期刊：
JOURNAL OF COMBINATORIAL THEORY SERIES B,2001年82(1):67-80 ISSN：0095-8956
通讯作者：
Hu, ZQ
作者机构：
[Hu, ZQ] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China.
通讯机构：
[Hu, ZQ] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
Cycle;linear forest;length;matching
摘要：
For a graph G and an integer k greater than or equal to1, let S(G)={x is an element ofV(G): d(G)(x)=0} and sigma (k)(G)=min{Sigma (k)(i=1) d(G)(v(i)) : {v(1),v(2),..., v(k)} is an independent set of G}. The main result of this paper is as follows. Let k greater than or equal to 3, m greater than or equal to 0, and 0 less than or equal to s less than or equal to k - 3. Let G be a (m + k - 1)-connected graph and let F be a subgraph of G with \E(F)\ = m and \S(F)\=s. If every component of F is a path, then G has a cycle of length greater than or equal to min {\V(G)\, 2/k sigma (k)(G)-m} passing through E(F) boolean OR V(F). This generalizes three related results known previously. (C) 2001 Academic Press.
摘要：
This paper studies the optimal design problem of a nonparametric regression model. A frame of the decision theory for nonparametric experimental designs is set up. Under this frame, the admissible minimaxity of the uniform design measure pi, which has a constant density over the experimental domain, is obtained. Furthermore, we prove that pi is the best design among a reasonable subclass of designs. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 62K05; 62K99.
关键词：
Predator-prey system;Global analysis;Bogdanov-takens bifurcation;Homoclinic orbit;Hopf bifurcation;Limit cycle;Paradox of enrichment;Bifurcation;Enrichment;Stability;Paradox
摘要：
A predator-prey system with nonmonotonic functional response is considered. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The bifurcation analysis of the model depending on all parameters indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and subcritical Hopf bifurcations, and the homoclinic bifurcation. It is shown that there are different parameter values for which the model has a limit cycle or a homoclinic loop, or exhibits the so-called paradox of enrichment phenomenon. Moreover, a limit cycle cannot coexist with a homoclinic loop for all parameters. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation) but for some specific parameter values it has a multiple focus of multiplicity at least 2.
期刊：
Journal of Differential Equations,2000年164(1):1-15 ISSN：0022-0396
通讯作者：
Xiao, DM
作者机构：
[Xiao, DM; Li, WX] Department of Mathematics, Central China Normal University, Wuhan, 430079, People's Republic of China
通讯机构：
[Xiao, DM ] ;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
In the first part of this paper, it is proved that the number of limit cycles of the competitive three-dimensional Lotka–Volterra system in R3+ is finite if this system has not any heteroclinic polycycles in R3+. In the second part of this paper, a 3D competitive Lotka–Volterra system with two small parameters is discussed. This system always has a heteroclinic polycycle with three saddles. It is proved that there exists one parameter range in which the system is persistence and has at least two limit cycles, and there exists other parameter ranges in which the system is not persistence and has at least one limit cycle.
期刊：
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS AND COMPUTATIONAL SIMULATIONS,2000年:176-180
通讯作者：
Liang, ZJ
作者机构：
[Yang, CH; Liang, ZJ] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Liang, ZJ] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
In this paper,we consider the Kolmogorov system which are the interaction of three species with the different intrinsic growth rates. We obtain the sufficient conditions to the existence of the non-constant periodic orbits of a Kolmogorov system in R-3.
摘要：
The optimality of controlled parabolic differential equations involving monotone graphs was discussed. The penalty function method for the pay-off function was developed by employing the state constraints. Some restrictions on the initial data for the state equations were placed due to the involvement of monotone graphs.
摘要：
In this paper, we investigate the quadratic Hamiltonian systems with non-Morsean point. It is proved that in this situation thr cyclicity or the period annulus tinder quadratic perturbations is equal to two. (C) 2000 Academic Press.
摘要：
This work deals with the necessary conditions of optimality for some optimal control problems governed by elliptic variational inequalities. Boundary control and state constrained problems are considered. The techniques used are based on those in Ref. 1 and a new penalty functional is defined in this paper.
期刊：
Journal of Differential Equations,2000年167(2):467-494 ISSN：0022-0396
通讯作者：
Zhao, HJ
作者机构：
[Zhao, HJ] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Zhao, HJ] Scuola Int Super Studi Avanzati,
通讯机构：
[Zhao, HJ] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
This paper, as a follow-up to the recent work of K. Nishihara (1997, J. Differential Equations 133, 384-395), is concerned with the asymptotic behaviors of the solution of quasilinear hyperbolic equation with linear damping V-u = a(V-chi)(chi) + V-1 = 0, a(1)(nu) > 0 for all nu is an element of R, which satisfies the following prescribed initial condition: (V(t, chi), V-1(t, chi))\ (1 = 0) = (V-0(chi), V-1(chi)), chi is an element of R. Compared with the results obtained by K. Nishihara, the main novelties of our present paper lie in the following: First, we recover all the results obtained by K. Nishihara under some other smallness assumptions on the initial data (V-0(chi), V-1(chi)) which are much weaker than those needed in K. Nishihara's arguments. Second, under some additional assumptions on the nonlinear function a(nu) and on the initial data (V-0(chi), V-1(chi)), when delta (0) = 0, delta (1) not equivalent to 0, we succeed in proving that phi (t, chi) is still sn asymptotic profile of V(t, chi) and this answers partially the open problem left by K. Nishihara. (C) 2000 Academic Press.
摘要：
This work is concerned with the Cauchy problem for a given class of nonlinear dispersive equations. Results for this problem are derived by employing the theory of Fourier analysis.
摘要：
This paper considers the existence of solutions for the following problem: -Delta u + u + v(x)u = (\u\(2) (*) 1/\x\)u + g(x), x is an element of R-3 where v(x) be a continuous function on R-3,v(x) < 0, v(x) --> 0, (as \x\ -->1 infinity); g(x) greater than or equal to 0,g(x) not equivalent to 0 and g(x) is an element of H-1(R-3). The author proves that there exists a constant C, such that \\g(x)\\(H-1) less than or equal to C, then there are at least two solutions for the above problem.
摘要：
This work deals with necessary conditions of optimality for optimal control problems governed by semilinear differential equations in Hilbert spaces.
摘要：
Abstract. Let \documentclass[12pt]{minimal}
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\begin{document}\end{document} is a decomposition of F such that\documentclass[12pt]{minimal}
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\begin{document}\end{document}Depending on F this might be a partition of F or almost a partition of F in the sense that \documentclass[12pt]{minimal}
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\begin{document}\end{document}. We prove that each Ft is dense in F, and \documentclass[12pt]{minimal}
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\begin{document}\end{document}. For \documentclass[12pt]{minimal}
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\begin{document}\end{document}-a.e. \documentclass[12pt]{minimal}
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\begin{document}\end{document} and Ft is an s-set when \documentclass[12pt]{minimal}
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\begin{document}\end{document}. Moreover, associated with this decomposition \documentclass[12pt]{minimal}
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\begin{document}\end{document} of F is a measurable function Y such that each Ft is a level set of Y. The fractal dimensions of the graph of Y are also determined.
作者机构：
[Zhang, XA] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;Acad Sinica, Inst Math, Beijing 100080, Peoples R China.;Bar Ilan Univ, Fac Life Sci, IL-52900 Ramat Gan, Israel.
通讯机构：
[Zhang, XA] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
Permanence;Extinction;Threshold of the harvesting;Maximum sustainable yield
摘要：
In this paper, we establish a mathematical model of two species with stage structure and the relation of predator-prey, to obtain the necessary and sufficient condition for the permanence of two species and the extinction of one species or two species. We also obtain the optimal harvesting policy and the threshold of the harvesting for sustainable development.
期刊：
Communications in Partial Differential Equations,2000年25(3-4):377-422 ISSN：0360-5302
通讯作者：
Zhao, HJ
作者机构：
[Zhao, HJ] Department of Mathematics, Central China Normal University, Wuhan 430079, China, Sc. Internazionale Superiore S., Via Beirut 2-4, 34014 Trieste, Italy
通讯机构：
[Zhao, HJ ] ;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
This paper considers the global existence and optimal temporal decay estimates of solutions to a class of multidimensional nonlinear evolution equations whose dispersive and dissipative terms have the same order p(p > 1). Such a class includes the multidimensional generalized Benjamin-Ono-Burgers equation and the multidimensional generalized Schrödinger-Burgers equations as special examples.
期刊：
Journal of Differential Equations,2000年163(1):198-222 ISSN：0022-0396
通讯作者：
Zhao, HJ
作者机构：
[Zhao, HJ] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Zhao, HJ] SISSA, ISAS,
通讯机构：
[Zhao, HJ] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
In this paper, we show that a strong planar rarefaction wave is nonlinear stable, namely it is an attractor for the relaxation approximation of the scalar conservation laws in several space dimensions. Compared with former results obtained by T. P. Liu (1987, Comm. Math. Phys.108, 153–175) and T. Luo (1997, J. Differential Equations133, 255–279), our main novelty lies in the fact that the planar rarefaction waves do not need to be small, and in the one-dimensional case, the initial disturbance can also be chosen arbitrarily large.
摘要：
Using the theory of singular perturbation of the ordinary differential equations, the special entropy-entropy flux pairs of Lax type, all terms of progression being the functions of a single variable, are constructed. By analyzing the progressing entropy waves, a convergence theorem for the method of artificial viscosity applied to the Cauchy problem is established.
期刊：
Journal of Differential Equations,2000年161(2):321-336 ISSN：0022-0396
通讯作者：
Yang, T
作者机构：
[Yang, T] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.;Cent China Normal Univ, Dept Math, Wuhan 430070, Peoples R China.
通讯机构：
[Yang, T] C;City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.
摘要：
In this paper, we consider the Cauchy problem for p-system with relaxation. Under the assumption that the relaxation time epsilon is sufficiently small, we prove the existence of the global smooth solution to the Cauchy problem with C-1-initial data provided the C-0-norm of the derivative of the initial data is of the order of xi/epsilon. Here xi is a small positive constant. On the other hand, when the initial density has compact support but is not identically zero, we prove the global regular solution for the Cauchy problem does not exist. (C) 2000 Academic Press.
期刊：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY,2000年68(2):145-154 ISSN：1446-7887
通讯作者：
Chen, Q
作者机构：
[Chen, Q] Mathematics Department Central China Normal University Wushan 430079 China<&wdkj&>School of Mathematical Science Wuhan University Wuhan 430072 China e-mail: qchen@mail.ccnu.edu.cn
通讯机构：
[Chen, Q ] ;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
Let M, N be Riemannian manifolds, f : M --> N a harmonic map with potential H, namely, a smooth critical point of the functional E-H(f) = integral(M)[e(f) - H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.
