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Table of Content
30 March 2015, Volume 30 Issue 1
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Differential-difference Complex and the Poincar\acute{e} Lemma
BAI Yong-qiang, YAN Guo-dong
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.
Quantum Cluster Algebra Structure on the Quantum Grothendieck Ring K
t−1
Yahia Badawi Bashir Meny, MA Hai-tao, YANG Yan-min
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-1
which is defined in section 2.
Normality Criteria of Meromorphic Functions Concerning Shared Fixed-points
YANG Qi
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）
）
n
and g（g
（k）
）
n
share z in D for each pair of functions f and g, then F is normal.
Stability Criteria for Continuous Systems with Two Different Time-varying Delays
CHENG Yuan-yuan, JIANG Wei
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.
The Boundedness of the Singular Integral Operator with Variable
Calderón-Zygmund
Kernel on Weighted Morrey Spaces
PAN Ya-li, LI Chang-wen, WEN Zong-liang
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.
The Berezin Transform and Radial Operators on the Weighted Bergman Space of the Unit Ball
LU Mei-lin, LI De-sheng, GUAN Hong-yan
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 A
2
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 L
1
symbol.
Triple Positive Solutions to a Third-order Three-point Boundary Value Problem with p-Laplacian Operator
TAN Hui-xuan, FENG Han-ying, FENG Xing-fang, DU Ya-tao
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-2
s 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.
Bifurcation Analysis of a Discrete Logistic System with Feedback Control
WU Dai-yong
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.
Gorensteinness and Tate Cohomology in Exact Categories
WANG Zhi-cheng
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.
Hopf Bifurcation and Stability Analysis for a Predator-prey Model with Time-delay
CHEN Hong-bing
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.
Global Stability of a Predator-prey Model with Stage Structure
WANG Li-li, XU Rui
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 Transform Method Applied to Solve Fractional Difference Equations
LI Xiao-yan, XIANG Jiang-ru, WU Ya-yun
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.
Optimal Route Selection Method Based on Vague Sets
GUO Rui, DU Li min, WANG Chun
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.
Some Geometric Inequalities for the Radii of Escribed Hyperspheres of a Simplex
YANG Shi-guo, WANG Wen
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.
A Maschke Type Theorem for Weak Hopf \pi-Comodules
JIA Ling, CHEN Xiao-yuan
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.
Permanence of a Nicholson's Blowflies Model with Feedback Control and Multiple Time-varying Delays
CHEN Xiao-ying, SHI Chun-ling
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.
