数学季刊

田宏根, 陈玮, 袁文俊

2015, 30(2): 159-165. doi:10.13371/j.cnki.chin.q.j.m.2015.02.001

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In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers bf,c_fsatisfying（i） b_f/c_fis a constant;（ii） min{σ（0,b_f）,σ（0,c_f）,σ（b_f,c_f）} ≥m for some m > 0;（iii） E_f’（S_f）\subseteq E_f（S_f）,where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and[7].

判定广义严格对角占优矩阵的新准则

张劲松

2015, 30(2): 166-171. doi:10.13371/j.cnki.chin.q.j.m.2015.02.002

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Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.

中立型非线性泛函差分方程三个正周期解的存在性

刘兴元

2015, 30(2): 172-183. doi:10.13371/j.cnki.chin.q.j.m.2015.02.003

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This paper is concerned with the nonlinear neutral functional difference equations△x（n） =-a（n）x（n） +h（n）f（n,x（n-T（n））,△x（n-δ（n）））,where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.

测地E-拟凸函数和测地E-图

林清英, 黄龙光

2015, 30(2): 184-189. doi:10.13371/j.cnki.chin.q.j.m.2015.02.004

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The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.

两个单形混合顶点角的广义正弦定理及应用

王文, 杨世国, 齐继兵

2015, 30(2): 190-198. doi:10.13371/j.cnki.chin.q.j.m.2015.02.005

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Some related problems of two n-dimensional simplices which are on an（n- 1）-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.

关于对偶均质积分的Dresher型不等式

魏波, 王卫东

2015, 30(2): 199-205. doi:10.13371/j.cnki.chin.q.j.m.2015.02.006

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In this paper, we establish two Dresher’s type inequalities for dual quermassintegral with Lp-radial Minkowski linear combination and L_p-harmonic Blaschke linear combination, respectively. Our results in special cases yield some new dual L_p-Brunn-Minkowski inequalities for dual quermassintegral.

关于NBUCA寿命分布的封闭性质

王丰效

2015, 30(2): 206-210. doi:10.13371/j.cnki.chin.q.j.m.2015.02.007

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In this paper, some results of the NBUCA class of life distribution are obtained.The preservation properties of NBUCA aging properties under anti-star-shaped transformation are investigated. The preservation of NBUCA aging properties under general accelerated life model are studied as well.

一个Theta函数恒等式的推广和相关模形式

薛琳, 张之正

2015, 30(2): 211-217. doi:10.13371/j.cnki.chin.q.j.m.2015.02.008

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In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.

对偶的Hom-型拟Hopf代数的Monoidal范畴解释

程永胜, 刘国敬

2015, 30(2): 218-226. doi:10.13371/j.cnki.chin.q.j.m.2015.02.009

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In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.

二阶脉冲积分微分方程周期边值问题

张林丽, 刘安平, 刘伟安

2015, 30(2): 227-235. doi:10.13371/j.cnki.chin.q.j.m.2015.02.010

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In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of periodic solution and the sufficient condition for uniform stability of trivial solution are obtained, which extend the previous results on integro-differential equation in periodic boundary value problem.

从混合范数空间到Bloch型空间的加权微分复合算子

刘光荣

2015, 30(2): 236-243. doi:10.13371/j.cnki.chin.q.j.m.2015.02.011

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The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.

具加权非局部源反应扩散方程解的渐近行为

蒋良军

2015, 30(2): 244-252. doi:10.13371/j.cnki.chin.q.j.m.2015.02.012

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In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t= △u + a（x）f（u） ∫_Ωh（u）dx,x∈Ω,t>0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f（s） = s^p,h（s） = s^q,0 ≤ p≤1,p + q >1,we obtain the asymptotic behavior of the blow up solution.

二阶p（t）-Laplacian微分系统的周期解

王奇, 陆地成, 马琪, 戴进

2015, 30(2): 253-266. doi:10.13371/j.cnki.chin.q.j.m.2015.02.013

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In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p（t）-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.

正规族与分担函数

王雪琴 , 雷春林

2015, 30(2): 267-273. doi:10.13371/j.cnki.chin.q.j.m.2015.02.014

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Let k be a positive integer,let h be a holomorphic function in a domain D,h \neq 0and let F be a family of nonvanishing meromorphic functions in D.If each pair of functions f and q in F,f^（k）and g^（k）share h in D,then F is normal in D.

基于重新排序时间错位限制下的最小化总完工时间的平行分批排序

许小艳, 慕运动, 郭晓, 郝赟

2015, 30(2): 274-279. doi:10.13371/j.cnki.chin.q.j.m.2015.02.015

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In the rescheduling on a single machine, a set of the original jobs has already been scheduled, in order to make a given objective function is optimal. The decision maker needs to insert the new jobs into the existing schedule without excessively disrupting it. A batching machine is a machine that can handle up to some jobs simultaneously. In this paper,we consider the total completion time under a limit on the sequence disruptions for parallel batching based on rescheduling. For the parallel batching problem based on rescheduling, we research the properties of feasible schedules and optimal schedules on the total completion time under a limit on the maximum time disruptions or total time disruptions, in which the jobs are sequenced in SPT order, and give out the pseudo-polynomial time algorithms on the number of jobs and the processing time of jobs by applying the dynamic programming method.

锥对称空间中的不动点定理

张屹

2015, 30(2): 280-286. doi:10.13371/j.cnki.chin.q.j.m.2015.02.016

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In this paper, some common fixed point theorems for general occasionally weakly compatible selfmaps and non-selfmaps on cone symmetric spaces were proved. The interesting point of this paper is that we do not assume that the cone is solid. Our results generalize and complete the corresponding results in [9-15].

具有接种和非局部扩散的流行病模型的行波解

王志平, 徐瑞, 张世华

2015, 30(2): 287-299. doi:10.13371/j.cnki.chin.q.j.m.2015.02.017

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An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder’s fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.

基于NOD误差的非参数回归模型估计的渐近性质

彭智庆, 郑璐璐, 刘艳芳, 潇如, 王学军

2015, 30(2): 300-307. doi:10.13371/j.cnki.chin.q.j.m.2015.02.018

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In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.

分裂图的区间图完全化问题

张振坤, 余敏

2015, 30(2): 308-316. doi:10.13371/j.cnki.chin.q.j.m.2015.02.019

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The interval graph completion problem on a graph G is to find an added edge set F such that G + F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated.

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