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中文
Table of Content
30 September 2016, Volume 31 Issue 3
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Global Existence, Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics
CAO Jie
2016, 31(3): 221-236. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.001
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In this paper,a third order（in time） partial differential equation in R
n
is considered.By using semigroup method and constructing Lyapunov function,we establish the global existence,asymptotic behavior and uniform attractors in nonhomogeneous case.In addition,we also obtain the results of well-posedness in semilinear case.
Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates
JIA Ying, LIU Jun-li
2016, 31(3): 237-247. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.002
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In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R
0
characterizes the disease transmission dynamics: if R
0
≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R
0
> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.
On Weak Braided T-category
S H I M e i - h u a , J I A L in g
2016, 31(3): 248-259. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.003
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Recently Turaev generalized the notion of a tensor category to that of a crossed group category.In[5]the authors constructed the representation category Rep（H） of a T-coalgebra H.In[2]the authors introduced the notions of a weak tensor category to characterize a weak bialgebra and a weak Hopf algebra.This paper is based on these ideas to naturally introduce the notions of a weak T-category and a weak braided T-category which are not under the usual way and prove that the categories of representations of a weak T-coalgebra and a weak braided T-coalgebra are a weak T-category and a weak braided T-category respectively.Furthermore we also discuss some properties of weak T-category.
Multiple Periodic Solutions for a Class of Fourth-order Difference Systems
ZHANG Shen-gui
2016, 31(3): 260-268. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.004
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By using critical point theory,we study periodic solutions for a class of fourthorder difference systems with partially periodic potential and linear nonlinearity.Some sufficient conditions for the existence of multiplicity of periodic solutions are obtained via generalized saddle point theorem.
Approximation by the
q-Baskakov-Schurer-Szász-Beta
Operators
WU Hua-ting, HU Xiao-min, LIU Rui-rui
2016, 31(3): 269-278. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.005
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In this paper we introduce a new kind of Baskakov-Schurer-Szász-Beta operators Mn,pq based on q-integers.We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0,∞].Then we obtain the estimates on the rate of convergence and weighted approximation of operators M
q
n,p
in terms of modulus of continuity.
Periodic Solutions of a Cooperative System with State Feedback Control
HUANG Ming-zhan, LIU Shou-zong, SONG Xin-yu
2016, 31(3): 279-287. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.006
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In this paper,we propose a semi-continuous dynamical system to study the cooperative system with feedback control.Based on geometrical analysis and the analogue of Poincaré criterion,the existence and stability of the positive order one periodic solutions are given.Numerical results are carried out to illustrate the feasibility of our main results.
The Parametric Representation for Starlike Mappings on Bounded Starlike Circular Domains
YAN Chun-yan , ZHANG Fang-fang
2016, 31(3): 288-297. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.007
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In this paper,the parametric representation of starlike mappings is given.As a direct application,the growth theorem is set up.Moreover,a character of starlike mappings is obtained.
On Complete Submanifolds in Space Forms
ZHANG Yun-tao
2016, 31(3): 298-306. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.008
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Let M
n
be an n（n≥4）-dimensional compact oriented submanifold in the nonnegative space forms N
n+p
（c） with S ≤ S（c,H）.Then M
n
is either homeomorphic to a standard n-dimensional sphere S
n
or isometric to a Clifford torus.We also prove that a2 xt-2compact oriented submanifold in any N
n+p
（c） is diffeomorphic to a sphere if S ≤（n
2
H
2
）/（n-1）+2c.
Global Existence, Asymptotic Behavior and Uniform Attractors of Timoshenko Systems with Gurtin-Pipkin Thermal Law
ZHENG Xiu-zhen
2016, 31(3): 307-330. doi:
10.13371/j.cnki.chin.q.j.m.2016.03.009
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In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.
