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.
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.
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.
摘要：
The optimal control problem governed by a state equation is addressed. Due to the involvement of the state constraint, a new kind of penalty functionals is constructed for the pay-off functional. Necessary conditions on the optimality for the problem are given and proven.
作者机构：
[Mao, JZ; Li, DY] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Jingzhong Mao] D;Department of Mathematics, Central China Normal University, Wuhan, Hubei, 430079, People's Republic of China
关键词：
Geodetic graph;Number of edges;Upper bound
摘要：
In this paper we investigate some structural characterizations of geodetic graphs and prove that if G is a central geodetic block on p vertices with diameter d greater than or equal to 3, and each vertex belongs to an induced cycle C2d+1, then the number q of edges equals p or q less than or equal to 1/6 p[p - 1/2(5d + 1) + 8]. Therefore the upper bounds of [3] have been considerably improved. (C) 1999 Elsevier Science B.V. All rights reserved.
摘要：
This paper has completely studied the dynamical properties of a class of epidemiological models, obtained the necessary and sufficient condition for a unique periodic solution which is asymptotically orbitally stable, and the necessary and sufficient conditions for the global asymptotic stability of the positive equilibrium.
期刊：
Numerical Functional Analysis and Optimization,1999年20(1):163-174 ISSN：0163-0563
通讯作者：
Wang, Gengsheng
作者机构：
Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;Wuhan Univ, Dept Phys, Wuhan 430072, Peoples R China.;[Chen, SR] Department of Physics, Wuhan University, 430072, Wuhan, China;[Wang, GS] Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China
通讯机构：
Huazhong Normal Univ, China
关键词：
maximum principle;optimal control problems;finite codimension;state constraint
摘要：
The maximum principle for optimal control problems of linear parabolic system with two point state constraint is discussed. Applications to some boundary periodic and distributed control problems are presented.
作者机构：
[Wang, GS; Deng, YB] Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, GS] H;Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
minimal positive solution;optimal control
摘要：
Some optimal control problems for the semilinear elliptic equation with critical exponent are presented. The semilinear elliptic equation in R<sup>N</sup> considered is as follows: -Δy+y = y<sup>2*</sup>+λf(x), xΕR<sup>N</sup>, N≥3 yΕH<sup>1</sup>(R<sup>N</sup>), y>0 in R<sup>N</sup>. The break of the uniqueness and the existence of the solutions makes the corresponding optimal control problems much more complicated since every control may correspond to more than one states or no state. This gap is filled by introducing the minimal positive solutions y<inf>λ</inf> as the states while the parameters λas the controls.
作者机构：
[Li, WX] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Li, WX] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
A/W-fractal;Open set conditions;S-set
摘要：
Corresponding to the irreducible 0–1 matrix (a
ij
)
n×n
, take similitude contraction mappingsϕ
ij
for eacha
ij
=1, ina
ij
=1, in R
d
with ratio 0<r
ij
<1. There are unique nonempty compact setsF
1,…,F
n
satisfying for each1≤i≤n, F
i. We prove that open set condition holds if and only ifF
i
is ans-set for some1≤i≤n, wheres is such that the spectral radius of matrix (r
3
)
n x n
is 1.
作者机构：
[Zhao, HJ; Xuan, BJ] CENT CHINA NORMAL UNIV,DEPT MATH,WUHAN 71007,PEOPLES R CHINA.;[Zhao, HJ] CHINESE ACAD SCI,WUHAN INST MATH SCI,YOUNG SCIENTIST LAB MATH PHYS,POB 71007,WUHAN 71007,PEOPLES R CHINA.
通讯机构：
[Zhao, HJ] C;CHINESE ACAD SCI,WUHAN INST MATH SCI,YOUNG SCIENTIST LAB MATH PHYS,POB 71007,WUHAN 71007,PEOPLES R CHINA.
摘要：
This work considers the existence of the global smooth solutions of several generalized BBM-Burgers equations. First, for n ≥1, the convergence results are discussed by employing a compact imbedding theorem. Following this, when n = 1, by exploiting the modified compact framework of Yunguang Lu, a convergence result is also obtained. Finally, it is pointed out that to get the strong convergence results, the second results do not ask f to be convex. This is due to the adoption of the modified compactness results of Yunguang Lu.
摘要：
In this paper we prove that there exist 4-{v, k, k, k, k; lambda} supplementary difference sets with v = q(2), q = 3(mod 8) a prime power, k = q(q - 1)/2, lambda = 4k - v, and Hadamard matrices of order 4v.
期刊：
International Journal of Control,1987年45(1):211-214 ISSN：0020-7179
通讯作者：
XIN, LX
作者机构：
[XIN, LX] Department of Mathematics , Huazhong Normal University , Wuhan, People's Republic of China.
通讯机构：
[XIN, LX] H;HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN,PEOPLES R CHINA.
摘要：
In this paper some necessary and sufficient conditions for stability, complete instability and composite stability type of a class of interval matrices are given.
