作者机构：
[Qin, Hong; Ou, Zujun] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Ou, Zujun] Jishou Univ, Coll Math & Comp Sci, Jishou 416000, Peoples R China.;[Chatterjee, Kashinath] Visva Bharati Univ, Dept Stat, Santini Ketan, W Bengal, India.
通讯机构：
[Qin, Hong] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
The foldover is a useful technique in construction of two-level factorial designs. A foldover design is the follow-up experiment generated by reversing the sign(s) of one or more factors in the initial design. The full design obtained by joining the runs in the foldover design to those of the initial design is called the combined design. In this paper, some lower bounds of various discrepancies of combined designs, such as centered L 2-discrepancy, symmetric L 2-discrepancy and wrap-around L 2-discrepancy, under a general foldover plan are obtained, which can be used as a benchmark for searching optimal foldover plans. Our results provide a theoretical justification for optimal foldover plans in terms of uniformity criterion. KeywordsDiscrepancy–Combined design–Lower bound–Optimal foldover plan–Uniformity
摘要：
In this paper, we prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: -Delta u = vertical bar u vertical bar(2)*(-2)u + g(u) in Omega, partial derivative u/partial derivative nu = 0 on partial derivative Omega, where Omega is a bounded domain in R-N with C-3 boundary, N >= 3, nu is the outward unit normal of partial derivative Omega, 2* = 2N/N-2, and g(t) = mu vertical bar t vertical bar(p-2)t - t, or g(t) = mu t, where p is an element of (2, 2*), mu > 0 are constants. We obtain the existence of infinitely many solutions under certain assumptions on N, p and partial derivative Omega. In particular, if g(t) = mu t with mu > 0, N >= 7, and Omega is a strictly convex domain, then the problem has infinitely many solutions. (C) 2011 Published by Elsevier Inc.
作者机构：
[Zhu, Chang Jiang; Yao, Lei] Cent China Normal Univ, Lab Nonlinear Anal, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Zhu, Chang Jiang] C;Cent China Normal Univ, Lab Nonlinear Anal, Dept Math, Wuhan 430079, Peoples R China.
摘要：
In this paper, we study a two-phase liquid-gas model with constant viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. Just as in Evje and Karlsen (Commun Pure Appl Anal 8:1867-1894, 2009) and Evje et al. (Nonlinear Anal 70:3864-3886, 2009), the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We use a new technique to get the upper and lower bounds of gas and liquid masses n and m. Then we get the global existence of weak solution by the line method. Also, we obtain the uniqueness of the weak solution.
摘要：
This paper presents an extension of the work of Yue and Chatterjee (2010) about U-type designs for Bayesian nonparametric response prediction. We consider nonparametric Bayesian regression model with p responses. We use U-type designs with n runs, m factors and q levels for the nonparametric multiresponse prediction based on the asymptotic Bayesian criterion. A lower bound for the proposed criterion is established, and some optimal and nearly optimal designs for the illustrative models are given. (C) 2011 Elsevier B.V. All rights reserved.
作者机构：
[Zhou, Zhen-Rong] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Zhou, Zhen-Rong] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
An F-stationary map is a critical point of the F-energy with respect to variations in the domain. It is a generalization of F-harmonic maps. In [11;we discuss the theorems of Liouville type and the monotonicity of F-stationary maps. In this paper;we discuss the stabilities of F-stationary maps from submanifolds of spheres and the Euclidean spaces. Published: June 2011 First available in Project Euclid: 5 July 2011 zbMATH: 1242.53078 MathSciNet: MR2811644 Digital Object Identifier: 10.2996/kmj/1309829550
摘要：
An F-stationary map is a critical point of the F-energy with respect to variations in the domain. It is a generalization of F-harmonic maps. In [11, 10], we discuss the theorems of Liouville type and the monotonicity of F-stationary maps. In this paper, we discuss the stabilities of F-stationary maps from submanifolds of spheres and the Euclidean spaces.
摘要：
Moderation analyses are widely used in biomedical and psychosocial research to investigate differential treatment effects, with moderators frequently identified through testing the significance of the interaction between the predictor and the potential moderator under strong parametric assumptions. Without imposing any parametric forms on how the moderators may affect the relationship between predictors and responses, varying coefficient models address this fundamental problem of strong parametric assumptions with the current practice of moderation analysis and provide a much broader class of models for complex moderation relationships. Local polynomial, especially local linear (LL), methods are commonly used in estimating the varying coefficient models. Recently, a double-smoothing (DS) LL method has been proposed for nonparametric regression models, with nice properties compared to LL and local cubic (LC) methods. In this paper, we generalise DS to varying coefficient models, and show that it holds similar advantages over LL and LC methods.
