I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
In this paper, a dissipative Zakharov equations are discretized by difference method. We make prior estimates for the algebric system of equations. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds of the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are dependent of the mesh size.
In this paper, a dissipative Zakharov equations are discretized by difference method. We make prior estimates for the algebric system of equations. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds of the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are dependent of the mesh size.
Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be
Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be
For the weakly inhomogeneous acoustic medium in Q={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.
For the weakly inhomogeneous acoustic medium in Q={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.
The purpose of the article is to formulate, under the lX risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.
The purpose of the article is to formulate, under the lX risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.
Positive solutions to the boundary value problem, are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)2(0, X), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong [1].
Positive solutions to the boundary value problem, are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)2(0, X), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong [1].
Versions of the multiple Nevanlinna-Pick interpolation problem in the class N-circumfiex involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description of their solutions.
Versions of the multiple Nevanlinna-Pick interpolation problem in the class N-circumfiex involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description of their solutions.
In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E_1.
In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E_1.
Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.
Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.
In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ~(1/2)) for Tikhonov-Browder regularization, where ' denotes the noise level of the data perturbation.
In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ~(1/2)) for Tikhonov-Browder regularization, where ' denotes the noise level of the data perturbation.
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the costruction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the costruction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of a "food-limited population model with toxicants and time delays. Some new results are obtained.
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of a "food-limited population model with toxicants and time delays. Some new results are obtained.
We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Liénard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove that if g is isochronous (see Definition 1.1), then the center is isochronous if and only if F=0. For the second class which is the Hamiltonian systems of the form x=-g(y), y=f(x) with a center at the origin, we prove that if f or g is isochronous, then the center is isochronous if and only if the other is also isochronous.
We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Liénard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove that if g is isochronous (see Definition 1.1), then the center is isochronous if and only if F=0. For the second class which is the Hamiltonian systems of the form x=-g(y), y=f(x) with a center at the origin, we prove that if f or g is isochronous, then the center is isochronous if and only if the other is also isochronous.
In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous difference equations x(n+1)-x(n)+∑ from (i=1) to m of pi(n)x(n-τ_i)(n)=0,which are the discrete analog of the delay differential equations considered in [1].
In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous difference equations x(n+1)-x(n)+∑ from (i=1) to m of pi(n)x(n-τ_i)(n)=0,which are the discrete analog of the delay differential equations considered in [1].
It is known that the study of the qualitative properties of a matrix A (which depend only on the sign pattern of A) can be turned into the study of the graph theoretical properties of the signed digraph S(A). The underlying digraph of the signed digraph of a strong sign nonsingular matrix (abbreviated S~2NS matrix) with a negative main diagonal is called an S~2NS digraph. In the study of S~2NS digraphs, the minimal forbidden configuration (or MFC for short) plays an important role. Three (classes of) MFS's were constructed by Thomassen, Brualdi and Shader, and Shao. In this paper, we show that a digraph D is an S2NS digraph if and only if its "cycle linear system" is solvable. This simplifies a parallel result obtained by Shao and Hu. As an application of the result, a graph theoretical characterization for a digraph to be an S~2NS digraph is given. At the end of the paper, we construct infinitely many new MFCs to show that for each even number k(k>0), there are basic MFCs with k terminal components (here, with no loss of generality, we assume that the number of the initial components of a digraph is no less than that of its terminal components throughout the following).
It is known that the study of the qualitative properties of a matrix A (which depend only on the sign pattern of A) can be turned into the study of the graph theoretical properties of the signed digraph S(A). The underlying digraph of the signed digraph of a strong sign nonsingular matrix (abbreviated S~2NS matrix) with a negative main diagonal is called an S~2NS digraph. In the study of S~2NS digraphs, the minimal forbidden configuration (or MFC for short) plays an important role. Three (classes of) MFS's were constructed by Thomassen, Brualdi and Shader, and Shao. In this paper, we show that a digraph D is an S2NS digraph if and only if its "cycle linear system" is solvable. This simplifies a parallel result obtained by Shao and Hu. As an application of the result, a graph theoretical characterization for a digraph to be an S~2NS digraph is given. At the end of the paper, we construct infinitely many new MFCs to show that for each even number k(k>0), there are basic MFCs with k terminal components (here, with no loss of generality, we assume that the number of the initial components of a digraph is no less than that of its terminal components throughout the following).
The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.
The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.
In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.
In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.