数学季刊

徐昌进, 陈大学

2013, 28(4): 475-484.

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A delayed predator-prey Gompertz model is investigated. The stability is analyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.

非线性Kirchhoff型波动方程解的能量衰减

宋志华

2013, 28(4): 485-491.

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The paper studies the asymptotic behavior of solution to the initial boundary value problem for a nonlinear hyperbolic equation of Kirchhoff type u_tt-M(∥A ^1/2u∥²)Au + u_t-|u|^au = 0: It proves the global existence of solution by constructing a stable set and the energy exponential decay estimate by applying a lemma of V Komornik.

一类多时滞三阶p-Laplacian方程周期解的存在性问题

周玲, 周宗福, 沈钦锐

2013, 28(4): 492-502.

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By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows (φp((x(t).. cx(t.. σ)) ′′)) ′ +f₁(x(t))x ′(t) + f₂(x ′(t))x ′′(t) +g(t, x(t), x(t.. τ(t)), ∫ ⁰_-rx(t + s) dm(s))=e(t). Some new results for existence of T-periodic solutions to such equations are obtained.

离散框架和相应于的连续框架之间的关系

刘春苔

2013, 28(4): 503-509.

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The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.

行负相依随机变量阵列的矩完全收敛性

吴永锋, 申广君

2013, 28(4): 510-521.

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In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.

一类三阶非线性微分方程耦合系统边值问题的正解

张豫川, 周宗福, 徐鑫

2013, 28(4): 522-531.

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By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.

关于伪小内射模

赵玉娥, 杜先能

2013, 28(4): 532-538.

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The denition of principally pseudo injectivity motivates us to generalize the notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are developed, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.

锥度量空间中一类压缩映射的一些不动点

黄华平, 许绍元, 韩艳

2013, 28(4): 539-545.

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In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric spaces and some previous results in cone metric spaces.

φ-混合矩阵阵列的完全收敛性

李静

2013, 28(4): 546-554.

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In the paper, the complete convergence for arrays of rowwise φ-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of rowwise φ-mixing random variables without assumptions of identical distribution and stochastic domination are presented.

模糊粗糙环及其性质

任必军, 付艳玲

2013, 28(4): 555-564.

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This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binary operation of ring was discussed.

锥度量空间的完备性

李克典

2013, 28(4): 565-572.

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Some topological properties of cone metric spaces are discussed and proved that every cone metric space (X; d) is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ∈ E; 0 《 c contains a set of diameter less that c has non-empty intersection.

一些二项式系数的交错二重和

郑德印, 唐培培

2013, 28(4): 573-577.

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We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.

φ-混合序列加权和的强大数律

刘婷婷, 陈志勇, 王学军, 王星惠

2013, 28(4): 578-584.

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Supported by the National Natural Science Foundation of China(11171001,11201001)； Supported by the Natural Science Foundation of Anhui Province(1208085QA03,1308085QA03)

一类时滞p-Laplacian中立型泛函微分方程周期解问题

陈文斌, 高芳, 鲁世平

2013, 28(4): 585-591.

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In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument (φ_p(x(t)-cx(t-σ)) ′) ′ + f(t, x ′(t)) + g(t, x(t-τ(t))) = e(t), some new results on the existence of periodic solutions is obtained.

一类二阶脉冲中立型微分方程的振动性质

黄先勇, 徐志庭

2013, 28(4): 592-604.

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Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et al[Li et al, Oscillation of second order self-conjugate differential equation with impulses. J Comput Appl Math 197(2006): 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.

关于凸体的Blaschke-Santalo不等式的逆形式

王卫东, 周艳平

2013, 28(4): 605-611.

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Reisner proved a reverse of the Blaschke-Santalo inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santalo inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty’s conjecture for projection bodies, respectively.

一类特殊的无限维李代数的单性与同构

余德民, 李爱华

2013, 28(4): 612-617.

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In this paper, a special innite dimensional Lie algebra is studied. The innite dimensional Lie algebra appears in the elds of conformal theory, mathematical physics, statistic mechanics and Hamilton operator. The innite dimensional Lie algebras is popularized Virasoro-like Lie algebra. Isomorphisms, homomorphisms, ideals of the innite dimensional Lie algebra are studied.

具有CTL免疫反应的HTLV-I感染模型的全局稳定性

宋强

2013, 28(4): 618-624.

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In this paper, a mathematical model for HTLV-I infection of CD4+ T cells that incorporates the CD8+ cytotoxic T-cell(CTL) response is studied. We establish two threshold parameters R0 and R1, the basic reproduction numbers for viral persistence and for CTL response, respectively. We also show that the parameter R1 can be used to distinguish asymptomatic carriers from HAM/TSP patients and as an important control parameter for preventing the development of HAM/TSP.

FI代数的模糊MP滤子格

刘春辉, 徐罗山

2013, 28(4): 625-632.

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In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-lters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.

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