射孔对破裂压力及裂缝形态影响数值模拟研究

针对射孔对水力压裂过程中的破裂压力以及裂缝形态的问题，通过建立不同射孔方位和不同远场主应力条件下裂缝扩展模型，将位移不连续方法（DDM）应用于水力压裂过程中的力学分析研究，同时在裂缝扩展准则上运用修正了的G准则—F准则并进行裂缝扩展规律研究。根据不同射孔方位和不同远场主应力条件下裂缝扩展的模拟计算，在地应力大小和方位确定的情况下，破裂压力随着射孔方位的增大而升高，并且随着方位角的增大，裂缝形态会发生转向，而且裂缝壁面粗糙，会增大压裂液摩阻。对于实际的射孔参数优化设计和压裂施工具有参考意义     

Sequence-compound estimation in scale-exponential families and speed of convergence

This paper deals with a sequence-compound estimation. The component problem is the squared error loss estimation of θ?[a,b] based on an observation X whose p.d.f. is of the form $\text{u(x)c(θ)}\text{exp}\text{(?}\text{x}\text{θ}\text{)}$. For each $\text{0<t<}\text{1}\text{2}$ a class of sequence-compound estimators $\text{ψ}\text{?}\text{=}\text{ψ}\text{?}{}_1\text{,}\text{ψ}\text{?}{}_2\text{,…)}$ is exhibited whose compound risk (average of risks) up to stage n differs from the Bayes envelope (in the component problem) w.r.t. the empiric distribution G_n of the parameters involved up to stage n by a quantity of order O(n^?δt) for a δ>0. It is also shown that at any stage i the difference of the risk of ψ?_i and the risk of the Bayes response w.r.t. G_i?1 is O(i^?δt). Examples of the above type of families are given where δ is min{1,$\text{2a}\text{b}$} and t is arbitrarily close to $\text{1}\text{2}$. Here it may be worthwhile to mention that a rate $\text{O}\text{(n}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{)}$ or better has not yet been obtained even in a very special family of densities.     

A Note on the Kuks-Olman Estimator

In the linear regression model the unknown parameter vector θ is supposed to vary in a known ellipsoid. Under this parameter constraint Kuks and Olman derived an estimator by demanding a minimax property. Since sometimes the Kuks-Olman estimator takes values outside of the ellipsoid a modification is proposed in the paper. It is shown that this modified variant is a least squares estimator in the restricted model.     

Generalized Linear Models with a Small Scale Parameter

We propose a study of asymptotic properties in an extension of the Nelder-Wedderburn generalized linear models (GLM) and we apply the results to a model choice in Mandel's models of analysis of variance (ANOVA). This study concerns the behaviour of the maximum likelihood estimators (MLE) when the scale parameter of the GLM tends to zero. Finally, to allow the use of our results, we give some specifications of this limit in three cases of the GLM.     

Generalized f variates in the general linear model

In this paper the theory of the generalized F variate is examined. A large class of statistics is constructed for linear for linear models when the errors are distributed N(0, ∑), where ∑ is positive definite. These statistics are shown to have a generalized F distribution. The role of the generalized F variate is then studied in detail for a linear model of constant intraclass correlation.     

On a theorem of graybill

Graybill (1976) gives a theorem for testing variance components in balanced random models. Unfortunately, the theorem does not hold true. We pin down the reason that causes the theorem to fail and give a correct version of it.     

Multilevel and nonlinear panel data models

Summary This paper presents a selective survey on panel data methods. The focus is on new developments. In particular, linear multilevel models, specific nonlinear, nonparametric and semiparametric models are at the center of the survey. In contrast to linear models there do not exist unified methods for nonlinear approaches. In this case conditional maximum likelihood methods dominate for fixed effects models. Under random effects assumptions it is sometimes possible to employ conventional maximum likelihood methods using Gaussian quadrature to reduce a T-dimensional integral. Alternatives are generalized methods of moments and simulated estimators. If the nonlinear function is not exactly known, nonparametric or semiparametric methods should be preferred. Helpful comments and suggestions from an unknown referee are gratefully acknowledged.