数学季刊

白永强, 阎国栋

2015, 30(1): 1-11. doi:10.13371/j.cnki.chin.q.j.m.2015.01.001

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Differential geometry play a fundamental role in discussing partial differential equations（PDEs） in mathematical physics. Recently discrete differential geometry is an active mathematical terrain, which aims at the development and application of discrete equivalents of the geometric notions and methods of differential geometry. In this paper, a discrete theory of exterior differential calculus and the analogue of the Poincar′e lemma for differential-difference complex are proposed. They provide an intrinsic idea for developing the theory to discuss the integrability of difference equations.

量子Grothendieck环K_t-1上的量子簇代数结构

Yahia Badawi Bashir Meny, 马海涛, 杨彦敏

2015, 30(1): 12-19. doi:10.13371/j.cnki.chin.q.j.m.2015.01.002

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In this paper, we give a quantum cluster algebra structure on the deformed Grothendieck ring K_t-1which is defined in section 2.

亚纯函数分担不动点的正规定则

杨祺

2015, 30(1): 20-29. doi:10.13371/j.cnki.chin.q.j.m.2015.01.003

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In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive integers. For every f ∈ F, all of whose zeros have multiplicity at least （nk+2）/（n-1）. If f（f^（k））ⁿand g（g^（k））ⁿshare z in D for each pair of functions f and g, then F is normal.

含两个不同时变时滞连续系统的稳定性判据

程媛媛, 蒋威

2015, 30(1): 30-38. doi:10.13371/j.cnki.chin.q.j.m.2015.01.004

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This paper presents a new result of stability analysis for continuous systems with two different time-varying delay components, new delay-dependent asymptotic stability criterion of continuous systems is proposed by exploiting an improved Lyapunov-Krasovskii functional candidate and an improved approximation method without resorting to any model transformation and free weighting matrix technique. This new criteria has advantages over some previous ones in that it involves few matrix variables and has less computational effort and conservatism. This criterion is expressed by a set of linear matrix inequalities, which can be tested by using the LMI toolbox in Matlab. Finally, illustrative example demonstrates the effectiveness and the advantage of the proposed method.

带变量Calderón-Zygmund核的奇异积分算子在加权Morrey空间上的有界性

潘亚丽, 李昌文, 温宗良

2015, 30(1): 39-46. doi:10.13371/j.cnki.chin.q.j.m.2015.01.005

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In this paper, we will study the boundedness of the singular integral operator with variable Calderón-Zygmund kernel on the weighted Morrey spaces L^p,κ（ω） for q′≤ p < ∞and 0 < κ < 1. Furthermore, the boundedness for the commutator with BMO functions is also obtained.

单位球加权Bergman空间上的Berezin变换与径向算子

鲁美麟, 李德生, 关洪岩

2015, 30(1): 47-54. doi:10.13371/j.cnki.chin.q.j.m.2015.01.006

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In this paper, we analyze a class of bounded radial operators on the weighted Bergman space A²_α(B_n, d V_α), we get that these kinds of operators are diagonal with respect to the standard orthonomal basis. We also investigate the connection between compactness of operators and the boundary behaviour of the corresponding Berezin transform. We further study a special class of radial operators, i.e., Toeplitz operators with a radial L¹ symbol.

带p-Laplacian算子的三阶三点边值问题的三个正解

谭惠轩, 封汉颍, 冯杏芳, 杜亚涛

2015, 30(1): 55-65. doi:10.13371/j.cnki.chin.q.j.m.2015.01.007

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In this paper, we consider the three-point boundary value problem \phi_p（u′′（t）））′+a（t）f（t, u（t）, u′（t）, u′′（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βu′（0）, u′（1） = αu′（η）, u′′（0） = 0, where \phi_p（s） = |s|^p-2s with p > 1, 0 < α, η < 1and 0 ≤β < 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.

具有反馈控制离散Logistic系统的分支分析

伍代勇

2015, 30(1): 66-78. doi:10.13371/j.cnki.chin.q.j.m.2015.01.008

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The paper studies the dynamical behaviors of a discrete Logistic system with feedback control. The system undergoes Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors of the system, such as the period-doubling bifurcation in periods 2, 4, 8 and 16, and quasi-periodic orbits and chaotic sets.

正合范畴中的Gorenstein性和Tate上同调

王志成

2015, 30(1): 79-92. doi:10.13371/j.cnki.chin.q.j.m.2015.01.009

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Motivated by the classical Gorenstein homological theory and structure of Tate cohomology, we develop a theory of Gorenstein projective objects and Tate cohomology in an exact category A with enough projectives. We study some properties of Gorenstein projective objects and establish Tate cohomology of objects with finite Gorenstein projective dimension.

具有时滞的食饵捕食系统的Hopf分支及分支周期解的稳定性

陈红兵

2015, 30(1): 93-106. doi:10.13371/j.cnki.chin.q.j.m.2015.01.010

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In this paper, a predator-prey model of three species is investigated, the necessary and sufficient of the stable equilibrium point for this model is studied. Further, by introducing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.

一类具有阶段结构的捕食-被捕食模型的全局稳定性

王丽丽, 徐瑞

2015, 30(1): 107-120. doi:10.13371/j.cnki.chin.q.j.m.2015.01.011

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A Holling type III predator-prey model with stage structure for prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. By using the uniformly persistence theory, the system is proven to be permanent if the coexistence equilibrium exists. By using Lyapunov functionals and La Salle’s invariance principle, it is shown that the two boundary equilibria is globally asymptotically stable when the coexistence equilibrium is not feasible. By using compound matrix theory, the sufficient conditions are obtained for the global stability of the coexistence equilibrium. At last, numerical simulations are carried out to illustrate the main results.

Laplace变换法求解分数阶差分方程

李晓艳, 项江如, 吴亚运

2015, 30(1): 121-129. doi:10.13371/j.cnki.chin.q.j.m.2015.01.012

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In this paper, we discuss the Laplace transform of the Caputo fractional difference and the fractional discrete Mittag-Leffler functions. On these bases, linear and nonlinear fractional initial value problems are solved by the Laplace transform method.

基于Vague集的最优路径选择方法

郭瑞, 杜利敏, 王淳

2015, 30(1): 130-136. doi:10.13371/j.cnki.chin.q.j.m.2015.01.013

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Optimal route selection is an important function of vehicle traffic flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting route. In this paper, subjective weighting method which relies on driver preference is used to determine the weight and the paper proposes the multi-criteria weighted decision method based on vague sets for selecting the optimal route. Examples show that, the usage of vague sets to describe route index value can provide more decision-making information for route selection.

有关单形旁切球半径的几何不等式

杨世国, 王文

2015, 30(1): 137-143. doi:10.13371/j.cnki.chin.q.j.m.2015.01.014

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In this paper, we study the problems of geometric inequality for the radii of escribed hyperspheres of an n-dimensional simplex in Euclidean space En. Some new geometric inequalities for the radii of escribed hyperspheres of a simplex are established.

弱Hopf群余代数的Maschke型定理

贾玲, 陈笑缘

2015, 30(1): 144-152. doi:10.13371/j.cnki.chin.q.j.m.2015.01.015

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In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sufficient conditions under which an epimorphism of weak（H, A）Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.

一类具有反馈控制与多变时滞Nicholson’s Blowflies模型的持久性

陈晓英, 施春玲

2015, 30(1): 153-158. doi:10.13371/j.cnki.chin.q.j.m.2015.01.016

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This paper covers the dynamic behaviors for a class of Nicholson’s blowflies model with multiple time-varying delay and feedback control. By using the differential inequality theory, a set of sufficient conditions are obtained to ensure the permanence of the system.Our result shows that feedback control variables have no influence on the permanence of the system.

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