期刊：
Journal of Fourier Analysis and Applications,2012年18(5):954-971 ISSN：1069-5869
通讯作者：
Li, Hai-Xiong
作者机构：
[Li, Hai-Xiong; He, Xing-Gang] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.;[Li, Hai-Xiong] HuBei Univ Educ, Coll Math & Quantitat Econ, Wuhan 430205, Peoples R China.
通讯机构：
[Li, Hai-Xiong] C;Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Weyl-Heisenberg frames;Riesz bases;Frame window function set
摘要：
Let {e
2πimx
g(x−n)}
m,n∈ℤ be a Weyl-Heisenberg system and let g be the characteristic function of a union of two separated intervals. We systematically study the window function g such that the Weyl-Heisenberg system consists of a Riesz basis of L
2(ℝ).
期刊：
Journal of Mathematical Analysis and Applications,2012年390(1):99-112 ISSN：0022-247X
通讯作者：
Li, Shuchao
作者机构：
[Li, Shuchao; Zhang, Meng] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Yu, Guihai; Feng, Lihua] Shandong Inst Business & Technol, Sch Math, Yantai 264005, Shandong, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
Let G = (V-G, E-G) be a simple connected graph. The eccentric distance sum of G is defined as xi(d)(G) = Sigma(v is an element of VG) epsilon(G)(V)D-G(v) where epsilon(G)(V) is the eccentricity of the vertex v and D-G (v) = Sigma(u is an element of VG) d(u, v) is the sum of all distances from the vertex v. In this paper we first characterize the extremal trees among n-vertex conjugated trees (trees with a perfect matching) having the minimal and second minimal eccentric distance sums. Then we identify the trees with the minimal and second minimal eccentric distance sums among the n-vertex trees with matching number m. Finally, we characterize the extremal tree with the second minimal eccentric distance sum among the n-vertex trees of a given diameter. Consequently, we determine the trees with the third and fourth minimal eccentric distance sums among the n-vertex trees, which is a continuance study as the results in [G.H. Yu, L.H. Feng, A. Ili& On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl. 375 (2011) 99-107]. (C) 2012 Elsevier Inc. All rights reserved.
摘要：
In this paper, we introduce three new classes of open sets in a general Euclidean space $\mathbb{R}^N$. 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. In this paper, we introduce three new classes of open sets in a general Euclidean space $\mathbb{R}^N$. 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.
期刊：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES,2012年85(3):809-837 ISSN：0024-6107
通讯作者：
Puig, Lluis
作者机构：
[Puig, Lluis] CNRS, Inst Math Jussieu, F-94340 Joinville Le Pont, France.;[Zhou, Yuanyang] Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.;[Puig, Lluis] CNRS, Inst Math Jussieu, 6 Av Bizet, F-94340 Joinville Le Pont, France.
通讯机构：
[Puig, Lluis] C;CNRS, Inst Math Jussieu, 6 Av Bizet, F-94340 Joinville Le Pont, France.
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.
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
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.
