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2016年 第31卷 第2期    刊出日期：2016-06-30

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具有s=5,6的距离整完全多部图

杨若松, 王力工

2016, 31(2):  111-117.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.001

摘要 ( 86 )   PDF (332KB) ( 123 )  

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Let D（G） =(d_ij)_n×n denote the distance matrix of a connected graph G with order n, where d_ij is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_{p1,p2,···,pr}=K_{a1·p1,a2·p2,···,as···ps} to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_{a1·p1,a2·p2,···,as·ps} with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_{a1·p1,a2·p2,···,as·ps} with s = 5, 6. The problem of the existence of such distance integral graphs K_{a1·p1,a2·p2,···,as·ps} with arbitrarily large number s remains open. 

环F_p+vF_p上的LCD循环码

张光辉, 刘青青

2016, 31(2):  118-124.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.002

摘要 ( 86 )   PDF (340KB) ( 83 )  

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In this paper,we characterize the necessary and sufficient conditions for a cyclic code of length n over F_p+ vF_p to be an LCD code,where p is an odd prime. 

退化和奇异抛物系统的一致爆破行为

刘丙辰, 张长城

2016, 31(2):  125-138.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.003

摘要 ( 65 )   PDF (492KB) ( 159 )  

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This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blowup exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases. 

Wick-型KdV-Burgcrs方程的精确解

刘绍庆, 高国成

2016, 31(2):  139-146.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.004

摘要 ( 72 )   PDF (358KB) ( 90 )  

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In this paper,we consider the wick-type Kd V-Burgers equation with variable coefficients. By using Tanh method with the aid of Hermite transformation, we deduce the exact solutions which include hyperbolic-exponential, trigonometric-exponential and exponential function solutions for the considered equation.

完全二部图K_8,n的点可区别IE-全染色

师瑾, 陈祥恩

2016, 31(2):  147-154.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.005

摘要 ( 82 )   PDF (363KB) ( 84 )  

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Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C（x） be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C（u） ≠ C（v） for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_vt^ie （G） and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K_8,n are discussed in this paper. Particularly, the VDIET chromatic number of K_8,n are obtained. 

带有Banach代数的非正规锥度量空间中的公共不动点定理

黄华平, 许绍元, 刘秋华, 明巍

2016, 31(2):  155-161.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.006

摘要 ( 76 )   PDF (316KB) ( 132 )  

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In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions. 

NSD随机变量阵列的L_r收敛性

朱华炎, 沈爱婷, 张颖

2016, 31(2):  162-170.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.007

摘要 ( 63 )   PDF (379KB) ( 154 )  

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Let {X_nk, k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r convergence of 1/a_n max 1≤j≤n |j∑k=1 X_nk| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. 

一般径向体的若干不等式

张平 , 王卫东

2016, 31(2):  171-177.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.008

摘要 ( 54 )   PDF (294KB) ( 125 )  

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Lutwak showed the radial bodies combining with the radial Minkowski linear combinations of star bodies. In this paper, the general radial bodies are introduced and its some properties and inequalities are established. 

竞争失效场合广义混合截尾寿命试验的似然分析

毛松, 师义民

2016, 31(2):  178-188.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.009

摘要 ( 85 )   PDF (458KB) ( 136 )  

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Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function（CMGF）. Furthermore, confidence intervals（CIs） are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here. 

依赖于导数项的非对称振子解的无界性

王丽霞, 马世旺, 汪小明

2016, 31(2):  189-200.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.010

摘要 ( 64 )   PDF (462KB) ( 69 )  

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In this paper, we consider the unboundedness of solutions for the asymmetric equation x^’’+ax⁺-bx^-+（x）ψ（x^’）+f（x）+g（x’）=p（t）,where x⁺= max{x, 0}, x^-= max{-x, 0}, a and b are two different positive constants,f（x） is locally Lipschitz continuous and bounded, （x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions: the resonance case 1/a^1/2+1/b^1/2∈Q and the nonresonance case 1/a^1/2+1/b^1/2∈Q 

超Geng-族的自相容源和守恒律

魏含玉, 崔仲远, 夏铁成

2016, 31(2):  201-210.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.011

摘要 ( 69 )   PDF (399KB) ( 141 )  

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Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrable super-Geng hierarchy. The methods derived by us can be generalized to other nonlinear equation hierarchies. 

抛物星形映射子族的增长定理和偏差定理

张晓飞, 闫春燕

2016, 31(2):  211-220.  doi:10.13371/j.cnki.chin.q.j.m.2016.02.012

摘要 ( 75 )   PDF (420KB) ( 179 )  

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In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established.