Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of an MHD micropolar fluid with wall effects

In this paper, the influence of magnetic field on the dispersion of a solute in peristaltic flow of an incompressible micropolar fluid is studied as a model of fluid transport in the human intestinal system with wall properties. Long wavelength approximation, Taylor's limiting condition, and dynamic boundary conditions at the flexible walls are used to obtain the average effective dispersion coefficient in the presence of combined homogeneous and heterogeneous chemical reactions. The effects of various pertinent parameters on the effective dispersion coefficient are discussed. Average effective dispersion coefficient increases with amplitude ratio, which implies that dispersion is more in the presence of peristalsis. It also increases with the cross‐viscosity coefficient, heterogeneous chemical reaction rate, and wall parameters. Further, dispersion decreases with micropolar parameter, magnetic parameter, and homogeneous chemical reaction rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian analysis of definitive screening designs when the response is nonnormal

Definitive screening designs (DSDs) are a class of experimental designs that allow the estimation of linear, quadratic, and interaction effects with little experimental effort if there is effect sparsity. The number of experimental runs is twice the number of factors of interest plus one. Many industrial experiments involve nonnormal responses. Generalized linear models (GLMs) are a useful alternative for analyzing these kind of data. The analysis of GLMs is based on asymptotic theory, something very debatable, for example, in the case of the DSD with only 13 experimental runs. So far, analysis of DSDs considers a normal response. In this work, we show a five‐step strategy that makes use of tools coming from the Bayesian approach to analyze this kind of experiment when the response is nonnormal. We consider the case of binomial, gamma, and Poisson responses without having to resort to asymptotic approximations. We use posterior odds that effects are active and posterior probability intervals for the effects and use them to evaluate the significance of the effects. We also combine the results of the Bayesian procedure with the lasso estimation procedure to enhance the scope of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).     

无重复因析试验中散度效应的ML估计

在无重复因析试验中,若因子A,B的散度效应显著,则不论其交互效应AB的散度效应是否显著,其散度效应的现有估计常常是有偏的,从而导致其被错误地识别为显著效应.提出了散度效应的一种新的估计方法(称为ML估计),并给出了ML估计的方差的精确表达形式,证明了在一类模型中,交互效应AB的散度效应的ML估计是无偏的.最后,将ML估计与现有的常用估计进行了比较.     

离散型指数族非线性模型的变离差检验

It is necessary to test for varying dispersion in generalized nonlinear models. Wei,et al (1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed ,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.     

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

§ 1　 Introduction and modelsThe general form of exponential family nonlinear models isg(μi) =f(xi,﹀) , (1 )where,g(· ) is a monotonic link function,f is a known differentiable nonlinear functionand﹀ is a p-vectoroffixed population parameters;μi=E(yi) and the density of response yiisp(yi) =exp{[yiθi -b(θi) -c(yi) ] -12 a(yi,) } ,(2 )whereθi is the natural parameter, is the dispersion parameter.From [1 1 ] ,μi=b(θi) ,Vi=Var(yi) =- 1 b(θi) .If f(xi,β) =x Ti ﹀,then mod…     

WFQEM‐based perturbation approach and its applications in analyzing nonlinear periodic structures

Based on the weak form quadrature element method, a perturbation approach is developed. Waves propagating in periodic beams on a nonlinear elastic foundation are studied by using the new proposed method. The feasibility and accuracy of the proposed method are verified by comparing the present results with those available in literatures in linear cases. Detailed modal analysis of the linear cases is conducted in order to obtain the dispersion relations of the nonlinear cases. The theoretical results show that the dispersion relations of the nonlinear cases are amplitude dependent. Furthermore, the effects of geometric parameters and degree of nonlinearity on the amplitude‐dependent dispersion relations are discussed in detail. This work provides a new method for analyzing the dispersion relations of nonlinear periodic structures and gives some useful guidelines for designing periodic beams or pipelines with nonlinear structure–foundation interaction. Copyright © 2016 John Wiley & Sons, Ltd.     

8×4×2~n设计纯净两因子交互作用成分最大数的界

混水平部分因析设计在各类试验中有广泛应用.纯净效应准则是用于选取最优部分因析设计的重要准则之一.本文考虑含有一个八水平因子、一个四水平因子和若干二水平因子的8×4×2~n混水平设计,给出了分辨度为Ⅲ和Ⅳ的该类混水平设计包含纯净两因子交互作用成分最大数的上界和下界.下界通过构造特定设计而得到.     

Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.     

无重复因析试验中一种估计散度效应的方法

自从Box和Meyer首次提出无重复因析试验中散度效应的识别和估计问题, 各种散度效应的估计方法(包括迭代和非迭代)被提出. 特别地, Brenneman 和Nair 给出了这些方法的一个综述, 并且他们验证了改进的Harvey方法优于其它的方法.本文中对于对数线性模型, 一个基于多个位置模型残差平均的非迭代的散度效应估计方法在模型选择阶段被提出. 在大多数的模拟实验模型中, 本文方法具有比MH方法更小的均方误差, 且它可以应用于MH方法不适用的0或小的绝对残差情形. 我们也考虑了这个估计的理论性质, 并进行了实例分析.     

Analysis of means approach in advanced designs

Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.     

The choice of screening design

A screening design is an experimental plan used for identifying the expectedly few active factors from potentially many. In this paper, we compare the performances of 3 experimental plans, a Plackett‐Burman design, a minimum run resolution IV design, and a definitive screening design, all with 12 and 13 runs, when they are used for screening and 3 out of 6 factors are active. The functional relationship between the response and the factors was allowed to be of 2 types, a second‐order model and a model with all main effects and interactions included. D‐efficiencies for the designs ability to estimate parameters in such models were computed, but it turned out that these are not very informative for comparing the screening performances of the 2‐level designs to the definitive screening design. The overall screening performance of the 2‐level designs was quite good, but there exist situations where the definitive screening design, allowing both screening and estimation of second‐order models in the same operation, has a reasonable high probability of being successful.     

Superpure digraph designs

A digraph design is a decomposition of a complete (symmetric) digraph into copies of pre‐specified digraphs. Well‐known examples for digraph designs are Mendelsohn designs, directed designs or orthogonal directed covers. A digraph design is superpure if any two of the subdigraphs in the decomposition have no more than two vertices in common. We give an asymptotic existence theorem for superpure digraph designs, which is a variation of an earlier result of Lamken and Wilson J Combin Theory Ser A 89: 149–200, 2000. As an immediate consequence, we obtain new results for supersimple designs and pure perfect Mendelsohn designs. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 239–255, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10013     

Comparing different fractions of a factorial design: a metal cutting case study

Full factorial designs of a significant size are very rarely performed in industry due to the number of trials involved and unavailable time and resources. The data in this paper were obtained from a six‐factor full factorial (2⁶) designed experiment that was conducted to determine the optimum operating conditions for a steel milling operation. Fractional‐factorial designs 2 (one‐eighth) and 2 (one‐fourth, using a fold‐over from the one‐eighth) are compared with the full 2⁶ design. Four of the 2 are de‐aliased by adding four more runs. In addition, two 12‐run Plackett–Burman experiments and their combination into a fold‐over 24‐run experiment are considered. Many of the one‐eighth fractional‐factorial designs reveal some significant effects, but the size of the estimates varies much due to aliasing. Adding four more runs improves the estimation considerably. The one‐quarter fraction designs yield satisfactory results, compared to the full factorial, if the ‘correct’ parameterization is assumed. The Plackett–Burman experiments, estimating all main effects, always perform worse than the equivalent regular designs (which have fewer runs). When considering a reduced model many of the different designs are more or less identical. The paper provides empirical evidence for managers and engineers that the choice of an experimental design is very important and highlights how designs of a minimal size may not always result in productive findings. Copyright © 2006 John Wiley & Sons, Ltd.     

无重复因析试验中多个散度效应检验的一种改进方法

在无重复因析试验的多个散度效应分析中,常常出现错误识别的现象,即两个显著的散度效应可能在它们的交互列上产生一个错误的散度效应,并且现有的许多方法都存在这样的问题.为了解决这种模棱两可性,McGrath和Lin(2001)提出了一种基于残差样本方差几何平均的检验方法(ML方法),但是这个方法不能应用于零残差样本方差的情形.鉴于此,提出了一种基于修改残差的改进方法,适用于零残差样本方差的情形,并且通过实例验证了方法的合理性.最后,通过模拟和ML方法做了比较.     

Construction of optimal supersaturated designs by the packing method

A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main effects is greater than the number of runs. It has received much recent interest because of its potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed. A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated. Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties.     

Enumeration of resolvable 2‐(10, 5, 16) and 3‐(10, 5, 6) designs

A backtracking over parallel classes with a partial isomorph rejection (PIR) is carried out to enumerate the resolvable 2‐(10,5,16) designs. Computational results show that the inclusion of PIR reduce substantially the CPU time for the enumeration of all designs. We prove first some results, which enable us to restrict the search space. Since every resolvable 2‐(10,5,16) design is also a resolvable 3‐(10,5,6) design and vice versa, the latter designs are also enumerated. There are 27, 121, 734 such designs with automorphism groups whose order range from 1 to 1,440. From these, designs 2,006,690 are simple. © 2004 Wiley Periodicals, Inc.     

Infinite families of 3‐designs from APN functions

Combinatorial $t$‐designs have nice applications in coding theory, finite geometries, and several engineering areas. A classical method for constructing $t$‐designs is by the action of a permutation group that is $t$‐transitive or $t$‐homogeneous on a point set. This approach produces $t$‐designs, but may not yield $\left(t+1\right)$‐designs. The objective of this paper is to study how to obtain 3‐designs with 2‐transitive permutation groups. The incidence structure formed by the orbits of a base block under the action of the general affine groups, which are 2‐transitive, is considered. A characterization of such incidence structure to be a 3‐design is presented, and a sufficient condition for the stabilizer of a base block to be trivial is given. With these general results, infinite families of 3‐designs are constructed by employing almost perfect nonlinear functions. Some 3‐designs presented in this paper give rise to self‐dual binary codes or linear codes with optimal or best parameters known. Several conjectures on 3‐designs and binary codes are also presented.     

Orthogonal designs,self‐dual codes,and the Leech lattice

Symmetric designs and Hadamard matrices are used to construct binary and ternary self‐dual codes. Orthogonal designs are shown to be useful in construction of self‐dual codes over large fields. In this paper, we first introduce a new array of order 12, which is suitable for any set of four amicable circulant matrices. We apply some orthogonal designs of order 12 to construct new self‐dual codes over large finite fields, which lead us to the odd Leech lattice by Construction A. © 2005 Wiley Periodicals, Inc. J Combin Designs 13: 184–194, 2005.     

The spectrum of additive BIB designs

In this article, the existence of additive BIB designs is discussed with direct and recursive constructions, together with investigation of a property of resolvability. Such designs can be used to construct infinite families of BIB designs. In particular, we obtain a series of B(sⁿ, ts^m, λt (ts^m ? 1) (s^n‐m ? 1)/[2(s^m ? 1)]) for any positive integer λ, such that sⁿ (sⁿ ? 1) λ ≡ 0 (mod s^m (s^m ? 1) and for any positive integer t with 2 ≤ t ≤ s^n‐m, where s is an odd prime power. Connections between additive BIB designs and other combinatorial objects such as multiply nested designs and perpendicular arrays are discussed. A construction of resolvable BIB designs with v = 4k is also proposed. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 235–254, 2007