摘要：
In this paper, we investigate large amplitude solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells. For the Cauchy problem and initial-boundary value problem, the global unique solvability is proved based on the energy method. In particular, our main purpose is to investigate the convergence rates as the diffusion parameter $\varepsilon$ goes to zero. It is shown that the convergence rates in $L^\infty$-norm are of the order $O\left(\varepsilon\right)$ and $O(\varepsilon^{1/2})$ corresponding to the Cauchy problem and the initial-boundary value problem respectively.
期刊：
Abstract and Applied Analysis,2012年2012:1-15 ISSN：1085-3375
通讯作者：
Xiao, Ti-Jun
作者机构：
[Zhang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Xiao, Ti-Jun] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China.;[Liang, Jin] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China.
通讯机构：
[Xiao, Ti-Jun] F;Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China.
关键词：
We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover;we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x ′ ( t ) = A x ( t ) + f ( t;x ( t ) );t ∈ \Bbb R;where A is the infinitesimal generator of an exponentially stable C 0 -semigroup. An application is also given to illustrate the abstract existence theorem. Published: 2012 First available in Project Euclid: 14 December 2012 zbMATH: 1244.34083 MathSciNet: MR2903805 Digital Object Identifier: 10.1155/2012/179525
期刊：
Journal of Statistical Planning and Inference,2012年142(5):1170-1177 ISSN：0378-3758
通讯作者：
Qin, Hong
作者机构：
[Qin, Hong; Wang, Zhenghong] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Chatterjee, Kashinath] Visva Bharati Univ, Dept Stat, Santini Ketan, W Bengal, India.;[Wang, Zhenghong] S Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.
通讯机构：
[Qin, Hong] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
General minimum aberration;Lower bound;Minimum moment aberration;Minimum uniformity aberration;Orthogonality;Projection discrepancy
摘要：
The objective of this paper is to study the issue of the projection discrepancy along the line of Liu (2002) and Fang and Qin (2005) based on discrete discrepancy measure proposed in Qin and Fang (2004), which has wide application to the field of fractional factorials. Here we also study the projection properties for q-level factorials and provide connection between minimum projection uniformity and other optimality criteria. A lower bound to projection discrepancy for q-level factorials is presented here. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.
摘要：
In this paper, we consider two classes of free boundary value problems of a viscous two-phase liquid-gas model relevant to the flow in wells and pipelines with mass-dependent viscosity coefficient. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. We obtain the asymptotic behavior and decay rates of the mass functions n(x, t), m(x, t) when the initial masses are assumed to be connected to vacuum both discontinuously and continuously, which improves the corresponding result about Navier-Stokes equations in Zhu (2010) [23]. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.
期刊：
Journal of Algebra,2012年355(1):80-92 ISSN：0021-8693
通讯作者：
Fan, Yun
作者机构：
[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Jin, Ping] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China.
通讯机构：
[Fan, Yun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
A module of a finite group over a finite field with a symmetric non-degenerate bilinear form which is invariant by the group action is called a symmetric module. In this paper, a characterization of indecomposable orthogonal decompositions of symmetric semisimple modules and a criterion for the hyperbolic symmetric modules are obtained, and some applications to the self-dual permutation codes are shown. (C) 2012 Elsevier Inc. All rights reserved.
作者机构：
华中师范大学数学与统计学学院,武汉430079 武汉工业学院数学与计算机学院,武汉430023;[刘春苔] Department of Mathematics Central China Normal University, Wuhan 430079, China, School of Mathematics and Computer Science Wuhan Polytechnic University, Wuhan 430023, China
通讯机构：
[Liu, C.] D;Department of Mathematics Central China Normal University, Wuhan 430079, China
摘要：
In this paper, we introduce three new classes of open sets in a general Euclidean space RN. It is shown that every class of open sets is compact under the Hausdorff distance. The result is then applied to a shape optimization problem of elliptic equation. The existence of the optimal solution is presented.
关键词：
Asymptotic distribution;empirical likelihood;partially linear single-index model;zero finite-order serial correlation
摘要：
The purpose of this paper is to test the underlying serial correlation in a partially linear single-index model. Under mild conditions, the proposed test statistics are shown to have standard chi-squared distribution asymptotically when there is no serial correlation in the error terms. To illustrate their finite sample properties, simulation experiments, as well as a real data example, are also provided. It is revealed that the finite sample performances of the proposed test statistics are satisfactory in terms of both estimated sizes and powers
作者机构：
[PENG Xiaojuan] School of Mathematics and Statistics, Central China Normal University, Wuhan, China;[LIU Yunxiao] Department of Mathematics, University of California San Diego, 9500, Gilman Dr, La Jolla, CA, United States
通讯机构：
School of Mathematics and Statistics, Central China Normal University, China
会议名称：
第七届科学计量学与大学评价国际研讨会
会议时间：
2012-10-27
会议地点：
武汉
会议论文集名称：
第七届科学计量学与大学评价国际研讨会论文集
关键词：
Information analysis;Operations research;Receiver operating characteristic curve;Statistical method
摘要：
A new and simple method is created to realize the analysis and cooperation of receiver operating characteristic (ROC) curves. Taking advantages of the cells' function in Excel, The formula of ROC curve analysis can be partitioned into a number of intermediate results and reasonably arranged in the cells of each worksheet. Eventually the calculation results of the formula, the ROC curve, statistical analysis and comparative judgments can be obtained ignoring any statistical formulas and commands via the new method. The ROC curve analysis and statistical conclusions can get immediately.
期刊：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2012年97(3):204-229 ISSN：0021-7824
通讯作者：
Zhu, Changjiang
作者机构：
[Wen, Huanyao; Zhu, Changjiang] Cent China Normal Univ, Hubei Key Lab Math Phys, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yao, Lei] Northwest Univ, Dept Math, Xian 710127, Peoples R China.;[Wen, Huanyao] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China.
通讯机构：
[Zhu, Changjiang] C;Cent China Normal Univ, Hubei Key Lab Math Phys, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, we get a unique local strong solution to a 3D viscous liquid–gas two-phase flow model in a smooth bounded domain. Besides, a blow-up criterion of the strong solution for 253μ>λ is obtained. The method can be applied to study a blow-up criterion of the strong solution to Navier–Stokes equations for 253μ>λ, which improves the corresponding result about Navier–Stokes equations in Sun et al. (2011) [15] where 7μ>λ. Moreover, all the results permit the appearance of vacuum.
Dans cet article, on démontre lʼexistence dʼune solution classique tridimensionelle pour un modèle dʼécoulement visqueux diphasique (liquide–gaz) dans un domaine borné et régulier. De plus, on établit un critère dʼexplosion de la solution lorsque 253μ>λ. La même méthode sʼapplique pour établir lʼexplosion de solution classique des équations de Navier–Stokes lorsque 253μ>λ, ce qui améliore le résultat correspondant obtenu dans Sun et al. (2011) [15] où lʼexplosion est établie pour 7μ>λ. Enfin, tous les résultats restent valables en présence de vide.
