数学季刊

何程, 林浩, 豆俊梅, 慕运动

2014, 29(2): 159-166. doi:10.13371/j.cnki.chin.q.j.m.2014.02.001

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It is known that the problem of minimizing total weighted completion time on a series-batching machine is NP-hard. We consider a series-batching bicriteria scheduling problem of minimizing makespan and total weighted completion time with equal length job simultaneously. A batching machine can handle up to b jobs in a batch, where b is called the batch capacity of the machine. We study the unbounded model with b ≥ n, where n denotes the number of jobs. A dynamic programming algorithm is proposed to solve the unbounded model, which can find all Pareto optimal schedules in O（n3） time.

一类奇完全数的一些结论

张四保

2014, 29(2): 167-170. doi:10.13371/j.cnki.chin.q.j.m.2014.02.002

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Define the total number of distinct prime factors of an odd perfect number n asω(n). We prove that if n is an odd perfect number which is relatively prime to 3 and 5 and7, then ω(n) ≥ 107. And using this result, we give a conclusion that the third largest prime factor of such an odd perfect number exceeds 1283.

带有p-Laplacian算子的四阶时滞微分方程边值问题的正解

张豫川, 周宗福

2014, 29(2): 171-179. doi:10.13371/j.cnki.chin.q.j.m.2014.02.003

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In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian（Φ_p（u））（t） + a（t）f（t, u（t- τ）, u（t）） = 0, 0 < t < 1;u（0） = u（0） = 0, u（1） = αu（η）;u（t） = 0,- τ≤ t ≤ 0.By using Schauder fixed-point theorem, some sufficient conditions are obtained which guarantee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.

Yang族一个新的非线性可积耦合及其哈密尔顿结构

魏含玉, 夏铁成

2014, 29(2): 180-188. doi:10.13371/j.cnki.chin.q.j.m.2014.02.004

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Based on a kind of non-semisimple Lie algebras, we establish a way to construct nonlinear continuous integrable couplings. Variational identities over the associated loop algebras are used to furnish Hamiltonian structures of the resulting continuous couplings.As an illustrative example of the scheme is given nonlinear continuous integrable couplings of the Yang hierarchy.

环 F₂+uF₂+vF₂

刘修生, 刘花璐

2014, 29(2): 189-194. doi:10.13371/j.cnki.chin.q.j.m.2014.02.005

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We study the structure of cyclic codes of an arbitrary length n over the ring F₂+ uF₂+ vF₂, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F₂+ uF₂+ vF₂ is a 3-quasi-cyclic code length 3n over F₂.

END随机变量的概率不等式及其应用

唐小峰

2014, 29(2): 195-202. doi:10.13371/j.cnki.chin.q.j.m.2014.02.006

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Some probability inequalities are established for extended negatively dependent（END） random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O（n^-1/2ln^1/2n） for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.

共振条件下2k阶微分方程周期边值问题解的存在唯一性

冯艳青, 王忠英

2014, 29(2): 203-209. doi:10.13371/j.cnki.chin.q.j.m.2014.02.007

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In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.

环F₂+uF₂+vF₂上循环码的一个刻画

张晓燕

2014, 29(2): 210-214. doi:10.13371/j.cnki.chin.q.j.m.2014.02.008

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In this work, we investigate the cyclic codes over the ring F2+ uF2+ vF2. We first study the relationship between linear codes over F₂+ uF₂+ vF₂ and that over F₂.Then we give a characterization of the cyclic codes over F₂+ uF₂+ vF₂ . Finally, we obtain the number of the cyclic code over F₂+ uF₂+ vF₂ of length n.

关于一个单形及其子单形的内切球半径的一些几何不等式

张晗方

2014, 29(2): 215-220. doi:10.13371/j.cnki.chin.q.j.m.2014.02.009

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In this paper, we obtain some geometric inequalities on the radii of inscribed sphere of a simplex and its subsimplex, as particular case of this paper, we obtain some main results of [1].

具有凸性的锥度量空间中可数个非自映射的公共不动点

朴勇杰, 李春花

2014, 29(2): 221-230. doi:10.13371/j.cnki.chin.q.j.m.2014.02.010

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A new common fixed point result for a countable family of non-self mappings defined on a closed subset of a cone metric space with the convex property is obtained, and from which, a more general result is given. Our main results improve and generalize many known common fixed point theorems.

一类可解李代数及其Hom-李代数结构

李小朝, 李东亚, 靳全勤

2014, 29(2): 231-237. doi:10.13371/j.cnki.chin.q.j.m.2014.02.011

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The finite-dimensional indecomposable solvable Lie algebras s with Q_2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q_2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.

刻画蕴含C₆+P₂的可图序列

胡黎莉

2014, 29(2): 238-243. doi:10.13371/j.cnki.chin.q.j.m.2014.02.012

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For a given graph H, a graphic sequence π =（d₁, d₂, ···, d_n） is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C₆+ P₂-graphic sequences where C₆+ P₂denotes the graph obtained from C₆ by adding two adjacent edges to the three pairwise nonadjacent vertices of C₆. Moreover, we use the characterization to determine the value of σ（C₆+ P₂, n）.

双列关联代数

韩国强, 姚海楼

2014, 29(2): 244-246. doi:10.13371/j.cnki.chin.q.j.m.2014.02.013

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Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods.

有限点集的m级连心线及其性质

周永国

2014, 29(2): 247-252. doi:10.13371/j.cnki.chin.q.j.m.2014.02.014

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In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.

非负曲率凯勒流形间隙现象的一个注记

焦振华

2014, 29(2): 253-256. doi:10.13371/j.cnki.chin.q.j.m.2014.02.015

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In this paper, we study the complex structure and curvature decay of Kahler manifolds with nonnegative curvature. Using a recent result obtained by Ni-Shi-Tam, we get a gap theorem of Ricci curvature on Kahler manifold.

由广义乘子变换定义的几个解析函数类的性质

李宗涛, 郭栋

2014, 29(2): 257-264. doi:10.13371/j.cnki.chin.q.j.m.2014.02.016

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In this paper, we introduce certain new subclasses of analytic functions defined by generalized multiplier transformation. By using the differential subordination, we study and investigate various inclusion properties of these classes. Also inclusion properties of these classes involving the integral operator are considered.

m-NA随机变量加权和的强收敛性

吴永锋

2014, 29(2): 265-273. doi:10.13371/j.cnki.chin.q.j.m.2014.02.017

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In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.

Hopf群余代数上的群扭曲张量双积

陈全国, 汤建钢

2014, 29(2): 274-282. doi:10.13371/j.cnki.chin.q.j.m.2014.02.018

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In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and sufficient conditions for the new object to be a Hopf group coalgebra.

乘子Hopf代数的广义交叉积与L-R smash积

赵利辉, 王彩虹

2014, 29(2): 283-291. doi:10.13371/j.cnki.chin.q.j.m.2014.02.019

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In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.

典型域上凸映射的一个映射性质

冯淑霞, 李鸿军

2014, 29(2): 292-297. doi:10.13371/j.cnki.chin.q.j.m.2014.02.020

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In this paper, we give a property of normalized biholomorphic convex mappings on the first, second and third classical domains: for any Z₀belongs to the classical domains, f maps each neighbourhood with the center Z₀, which is contained in the classical domains, to a convex domain.

外P_(ρ,σ)-集合的随机特性与应用

张环理, 王冬梅

2014, 29(2): 298-306. doi:10.13371/j.cnki.chin.q.j.m.2014.02.021

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Based on the conception of P_(ρ,σ)-set(X^P-F_ρ, X^PF_σ), this paper studied the relation between outer P_(ρ,σ)-set and outer P-set: give outer P_(ρ,σ)-set and outer P-set relation theorem, outer P_(ρ,σ)-set and numerical value σ relation theorem, outer P_(ρ,σ)-set’s range; studied other characteristics of outer P_(ρ,σ)-set: give the finiteness theorem of outer P_(ρ,σ)-set, the set chain theorem of outer P_(ρ,σ)-set, the outer P_(ρ,σ)-set probability interval finite partition theorem, and its corollary; also give generation, reduction, identification theorem of outer P(ρ,σ)-set, filter generation theorem of outer P_(ρ,σ)-set; finally give its application.

基于Gabor小波的纹理图像分类

邓未冰, 李海飞, 史亚莉, 杨晓慧

2014, 29(2): 307-316. doi:10.13371/j.cnki.chin.q.j.m.2014.02.022

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For a texture image, by recognizining the class of every pixel of the image, it can be partitioned into disjoint regions of uniform texture. This paper proposed a texture image classification algorithm based on Gabor wavelet. In this algorithm, characteristic of every image is obtained through every pixel and its neighborhood of this image. And this algorithm can achieve the information transform between different sizes of neighborhood. Experiments on standard Brodatz texture image dataset show that our proposed algorithm can achieve good classification rates.

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