摘要：
In this paper, we get a blow-up criterion for the strong solutions to the 3D viscous liquid–gas two-phase flow model with vacuum. More precisely, we prove that the bound of Lt1Lx∞ norm of the deformation tensor of velocity gradient controls the possible breakdown of the strong solutions.
作者机构：
[Sun, Hao] Huazhong Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.;[Sun, Hao] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China.
通讯机构：
[Sun, Hao] H;Huazhong Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
摘要：
We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.
作者：
FAN Qiong1,2, QI Huan1 1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China;2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China
作者机构：
[Huan Qi] Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China;School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China;[Qiong Fan] Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China
通讯机构：
[Huan Qi] D;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China
关键词：
main eigenvalues;2-walk linear graph;path;cycle
摘要：
A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can estimate and characterize more 2-walk linear graphs that have exactly two main eigenvalues.
期刊：
Journal of Complexity,2012年28(2):224-237 ISSN：0885-064X
通讯作者：
Zhou, Yong-Dao
作者机构：
[Zhou, Yong-Dao] Sichuan Univ, Coll Math, Chengdu 610064, Peoples R China.;[Fang, Kai-Tai] BNU HKBU United Int Coll, Zhuhai 519085, Peoples R China.;[Fang, Kai-Tai] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China.;[Ning, Jian-Hui] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, the wrap-around L"2-discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs n is smaller than the number of all level-combinations m, the construction problem can be transferred to a zero-one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When n>=m, another algorithm is proposed. Empirical study shows that when n is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs. In this paper, the wrap-around L"2-discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs n is smaller than the number of all level-combinations m, the construction problem can be transferred to a zero-one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When n>=m, another algorithm is proposed. Empirical study shows that when n is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs.
作者机构：
[Jiang, Daijun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Feng, Hui] Wuhan Univ, Sch Math Sci, Wuhan 430072, Peoples R China.;[Zou, Jun] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China.
通讯机构：
[Jiang, Daijun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
We shall study the convergence rates of the Tikhonov regularizations for the identification of the diffusivity q(x) in a parabolic-elliptic system. The H~1 regularization and a mixed L~P-H~1 regularization are considered. For the H~1 regularization, we present a simple and easily interpretable source condition, under which the regularized solutions will be shown to converge at the standard rate in terms of the noise level of the data. The convergence is analyzed in three different approaches, which result in the same convergence rate but require quite different conditions on the measurement time and the identifying parameters. For the mixed L~P-H~1 regularization, we will achieve some desired convergence rate by using the Bregman distance and some new source condition and nonlinearity condition.
作者机构：
[Hu, Jianwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Runchu] NE Normal Univ, KLAS, Changchun 130024, Peoples R China.;[Zhang, Runchu] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China.;[Zhang, Runchu] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China.;[Zhang, Runchu] Nankai Univ, LPMC, Tianjin 300071, Peoples R China.
通讯机构：
[Hu, Jianwei] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
For two-level regular designs, we obtain the structures of Fisher information matrices for estimating main effects and two-factor interactions (2fi's). Based on these results, we propose the definition of minimal sufficient confounding information among main effects and 2fi's. As an application, we demonstrate that minimum aberration (MA) designs must be (M,S)-optimal designs for two-level regular designs. In addition, we show that sequentially minimizing M-(1,M-2)1, M-(2,M-2)2 and M-(2,M-2)1, as the core of the minimum M-aberration criterion proposed by Zhu and Zeng (2005), is equivalent to sequentially minimizing word length pattern A(3) and A(4). In particular, we show that sequentially minimizing A(3) and A(4) is equivalent to sequentially maximizing the first two components of the maximum estimation capacity, E-1(d) and E-2(d), defined in Cheng, Steinberg, and Sun (1999).
期刊：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2012年44(1):102-133 ISSN：0036-1410
通讯作者：
Zhu, Changjiang
作者机构：
[Duan, Renjun] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China.;[Liu, Qingqing; Zhu, Changjiang] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Zhu, Changjiang] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China.
关键词：
35Q35;35P20;bipolar Euler–Maxwell system;plasma physics;Euler equation with damping;time-decay rate
摘要：
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The global unique solvability is proved based on the energy method. In particular, our main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter $\beta$ goes to zero. We show that the boundary layer thickness is of the order $O\left(\beta^\gamma\right)$ with $0<\gamma<\frac{1}{2}$.
期刊：
Mathematical Methods in the Applied Sciences,2012年35(1):84-96 ISSN：0170-4214
通讯作者：
Yan, Guozheng
作者机构：
[Yan, Guozheng] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Ye, Jianguo] Kashigar Teachers Coll, Dept Math, Xinjiang, Peoples R China.
通讯机构：
[Yan, Guozheng] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Helmholtz equation;scattering problem;boundary integral equation
作者机构：
[Shen, Jing] Naval Univ Engn, Sch Sci, Wuhan 430033, Hubei, Peoples R China.;[Fan, Yun] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
会议名称：
IEEE 5th International Conference on Advanced Computational Intelligence (ICACI)
会议时间：
OCT 18-20, 2012
会议地点：
Nanjing, PEOPLES R CHINA
会议主办单位：
[Shen, Jing] Naval Univ Engn, Sch Sci, Wuhan 430033, Hubei, Peoples R China.^[Fan, Yun] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
摘要：
This paper exhibits a distinguishing algorithmic feature of a phase transition point of a random system I of m linear equations over a finite field with n variables: the complexity of Gaussian elimination for testing satisfiability of the systems approaches maximum at the satisfiability threshold point m/n = 1, and the worst instances should be found at the point. It is very interesting that the algorithm exactly undergoes an easy/hard transition at the satisfiability threshold point.
作者机构：
[Chen, Gang; Chen, G] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, Gang] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
character ring;induction theorem;p-elementary subgroups;characteristic class function
摘要：
Let G be a finite group, S a unitary subring of the complex number field ℂ and R(G) the character ring of G. Let π be the set of rational prime numbers whose inverses do not belong to S. Denote the family of all p-elementary subgroups of G by W(π), where p runs over π. It is proved that, in the sense of conjugation, W(π) is the least family of subgroups of G such that the S-linear map is surjective.
期刊：
Communications in Algebra,2012年40(4):1547-1562 ISSN：0092-7872
通讯作者：
Blau, Harvey I.
作者机构：
[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA.;[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Blau, Harvey I.] No Illinois Univ, Dept Math Sci, 1425 W Lincoln Hwy, De Kalb, IL 60115 USA.
通讯机构：
[Blau, Harvey I.] N;No Illinois Univ, Dept Math Sci, 1425 W Lincoln Hwy, De Kalb, IL 60115 USA.
期刊：
Ars Combinatoria,2012年107:141-160 ISSN：0381-7032
通讯作者：
Choie, YoungJu
作者机构：
[Choie, YoungJu] POSTECH, Dept Math, Pohang 790784, South Korea.;[Dougherty, Steven] Univ Scranton, Dept Math, Scranton, PA 18510 USA.;[Liu, Hongwei] Huazhong Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Choie, YoungJu] P;POSTECH, Dept Math, Pohang 790784, South Korea.
关键词：
Codes over rings;Hilbert modular form;Jacobi hilbert modular form;Polynomial ring;Totally real field
摘要：
In this paper, we study codes over polynomial rings and give a connection to Jacobi Hubert modular forms, in particular, Hubert modular forms over the totally real field via the complete weight enumerators of codes over polynomial rings.
