In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmo...In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter e is given, and error estimate and numerical result are also given.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform...In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.展开更多
In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the t...In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of lite difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results.展开更多
Multi-objective genetic algorithm is much suitable for solving multi-objective optimization problems. By use of Genetic algorithm, the optimization of S-boxes is explored in this paper. Results of the experiments show...Multi-objective genetic algorithm is much suitable for solving multi-objective optimization problems. By use of Genetic algorithm, the optimization of S-boxes is explored in this paper. Results of the experiments show that, with heuristic mutation strategy, the algorithm has high searching efficiency and fast convergence speed. Meanwhile, we also have take the avalanche probability of S-boxes into account, besides nonlinearity and difference uniformity. Under this method, an effective genetic algorithm for 6×6 S-boxes is provided and a number of S-boxes with good cryptographic capability can be obtained.展开更多
The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi...The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.展开更多
Because ring-stiffened cylindrical shell structures have many merits, they are widely used in many areas. However, as the strength of steel increase continuously, ensuring of the structure stability is becoming more a...Because ring-stiffened cylindrical shell structures have many merits, they are widely used in many areas. However, as the strength of steel increase continuously, ensuring of the structure stability is becoming more and more important. Therefore, it is necessary to carry on a more particular analysis. Based on the understanding and analysis of the characteristics of stability for a ring-stiffened cylindrical shell under uniform external pressure and under external single pressure, the characteristics under different cross uniform external pressures are analyzed, and the regularity of it is also gotten. The curve of stability given various geometrical parameters under different cross uniform external pressures is protracted by the analysis of the theory. The conclusion not only improves the theory structural mechanics, it also was important effects on engineering calculation and design.展开更多
In this work, we first define the notions of almost periodic sequences, asymptotically almost periodic sequences, as well as uniformly almost periodic sequences,and reveal their basic properties. Then for the almost p...In this work, we first define the notions of almost periodic sequences, asymptotically almost periodic sequences, as well as uniformly almost periodic sequences,and reveal their basic properties. Then for the almost periodic difference systems of general form we establish the criteria of existence for almost periodic solutions.Especially, several existence theorems are proved in terms of discrete Liapunov functions.展开更多
We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of...We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.展开更多
文摘In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter e is given, and error estimate and numerical result are also given.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
文摘In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.
文摘In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of lite difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results.
基金Supported by the National Natural Science Foundation of China (60473012)
文摘Multi-objective genetic algorithm is much suitable for solving multi-objective optimization problems. By use of Genetic algorithm, the optimization of S-boxes is explored in this paper. Results of the experiments show that, with heuristic mutation strategy, the algorithm has high searching efficiency and fast convergence speed. Meanwhile, we also have take the avalanche probability of S-boxes into account, besides nonlinearity and difference uniformity. Under this method, an effective genetic algorithm for 6×6 S-boxes is provided and a number of S-boxes with good cryptographic capability can be obtained.
文摘The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.
文摘Because ring-stiffened cylindrical shell structures have many merits, they are widely used in many areas. However, as the strength of steel increase continuously, ensuring of the structure stability is becoming more and more important. Therefore, it is necessary to carry on a more particular analysis. Based on the understanding and analysis of the characteristics of stability for a ring-stiffened cylindrical shell under uniform external pressure and under external single pressure, the characteristics under different cross uniform external pressures are analyzed, and the regularity of it is also gotten. The curve of stability given various geometrical parameters under different cross uniform external pressures is protracted by the analysis of the theory. The conclusion not only improves the theory structural mechanics, it also was important effects on engineering calculation and design.
文摘In this work, we first define the notions of almost periodic sequences, asymptotically almost periodic sequences, as well as uniformly almost periodic sequences,and reveal their basic properties. Then for the almost periodic difference systems of general form we establish the criteria of existence for almost periodic solutions.Especially, several existence theorems are proved in terms of discrete Liapunov functions.
基金supported by the National Science Foundation of the United States (Grant No. CMMI-1435864)
文摘We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.
