数学季刊

邢杰

2015, 30(3): 317-322. doi:10.13371/j.cnki.chin.q.j.m.2015.03.001

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Let（M,g） be a smooth compact Riemannian manifold of dimension n.Denote△f=△-▽f.▽ the weighted Laplacian operator,where f is a smooth real valued function on M.When N is finite and the N-Bakry-Emery Ricci tensor is bounded from below by a constant,we establish local gradient estimates for positive solutions of the following simple Lichnerowicz equation△fu+cu^-α=0 on a compact Riemannian manifold,where α is a positive constant and c is a smooth function.

(2+1)维AKNS方程的行波解研究

程智龙, 郝晓红

2015, 30(3): 323-329. doi:10.13371/j.cnki.chin.q.j.m.2015.03.002

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Based on the travelling wave method, a（2 + 1）-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.

基于多客户的工件可转包排序问题

冯艳玲, 张玉忠, 贾国柱

2015, 30(3): 330-338. doi:10.13371/j.cnki.chin.q.j.m.2015.03.003

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In this paper, we study a new scheduling and outsourcing model with multiple customers in which jobs can be processed by either in-house machine or outsourcing machine.All processed jobs have to be delivered in batches to their respective customers and each shipment incurs a delivery cost as well as a fixed amount of time. We discuss three commonly used objective functions, analyze their complexity and solve them by dynamic programming algorithms.

三维不可压霍尔磁流体方程组弱解的正则性准则

刘坤红, 原保全

2015, 30(3): 339-348. doi:10.13371/j.cnki.chin.q.j.m.2015.03.004

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In this paper,we study the regularity criterion of weak solutions to the3 D incompressible Hall-magnetohydrodynamics,which is ifu and Bsatisfy the condition∫₀^T‖\alpha_x3u（t）‖^q_LP+‖▽B‖γLβdt<∞ with 3/p+2/q≤1,3/β+2/γ≤1,p>3,β>3,then the weak solution（u,B） is a smooth one on(0,T].

模糊软集的相似测度和距离测度

刘雅雅, 秦克云, 王玲

2015, 30(3): 349-357. doi:10.13371/j.cnki.chin.q.j.m.2015.03.005

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In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.

非线性奇异二阶三点边值问题的对称正解

吴红萍

2015, 30(3): 358-365. doi:10.13371/j.cnki.chin.q.j.m.2015.03.006

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In this paper, the second-order three-point boundary value problem {u"（t）+λa（t）f（t,u（t））=0,0<t<1,u（t）=u（1-t）,u′（0）-u′（1）=u（1/2）is studied,where λ is a positive parameter,under various assumption on a and f,we establish intervals of the parameter λ,which yield the existence of positive solution,our proof based on Krasnosel’skii fixed-point theorem in cone.

涉及两个质点组的一个恒等式及应用

周永国

2015, 30(3): 366-372. doi:10.13371/j.cnki.chin.q.j.m.2015.03.007

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In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for two mass-points systems and its radius of the circumscribed sphere and an inequality for distance between mass-points of two mass-points systems and its k-dimensional volume.

BCK代数的广义（∈,∈∨q）-模糊理想

刘春辉

2015, 30(3): 373-380. doi:10.13371/j.cnki.chin.q.j.m.2015.03.008

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In this paper, as a generalization of the notion of（∈, ∈∨ q）-fuzzy ideals, we introduced the notion of（∈, ∈∨ qδ）-fuzzy ideals and investigated their properties in BCKalgebras. Several equivalent characterizations of（∈, ∈∨ qδ）-fuzzy ideals are obtained and relations between（∈, ∈∨ qδ）-fuzzy ideals and ideals are discussed in BCK-algebras.

关于有限群的极大子群的s^*-完备

高辉, 高胜哲, 尹丽

2015, 30(3): 381-388. doi:10.13371/j.cnki.chin.q.j.m.2015.03.009

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Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.

二元Hamming结合方案的紧相对6-设计

李增提, 高锁刚, 冯光辉

2015, 30(3): 389-407. doi:10.13371/j.cnki.chin.q.j.m.2015.03.010

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The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte（Philips Res Rep 32: 373C411, 1997）. In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very explicitly for binary Hamming association schemes H（n, 2）.

一种杂交共轭梯度方法的全局收敛性

吴雪莎

2015, 30(3): 408-415. doi:10.13371/j.cnki.chin.q.j.m.2015.03.011

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Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed. Under the general Wolfe linear searches, the proposed method can generate the sufficient descent direction at each iterate,and its global convergence property also can be established. Some preliminary numerical results show that the proposed method is effective and stable for the given test problems.

多复变ε星形映射的系数

闫春燕, 孙林坡, 安曼

2015, 30(3): 416-419. doi:10.13371/j.cnki.chin.q.j.m.2015.03.012

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In this paper, we study ε-starlike mappings on the unit ball in \mathbb{C}^{n}, the upper bounds of coefficients of kth item of homogeneous expansion for ε-starlike mappings are obtained.

考虑毛管形状的幂律流体等效渗透率计算方法

杨二龙, 李欢, 高慧娟, 谷婷婷

2015, 30(3): 420-428. doi:10.13371/j.cnki.chin.q.j.m.2015.03.013

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While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.

基于融合特征的商品图像分类

杨晓慧, 刘静静, 杨利军

2015, 30(3): 429-441. doi:10.13371/j.cnki.chin.q.j.m.2015.03.014

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Two key challenges raised by a product images classification system are classification precision and classification time. In some categories, classification precision of the latest techniques, in the product images classification system, is still low. In this paper, we propose a local texture descriptor termed fan refined local binary pattern, which captures more detailed information by integrating the spatial distribution into the local binary pattern feature. We compare our approach with different methods on a subset of product images on Amazon/e Bay and parts of PI100 and experimental results have demonstrated that our proposed approach is superior to the current existing methods. The highest classification precision is increased by 21% and the average classification time is reduced by 2/3.

一类解析函数的Fekete-Szeg\"{o}不等式

郭栋, 李宗涛, 黄金超

2015, 30(3): 442-449. doi:10.13371/j.cnki.chin.q.j.m.2015.03.015

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The Fekete-Szego inequality for a subclass H（α,λ,A,B） of the class H of normalized analytic functions is studied.For each f（z）=z+∞∑n=2α_nzⁿ ∈ H（α,λ,A,B）,the sharp upper bounds of |α₃-α₂²|for any complex parameter u are obtained by using the fundamental inequalities of analytic functions and analytical techniques and the applications of the inequality of functions defined with Hadaniard product are proved.

一类具有接种和时滞的非自治捕食-食饵的SIR传染病模型

康瑞妮, 张太雷, 刘俊利

2015, 30(3): 450-461. doi:10.13371/j.cnki.chin.q.j.m.2015.03.016

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A non-autonomous SIR epidemic model of prey-predator with vaccination and time delay is investigated in this paper. And an infectious disease is only considered to spread among the prey population. By using comparison principle and Lyapunov functional methods, we obtain the sufficient criteria for the permanence, extinction of infectious disease and the global attractively of the model. Furthermore, some numerical simulations illustrate that the vaccination has a better effect for disease controlling of infective prey.

B₃型量子包络代数典范基中t值≤6时的单项式

胡余旺, 耿亚军

2015, 30(3): 462-474. doi:10.13371/j.cnki.chin.q.j.m.2015.03.017

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All monomials with t-value ≤ 6 in Canonical basis of quantized enveloping algebra of type B₃ are determined in this paper.

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