期刊：
Ars Combinatoria,2014年114:213-222 ISSN：0381-7032
通讯作者：
Wu, Yaping
作者机构：
[Wu, Yaping] Jianghan Univ, Fac Math & Comp, Wuhan, Peoples R China.;[Fan, Qiong] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Wu, Yaping] J;Jianghan Univ, Fac Math & Comp, Wuhan, Peoples R China.
关键词：
Bicyclic graph;Lexicographical order;Spectral moment
摘要：
A graph G of order n is called a bicyclic graph if G is connected and the number of edges of G is n + 1. In this paper, we study the lexicographic ordering of bicyclic graphs by spectral moments. For each of the three basic types of bicyclic graphs on a fixed number of vertices maximal and minimal graphs in the mentioned order are determined.
摘要：
Let a, b, c > 0. We investigate the characterization problem which asks for a classification of all the triples (a, b, c) such that the Weyl-Heisenberg system
$$\left\{ {{e^{2\pi imbx}} \times {\chi _{[na,na + c)}}:m,n \in {\Bbb Z}} \right\}$$
is a frame for L
2(ℝ). It turns out that the answer to the problem is quite complicated, see Gu and Han (2008) and Janssen (2003). Using a dilation technique, one can reduce the problem to the case where b = 1 and only let a and c vary. In this paper, we extend the Zak transform technique and use the Fourier analysis technique to study the problem for the case of a being a rational number. We prove some special cases of values for c and a that do not produce a frame, which expands earlier works.
摘要：
<正>1问题的提出芝加哥大学学校数学方案（The University of Chicago School Mathematics Project）成立于1983年,是由美国科学基金会和Amoco基金会赞助,一批数学教育领域的专家和教师共同编写的一套中学数学教材（简称UCSMP教材）.该教材旨在改变当时美国学校数学教育滞后于现代科技和数学发展的状况,使中小学数学课程体现时代要求和数学发展状况.这套教材强调通过学生的阅读学习数学,着眼于培养学生独立学习和应
作者机构：
[Liu, Hongwei; Chen, Bocong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Dinh, Hai Q.] Kent State Univ, Dept Math Sci, Warren, OH 44483 USA.;[Chen, Bocong] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637616, Singapore.
通讯机构：
[Chen, Bocong] N;Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637616, Singapore.
期刊：
Journal of Graph Theory,2014年77(3):237-250 ISSN：0364-9024
通讯作者：
Chen, Guantao
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Ferrara, Michael; Jacobson, Michael] Univ Colorado Denver, Dept Math & Stat Sci, Denver, CO USA.;[Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Liu, Huiqing] Hubei Univ, Sch Math & Comp Sci, Wuhan, Peoples R China.
通讯机构：
[Chen, Guantao] G;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.
关键词：
extremal spanning tree;broom
摘要：
A broom is a tree obtained by subdividing one edge of the star an arbitrary number of times. In (E. Flandrin, T. Kaiser, R. Kužel, H. Li and Z. Ryjáček, Neighborhood Unions and Extremal Spanning Trees, Discrete Math 308 (2008), 2343–2350) Flandrin et al. posed the problem of determining degree conditions that ensure a connected graph G contains a spanning tree that is a broom. In this article, we give one solution to this problem by demonstrating that if G is a connected graph of order with , then G contains a spanning broom. This result is best possible.
期刊：
Applied Mechanics and Materials,2014年687-691:4946-4949 ISSN：1662-7482
通讯作者：
Cheng, Y.
作者机构：
[Wang Q.; Cheng Y.; Zhao D.] School of Mathematics and Statistics, Central China Normal University, Wuhan, China;[Tan K.] School of Economics and Business Administration, Central China Normal University, Wuhan, China
通讯机构：
[Cheng, Y.] S;School of Mathematics and Statistics, Central China Normal UniversityChina
会议名称：
2014 International Conference on Manufacturing Technology and Electronics Applications, ICMTEA 2014
期刊：
Journal of Differential Equations,2014年257(6):1721-1752 ISSN：0022-0396
通讯作者：
Huang, Jicai
作者机构：
[Huang, Jicai; Song, Jing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Ruan, Shigui] Univ Miami, Dept Math, Coral Gables, FL 33124 USA.
通讯机构：
[Huang, Jicai] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Predator–prey system;Holling type-III functional response;Hopf bifurcation;Bogdanov–Takens bifurcation;Degenerate focus type BT bifurcation of codim 3
摘要：
We consider a predator-prey system of Leslie type with generalized Holling type III functional response p(x) = mx(2)/ax(2)+bx+1. By allowing b to be negative (b > -2 root a), p(x) is monotonic for b > 0 and nonmonotonic for b < 0 when x >= 0. The model has two non-hyperbolic positive equilibria (one is a multiple focus of multiplicity one and the other is a cusp of codimension 2) for some values of parameters and a degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3 for other values of parameters. When there exist a multiple focus of multiplicity one and a cusp of codimension 2, we show that the model exhibits subcritical Hopf bifurcation and Bogdanov-Takens bifurcation simultaneously in the corresponding small neighborhoods of the two degenerate equilibria, respectively. Different phase portraits of the model are obtained by computer numerical simulations which demonstrate that the model can have: (i) a stable limit cycle enclosing two non-hyperbolic positive equilibria; (ii) a stable limit cycle enclosing an unstable homoclinic loop; (iii) two limit cycles enclosing a hyperbolic positive equilibrium; (iv) one stable limit cycle enclosing three hyperbolic positive equilibria; or (v) the coexistence of three stable states (two stable equilibria and a stable limit cycle). When the model has a Bogdanov-Takens singularity of codimension 3, we prove that the model exhibits degenerate focus type Bogdanov-Takens bifurcation of codimension 3. These results not only demonstrate that the dynamics of this model when b > -2 root a are much more complex and far richer than the case when b > 0 but also provide new bifurcation phenomena for predator-prey systems. (C) 2014 Elsevier Inc. All rights reserved.
作者机构：
[Hou, Ailin] Tianjin Med Univ, Sch Med Imaging, Tianjin 300203, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
A connected graph G is a cactus if any two of its cycles have at most one common vertex. Denote by Cn,q the set of n-vertex cacti with matching number q. Huang, Deng and Simic [23] identified the unique graph with the maximum spectral radius among 2q-vertex cacti with perfect matchings. In this paper, as a continuance of it, the largest and second largest spectral radii together with the corresponding graphs among Cn,q are determined. Consequently, the first two largest spectral radii together with cacti having perfect matchings are also determined.Quaestiones Mathematicae 37(2014), 401-414
期刊：
Insurance: Mathematics and Economics,2014年59(Nov.):325-336 ISSN：0167-6687
通讯作者：
Li, Bo
作者机构：
[Li, Bo; Zhang, Huiming] Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.;[Liu, Yunxiao] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 USA.
通讯机构：
[Li, Bo] C;Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Compound Poisson distribution;Integer-valued Levy process;CreditRisk plus model;Geometric Brownian motion with jumps;Pseudo compound Poisson distribution;Wiener-Levy theorem
摘要：
Probability generating function (p.g.f.) is a powerful tool to study discrete compound Poisson (DCP) distribution. By applying inverse Fourier transform of p.g.f., it is convenient to numerically calculate probability density and do parameter estimation. As an application to finance and insurance, we firstly show that in the generalized CreditRisk+ model, the default loss of each debtor and the total default of all debtors are both approximately equal to a DCP distribution, and we give Le Cam's error bound between the total default and a DCP distribution. Next, we consider geometric Brownian motion with DCP jumps and derive its rth moment. We establish the surplus process of the difference of two DCP distributions, and numerically compute the tail probability. Furthermore, we define the discrete pseudo compound Poisson (DPCP) distribution and give the characterizations and examples of DPCP distribution, including the strictly decreasing discrete distribution and the zero-inflated discrete distribution with P(X = 0) > 0.5. (C) 2014 Elsevier B.V. All rights reserved.
