In this paper,using the monotone iterative method,we study the existence of extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces.Some existence theorems of extreme solutions are obtained.
In this paper,using the monotone iterative method,we study the existence of extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces.Some existence theorems of extreme solutions are obtained.
In this paper,we propose a general path following method,in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap.The algorithm maintains the O(〖KF(〗n〖KF)〗L) iteration complexity.It enjoys quadratic convergence if the optimal vertex is nondegenerate.
In this paper,we propose a general path following method,in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap.The algorithm maintains the O(〖KF(〗n〖KF)〗L) iteration complexity.It enjoys quadratic convergence if the optimal vertex is nondegenerate.
In this paper,we study the stochastic comparisons of minimal repair replacement policies in repairable case.We give some results on comparisons of the same unit for different policies and on comparisons of the same policies for different units.
In this paper,we study the stochastic comparisons of minimal repair replacement policies in repairable case.We give some results on comparisons of the same unit for different policies and on comparisons of the same policies for different units.
The parametric representation for finite-band solutions of a stationary soliton equation is discussed.This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense.The nonconfocal involutive integral representations {F_m} are obtained also.The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.
The parametric representation for finite-band solutions of a stationary soliton equation is discussed.This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense.The nonconfocal involutive integral representations {F_m} are obtained also.The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.
By the interpolation inequality and a priori estimates in the weighted space,the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,and the existence of the maximal attractor is obtained.
By the interpolation inequality and a priori estimates in the weighted space,the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,and the existence of the maximal attractor is obtained.
To solve the shell problem,we propose a mixed finite element method with bubble-stabilization term and discrete Riesz-representation operators.It is shown that this new method is coercive,implying the well-known K-ellipticity and the Inf-Sup condition being circumvented,and the resulting linear system is symmetrically positively definite,with a condition number being at most O(h~(-2)).Further,an optimal error bound is attained.
To solve the shell problem,we propose a mixed finite element method with bubble-stabilization term and discrete Riesz-representation operators.It is shown that this new method is coercive,implying the well-known K-ellipticity and the Inf-Sup condition being circumvented,and the resulting linear system is symmetrically positively definite,with a condition number being at most O(h~(-2)).Further,an optimal error bound is attained.
In this paper,we study a nonlinear Dirichlet problem on a smooth bounded domain,in which the nonlinear term is asymptotically linear,not superlinear,at infinity and sublinear near the origin.By using Mountain Pass Theorem,we prove that there exist at least two positive solutions under suitable assumptions on the nonlinearity.
In this paper,we study a nonlinear Dirichlet problem on a smooth bounded domain,in which the nonlinear term is asymptotically linear,not superlinear,at infinity and sublinear near the origin.By using Mountain Pass Theorem,we prove that there exist at least two positive solutions under suitable assumptions on the nonlinearity.
In this paper we prove that Sands' topological condition for Collet-Eckmann maps implies Tsujii's metrical condition;on the other hand,if a Collet-Eckmann map satisfies Tsujii's metrical condition,then it satisfies Sands' topological condition.Thus we obtain three different versions of Benedicks-Carleson Theorem by using topological conditions.
In this paper we prove that Sands' topological condition for Collet-Eckmann maps implies Tsujii's metrical condition;on the other hand,if a Collet-Eckmann map satisfies Tsujii's metrical condition,then it satisfies Sands' topological condition.Thus we obtain three different versions of Benedicks-Carleson Theorem by using topological conditions.
A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path.This concept is a generalization of a directed cycle.We show that if T is an almost regular n-partite (n≥8) tournament with each partite set having at least two vertices,then every arc of T has a k-outpath for all k,3≤k≤n-1.
A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path.This concept is a generalization of a directed cycle.We show that if T is an almost regular n-partite (n≥8) tournament with each partite set having at least two vertices,then every arc of T has a k-outpath for all k,3≤k≤n-1.
A matrix splitting method is presented for minimizing a quadratic programming (QP) problem,and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points.We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate,and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region,and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
A matrix splitting method is presented for minimizing a quadratic programming (QP) problem,and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points.We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate,and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region,and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
A system of three-unit networks with no-self-connection is investigated,the general formula for bifuraction direction of Hopf bifurcation is calculated,and the estimation formula of the period for periodic solution is given.
A system of three-unit networks with no-self-connection is investigated,the general formula for bifuraction direction of Hopf bifurcation is calculated,and the estimation formula of the period for periodic solution is given.
In this paper,we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form.We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form.This helps us to explicate the difficulty of constructing the non-separable variate wavelet basis and to hint how to construct non-separable variate wavelet basis.
In this paper,we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form.We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form.This helps us to explicate the difficulty of constructing the non-separable variate wavelet basis and to hint how to construct non-separable variate wavelet basis.
The uniqueness for unbounded classical solutions of the evolution system describing geophysical flow within the earth and its associated systems is investigated.Under suitable growth conditions,it is shown that the solution to the initial value problem is unique.Moreover,a counterexample is given if the growth conditions are not satisfied.
The uniqueness for unbounded classical solutions of the evolution system describing geophysical flow within the earth and its associated systems is investigated.Under suitable growth conditions,it is shown that the solution to the initial value problem is unique.Moreover,a counterexample is given if the growth conditions are not satisfied.
The asymptotic behavior of the nonoscillatory solutions of the difference equations Δ[r(n)Δx(n)]+f(n,x(n),x(τ(n,x(n))))=0 (1) is considered.In the case when f is a strongly sublinear (superlinear) function,conditions for oscillations of (1) are also found.
The asymptotic behavior of the nonoscillatory solutions of the difference equations Δ[r(n)Δx(n)]+f(n,x(n),x(τ(n,x(n))))=0 (1) is considered.In the case when f is a strongly sublinear (superlinear) function,conditions for oscillations of (1) are also found.
Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied.An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model.Also,an appropriate statistic for test variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied.An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model.Also,an appropriate statistic for test variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
In this paper,we give some conditions for line search,and prove that under these line search conditions the DFP algorithm is globally convergent and Q-superlinearly convergent.We show that the conditions are weaker than those in [6].
In this paper,we give some conditions for line search,and prove that under these line search conditions the DFP algorithm is globally convergent and Q-superlinearly convergent.We show that the conditions are weaker than those in [6].