作者机构：
[Zhang, Xing An; Yin, Hong Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yin, Hong Yan] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.;[Zhou, Da] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
通讯机构：
[Zhang, Xing An] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, we investigate the isolated closed orbits of two types of cubic vector fields in Double-struck capital R-3 by using the idea of central projection transformation, which sets up a bridge connecting the vector field X (x) in Double-struck capital R-3 with the planar vector fields. We have proved that the cubic vector field in Double-struck capital R-3 can have two isolated closed orbits or one closed orbit on the invariant cone. As an application of this result, we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones, and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.
作者机构：
[Song, Fei-fei] Henan Agr Univ, Dept Informat & Computat Sci, Zhengzhou 450002, Peoples R China.;[Hu, Zhi-quan] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
作者机构：
华中师范大学数学与统计学学院,武汉430079;Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, UMR 7352, CNRS, Université de Picardie Jules Verne, Amiens 80039, France;华中师范大学数学与统计学学院,武汉,430079;Laboratoire d'Analyse et de Mathématiques Appliquées, UMR 8050, CNRS, Université Paris-Est Créteil, Créteil 94010,France;深圳大学数学与统计学院,深圳518060
作者机构：
[Min Liu] College of Economics, Northwest University of Political Science and Law, Xi’an, Shaanxi, China;[Zhiquan Hu] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China
通讯机构：
[Min Liu] C;College of Economics, Northwest University of Political Science and Law, Xi’an, Shaanxi, China
摘要：
For a fixed graph $F$, a graph $G$ is $F$-saturated if it has no $F$ as a subgraph, but does contain $F$ after the addition of any new edge. The saturation number, sat$\left( {n,F} \right)$, is the minimum number of edges of a graph in the set of all $F$-saturated graphs with order $n$. In this paper, we determine the saturation number sat$\left( {n,2{P_3} \cup t{P_2}} \right)$ and characterize the extremal graphs for $n \ge 6t + 8$.
作者机构：
[Peng, Shuangjie; An, Xiaoming] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xie, Chaodong] Guizhou Univ Ethin Minor, Sch Econ Management, Guiyang 550025, Peoples R China.
通讯机构：
[Peng, Shuangjie] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Hardy-Littlewood-Sobolev inequality;achievability of a supremum;supercritical exponent
摘要：
In this paper, we prove that the supremum sup {integral(B)integral(B) vertical bar u(y)vertical bar(p(vertical bar y vertical bar))vertical bar u(x)vertical bar(p(vertical bar x vertical bar)) /vertical bar x - y vertical bar(mu) dxdy : u is an element of H-0,H- (1)(rad) (B), parallel to del u parallel to(L2(B)) = 1} is attained, where B denotes the unit ball in R-N (N >= 3), mu is an element of (0,N), p(r) = 2(mu)* + r(t), t is an element of (0, min{N/2 - mu/4, N - 2}) and 2(mu)* = (2N - mu)/(N - 2) is the critical exponent for the Hardy-Littlewood-Sobolev inequality.
作者机构：
[Qin, Hong; Jiang, Qin] Cent China Normal Univ, Dept Stat, Wuhan 430079, Hubei, Peoples R China.;[Jiang, Qin] Huanggang Normal Univ, Dept Math, Huanggang 438000, Peoples R China.;[Zhao, Hui] Zhongnan Univ Econ & Law, Dept Stat, Wuhan 430073, Hubei, Peoples R China.
通讯机构：
[Jiang, Qin] C;[Jiang, Qin] H;Cent China Normal Univ, Dept Stat, Wuhan 430079, Hubei, Peoples R China.;Huanggang Normal Univ, Dept Math, Huanggang 438000, Peoples R China.
关键词：
gap times;model checking;recurrent events;estimating equations;semiparametric model
摘要：
In the article, we investigate a general class of semiparametric hazards regression models for recurrent gap times. The general class includes the proportional hazards model, the accelerated failure time model and the accelerated hazards models as special cases. The model is flexible in modelling recurrent gap times since a covariate effect is identified as having two separate components, namely a time-scale change on hazard progression and a relative hazards ratio. In order to infer the model parameters, the procedure is proposed based on estimating equations. The asymptotic properties of the proposed estimators are established and the finite sample properties are investigated via simulation studies. In addition, a lack of fit test is presented to assess the adequacy of the model and an application of data from a bladder cancer study is reported for illustration.
作者机构：
Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China;University of Chinese Academy of Sciences, Beijing 100049, China;Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;[Rao Yongsheng] 广州大学
关键词：
web;Canvas;dynamic geometry;subject tools
摘要：
Dynamic geometry software, as a piece of computer-assisted instruction（CAI） software, is closely and deeply associated with mathematics, and is widely applied to mathematics teaching activities in primary and secondary schools. Meanwhile, web technology also has become an important technology for assisting education and teaching. This paper expounds a web-based dynamic geometry software development process, and analyses specific requirements regarding graphical application programming interface（API） required by dynamic geometry software. With experiments and comparison on the two different hypertext markup language（HTML）5 graphical API technologies, i.e., scalable vector graphics（SVG） and Canvas, on different apparatuses and browsers, we draw the conclusion that it is more suitable to adopt Canvas as the graphical API technology for the web-based dynamic geometry software, thus further proposed the principles and methods for an object-oriented Canvas design. The dynamic geometry software based on the newly-designed Canvas has technical advantages and educational value, well incorporating aesthetic education into mathematics education.
作者机构：
[Wang, Zheng-hong] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China.;[Qin, Hong; Wang, Zheng-hong] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Qin, Hong] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
作者机构：
[Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Lim, Meng Fai] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
关键词：
11R20;11R23;11R29;Iwasawa asymptotic class number formula;MH(G) -property;p-adic Lie extension
