A note on the ellipticity of the single layer potential in two-dimensional linear elastostatics

We prove that the single layer potential operator of planar linear elastostatics is elliptic in [H^−1/2(Γ)]², if the domain Ω is scaled appropriately.     

On a sharpened form of the Leray-Lions' ellipticity criterion

The well-known ellipticity criterion of Leray-Lions for solvability of a nonlinear equation in divergence form is sharpened, eliminating any coercivity hypothesis, by using a remark on the asymptotic strong monotonicity of strictly monotone mappings in finite dimensional spaces, and extending the result to non-local mappings.     

On the use of piecewise linear models in nonlinear programming

This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming and sequential linear-quadratic programming methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian.     

On the estimation of prediction errors in linear regression models

Estimating the prediction error is a common practice in the statistical literature. Under a linear regression model, lete be the conditional prediction error andê be its estimate. We use (ê, e), the correlation coefficient betweene andê, to measure the performance of a particular estimation method. Reasons are given why correlation is chosen over the more popular mean squared error loss. The main results of this paper conclude that it is generally not possible to obtain good estimates of the prediction error. In particular, we show that (ê, e)=O(n ^–1/2) whenn . When the sample size is small, we argue that high values of (ê, e) can be achieved only when the residual error distribution has very heavy tails and when no outlier presents in the data. Finally, we show that in order for (ê, e) to be bounded away from zero asymptotically,ê has to be biased.     

On ellipticity of balance equations for atmospheric dynamics

Initial data for atmospheric multi-scale models need to be adjusted in order to ensure small amplitudes of high-frequency oscillations. Different adjustment methods lead to balance conditions in the form of time-independent partial differential systems with appropriate boundary conditions. One of the issues of such systems is a violation of the ellipticity conditions in a part of the problem domain. In this study we present the ellipticity conditions for balance equations based on diagnostic divergence relation with different levels of complexity and explore the existence of non-elliptic regions in the gridded fields of the atmospheric analysis data. It is shown that more physically justifiable balance equations are associated with much sparser and less intensive non-elliptic regions. The obtained results confirm Kasahara’s assumption that ellipticity conditions are violated in the actual atmospheric fields essentially due to approximations made under deriving balance equations.     

On estimating the hidden periodicities in linear time series models

In this paper the tollowing modelX(n)=sum from j=1 to p α_je~(inλj)+ξ_nis considered,where p,λ_1,λ_2,…,λ_p,are constants α=(α_1,α_2,…,α_p) is a random vector and {ξ_n;n=0,±1,±2,…} is a wide-sense stationary sequence with zero means.In [4],theorem about thestrong consistent estimates of λ_1,λ_2.…,λ_p and α are proved under the assumption that α is a constantvector and p and δ are known constants such that0<δ<(?){λ_i-λ_j}.The main purpose of the present paper is to prove theorems on the strong consistent estimates ofparameters p,λ_1,λ_2,…,λ_p and random vector α without knowing p and δ.Numerical examples arealso given to illustrate our method of estimation.     

On sparse estimation for semiparametric linear transformation models

Semiparametric linear transformation models have received much attention due to their high flexibility in modeling survival data. A useful estimating equation procedure was recently proposed by Chen et al. (2002) [21] for linear transformation models to jointly estimate parametric and nonparametric terms. They showed that this procedure can yield a consistent and robust estimator. However, the problem of variable selection for linear transformation models has been less studied, partially because a convenient loss function is not readily available under this context. In this paper, we propose a simple yet powerful approach to achieve both sparse and consistent estimation for linear transformation models. The main idea is to derive a profiled score from the estimating equation of Chen et al. [21], construct a loss function based on the profile scored and its variance, and then minimize the loss subject to some shrinkage penalty. Under regularity conditions, we have shown that the resulting estimator is consistent for both model estimation and variable selection. Furthermore, the estimated parametric terms are asymptotically normal and can achieve a higher efficiency than that yielded from the estimation equations. For computation, we suggest a one-step approximation algorithm which can take advantage of the LARS and build the entire solution path efficiently. Performance of the new procedure is illustrated through numerous simulations and real examples including one microarray data.     

On the quadratic estimation of covariance matrices in multivariate linear models

This paper investigates the estimation of covariance matrices in multivariate mixed models. Some sufficient conditions are derived for a multivariate quadratic form and a linear combination of multivariate quadratic forms to be the BQUE (quadratic unbiased and severally minimum varianced) estimators of its expectations.     

On linear models with long memory and heavy-tailed errors

We consider the robust estimation of regression parameters in linear models with long memory and heavy-tailed errors. Asymptotic Bahadur-type representations of robust estimates are developed and their limiting distributions are obtained. It is shown that the limiting distributions are very different from those obtained under short memory. A simulation study is carried out to compare the performance of various asymptotic representations.     

On homogeneity and small extensions of models of the theory of linear ordering

Some properties concerning homogeneity and the existence of small extensions proved earlier for models of superstable theories, are proved here for models of the theory of linear ordering.     

广义线性模型(三)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(二)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(一)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(十)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分3部分:建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L.Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(八)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分3部分:建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L.Fahrmeir等人的《MultivariateStatisticalModel ingBasedonGeneralizedLinearModels》     

On response functions in linear thermoelastic models of shape memory polymers

This paper is concerned with the broad class of Liner Thermoelastic (LTE) models for Shape Memory Polymers (SMPs) which unifies numerous constitutive theories proposed in the literature for this kind of smart material. It is shown that the response functions for the general model of this class may be determined directly from experimental data measured in standard thermomechanical cyclic tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Intrinsic formulation of the displacement-traction problem in linear shell theory

We recast the Dirichlet boundary conditions satisfied by the displacement field of the middle surface of a linearly elastic shell as boundary conditions satisfied by the corresponding linearized change of metric and of curvature tensor fields. This in turn allows us to give an intrinsic formulation of the linear shell model of W.T. Koiter with these two tensor fields as the sole unknowns.     

Quasilinear ellipticity and the dirichlet problem

In this paper we prove some existence theorems for the Dirichlet problem in ^1,2(Q) for a quasilinear elliptic equation under assumptions of the Ambrosetti-Prodi type. We also discuss the solvability of this problem, in a nonresonant case, with boundary data inL ²(∂Q) which leads in a natural way to the Dirichlet problem in a weighted Sobolev space.