数学季刊

曹洁

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 Rⁿ 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.

一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

贾滢, 刘俊利

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 R₀ characterizes the disease transmission dynamics: if R₀≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R₀> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.

弱辫子T-范畴

史美华 , 贾玲

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.

一类四阶差分系统的多重周期解

张申贵

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.

q-Baskakov-Schurer-Szász-Beta算子的逼近

吴华亭, 胡晓敏, 刘蕊蕊

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,pin terms of modulus of continuity.

具有状态反馈控制的合作系统的周期解

黄明湛, 刘守宗, 宋新宇

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.

有界星形圆形域上星形映射的参数表示

闫春燕, 张芳芳

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.

空间形式中的完备子流形

张运涛

2016, 31(3): 298-306. doi:10.13371/j.cnki.chin.q.j.m.2016.03.008

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Let Mⁿ be an n（n≥4）-dimensional compact oriented submanifold in the nonnegative space forms N^n+p（c） with S ≤ S（c,H）.Then Mⁿ is either homeomorphic to a standard n-dimensional sphere Sⁿ 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 ≤（n²H²）/（n-1）+2c.

Timoshenko系统在Gurtin-Pipkin热能定律下解的整体存在性、渐进性及一致吸引子

郑秀珍

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.

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