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2014年 第29卷 第1期    刊出日期：2014-03-30

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图的最小控制树问题

林浩, 林澜

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

摘要 ( 47 )   PDF (644KB) ( 15 )  

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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.

单位多圆柱上加权Bergman空间上的复合算子

胡蓉, 胡鹏彦

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

摘要 ( 57 )   PDF (289KB) ( 23 )  

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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.

二阶微分方程解的下级与型

张少华, 吴昭君, 孙道椿

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

摘要 ( 37 )   PDF (393KB) ( 16 )  

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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)=a_dz^d, 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)=a_dz^d+a_d-1z^d-1+…+a₁z+a₀, a_d>0, a_d-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.

解凸可行问题的一个带中心技术的外推平行次梯度投影算法

党亚峥, 韩学峰, 高岩

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

摘要 ( 40 )   PDF (468KB) ( 26 )  

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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. 

形式幂级数环上的自对偶码 

刘修生, 刘花璐

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

摘要 ( 47 )   PDF (534KB) ( 13 )  

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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 R_i={a₀+a₁r+…+a_i-1\gamma^i-1|a_i∈\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 R_i,  and give some characterizations of self-dual codes over R_∞.

复双球垒域上一些奇异积分方程的直接求解

龚定东, 郭玉琴

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

摘要 ( 37 )   PDF (384KB) ( 38 )  

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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.








一类具有时滞、脉冲效应和阶段结构的捕食者-食饵模型

杜艳可, 吴向东, 徐瑞

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

摘要 ( 48 )   PDF (1383KB) ( 33 )  

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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. 

无穷区间上具积分边值条件的二阶非线性奇异微分方程组正解存在性

李耀红

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

摘要 ( 42 )   PDF (607KB) ( 14 )  

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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.

BL-代数的 (∈_γ ,∈_γVq_δ)-直觉模糊(软)滤子

杨永伟, 辛小龙, 贺鹏飞

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

摘要 ( 50 )   PDF (678KB) ( 38 )  

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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.

K₄VK_n的Smarandachely邻点可区别正常边染色

陈祥恩, 姚兵

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

摘要 ( 48 )   PDF (838KB) ( 60 )  

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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 S_f(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. 

关于复阶k一致α-凸p叶函数类的新积分算子的凸性

李书海, 马丽娜, 敖恩

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

摘要 ( 40 )   PDF (518KB) ( 13 )  

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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.

关于拟-Jacobi双代数胚及其Dirac-Jacobi结构

刘玲, 苏农

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

摘要 ( 30 )   PDF (627KB) ( 6 )  

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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.

某些类具有反射与平移移位的卷积型奇异积分方程的解法

李平润

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

摘要 ( 40 )   PDF (534KB) ( 43 )  

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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}.



整循环图的秩

周后卿

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

摘要 ( 50 )   PDF (562KB) ( 16 )  

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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. 

套代数上Lie同态的一个局部刻画

杨妙霞, 张建华

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

摘要 ( 47 )   PDF (244KB) ( 19 )  

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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.

带有非齐次温度边界的一维可压缩粘性微极流体模型的局部正则性

孙林林, 梁铁旺, 张建朋

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

摘要 ( 43 )   PDF (743KB) ( 20 )  

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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].

一种修正的LS共轭梯度方法及其收敛性

刘金魁

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

摘要 ( 45 )   PDF (534KB) ( 31 )  

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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. 

强耗散可拉伸梁方程解的一致衰减性

冯保伟, 张明, 梁铁旺, 李海燕

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

摘要 ( 37 )   PDF (463KB) ( 41 )  

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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.