Chinese Quarterly Journal of Mathematics

Minimum Dominating Tree Problem for Graphs

LIN Hao, LIN Lan

2014, 29(1): 1-8. doi:10.13371/j.cnki.chin.q.j.m.2014.01.001

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A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which is an NP-hard problem.This paper studies some polynomially solvable cases,including interval graphs,Halin graphs,special outer-planar graphs and others.

Composition Operators on the Weighted Bergman Space in the Unit Polydisk

HU Rong, HU Peng-yan

2014, 29(1): 9-13. doi:10.13371/j.cnki.chin.q.j.m.2014.01.002

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We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for the proof of the boundedness of composition operators,and then obtain an upper bound for the special operator norm on Bergman space.

The Lower Order and Type of Solutions of Second Order Differential Equation

ZHANG Shao-hua, WU Zhao-jun, SUN Dao-chun

2014, 29(1): 14-21. doi:10.13371/j.cnki.chin.q.j.m.2014.01.003

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The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0, where A(z) is a polynomial. In the case of A(z)=adzd, the authors prove that the lower order and the type of all non-trivial solutions w of w"(z)-A(z)w=0 are equal to (d+2)/2 and 2\sqrt{|a_{d}|}/(d+2) respectively. In the case of A(z)=adzd+ad-1zd-1+…+a1z+a0, ad>0, ad-1≥0,…, a1≥0, a0≥0, the authors prove that the lower order of all non-trivial solutions w of w"(z)-A(z)w=0 is (d+2)/2.

An Extrapolated Parallel Subgradient Projection Algorithm with Centering Technique for the Convex Feasibility Problem

DANG Ya-zheng, HAN Xue-feng, GAO Yan

2014, 29(1): 22-29. doi:10.13371/j.cnki.chin.q.j.m.2014.01.004

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In this paper, we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem, the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence. To prove the convergence in a simply way, we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space. Thus, the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions. Numerical results show that the new algorithm has better convergence than the existing algorithms.

The Self-dual Codes over Formal Power Series Rings

LIU Xiu-sheng, LIU Hua-lu

2014, 29(1): 30-38. doi:10.13371/j.cnki.chin.q.j.m.2014.01.005

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The codes of formal power series rings R_{\infty}=\mathbb{F}[[\gamma]]=\Sigma_{l=0}^{\infty}a_{l}\gamma_{l}|a_{l}\in\mathbb{F}} and finite chain rings

Ri={a0+a1r+…+ai-1\gamma^i-1|ai∈\mathbb{F}} have close relationship in lifts and projection. In this paper, we study self-dual codes over R∞ by means of self-dual codes over Ri, and give some characterizations of self-dual codes over R∞.

Direct Solutions of Some Singular Integral Equations on the Building Domain of Complex Biballs

GONG Ding-dong, GUO Yu-qin

2014, 29(1): 39-44. doi:10.13371/j.cnki.chin.q.j.m.2014.01.006

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By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs, direct solutions of some singular integral equations with variable coefficients are discussed and the explicit formulas for these solutions are obtained.

A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects

DU Yan-ke, WU Xiang-dong, XU Ru

2014, 29(1): 45-54. doi:10.13371/j.cnki.chin.q.j.m.2014.01.007

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A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated, in which both the prey and the predator have a history that takes them through two stages: immature and mature. The global attractiveness of the pest-eradication periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Further, numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

Existence of Positive Solutions for Systems of Second-order Nonlinear Singular Differential Equations with Integral Boundary Conditions on Infinite Interval

LI Yao-hong

2014, 29(1): 55-64. doi:10.13371/j.cnki.chin.q.j.m.2014.01.008

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By using cone theory and the Monch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.

(∈_γ ,∈_γVq_δ) -intuitionistic Fuzzy(Soft) Filter of BL-algebras

YANG Yong-wei, XIN Xiao-long, HE Peng-fei

2014, 29(1): 65-75. doi:10.13371/j.cnki.chin.q.j.m.2014.01.009

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In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the (∈_γ,∈_γVq_δ)-intuitionistic fuzzy filters and (∈_γ,∈_γVq_δ)-intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we discuss the properties of images and inverse images of (∈_γ,∈_γVq_δ)-intuitionistic fuzzy soft filters of BL-algebras.

Smarandachely Adjacent-vertex-distinguishing Proper Edge Coloring of K₄ V K_n

CHEN Xiang-en, YAO Bing

2014, 29(1): 76-87. doi:10.13371/j.cnki.chin.q.j.m.2014.01.010

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Let f be a proper edge coloring of G using k colors. For each x∈V(G), the set of the colors appearing on the edges incident with x is denoted by Sf(x) or simply S(x) if no confusion arise. If S(u)■S(v) and S(v)■S(u) for any two adjacent vertices u and v, then f is called a Smarandachely adjacent vertex distinguishing proper edge coloring using k colors, or k-SA-edge coloring. The minimum number k for which G has a Smarandachely adjacent-vertex-distinguishing proper edge coloring using k colors is called the Smarandachely adjacent-vertex-distinguishing proper edge chromatic number, or SAedge chromatic number for short, and denoted by χ’_sa(G). In this paper, we have discussed the SA-edge chromatic number of K₄∨K_n.

Convexity for New Integral Operator on k-uniformly p-valent α-convex Functions of Complex Order

LI Shu-hai, MA Li-na, AO-en

2014, 29(1): 88-96. doi:10.13371/j.cnki.chin.q.j.m.2014.01.011

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In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent α-convex functions of complex order. These results extend some known theorems.

On Quasi-Jacobi Bialgebroid and Its Dirac-Jacobi Structure

LIU Ling, SU Nong

2014, 29(1): 97-106. doi:10.13371/j.cnki.chin.q.j.m.2014.01.012

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Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced. The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved. Meanwhile several special examples are presented.

The Method of Solutions for some Kinds of Singular Integral Equations of Convolution Type with Both Reflection and Translation Shift

LI Ping-run

2014, 29(1): 107-115. doi:10.13371/j.cnki.chin.q.j.m.2014.01.013

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In this paper, some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform. In spite of the classical method for solution, we are to give another method, therefore the general solution and condition of solvability are obtained in class {0}.

The Rank of Integral Circulant Graphs

ZHOU Hou-qing

2014, 29(1): 116-124. doi:10.13371/j.cnki.chin.q.j.m.2014.01.014

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A graph is called an integral graph if it has an integral spectrum i.e., all eigenvalues are integers. A graph is called circulant graph if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. The rank of a graph is defined to be the rank of its adjacency matrix. This importance of the rank, due to applications in physics, chemistry and combinatorics. In this paper, using Ramanujan sums, we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.

A Local Characterization of Lie Homomorphisms of Nest Algebras

YANG Miao-xia, ZHANG Jian-hua

2014, 29(1): 125-128. doi:10.13371/j.cnki.chin.q.j.m.2014.01.015

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In this paper, linear maps preserving Lie products at zero points on nest algebras are studied. It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism. As an application, the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.

Local Regularity for a ID Compressible Viscous Micropolar Fluid Model with Non-homogeneous Temperature Boundary

SUN Lin-lin, LIANG Tie-wang, ZHANG Jian-peng

2014, 29(1): 129-141. doi:10.13371/j.cnki.chin.q.j.m.2014.01.016

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In this paper, we discuss the local existence of Hi(i=2,4) solutions for a 1D compressible viscous micropolar fluid model with non-homogeneous temperature boundary. The proof is based on the local existence of solutions in [1].

A Descent Gradient Method and Its Global Convergence

LIU Jin-kui

2014, 29(1): 142-150. doi:10.13371/j.cnki.chin.q.j.m.2014.01.017

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Y Liu and C Storey(1992) proposed the famous LS conjugate gradient method which has good numerical results. However, the LS method has very weak convergence under the Wolfe-type line search. In this paper, we give a new descent gradient method based on the LS method. It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search. Finally, we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP+ method.

On Uniform Decay of Solutions for Extensible Beam Equation with Strong Damping

FENG Bao-wei, ZHANG Ming, LIANG Tie-wang, LI Hai-yan

2014, 29(1): 151-158. doi:10.13371/j.cnki.chin.q.j.m.2014.01.018

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This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.

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