湍流模型和施密特数对街谷内污染扩散模拟的影响

选取不同的湍动施密特数,分别采用标准κ-ε模型和realizable κ-ε模型对孤立街道峡谷内的气流运动和污染物扩散进行了数值模拟.计算得到的气流速度场和污染物浓度分布表明,标准κ-ε模型和realizable κ-ε模型预测出极为相似的气流旋涡结构,即在峡谷内生成一个中心大致位于峡谷中央的顺时针大旋涡,并在此大旋涡的作用下污染物往峡谷的背风侧积聚.通过对比分析峡谷迎风面和背风面上的无量纲污染物浓度计算结果与风洞试验数据表明,湍动施密特数的改变并不影响计算空气流场,但改变污染物扩散方程中的湍动扩散率,增大湍动施密特数将减弱污染物的湍动扩散作用,使得峡谷顶部污染物外溢减少,从而导致峡谷内的污染物浓度计算值增大;只要给定合适的计算参数,标准κ-ε模型和realizable κ-ε模型均能预测出峡谷内的污染物扩散分布,标准κ-ε模型合适的湍动施密特数为0.4～0.6,而realizable κ-ε模型则为0.3～0.5;当取湍动施密特数为0.7(Fluent软件系统中的默认值)时,标准κ-ε模型的计算精度高于realizable κ-ε模型的计算精度.     

Likelihood ratio ordering of order statistics,mixtures and systems

Let X=(_X1,_X2,…,_Xn)$\mathit{X}=(X_1,X_2,\dots ,X_n)$ be an exchangeable random vector, and denote _X1:i=min{_X1,_X2,…,_Xi}$X_{1:i}=\min \{X_1,X_2,\dots ,X_i\}$ and _Xi:i=max{_X1,_X2,…,_Xi}$X_{i:i}=\max \{X_1,X_2,\dots ,X_i\}$, 1?i?n$1?i?n$. These order statistics represent the lifetimes of the series and the parallel systems, respectively, with component lifetimes _Xi$X_i$. In this paper we obtain conditions under which _X1:i$X_{1:i}$ (or _Xi:i$X_{i:i}$) decreases (increases) in i in the likelihood ratio (lr) order. An even more general result involving general (that is, not necessary exchangeable) random vectors is also derived for general series (or parallel) systems. We show that the series (parallel) systems are not necessarily lr-ordered even if the components are independent.     

Prediction in moving average processes

For the stationary invertible moving average process of order one with unknown innovation distribution F, we construct root-n   consistent plug-in estimators of conditional expectations E(h(_Xn+1)|_X1,…,_Xn)$E(h(X_{n+1})|X_1,\dots ,X_n)$. More specifically, we give weak conditions under which such estimators admit Bahadur-type representations, assuming some smoothness of h or of F. For fixed h it suffices that h   is locally of bounded variation and locally Lipschitz in _L2(F)$L_2(F)$, and that the convolution of h and F   is continuously differentiable. A uniform representation for the plug-in estimator of the conditional distribution function P(_Xn+1?·|_X1,…,_Xn)$P(X_{n+1}?·|X_1,\dots ,X_n)$ holds if F has a uniformly continuous density. For a smoothed version of our estimator, the Bahadur representation holds uniformly over each class of functions h that have an appropriate envelope and whose shifts are F-Donsker, assuming some smoothness of F. The proofs use empirical process arguments.     

Asymptotic results in canonical discriminant analysis when the dimension is large compared to the sample size

This paper deals with the distributions of test statistics for the number of useful discriminant functions and the characteristic roots in canonical discriminant analysis. These asymptotic distributions have been extensively studied when the number p   of variables is fixed, the number q+1$q+1$ of groups is fixed, and the sample size N tends to infinity. However, these approximations become increasingly inaccurate as the value of p increases for a fixed value of N. On the other hand, we encounter to analyze high-dimensional data such that p is large compared to n. The purpose of the present paper is to derive asymptotic distributions of these statistics in a high-dimensional framework such that q   is fixed, p→∞$p\to \infty$, m=n-p+q→∞$m=n-p+q\to \infty$, and p/n→c∈(0,1)$p/n\to c\in (0,1)$, where n=N-q-1$n=N-q-1$. Numerical simulation revealed that our new asymptotic approximations are more accurate than the classical asymptotic approximations in a considerably wide range of (n,p,q)$(n,p,q)$.     

Ordered ranked set samples and applications to inference

Ranked set sampling (RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian J. Agricultural Res. 3, 385–390] as an effective way to estimate the unknown population mean. Chuiv and Sinha [1998. On some aspects of ranked set sampling in parametric estimation. In: Balakrishnan, N., Rao, C.R. (Eds.), Handbook of Statistics, vol. 17. Elsevier, Amsterdam, pp. 337–377] and Chen et al. [2004. Ranked Set Sampling—Theory and Application. Lecture Notes in Statistics, vol. 176. Springer, New York] have provided excellent surveys of RSS and various inferential results based on RSS. In this paper, we use the idea of order statistics from independent and non-identically distributed (INID) random variables to propose ordered ranked set sampling (ORSS) and then develop optimal linear inference based on ORSS. We determine the best linear unbiased estimators based on ORSS (BLUE-ORSS) and show that they are more efficient than BLUE-RSS for the two-parameter exponential, normal and logistic distributions. Although this is not the case for the one-parameter exponential distribution, the relative efficiency of the BLUE-ORSS (to BLUE-RSS) is very close to 1. Furthermore, we compare both BLUE-ORSS and BLUE-RSS with the BLUE based on order statistics from a simple random sample (BLUE-OS). We show that BLUE-ORSS is uniformly better than BLUE-OS, while BLUE-RSS is not as efficient as BLUE-OS for small sample sizes (n<5$n<5$).     

Characterizations based on record values and order statistics

Consider a sequence of independent and identically distributed random variables {_Xi,i?1}$\{X_i,i?1\}$ with a common absolutely continuous distribution function F  . Let _X1:n?_X2:n???_Xn:n$X_{1:n}?X_{2:n}???X_{n:n}$ be the order statistics of {_X1,_X2,…,_Xn}$\{X_1,X_2,\dots ,X_n\}$ and {_Yl,l?1}$\{Y_l,l?1\}$ be the sequence of record values generated by {_Xi,i?1}$\{X_i,i?1\}$. In this work, the conditional distribution of _Yl$Y_l$ given _Xn:n$X_{n:n}$ is established. Some characterizations of F   based on record values and _Xn:n$X_{n:n}$ are then given.     

A note on the queue with a random set-up time under a restricted admissibility policy with a Bernoulli vacation schedule

This paper deals with the queue size distribution of an M^x/G/1 queue with a random set-up time and with a Bernoulli vacation schedule under a restricted admissibility policy. This generalizes the model studied by Madan and Choudhury [Sankhyá 66 (2004) 175–193].     

Gesellschafterausstieg in großen Familienunternehmen

Zusammenfassung  Dieser Beitrag befasst sich mit dem Ausstieg von Gesellschaftern aus Familienunternehmen als bedeutendes Corporate Governance-Problem. Im Mittelpunkt steht die Untersuchung der Wirkung von Ausstiegsmotiven, Rahmenbedingungen sowie Ausstiegsbarrieren auf die Belastung von Unternehmen und Familie durch den Gesellschafterausstieg. Eine explorative empirische Untersuchung von 55 gro?en deutschen Familienunternehmen liefert Ans?tze für eine Organisationstheorie des Familienunternehmens und für praktische Empfehlungen bei der Gestaltung von Satzung und Ausstiegsverhandlung.

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Summary  This article deals with the exit of shareholders in family owned businesses as an important corporate governance problem. We mainly analyse the effect of exit motivations, exit conditions, and barriers to exit on the exit’s burden for the company and the family. An explorative empirical study of 55 large German family owned businesses comes up with ideas for an organization theory of family owned businesses as well as some practical recommendations for statutes and exit negotiations.

     

A sequential design for a clinical trial with a linear prognostic factor

We study a randomized adaptive design to assign one of the L$L$ treatments to patients who arrive sequentially by means of an urn model. At each stage n$n$, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0?_Yn?1$0?Y_n?1$, and 1-_Yn$1-Y_n$ is distributed among the other treatments according to their performance until stage n-1$n-1$. Patients can be classified in K+1$K+1$ levels and we assume that the effect of this level in the response to the treatments is linear. We study the asymptotic behavior of the design when the ordinary least square estimators are used as a measure of performance until stage n-1$n-1$.     

Multivariate Matsumoto–Yor property is rather restrictive

Matsumoto and Yor [2001. An analogue of Pitman's 2M-X$2M-X$ theorem for exponential Wiener functionals. Part II: the role of the GIG laws. Nagoya Math. J. 162, 65–86] discovered an interesting invariance property of a product of the generalized inverse Gaussian (GIG) and the gamma distributions. For univariate random variables or symmetric positive definite random matrices it is a characteristic property for this pair of distributions. It appears that for random vectors the Matsumoto–Yor property characterizes only very special families of multivariate GIG and gamma distributions: components of the respective random vectors are grouped into independent subvectors, each subvector having linearly dependent components. This complements the version of the multivariate Matsumoto–Yor property on trees and related characterization obtained in Massam and Weso?owski [2004. The Matsumoto–Yor property on trees. Bernoulli 10, 685–700].