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Table of Content
30 June 2015, Volume 30 Issue 2
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Normal Families of Meromorphic Functions and Shared Set
TIAN Hong-gen, CHEN Wei, YUAN Wen-jun
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
f
satisfying（i） b
f
/c
f
is 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].
New Criteria for Judging Generalized Strictly Diagonally Dominant Matrix
ZHANG Jin-song
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.
Existence of Three Positive Periodic Solutions of Neutral Nonlinear Functional Difference Equations
LIU Xing-yuan
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.
On Geodesic E-quasiconvex Functions and Geodesic E-epigraphs
LIN Qing-ying, HUANG Long-guang
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.
The Generalized Sine Theorem for Mixed Vertex Angle of Two Simplices and Applications
WANG Wen, YANG Shi-guo, QI Ji-bing
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.
Dresher's Type Inequalities for Dual Quermassintegral
WEI Bo, WANG Wei-dong
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.
Preservation Property of NBUCA Life Distributions
WANG Feng-xiao
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.
A General Theta Function Identity and Modular Equations
XUE Lin, ZHANG Zhi-zheng
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.
Monoidal Category Approach to Dual Hom-quasi-Hopf Algebras
CHENG Yong-sheng, LIU Guo-jing
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.
Periodic Boundary Value Problem for Second-order Impulsive Integro-differential Equation
ZHANG Lin-li, LIU An-ping, LIU Wei-an
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.
Weighted Differentiation Composition Operators from Mixed-norm Spaces to Bloch-type Spaces
LIU Guang-rong
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.
Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlocal Source
JIANG Liang-jun
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） ∫
Ω
h（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.
Periodic Solutions for Some Second-order Differential System with p(t)-Laplacian
WANG Qi, LU Di-cheng, MA Qi, DAI Jin
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.
Normal Families and Shared Functions
WANG Xue-qin, LEI Chun-lin
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.
Rescheduling to Minimize Total Completion Time Under a Limit Time Disruption for the Parallel Batch
XU Xiao-yan, MU Yun-dong, GUO Xiao, HAO Yun
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.
Fixed Point Theorems in Cone Symmetric Spaces
ZHANG Yi
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].
Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion
WANG Zhi-ping, XU Rui, ZHANG Shi-hua
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.
Asymptotic Property for the Estimator of Nonparametric Regression Models Under Negatively Orthant Dependent Errors
PENG Zhi-qing, ZHENG Lu-lu, LIU Yan-fang, XIAO Ru, WANG Xue-jun
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.
The Interval Graph Completion Problem on Split Graphs
ZHANG Zhen-kun, YU Min
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.
