摘The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.
文摘The singularly perturbed nonlinear problem where y,f, A, B are n-dimensional vectors is considered. Under the appropriate assump- tions the authors prove that there exists a solution y(x, ) and the estimation of y(x,) is obtained using the method of differential inequalities.
基金supported by National Natural Science Foundation of China(Grant Nos.11371125,11171307 and 61374086)Natural Science Foundation of the Hunan Province(Grant No.14JJ2127)Natural Science Foundation of the Zhejiang Province(Grant No.LY13A010004)
文摘we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(-1/2,1/2;1;1- xc) and F(-1/2- δ,1/2 + δ;1;1- xd) on(0,1) for given 0 < c 5d/6 < ∞ andδ∈(-1/2,1/2),and find the largest value δ1 = δ1(c,d) such that inequality F(-1/2,1/2;1;1- xc) <F(-1/2- δ,1/2 + δ;1;1- xd) holds for all x ∈(0,1). Besides,we also consider the Gaussian hypergeometric functions F(a- 1- δ,1- a + δ;1;1- x3) and F(a- 1,1- a;1;1- x2) for given a ∈ [1/29,1) and δ∈(a- 1,a),and obtain the analogous results.
基金supported by the Science and Technology Foundation of Guizhou Province under Grant No.20102133
文摘This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.
基金supported by the National Science Foundation of China under Grant Nos.71171164 and 70471057the Doctorate Foundation of Northwestern Polytechnical University under Grant No.CX201235
文摘This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem(i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality' solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.
基金supported partially by the National Natural Science Foundation of China under Grant Nos.10871195 and 60821002/F02National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences
文摘This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result.By computing the geometric error directly without accumulating the approximation error and chord error,the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.
