Abstract This paper investigates the set partitioning containing kernels. This problem can also be considered as the identical machine scheduling problem with nonsimultaneous machine release times. That the algorithm ...Abstract This paper investigates the set partitioning containing kernels. This problem can also be considered as the identical machine scheduling problem with nonsimultaneous machine release times. That the algorithm MULTIFIT has a worst case bound of 6/5 is proved. Through combining MULTIFIT and LPT, an algorithm MULTILPT with a worst case bound of 7/6 has been obtained.展开更多
Abstract It is proved that the quadratic system with a weak focus and a strong focus has a unique limit cycle around one of the two foci, if there exists simultaneously limit cycles around each of the two foci for the...Abstract It is proved that the quadratic system with a weak focus and a strong focus has a unique limit cycle around one of the two foci, if there exists simultaneously limit cycles around each of the two foci for the system.展开更多
Abstract In this paper,the almost periodic nonautonomous diffusive food chain system of three species is discussed.By using the comparison theorem and V function method,the author proves the existence and uniquene...Abstract In this paper,the almost periodic nonautonomous diffusive food chain system of three species is discussed.By using the comparison theorem and V function method,the author proves the existence and uniqueness of a positive almost periodic solution,and its stability under disturbances from the hull.展开更多
In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke compari...In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).展开更多
The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivi...The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivial bell-profile traveling solitary waves, nor periodic waves. In the present paper, we show two approaches for the study of traveling solitary waves of the Burgers-Korteweg-de Vries equation: one is a direct method which involves a few coordinate transformations, and the other is the Lie group method. Our study indicates that the Burgers-Korteweg-de Vries equation indirectly admits one-parameter Lie groups of transformations with certain parametric conditions and a traveling solitary wave solution with an arbitrary velocity is obtained accordingly. Some incorrect statements in the recent literature are clarified.展开更多
By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vec...By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vector. We show that if the Melnikov-type vector satisfies some conditions then autonomous differential equations have homoclinic solutions. Moreover, our result holds only for autonomous differential equations.展开更多
We discuss a clacks of predator-prey systems under a sparse effect, which possess a dense dependence of the predator species. We prove that this system hasjust one singular point in the first quadrant and it must be a...We discuss a clacks of predator-prey systems under a sparse effect, which possess a dense dependence of the predator species. We prove that this system hasjust one singular point in the first quadrant and it must be a focus (or node).When it is stable, there can .at least exist two limit cycles surrounding it. Alsoa non-existential condition of limit cycles is given. When it is unstable, theremust exist a unique limit cycle surf.ounding it. Thus, the qualitative analysis ofthe system obtained is complete.展开更多
In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the ...In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.展开更多
This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is p...This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is provided. One examplefrom practicc electrical network problem is used to test all these theory.展开更多
Consider the general sublinear ordinary differential equations of second order of theform X(t) + a(t)f(X(t)) =0, where a(t)∈C[t0,∞),f(x)∈C(R)and xf(x)>0,f'(x) ≥ 0 for x ≠ 0.Furthermore,f(x) also satisfies ...Consider the general sublinear ordinary differential equations of second order of theform X(t) + a(t)f(X(t)) =0, where a(t)∈C[t0,∞),f(x)∈C(R)and xf(x)>0,f'(x) ≥ 0 for x ≠ 0.Furthermore,f(x) also satisfies sublinear condition, which coversthe prototype nonlinear function f(x)=|x|γ sgnx with 0<γ<1 known as the EmdenFowler case. The coefficient α(t) is not assumed to be eventually nonnegative. A new oscillation criterion involving integral averages of α(t) due to Kamenev (Math. Zametki 23(1978), 249 - 251 ) for linear equation and Wong (Conference Proceedings, Canad. Math.Soc. 8(1987), 299-302) for Emder-Fowler equation with 0<γ<1 is shown to remainvalid for general sublinear equation.展开更多
In this paper, the existence and uniqueness of periodic solutions of linearfunctional differential equat,ions, including neutral equations, with constant coef-ficients are investigated, necessary and sufficient condit...In this paper, the existence and uniqueness of periodic solutions of linearfunctional differential equat,ions, including neutral equations, with constant coef-ficients are investigated, necessary and sufficient conditions for the existence anduniqueness of periodic solutions of linear neutral functional differential equationsand some of their special oases are given via systems of linear algebraic equations. Especially, the problems of existonce and Uniqueness of periodic solutions ofgeneral linear functional differential equations of non-neutral type are completelysolved.展开更多
In this artical the existence, stability and asymptoticity of periodic solutionfor Abel equation :as well as ones for its special cases are discussed, where a(t), b(t), c(t) and d(t)are real periodic functions.
文摘Abstract This paper investigates the set partitioning containing kernels. This problem can also be considered as the identical machine scheduling problem with nonsimultaneous machine release times. That the algorithm MULTIFIT has a worst case bound of 6/5 is proved. Through combining MULTIFIT and LPT, an algorithm MULTILPT with a worst case bound of 7/6 has been obtained.
文摘Abstract It is proved that the quadratic system with a weak focus and a strong focus has a unique limit cycle around one of the two foci, if there exists simultaneously limit cycles around each of the two foci for the system.
文摘Abstract In this paper,the almost periodic nonautonomous diffusive food chain system of three species is discussed.By using the comparison theorem and V function method,the author proves the existence and uniqueness of a positive almost periodic solution,and its stability under disturbances from the hull.
基金Supported by the Research Foundation of Education Department of Zhejiang Province( 2 0 0 380 4 9)
文摘In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).
基金This work was supported by US National Science Foundation(Grant No.CCF-0514768)partly supported by UTPA Faculty Research Council(Grant No.119100)
文摘The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivial bell-profile traveling solitary waves, nor periodic waves. In the present paper, we show two approaches for the study of traveling solitary waves of the Burgers-Korteweg-de Vries equation: one is a direct method which involves a few coordinate transformations, and the other is the Lie group method. Our study indicates that the Burgers-Korteweg-de Vries equation indirectly admits one-parameter Lie groups of transformations with certain parametric conditions and a traveling solitary wave solution with an arbitrary velocity is obtained accordingly. Some incorrect statements in the recent literature are clarified.
文摘By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vector. We show that if the Melnikov-type vector satisfies some conditions then autonomous differential equations have homoclinic solutions. Moreover, our result holds only for autonomous differential equations.
文摘We discuss a clacks of predator-prey systems under a sparse effect, which possess a dense dependence of the predator species. We prove that this system hasjust one singular point in the first quadrant and it must be a focus (or node).When it is stable, there can .at least exist two limit cycles surrounding it. Alsoa non-existential condition of limit cycles is given. When it is unstable, theremust exist a unique limit cycle surf.ounding it. Thus, the qualitative analysis ofthe system obtained is complete.
基金supported by National Security Agency,United States Army Research Offfice and a Hong Kong RGC Competitive Earmarked Research (Grant No. 600607)
文摘In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.
文摘This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is provided. One examplefrom practicc electrical network problem is used to test all these theory.
文摘Consider the general sublinear ordinary differential equations of second order of theform X(t) + a(t)f(X(t)) =0, where a(t)∈C[t0,∞),f(x)∈C(R)and xf(x)>0,f'(x) ≥ 0 for x ≠ 0.Furthermore,f(x) also satisfies sublinear condition, which coversthe prototype nonlinear function f(x)=|x|γ sgnx with 0<γ<1 known as the EmdenFowler case. The coefficient α(t) is not assumed to be eventually nonnegative. A new oscillation criterion involving integral averages of α(t) due to Kamenev (Math. Zametki 23(1978), 249 - 251 ) for linear equation and Wong (Conference Proceedings, Canad. Math.Soc. 8(1987), 299-302) for Emder-Fowler equation with 0<γ<1 is shown to remainvalid for general sublinear equation.
文摘In this paper, the existence and uniqueness of periodic solutions of linearfunctional differential equat,ions, including neutral equations, with constant coef-ficients are investigated, necessary and sufficient conditions for the existence anduniqueness of periodic solutions of linear neutral functional differential equationsand some of their special oases are given via systems of linear algebraic equations. Especially, the problems of existonce and Uniqueness of periodic solutions ofgeneral linear functional differential equations of non-neutral type are completelysolved.
文摘In this artical the existence, stability and asymptoticity of periodic solutionfor Abel equation :as well as ones for its special cases are discussed, where a(t), b(t), c(t) and d(t)are real periodic functions.
