Table of Content

30 December 2013, Volume 28 Issue 4

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Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gompertz Model

XU Chang-jin, CHEN Da-xue

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.

Energy Decay of Solution to a Nonlinear Wave Equation of Kirchhoff Type

SONG Zhi-hua

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 utt-M(∥A 1/2 u∥2)Au + ut-|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 Komorn

Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

ZHOU Ling, ZHOU Zong-fu, SHEN Qin-rui

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.

The Relations between Discrete Frames and Continuous Frames with Respect to (N,u)

LIU Chun-tai

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.





Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables

WU Yong-feng, SHEN Guang-jun

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.





Positive Solutions of Boundary Value Problem for a Coupled System of Nonlinear Third-order Differential Equations

ZHANG Yu- chuan, ZHOU Zong-fu, XU Xin

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.





On Pseudo Small Injective Modules

ZHAO Yu- e, DU Xian-neng

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.





Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

HUANG Hua-ping, XU Shao-yuan , HAN Yan

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.





Complete Convergence for Arrays of Rowwise φ-mixing Random Variables

LI Jing

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.

Fuzzy Rough Ring and Its Properties

REN Bi-jun, FU Yan-ling

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.





The Completeness of Cone Metric Spaces

LI Ke- dian

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.





Some Alternating Double Binomial Sums

ZHENG De-yin, TANG Pei-pei

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.





Strong Laws of Large Numbers for Weighted Sums of φ-mixing Sequence

LIU Ting-ting, CHEN Zhi-yong, WANG Xue-jun, WANG Xing-hui

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)

Periodic Solutions for p-Laplacian Neutral Functional Differential Equation with a Deviating Argument

CHEN Wen- bin, GAO Fang, LU Shi-ping

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 (φp(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.

Oscillation of a Second-order Impulsive Neutral Differential Equation 

HUANG Xian-yong, XU Zhi-ting

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.



On Reverses of the Blaschke-Santalo Inequality for Convex Bodies

WANG Wei- dong, ZHOU Yan-ping

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.





Simplicities and Automorphisms of a Special Infinite Dimensional Lie Algebra

YU De-min, LI Ai-hua

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.



Global Stability in a Model for CTL Response to HTLV-I Infection

SONG Qiang

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.



Fuzzy MP-filters Lattice on a Given FI-algebra

LIU Chun-hui, XU Luo-shan

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.