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Table of Content
30 June 2018, Volume 33 Issue 2
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Admissible Periodic Bouncing Solutions for A Class of Semi-linear and Non-conservative Impact Oscillators
HANG Wei-tao, WANG Chao, LI Qi, YANG Xiao
2018, 33(2): 111-121. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.001
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In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.
Bayesian Inference on Type-I Progressively Hybrid Competing Risks Model
ZHANG Chun-fang, SHI Yi-min, WU Min
2018, 33(2): 122-131. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.002
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In this paper, we construct a Bayesian framework combining Type-Ⅰ progressively hybrid censoring scheme and competing risks which are independently distributed as exponentiated Weibull distribution with one scale parameter and two shape parameters. Since there exist unknown hyper-parameters in prior density functions of shape parameters, we consider the hierarchical priors to obtain the individual marginal posterior density functions,Bayesian estimates and highest posterior density credible intervals. As explicit expressions of estimates cannot be obtained, the componentwise updating algorithm of Metropolis-Hastings method is employed to compute the numerical results. Finally, it is concluded that Bayesian estimates have a good performance.
Some Basic Properties for Certain Classes of p-valent Analytic Functions Using Differential Operator
ZHANG Hai-Yan, TANG Huo, LI Shu-Hai, MA Li-Na
2018, 33(2): 132-139. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.003
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In this paper, we introduce new subclasses of p-valent analytic functions defined by using differential operator in the open unit disc. We study coefficient inequality, distortion theorem, radius of close to-convexity, starlikeness and convexity, extreme points and integral operator for functions in these new subclasses.
A Note on the Matching Polynomials of Paths and Cycles
ZHANG Hai-liang
2018, 33(2): 140-143. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.004
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The spectra of matching polynomials which are useful in the computations of resonance energy and grand canonical partition functions of molecular’s. It also present other properties for certain classes of graphs and lattices. In [1] Balasubramanian calculates several matching polynomials and matching roots of several molecular graphs. He found that the matching polynomial of C
6
, C
10
, C
14
, C
18
and C
22
are divided by x
2
-2. In this note,we prove that x
2
-2 divides MC
4k+2
（x）, k = 1, 2,..., n and obtain some other properties of matching polynomials of paths and cycles.
The Lattice of （∈, ∈ ∨ q
k
)-fuzzy Filters in a Given R
0
-algebra
LIU Chun-hui
2018, 33(2): 144-155. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.005
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The purpose of this paper is to further study the
（∈, ∈ ∨ q
k
)
-fuzzy filter theory in R0-algebras. Some new properties of
（∈, ∈ ∨ q
k
)
-fuzzy filters are given. Representation theorem of
（∈, ∈ ∨ q
k
)
-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all
（∈, ∈ ∨ q
k
)
-fuzzy filters on a given R0-algebra, under the partial order, forms a complete distributive lattice.
Inequalities for L
p
Mixed Intersection Bodies
LIU Li-juan, WANG Wei
2018, 33(2): 156-165. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.006
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Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.
Existence and Uniqueness of Almost Periodic Solutions for Some Infinite Delay Integral Equations
XU Jian-zhong, ZHANG Yu-chuan, ZHOU Zong-fu
2018, 33(2): 166-171. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.007
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In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
The Strong Convergence Properties for Partial Sums of m-NA Random Variables
WANG Meng-hang, PEI Wen-chen, ZHANG Yu-heng, YING Han-lu, WANG Xue-jun
2018, 33(2): 172-180. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.008
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In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.
Nonlinear Super Integrable Couplings of A Super Integrable Hierarchy and Its Super Hamiltonian Structures
TAO Si-xing
2018, 33(2): 181-193. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.009
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Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.
Discreteness Criterion for Subgroups in PU(1; n;C)
YANG Juan, WANG hua
2018, 33(2): 194-198. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.010
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In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.
Applications of the Di®erential Operator to the Class of p-Valent Functions
ZHOU Cong-hui
2018, 33(2): 199-205. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.011
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In this paper, we define some new subclasses of strongly close-to-star and strongly close-to-convex p-valent functions defined in the open unit disc by using a differential operator. Some inclusion results, convolution properties are studied.
A Note on DP Algorithm for Batching Scheduling to Minimize Maximum Lateness
LIN Hao, HE Cheng
2018, 33(2): 206-211. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.012
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In parallel-batching machine scheduling, all jobs in a batch start and complete at the same time, and the processing time of the batch is the maximum processing time of any job in it. For the unbounded parallel-batching machine scheduling problem of minimizing the maximum lateness, denoted 1|p-batch|L
max,
a dynamic programming algorithm with time complexity O（n
2
） is well known in the literature.Later, this algorithm is improved to be an O（n log n） algorithm. In this note, we present another O（n log n） algorithm with simplifications on data structure and implementation details.
B-Implicit Contractive Conditions and Unique (Common) Fixed Points on Complex Valued Metric Spaces
PIAO Yong-jie
2018, 33(2): 212-220. doi:
10.13371/j.cnki.chin.q.j.m.2018.02.013
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A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.
