摘要：
We consider the reduced-gravity two-and-a-half model in oceanic fluid dynamics, and prove the stability of weak solutions in periodic domain Omega = T(2). The proof is based on the uniform a priori estimates and the method of weak convergence, and the limit is carried out with the help of a new higher regularity estimate of the velocity, which is derived by constructing a special test function. (C) 2012 Elsevier Inc. All rights reserved.
作者：
CAO Li1, HE Xinggang2 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072 , Hubei, China;2. College of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China
作者机构：
[Li Cao] School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China;[Xinggang He] College of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China
通讯机构：
[Li Cao] S;School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China
摘要：
In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the technique of Moran set, the Hausdorff, packing, and upper box dimensions of the Moran-Sierpinski gasket are given. The dimensional results of the Sierpinski gasket can be seen as a special case of this paper.
期刊：
Journal of Geometry and Physics,2012年62(10):1999-2008 ISSN：0393-0440
通讯作者：
Chen, Yongfa
作者机构：
[Chen, Yongfa] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Xu, Xu] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
通讯机构：
[Chen, Yongfa] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, we get optimal lower bounds for the eigenvalues of the Dirac–Witten operator. These estimates are given in terms of the intrinsic and extrinsic curvature expressions. In the limiting case, we prove that the spacelike submanifold is Einstein if the normal bundle is flat.
期刊：
Journal of Mathematical Physics,2012年53(10):103703 ISSN：0022-2488
通讯作者：
Yin, Haiyan
作者机构：
[Yin, Haiyan; Ruan, Lizhi] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Yin, Haiyan] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China.
关键词：
convergence;damping;diffusion;hyperbolic equations;initial value problems;nonlinear equations
摘要：
The aim of this paper is to study the global unique solvability on C-infinity-solution to the Cauchy problem of a special 2 x 2 nonlinear hyperbolic system with damping and diffusion. Furthermore, we also investigate the convergence rates as the diffusion parameter beta goes to zero. It is shown that the convergence rates in C-infinity-norm is of the order O(beta). The novelty of analysis taken in the present article is to obtain the uniform-in-beta a priori estimates on H-s-norm for any s is an element of N, which are implemented by introducing induction. We focus on two cases in this paper: both alpha = beta and alpha not equal beta since the uniform-in-beta a priori estimates obtained are distinctly different for different cases. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4751283]
摘要：
Given an n-vertex graph G, the matrix Omega(G) = (I-n + L(G))(-1) = (omega(ij)) is called the doubly stochastic graph matrix of G, where I-n is the n x n identity matrix and L(G) is the Laplacian matrix of G. Let omega(G) be the smallest element of Omega(G). Zhang and Wu [X.D. Zhang and J.X. Wu. Doubly stochastic matrices of trees. Appl. Math. Lett., 18:339-343, 2005.] determined the tree T with the minimum omega(T) among all the n-vertex trees. In this paper, as a continuance of the Zhang and Wu's work, we determine the first. inverted left perepndiculern-1/2inverted right perpendicular trees T-1, T-2, ... Tinverted left perpendicularn-1/2inverted right perpendicular such that omega(T-1) < omega(T-2) < ... < omega (Tleft perpendicularn-1/2right perpendicular) <= omega(Tinverted left perpendicularn-1/2inverted right perpendicular) < omega(T), where T-i is obtained by attaching a pendant vertex to v(i) of path Pn-1 = v(1)v(2) ... v(i) ... v(n-1) and T is an n-vertex tree different from the trees T-1, T-2, ... T vertical bar n-1/2 vertical bar
期刊：
Industrial Engineering and Management Systems,2012年11(1):18-25 ISSN：1598-7248
作者机构：
[Bo Zhang] School of Mathematics and Statistics, Huazhong Normal University;[Jin Peng] Institute of Uncertain Systems, Huanggang Normal University
关键词：
Chinese Postman Problem;Uncertainty Theory;Uncertain Programming
摘要：
IChinese postman problem is one of the classical combinatorial optimization problems with many applications. However, in application, some uncertain factors are frequently encountered. This paper employs uncertain programming to deal with Chinese postman problem with uncertain weight Within the framework of uncertainty theory, the concepts of expected shortest route, ${\alpha}$-shortest route, and distribution shortest route are proposed. After that, expected shortest model, and ${\alpha}$-shortest model are constructed. Taking advantage of properties of uncertainty theory, these models can be transf-ormed into their corresponding deterministic forms, which can be solved by classical algorithm..
摘要：
In this paper, we are concerned with the following nonlinear Schrodinger equations with inverse square potential and critical Sobolev exponent -Delta u - mu u/vertical bar x vertical bar(2) + a(x)u = vertical bar u vertical bar(2)*(-2)u + f(x, u), u is an element of H-1(R-N), (P) where 2* = 2N/(N - 2) is the critical Sobolev exponent, 0 <= mu < <(mu)over bar> := (N-2)(2)/4, a(x) is an element of C(R-N). We first give a representation to the Palais-Smale sequence related to (P) and then obtain an existence result of positive solutions of (P). Our assumptions on a(x) and f(x, u) are weaker than the known cases even if mu = 0. (C) 2012 Elsevier Inc. All rights reserved.
作者机构：
[Zhao, Hui] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Jiang, Ningning] Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China.
通讯机构：
[Zhao, Hui] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Current status data;nonparametric maximum likelihood estimation;success-failure life test
摘要：
Success-failure life tests are widely used in reliability engineering research to evaluate the storage life of products, where the observed data are the current status data, usually summarized as the form of "binomial life data". For this type of data, this paper proposes a two-stage algorithm to estimate some commonly used lifetime distributions. This algorithm is automatic, intuitively appealing and simple to implement. Simulation studies show that compared with some existing methods, the proposed algorithm is more stable and efficient, especially in small sample situations, and it can also be extended to deal with some complicated lifetime distributions.
