By studying the properties of Chebyshev polynomials, some specific and mean-ingful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbersand Lucas numbers are obtained.
A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discr...A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.展开更多
The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of ...The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.展开更多
Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a ...Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutions with five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.展开更多
An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transforma...An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.展开更多
We verify that the total angular momentum 3-vector defined by the author [X. Zhang, Commun. Math.Phys. 206 (1999) 137] is equal to (0, 0, ma) forany time slice in both the Kerr and the Kerr-Newman spacetimes.
In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bre...In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest.展开更多
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by u...Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.展开更多
The bilinear form for a nonisospectral and variable-coefficient KdV equation is obtained and some exact soliton solutions are derived through Hirota method and Wronskian technique. We also derive the bilmear transform...The bilinear form for a nonisospectral and variable-coefficient KdV equation is obtained and some exact soliton solutions are derived through Hirota method and Wronskian technique. We also derive the bilmear transformation from its Lax pairs and End solutions with the help of the obtained bilinear transformation.展开更多
Two new applications of homogeneous balance(HB) method are presented.It is shown that HB method can be extended to search for the Baecklund transformations and similarity reductions of nonlinear partial differential e...Two new applications of homogeneous balance(HB) method are presented.It is shown that HB method can be extended to search for the Baecklund transformations and similarity reductions of nonlinear partial differential equations.The close relations among the HB method,Weiss-Tabor-Carnevale method and Clarkson-Kruskal direct reduction method are also found.KdV-MKdV equation is considered as an illustrative example,and its on kind of Backlund transformation,three kinds of similarity reductions and several kinds of travelling wave solutions are obtained by using extended HB method.展开更多
By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified wa...By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).展开更多
In 1979,Jurek gave a characterization of the moment of a full operator-stable μ by eigenvalues of exponent matrix of μ. Here, a characterization of the moment of Lévy measure (restricted on a neighbor of 0) of ...In 1979,Jurek gave a characterization of the moment of a full operator-stable μ by eigenvalues of exponent matrix of μ. Here, a characterization of the moment of Lévy measure (restricted on a neighbor of 0) of a full operator-stable μ by eigenvalues of exponent matrix of μ is given.展开更多
Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction...Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction flA can be topologically conjugate the n-adic system.展开更多
In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Mu...In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.展开更多
One of the central questions in CAGD is blending of pipe surfaces. Wu Wen-tsun[1]studied the problem by using the characteristic set method and derived a sufficient andnecessary condition for the existence of a GC1 bl...One of the central questions in CAGD is blending of pipe surfaces. Wu Wen-tsun[1]studied the problem by using the characteristic set method and derived a sufficient andnecessary condition for the existence of a GC1 blending cubic surface of two cylinders whose展开更多
Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) ...Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) < R}. Recall that a slowly oscillating function on X is a function f G C*(X) satisfying the following condition:展开更多
For α ∈ (0, ∞), let Hα∞ (or Hα,0∞) denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|2)α = O(1) (or |f(z)|(1 - |z|2)α = o(1) as |z| → 1). Hα∞(or Hα,0∞...For α ∈ (0, ∞), let Hα∞ (or Hα,0∞) denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|2)α = O(1) (or |f(z)|(1 - |z|2)α = o(1) as |z| → 1). Hα∞(or Hα,0∞) is called a Bers-type space (or a little Bers-type space).In this paper, we give some basic properties of Hα∞. C, the composition operator associated with a symbol function which is an analytic self map of D, is difined by Cf = f o . We characterize the boundedness and compactness of C which sends one Bers-type space to another function space.展开更多
基金Supported by the Natural Science Foundation of Shaanxi Province(2002A11)Supported by the Shangluo Teacher's College Research Foundation(SKY2106)
文摘By studying the properties of Chebyshev polynomials, some specific and mean-ingful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbersand Lucas numbers are obtained.
基金The project supported by the Scientific Research Award Foundation for Outstanding Young and Middle-Aged Scientists of Shandong Province of China
文摘A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.
文摘The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.
基金Chinese Key Research Plan 'Mathematical Mechanization and a Platform for Automated Reasoning'，上海市科委资助项目，中国博士后科学基金
文摘Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutions with five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.
文摘An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.
文摘We verify that the total angular momentum 3-vector defined by the author [X. Zhang, Commun. Math.Phys. 206 (1999) 137] is equal to (0, 0, ma) forany time slice in both the Kerr and the Kerr-Newman spacetimes.
文摘In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest.
文摘Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.
文摘The bilinear form for a nonisospectral and variable-coefficient KdV equation is obtained and some exact soliton solutions are derived through Hirota method and Wronskian technique. We also derive the bilmear transformation from its Lax pairs and End solutions with the help of the obtained bilinear transformation.
文摘Two new applications of homogeneous balance(HB) method are presented.It is shown that HB method can be extended to search for the Baecklund transformations and similarity reductions of nonlinear partial differential equations.The close relations among the HB method,Weiss-Tabor-Carnevale method and Clarkson-Kruskal direct reduction method are also found.KdV-MKdV equation is considered as an illustrative example,and its on kind of Backlund transformation,three kinds of similarity reductions and several kinds of travelling wave solutions are obtained by using extended HB method.
文摘By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
文摘In 1979,Jurek gave a characterization of the moment of a full operator-stable μ by eigenvalues of exponent matrix of μ. Here, a characterization of the moment of Lévy measure (restricted on a neighbor of 0) of a full operator-stable μ by eigenvalues of exponent matrix of μ is given.
文摘Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction flA can be topologically conjugate the n-adic system.
基金The NNSF (10171010) of China Major Project of Education Ministry (01061) of China, Key Library for Vegetation Ecology, Education Ministry of China.
文摘In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.
基金The State Major Key Project for Basic Rearches of China.
文摘One of the central questions in CAGD is blending of pipe surfaces. Wu Wen-tsun[1]studied the problem by using the characteristic set method and derived a sufficient andnecessary condition for the existence of a GC1 blending cubic surface of two cylinders whose
文摘Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) < R}. Recall that a slowly oscillating function on X is a function f G C*(X) satisfying the following condition:
文摘For α ∈ (0, ∞), let Hα∞ (or Hα,0∞) denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|2)α = O(1) (or |f(z)|(1 - |z|2)α = o(1) as |z| → 1). Hα∞(or Hα,0∞) is called a Bers-type space (or a little Bers-type space).In this paper, we give some basic properties of Hα∞. C, the composition operator associated with a symbol function which is an analytic self map of D, is difined by Cf = f o . We characterize the boundedness and compactness of C which sends one Bers-type space to another function space.
