摘要：
In this short note, we study the asymptotic property of Huisken's functional for mean curvature flow on the minimal submanifolds of Euclidean space. We prove that the limit of Huisken's functional equals to the extrinsic asymptotic volume ratio on the minimal submanifold of Euclidean space. (C) 2013 Elsevier Inc. All rights reserved.
期刊：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2013年141(8):2859-2868 ISSN：0002-9939
通讯作者：
Cheng, Liang
作者机构：
[Cheng, Liang] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhu, Anqiang] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
通讯机构：
[Cheng, Liang] H;Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Ricci flow;weighted forward reduced volume;Type III singularities;gradient expanding soliton
摘要：
In this paper, we introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which is related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone nonincreasing under Ricci flow. Moreover, we show that, just the same as Perelman's reduced volume, the weighted reduced volume entropy has the value $(4\mathrm{\pi }{)}^{\frac{\mathrm{n}}{2}}$ if and only if the Ricci flow is the trivial flow on flat Euclidean space.
作者机构：
[Yan, Ting] Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.;[Xu, Jinfeng] NYU, Div Biostat, Dept Populat Hlth, Sch Med, New York, NY 10016 USA.
通讯机构：
[Yan, Ting] C;Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.
关键词：
beta-model;Central limit theorem;Fisher information matrix
摘要：
Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β-model for undirected random graphs when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we prove asymptotic normality of the maximum likelihood estimator under mild conditions. Simulation studies and a data example illustrate the theoretical results.
期刊：
Advances in Mathematics,2013年242:187-208 ISSN：0001-8708
通讯作者：
He, Xing-Gang
作者机构：
[Dai, Xin-Rong] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China.;[He, Xing-Gang] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.;[Lai, Chun-Kit] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada.
通讯机构：
[He, Xing-Gang] C;Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Cantor measures;Spectral measures;Spectra;Trees
摘要：
We consider equally-weighted Cantor measures mu(q,b) arising from iterated function systems of the form b(-1)(x + i), i = 0, 1, ..., q - 1, where q < b. We classify the (q, b) so that they have infinitely many mutually orthogonal exponentials in L-2(mu(q,b)). In particular, if q divides b, the measures have a complete orthogonal exponential system and hence spectral measures. Improving the construction by Dutkay et al. (2009) [3], we characterize all the maximal orthogonal sets Lambda when q divides b via a maximal mapping on the q-adic tree in which all elements in Lambda are represented uniquely in finite b-adic expansions and we can separate the maximal orthogonal sets into two types: regular and irregular sets. For a regular maximal orthogonal set, we show that its completeness in L-2(mu(q,b)) is crucially determined by the certain growth rate of non-zero digits in the tail of the b-adic expansions of the elements. Furthermore, we exhibit complete orthogonal exponentials with zero Beurling dimensions. These examples show that the technical condition in Theorem 3.5 of Dutkay et al. (2011) [4] cannot be removed. For an irregular maximal orthogonal set, we show that under some conditions, its completeness is equivalent to that of the corresponding regularized mapping. (C) 2013 Elsevier Inc. All rights reserved.
期刊：
SIAM JOURNAL ON DISCRETE MATHEMATICS,2013年27(2):597-618 ISSN：0895-4801
通讯作者：
Law, Ka Ho
作者机构：
[Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Law, Ka Ho; Zang, Wenan] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.
通讯机构：
[Law, Ka Ho] U;Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.
摘要：
Let G = (V-1, V-2, E) be a balanced bipartite graph with 2n vertices. The bipartite binding number of G, denoted by B(G), is defined to be n if G = K-n,K-n and min(i is an element of {1,2}) min (empty set not equal S subset of Vi vertical bar N(S)vertical bar < n) vertical bar N(S)vertical bar/vertical bar S vertical bar otherwise. We call G bipancyclic if it contains a cycle of every even length m for 4 <= m <= 2n. The purpose of this paper is to show that if B(G) > 3/2 and n >= 139, then G is bipancyclic; the bound 3/2 is best possible in the sense that there exist infinitely many balanced bipartite graphs G that have B(G) = 3/2 but are not Hamiltonian.
期刊：
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA,2013年38(1):515-534 ISSN：1239-629X
通讯作者：
Li, Gongbao
作者机构：
[Li, Gongbao; Ye, Hongyu] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Cohomological index;Fountain theorem over cones;Infinitely many solutions;p-Laplace equation
摘要：
In this paper, we study the existence of infinitely many solutions to the following quasilinear equation of p-Laplacian type in R-N (0.1) -Delta(p)u + vertical bar u vertical bar(p-2)u = lambda V(x)vertical bar u vertical bar(p-2)u + g(x,u), u is an element of W-1,W-p(R-N) with sign-changing radially symmetric potential V(x), where 1 < p < N, lambda is an element of R and Delta(p)u = div(vertical bar Du vertical bar(p-2) Du) is the p-Laplacian operator, g(x,u) is an element of C(R-N x R, R) is subcritical and p-superlinear at 0 as well as at infinity. We prove that under certain assumptions on the potential V and the nonlinearity g, for any lambda is an element of R, the problem (0.1) has infinitely many solutions by using a fountain theorem over cones under Cerami condition. A minimax approach, allowing an estimate of the corresponding critical level, is used. New linking structures, associated to certain variational eigenvalues of -Delta(p)u + vertical bar u vertical bar(p-2)u = lambda V(x)vertical bar u vertical bar(p-2)u are recognized, even in absence of any direct sum decomposition of W-1,W-p(R-N) related to the eigenvalue itself. Our main result can be viewed as an extension to a recent result of Degiovanni and Lancelotti in [10] concerning the existence of nontrivial solutions for the quasilinear elliptic problem: (0.2) {-Delta(p)u = lambda V(x)vertical bar u vertical bar(p-2)u + g(x,u), in Omega, u = 0, on partial derivative Omega, where Omega subset of R-N is a bounded open domain.
期刊：
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY,2013年155(1):73-86 ISSN：0305-0041
通讯作者：
Lau, Ka-Sing
作者机构：
[Lau, Ka-Sing] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.;[Luo, Jun Jason] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China.;[Rao, Hui] Hua Zhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Lau, Ka-Sing] C;Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.
摘要：
Given an integer $n\geq 2$ and a digit set ${\mathcal D}\subsetneq {0,1,...,n-1}^2$, there is a self-similar set $F \subset {\Bbb R}^2$ satisfying the set equation: $F=(F+{\mathcal D})/n$. We call such $F$ a fractal square. By studying a periodic extension $H= F+ {\mathbb Z}^2$, we classify $F$ into three types according to their topological properties. We also provide some simple criteria for such classification.
摘要：
The blow-up behavior of the solution to a semilinear equation with critical exponent {u(t) = Delta u + vertical bar u vertical bar(p-1)u in Omega x (0, T), u = 0 on partial derivative Omega x (0, T), u(., 0) = u0 on Omega is established. We obtain that if Omega is star-shaped about a is an element of Omega and n >= 3, p = n+2/n-2, then lim(t -> T)(T - t)(beta)u(a + y root T - t, t) exists and equals 0 or +/-kappa in L-loc(2) (R-n), where beta = 1/p-1, kappa = beta(beta) . (C) 2013 Elsevier Inc. All rights reserved.
期刊：
Journal of Function Spaces and Applications,2013年 ISSN：2090-8997
通讯作者：
Li, F
作者机构：
[Li, Fang; Wang, Huiwen] Yunnan Normal Univ, Sch Math, Kunming 650092, Peoples R China.;[Zhang, Jun] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Li, F ] ;Yunnan Normal Univ, Sch Math, Kunming 650092, Peoples R China.
摘要：
We obtain the multiplicative perturbation theorems for convoluted C-cosine functions (resp., convoluted C-semigroups) and n-times integrated C-cosine functions ( resp., n-times integrated C-semigroups) for n is an element of N. Moreover, we obtain some new results for perturbations on C-cosine functions ( resp., C-semigroups). Some examples are presented.
期刊：
Statistics & Probability Letters,2013年83(9):2060-2066 ISSN：0167-7152
通讯作者：
Xie, Minyu
作者机构：
[Xie, Minyu; Chen, Wangxue; Wu, Ming] Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Xie, Minyu] C;Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Ranked set sample;Moving extremes ranked set sampling;Maximum likelihood estimator
摘要：
A modification of ranked set sampling (RSS) called moving extremes ranked set sampling (MERSS) is considered for the estimation of the scale parameter of scale distributions. A maximum likelihood estimator (MLE) is studied and its properties are obtained. We prove the MLE is an equivariant estimator under scale transformation. In order to give more insight into the performance of MERSS with respect to (w.r.t.) simple random sampling (SRS), the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for some usual scale distributions. The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS, when the same sample size is used. (C) 2013 Elsevier B.V. All rights reserved.
期刊：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2013年23(10):1350164 ISSN：0218-1274
通讯作者：
Huang, Jicai
作者机构：
[Gong, Yijun; Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Chen, Jing] Univ Miami, Dept Math, Coral Gables, FL 33124 USA.
通讯机构：
[Huang, Jicai] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Predator–prey system of Holling and Leslie type;constant-yield harvesting;cusp of codimension at least 4;Hopf bifurcation;Bogdanov–Takens bifurcations of codimensions 2 and 3
摘要：
The bifurcation analysis of a predator–prey system of Holling and Leslie type with constant-yield prey harvesting is carried out in this paper. It is shown that the model has a Bogdanov–Takens singularity (cusp case) of codimension at least 4 for some parameter values. Various kinds of bifurcations, such as saddle-node bifurcation, Hopf bifurcation, repelling and attracting Bogdanov–Takens bifurcations of codimensions 2 and 3, are also shown in the model as parameters vary. Hence, there are different parameter values for which the model has a limit cycle, a homoclinic loop, two limit cycles, or a limit cycle coexisting with a homoclinic loop. These results present far richer dynamics compared to the model with no harvesting. Numerical simulations, including the repelling and attracting Bogdanov–Takens bifurcation diagrams and corresponding phase portraits, and the existence of two limit cycles or an unstable limit cycle enclosing a stable multiple focus with multiplicity one, are also given to support the theoretical analysis.
作者机构：
[He, Sui; Wang, Fen] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Sun, Liu-quan] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China.
通讯机构：
[Sun, Liu-quan] C;Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China.
关键词：
additive rates;clustered failure time data;estimating equation;marginal model;recurrent events
摘要：
Recurrent event data often arises in biomedical studies, and individuals within a cluster might not be independent. We propose a semiparametric additive rates model for clustered recurrent event data, wherein the covariates are assumed to add to the unspecified baseline rate. For the inference on the model parameters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established.
作者机构：
[Wang, Chengyong] Hubei Univ Arts & Sci, Sch Math & Comp Sci, Xiangyang 441053, Peoples R China.;[Li, Shuchao; Yan, Lixia] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yan, Lixia] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. Let J(n)(g) is be the class of all n-vertex tricyclic graphs with girth g. This paper determines the unique graph with the maximal Laplacian spectral radius among all graphs in J(n)(g) with exactly three (resp. four) cycles. Furthermore, the upper bound of the Laplacian spectral radius and the extremal graph in J(n)(g) are also obtained, where g is even.
