Chinese Quarterly Journal of Mathematics

Bicriteria Scheduling on a Series-Batching Machine to Minimize Makespan and Total Weighted Completion Time with Equal Length Job

HE Cheng, LIN Hao, DOU Jun-mei, MU Yun-dong

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.

Some Results of a Certain Odd Perfect Number

ZHANG Si-bao

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.

Positive Solutions for Fourth-order Delay Differential Equation of Boundary Value Problem with p-Laplacian

ZHANG Yu-chuan, ZHOU Zong-fu

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.

A New Nonlinear Integrable Couplings of Yang Equations Hierarchy and Its Hamiltonian Structure

WEI Han-yu, XIA Tie-cheng

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.

Cyclic Codes over F₂ + uF₂ + vF₂

LIU Xiu-sheng, LIU Hua-lu

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.

Probability Inequalities for Extended Negatively Dependent Random Variables and Their Applications

TANG Xiao-feng

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.

The Existence and Uniqueness of the Solution for Periodical Boundary Value Problems of 2kth Order Differential Equations with Resonance

FENG Yan-qing, WANG Zhong-ying

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.

On the Characterization of Cyclic Codes over Ring F₂+uF₂+vF₂

ZHANG Xiao-yan

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.

Some Geometric Inequalities on the Radii of Inscribed Sphere of a Simplex and Its Subsimplex

ZHANG Han-fang

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].

Common Fixed Points for a Countable Family of Non-self Mappings in Cone Metric Spaces with the Convex Property

PIAO Yong-jie, LI Chun-hua

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.

A Class of Solvable Lie Algebras and Their Hom-Lie Algebra Structures

LI Xiao-chao, LI Dong-ya, JIN Quan-qin

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.

Characterizing C₆ + P₂graphic Sequences

HU Li-li

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）.

Biserial Incidence Algebras

HAN Guo-qiang, YAO Hai-lou

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.

m-degree Center-connecting Line of Finite Points Set and Its Properties

ZHOU Yong-guo

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.

A Note on Gap Phenomena of Kahler Manifolds with Nonnegative Curvature

JIAO Zhen-hua

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.

Properties for Certain Subclasses of Analytic Functions Associated with Generalized Multiplier Transformation

LI Zong-tao, GUO Dong

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.
77.6

On the Strong Laws for Weighted Sums of m-negatively Associated Random Variables

WU Yong-feng

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.

Group Twisted Tensor Biproducts over Hopf Group Coalgebras

CHEN Quan-guo, TANG Jian-gang

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.

Generalized Crossed Products and L-R Smash Products of Multiplier Hopf Algebras

ZHAO Li-hui, WANG Cai-hong

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.

A Property of Convex Mappings on the Classical Domains

FENG Shu-xia, LI Hong-jun

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.

Outer P_(ρ,σ)-set’s Random Characteristic and Application

ZHANG Huan-li, WANG Dong-mei

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.

Texture Image Classification Based on Gabor Wavelet

DENG Wei-bing, LI Hai-fei, SHI Ya-li, YANG Xiao-hui

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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