This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2...This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.展开更多
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is establishe...In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.展开更多
We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the solit...We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.展开更多
This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matr...This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.展开更多
This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent...This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.展开更多
Singular value system is applied to construct a new class of improved regularizing methods for solving the first kind of Fredholm integral equations with noisy data. By a priori choosing regularizing parameters, optim...Singular value system is applied to construct a new class of improved regularizing methods for solving the first kind of Fredholm integral equations with noisy data. By a priori choosing regularizing parameters, optimal convergence order of the regularized solution is obtained. And with aids of MATLAB software, numerical results are presented which roughly coincide with the theoretical analysis.展开更多
The garment industry in Vietnam is one of the country’s strongest industries in the world.However,the production process still encounters problems regarding scheduling that does not equate to an optimal process.The p...The garment industry in Vietnam is one of the country’s strongest industries in the world.However,the production process still encounters problems regarding scheduling that does not equate to an optimal process.The paper introduces a production scheduling solution that resolves the potential delays and lateness that hinders the production process using integer programming and order allocation with a make-to-order manufacturing viewpoint.A number of constraints were considered in the model and is applied to a real case study of a factory in order to viewhowthe tardiness and latenesswould be affected which resulted in optimizing the scheduling time better.Specifically,the constraints considered were order assignments,production time,and tardiness with an objective function which is to minimize the total cost of delay.The results of the study precisely the overall cost of delay of the orders given to the plant and successfully propose a suitable production schedule that utilizes the most of the plant given.The study has shown promising results that would assist plant and production managers in determining an algorithm that they can apply for their production process.展开更多
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The...This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.展开更多
In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosin...In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.展开更多
文摘This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
基金the National Science Foundation(Grant Nos.DMS0409297,DMR0205232,CCF-0430349)US National Institute of Health-National Cancer Institute(Grant No.1R01CA125707-01A1)+2 种基金the National Natural Science Foundation of China(Grant No.10571172)the National Basic Research Program(Grant No.2005CB321704)the Youth's Innovative Program of Chinese Academy of Sciences(Grant Nos.K7290312G9,K7502712F9)
文摘In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
基金supported by the National Natural Science Foundation of China under Grant Nos.12175111,12275144 and 12235007the KC Wong Magna Fund in Ningbo University。
文摘We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.
基金Project supported by the National Natural Science Foundation of China(No.10672194)the China-Russia Cooperative Project(the National Natural Science Foundation of China and the Russian Foundation for Basic Research)(No.10811120012)
文摘This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.
基金supported by the National Natural Science Foundation of China(11301492)the Ph.D.Programs Foundation of Ministry of Education of China(20130145120005)the TianYuan Special Funds of the National Natural Science Foundation of China(11226134)
文摘This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.
基金Natural Science Foundation of Shandong Province (Y2001E03)
文摘Singular value system is applied to construct a new class of improved regularizing methods for solving the first kind of Fredholm integral equations with noisy data. By a priori choosing regularizing parameters, optimal convergence order of the regularized solution is obtained. And with aids of MATLAB software, numerical results are presented which roughly coincide with the theoretical analysis.
文摘The garment industry in Vietnam is one of the country’s strongest industries in the world.However,the production process still encounters problems regarding scheduling that does not equate to an optimal process.The paper introduces a production scheduling solution that resolves the potential delays and lateness that hinders the production process using integer programming and order allocation with a make-to-order manufacturing viewpoint.A number of constraints were considered in the model and is applied to a real case study of a factory in order to viewhowthe tardiness and latenesswould be affected which resulted in optimizing the scheduling time better.Specifically,the constraints considered were order assignments,production time,and tardiness with an objective function which is to minimize the total cost of delay.The results of the study precisely the overall cost of delay of the orders given to the plant and successfully propose a suitable production schedule that utilizes the most of the plant given.The study has shown promising results that would assist plant and production managers in determining an algorithm that they can apply for their production process.
文摘This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
基金This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai.
文摘In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
