关键词：
Global analysis;hyperbolic-parabolic system;decay rate;convex entropy
摘要：
We investigate a model arising from biology, which is a hyperbolic-parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the H
s
∩ L
1-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L
2 decay rate of the solution and the almost optimal L
2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.
作者机构：
School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430000, China;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079 China
摘要：
In view of the existing situation of graduates' education, this essay analyzes several problems such as the weak supervisor force, the lack of academic atmosphere, the low level in management and the decline of graduates' quality, in the light of which, it raises a fundamental principle of cultivating graduates "double-core education, two-way development" That is to educate creative specialized talents with scientific research capacity as the core and comprehensive inter-disciplinary elites with the core of professional skills.With further and detailed study, it comes to a conclusion that scientific research capacity is oriented around professional ability which is based on the former one in reverse.
期刊：
Journal of Scientific Computing,2013年56(1):1-13 ISSN：0885-7474
通讯作者：
Tang, Tao
作者机构：
[Tang, Tao] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China.;[Xie, Hehu] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC,NCMIS, Beijing 100190, Peoples R China.;[Yin, Xiaobo] Cental China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Tang, Tao] H;Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China.
摘要：
It has been demonstrated that spectral deferred correction (SDC) methods can achieve arbitrary high order accuracy and possess good stability properties. There have been some recent interests in using high-order Runge-Kutta methods in the prediction and correction steps in the SDC methods, and higher order rate of convergence is obtained provided that the quadrature nodes are uniform. The assumption of the use of uniform mesh has a serious practical drawback as the well-known Runge phenomenon may prevent the use of reasonably large number of quadrature nodes. In this work, we propose a modified SDC methods with high-order integrators which can yield higher convergence rates on both uniform and non-uniform quadrature nodes. The expected high-order of accuracy is theoretically verified and numerically demonstrated.
摘要：
In this paper, we study a nonlinear Schrodinger equations with magnetic potentials in R-N involving subcritical growth. Under some decaying and weak symmetry conditions of both electric and magnetic potentials, we prove that the equation has infinitely many nonradial complex-valued solutions by applying the finite reduction method. (C) 2013 AIP Publishing LLC.
关键词：
Coordinated charging;load variance;microgrid;plug-in hybrid electric vehicle (EV) (HEV) (PHEV);regulated charging;smart grid;vehicle to grid (V2G)
摘要：
With the advent of the plug-in hybrid electric vehicles (PHEVs), the vehicle-to-grid (V2G) technology is attracting increasing attention recently. It is believed that the V2G option can aid to improve the efficiency and reliability of the power grid, as well as reduce overall cost and carbon emission. In this paper, the possibility of smoothing out the load variance in a household microgrid by regulating the charging patterns of family PHEVs is investigated. First, the mathematic model of the problem is built up. Then, the case study is conducted, which demonstrates that, by regulating the charging profiles of the PHEVs, the variance of load power can be dramatically reduced. Third, the energy losses and the subsidy mechanism are discussed. Finally, the impacts of the requested net charging quantities and the battery capacity of PHEVs on the performance of the regulated charging are investigated.
期刊：
Journal of Differential Equations,2013年254(10):4109-4121 ISSN：0022-0396
通讯作者：
Yan, Guozheng
作者机构：
[Yan, Guozheng; Guo, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yan, Guozheng] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Maxwell equations;Scattering problem;Boundary integral equations
摘要：
In this paper we consider the scattering of time-harmonic electromagnetic plane waves by an impenetrable obstacle which is embedded in a piecewise homogeneous medium. Applying potential theory, the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of the solution to the system by using the generalized Girding inequality and the Fredholm theory. (C) 2013 Elsevier Inc. All rights reserved.
期刊：
Computational and Mathematical Methods in Medicine,2013年2013(2):469373:1-469373:9 ISSN：1748-6718
通讯作者：
Li, Gang
作者机构：
[Fang, Kai-Tai] Hong Kong Baptist Univ, Beijing Normal Univ, United Int Coll, Zhuhai 519085, Peoples R China.;[Li, Gang; Lu, Xuyang] Univ Calif Los Angeles, Sch Publ Hlth, Dept Biostat, Los Angeles, CA 90095 USA.;[Qin, Hong] Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gang] U;Univ Calif Los Angeles, Sch Publ Hlth, Dept Biostat, Los Angeles, CA 90095 USA.
期刊：
Journal of Probability and Statistics,2013年2013(309) ISSN：1687-952X
通讯作者：
Tian, G.-L.
作者机构：
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China;School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China;Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong
通讯机构：
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong
摘要：
Let G be a 2-edge-connected simple graph, and let A denote an abelian group with the identity element 0. If a graph G
* is obtained by repeatedly contracting nontrivial A-connected subgraphs of G until no such a subgraph left, we say G can be A-reduced to G*. A graph G is bridged if every cycle of length at least 4 has two vertices x, y such that d
G
(x, y) < d
C
(x, y). In this paper, we investigate the group connectivity number Λ
g
(G) = min{n: G is A-connected for every abelian group with |A| ≥ n} for bridged graphs. Our results extend the early theorems for chordal graphs by Lai (Graphs Comb 16:165–176, 2000) and Chen et al. (Ars Comb 88:217–227, 2008).
期刊：
Journal of Applied Mathematics,2013年2013:192732:1-192732:11 ISSN：1110-757X
通讯作者：
Xiang, Zhong-Qi
作者机构：
[Xiang, Zhong-Qi; Xiang, ZQ] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Xiang, Zhong-Qi] C;Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
关键词：
We introduce the modular continuous g-Riesz basis to improve one existing result for continuous g-Riesz basis in Hilbert C* -modules;and then we study the equivalency relations between continuous g-frames in Hilbert C* -modules;and;in particular;we obtain two necessary and sufficient conditions under which two continuous g-frames are similar. Finally;we generalize a stability result for alternate duals of g-frames in Hilbert spaces to alternate duals of continuous g-frames in Hilbert C* -modules. Published: 2013 First available in Project Euclid: 14 March 2014 zbMATH: 06950546 MathSciNet: MR3108947 Digital Object Identifier: 10.1155/2013/192732
摘要：
We introduce the modular continuous g-Riesz basis to improve one existing result for continuous g-Riesz basis in Hilbert C* -modules, and then we study the equivalency relations between continuous g-frames in Hilbert C* -modules, and, in particular, we obtain two necessary and sufficient conditions under which two continuous g-frames are similar. Finally, we generalize a stability result for alternate duals of g-frames in Hilbert spaces to alternate duals of continuous g-frames in Hilbert C* -modules.
作者机构：
School of Mathematics, Yunnan Normal University, Kunming 650092, China;Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China;Department of Mathematics, Central China Normal University, Wuhan 430079, China
通讯机构：
Department of Mathematics, Shanghai Jiao Tong University, China
关键词：
Measure of non compactness;Mild solutions;Nonlinear evolution equations
期刊：
Abstract and Applied Analysis,2013年2013(SI44):1-11 ISSN：1085-3375
通讯作者：
Zhang, Weipeng
作者机构：
[Zhang, Weipeng; Li, Xiaodong] NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China.;[Geng, Fengjie] China Univ Geosci, Sch Informat Engn, Beijing 100083, Peoples R China.;[Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Zhang, Weipeng] N;NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China.
关键词：
The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally;the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover;the methods adopted in this paper can be extended to a higher dimensional system. Published: 2013 First available in Project Euclid: 26 February 2014 zbMATH: 1280.37050 MathSciNet: MR3055977 Digital Object Identifier: 10.1155/2013/152518
摘要：
The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system.
