two dimensional transient wave propagation in viscoelastic layered media propagation of two dimensional transient waves in multilayered viscoelastic media is investigated the multilayered medium consists of n different isotropic homogeneous and linearly viscoelastic layers with more than one discrete relaxation time the top surface of the layered medium is subjected to dynamic in plane surface tractions whereas the lower surface is free or fixed a numerical technique which combines the fourier transform with the method of characteristics is employed to obtain the solutions the numerical results are displayed in curves denoting the variations of the stress and displacement components with time at different locations these curves reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers the curves also display the effects of viscous damping in the wave profiles by suitably adjusting the material constants curves for the cases of elastic layers and viscoelastic layers with one relaxation time standard linear solid are also obtained the curves further show that the numerical technique applied in this study is capable of predicting the sharp variations in the field variables in the neighborhood of the wave fronts solutions for some special cases including lamb s problem for the elastic half space are obtained and compared with the existing solutions in the literature very good agreement is found

axisymmetric elastic waves in weakly coupled layered media of infinite radial extent abstract the propagation of axisymmetric waves in layered periodic elastic media of infinite radial extent is investigated hankel and laplace transforms are employed to convert radial and time dependence of displacement and stress within a layer to frequency and radial wavenumber continuity of stress and displacement is imposed at the interface between layers yielding transfer matrices the structure of propagation and attenuation zones pz s and az s of the system with infinite number of layers is studied when the ratios of shear and longitudinal mechanical impedances t l of the two layers are large the pz s of the layered system become narrow approaching certain limiting curves in the frequency wavenumber plane for large t l an asymptotic analysis is employed analytically to approximate the width of the pz s numerical computations of pz s are given which are in good agreement with the analytical predictions the spacing of the resonance points of a layered system with finite number of layers is found to depend mainly on the structure of the pz s of the corresponding system with an infinite number of layers

elastodynamic direct boundary element methods with enhanced numerical stability properties evidence of numerical instabilities in two dimensional time domain direct boundary element methods is presented the e ects of numerical versus analytical integration of spatial integrals on stability are shown and two new time stepping algorithms are introduced and compared to existing formulations the so called new direct half step scheme and the epsilon scheme are shown to improve the numerical stability of direct boundary element methods copyright 1999 john wiley sons ltd

multi domain bem for two dimensional problems of elastodynamics an advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two dimensional elastic or visco elastic solids of arbitrary shape and connectivity is presented for transient dynamic analysis the problem is first solved in the laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions the present analysis is capable of treating very large multi domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces with the help of this substructuring capability problems related to the layered media and soil structure interaction can all be analysed this paper also introduces a new type of element called enclosing element which has been developed and used to model the infinitely extending boundaries of a half space or a layered medium a number of numerical examples are presented and through comparisons with available analytical and numerical results the accuracy stability and efficiency of the present analysis are established

geometric properties of heisenberg type groups on montre qu il y a une certaine metrique riemannienne contravariante qui induit une longueur d arc

near field transient axisymmetric waves in layered structures effects of weak coupling axisymmetric stress wave transmission through the leading layers of layered structures of infinite radial but finite axial extent is numerically studied by employing two different computational approaches a technique based on the numerical inversion of double integral transformations dit and a finite element fe analysis considering the first approach careful selections of the limits of the numerical inversions and the sampling rates are required in order to overcome inherent numerical instabilities associated with exponential dichotomy this type of numerical instability is more evident in layered media with weak coupling in such systems direct multiplications of layer transfer matrices are avoided by employing a global scheme to assemble well conditioned global transfer matrices moreover the specific structure of the propagation and attenuation zones of the structure are taken into account for increasing the efficiency and effectiveness of the transfer matrix manipulations satisfactory agreement between the dit and fe numerical results is observed at least for early times close to the region of application of the external pressure the fe simulations suffer from the discretization of the applied load node to node oscillations and reflections from infinite elements silent boundaries using the aforementioned numerical techniques transient wave transmission in two layered systems one with weak and one with strong interlayer coupling is considered and the effects of weak coupling on the wave transmission is studied we show that at early times weak coupling results in stress localization in the region close to the applied pressure a result which can have potential application in the use of layered media as shock isolators 1997 by john wiley sons ltd

estimating departure from normality departure of a sample from a normal distribution should be assessed by a quantity that is meaningful in terms of the data rather than merely by the p value from a test statistic indices of departure based on the shapiro francia w and the shapiro wilk w statistics are derived and shown to have a natural interpretation in relation to the normal probability plot a new diagnostic plot is proposed an example is given which shows the relationship between one of the new indices and errors in calculated reference ranges due to non normality of the data

overweight tails are inefficient test statistics which are almost determined by o n tail order statistics are shown to provide tests of asymptotic relative efficiency 0 against the usual type of contiguous alternative the result is applied to several goodness of fit tests the variance weighted kolmogorov smirnov statistic the kolmogorov smirnov statistic in the stabilized probability plot and the correlation coefficient in a q q plot for a variety of distributions with exponential tails

a precise numerical method for rayleigh waves in a stratified half space this paper presents theory and results for rayleigh waves propagating in a transversely isotropic stratified solid resting on an elastic semi infinite space it uses the precise integration method pim and the extended wittrick williams w w algorithm this problem can be reduced into the eigenvalue problem of ordinary differential equations odes in the frequency wavenumber domain the pim used here is a precise method for solving the odes with two point boundary conditions and the eigenvalue counting method of the extended w w algorithm is used to ensure that all eigenvalues are found without the possibility of any being missed hence the theory presented in this paper is exact in the sense that its precision is limited only by the precision of the computer used

the stabilized probability plot summary the stabilized probability plot is introduced an attractive feature of the plot that enhances its interpretability is that the variances of the plotted points are approximately equal this prompts the definition of a new and powerful goodness of fit statistic dsp which analogous to the standard kolmogorov smirnov statistic d is defined to be the maximum deviation of the plotted points from their theoretical values using either d or dsp it is shown how to construct acceptance regions for qq pp and the new plots acceptance regions can help remove much of the subjectivity from the interpretation of these probability plots

estimating fatigue curves with the random fatigue limit model in a fatigue limit model units tested below the fatigue limit also known as the threshold stress theoretically will never fail this article uses a random fatigue limit model to describe a the dependence of fatigue life on the stress level b the variation in fatigue life and c the unit tounit variation in the fatigue limit we fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions small quantiles of the life distribution are often of interest to designers lower confidence bounds based on likelihood ratio methods are obtained for such quantiles to assess the fits of the model we construct diagnostic plots and perform goodness of fit tests and residual analyses

h type groups and iwasawa decompositions since their introduction by a kaplan kpl some ten years ago generalised heisenberg groups also known as groups of heisenberg type or h type groups have provided a framework in which to construct interesting examples in geometry and analysis see for instance c2 kp2 kp3 kpr k2 rl r2 tl tv the iwasawa n groups associated to all the real rank one simple lie groups are h type so one has a convenient vehicle for studying these in a unified way many problems on these simple lie groups can be reduced to a problem on h type groups via the so called noncompact picture and often problems on h type groups can be solved on all the groups of the family in one fell swoop as in for example ch ck dr out of this approach to studying simple lie groups several problems arise such as why only some h type groups correspond to simple lie groups of real rank one in this paper we discuss various features of iwasawa n groups which distinguish them in the class of all h type groups we shall show that all h type groups which possess certain geometric properties clearly possessed by iwasawa n groups satisfy a lie algebraic condition implicit in the work of b kostant kt2 that we shall call the j condition we shall also use elementary clifford algebra to classify the

simultaneous non parametric confidence intervals for survival probabilities from censored data in medical studies with censored data kaplan and meier s product limit estimator has frequent use as the estimate of the survival function simultaneous confidence intervals for the survival function at various time points constitute a useful addition to the analysis this study compares several such methods we consider in a simulation investigation two whole curve confidence bands and four methods based on the bonferroni inequality the results show that three bonferroni type methods are essentially equivalent all being better than the other methods when the number of time points is small 3 or 5

goodness of fit tests based on p p probability plots percentage percentage p p probability plots constructed from standardized observations possess some attractive features that are not shared by more commonly used quantile quantile q q plots in particular the identification of viable alternatives to a proposed probability model can be greatly facilitated by displaying curves on p p plots to represent families of alternative models a single curve can represent an entire family of alternatives indexed by both location and scale parameters two goodness of fit statistics based on measures of linearity for standardized p p plots are proposed and simple approximations for percentage points of these statistics are presented for testing the fit of exponential gumbel weibull and normal lognormal probability models with unknown parameters results of extensive monte carlo power comparisons with other goodness of fit tests are summarized the proposed tests are shown to have superior power for detecting light tailed and moderate tailed alternatives to

tests for the exponential weibull and gumbel distributions based on the stabilized probability plot goodness of fit procedures for composite testing of the exponential weibull and gumbel distributions are investigated these procedures are such that they can be used graphically with and to aid interpretation of probability plots in the situations of interest here the new procedure is generally more powerful than the kolmogorovsmirnov test which appears to be the only other readily available goodness of fit procedure that can be used graphically with probability plots

an indirect elastodynamic boundary element method with analytic bases an indirect time domain boundary element method bem is presented here for the treatment of 2d elastodynamic problems the approximated solution in this method is formulated as a linear combination of a set of particular solutions which are called bases the displacement and stress fields of a basis are analytically derived by means of solving lame s displacement potentials a semi collocation method is proposed to be the time stepping algorithm this method is equivalent to a displacement discontinuity method with piecewise linear discontinuities in both space and time the resulting time stepping scheme is explicit the bem is implemented to solve three numerical examples lamb s problem half plane with a buried crack and selberg s problem though lamb s problem is considered a difficult problem for numerical methods the current numerical results for the surface displacements show accurately the characteristics of the rayleigh wave this method is efficient and accurate copyright 2003 john wiley sons ltd

a clifford algebra approach to real simple lie algebras ii the algebras with root system bcr the algebras with root system bcr

a dispersive effective medium for wave propagation in periodic composites the problem of wave propagation through a periodic medium is considered it is assumed that the ratio between the cell size and the shortest wavelength of the initial disturbance is small within this regime an effective medium model of the propagation phenomena is obtained using the bloch expansion the effective medium obtained is shown to be dispersive it is known that a dominant feature of the transient wave train in a periodic medium is that of dispersion it is shown that our model recovers homogenization formally when the cell size approaches zero explicit formula for the constants appearing in the effective medium equation is derived for the case of one dimension the accuracy of the resulting approximation is assessed in numerical simulations

on goodness of fit tests for the two parameter weibull distribution derived from the stabilized probability plot summary michael s statistic dsp based on the stabilized probability plot is considered for the assessment of goodness of fit of a two parameter weibull distribution this statistic is shown to have high power when the parameters are estimated using a procedure due to blom 1958 the correlation coefficient of the stabilized plot rsp is also proposed as a test statistic for this situation finally a family of transformations is obtained to reduce the null distribution of rsp to standard normality

transformations and influential observations in minimum sum of absolute errors regression the box cox power transformation model is considered for minimum sum of absolute errors msae regression a long tailed error distribution specifically the laplace distribution is included and could accommodate observations that in the normal case are outlying or unduly influencing a choice of transformation the log likelihood procedure of box and cox 1964 for obtaining the optimal transformation parameter is adapted for laplace errors and msae regression graphical methods for detecting the influence of individual observations on the choice of transformation are described application to examples illustrates that this approach can provide valuable additional information to the data analyst

two dimensional transient wave propagation problems by time domain bem abstract in this paper an advanced formulation of time domain boundary element method bem for linear elastodynamics is used to study a number of problems involving wave propagation through half space as well as multi layered soils the algorithm incorporates isoparametric quadratic elements which facilitate proper modelling of problem geometry and can represent the field variables in dynamic problems very accurately which are very often wavy in nature also higher order temporal variation of functions is introduced improved techniques are employed for the accurate evaluation of both the singular and non singular spatial integrals most importantly this formulation incorporates simpler and better behaved kernels compared to those that have appeared in the recent bem literature by the present and other previous researchers with all these new and efficient features the present formulation is superior to the existing ones and as such represents a very effective tool for solving 2d transient wave propagation problems especially in infinite and semi infinite domains where other numerical methods have considerable difficulty in producing accurate solutions

confidence bands for survival functions with censored data a comparative study consider the problem of obtaining simultaneous confidence bands for the survival function s x when the data are arbitrarily right censored the usual pointwise confidence intervals based on greenwood s variance formula can be adapted to yield a large sample confidence band this band has in a certain sense equal precision at each point of s x it is compared with the censored versions of the kolmogorov band and the renyi band the comparisons are made in terms of the widths and the adequacy of large sample approximations and are carried out under various censoring models and degrees of censoring the bands are illustrated by applying them to data from a mechanical switch life test

advanced time domain formulation of bem for two dimensional transient elastodynamics the traction kernel is derived by using the causality of the waves and the resulting kernel is explicite an appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated the algorithm has a capability of handling problems with multiply connected regions this above algorithm is now a part of the general purpose bem code known as gpbest

elastodynamic boundary element method for piecewise homogeneous media a general higher order formulation for the time domain elastodynamic direct boundary element method is presented for computing the transient displacements and stresses in multiply connected two dimensional solids the displacement and traction interpolation functions are linear in time and quadratic in space all integrations are analytical and are expressed in terms of twelve basic recurring integrals causality is ensured by integrating only over the dynamically active parts of each element and the algorithm presented is time marching and implicit the use of analytical integrations allows both unbounded and bounded domain problems to be solved without having to introduce special enclosing elements all of these improved features allow for a formulation that is very efficient and accurate the stability and accuracy of the elastodynamic boundary element algorithm is demonstrated by solving several example problems and comparing the results with available analytical and numerical solutions 1998 john wiley sons ltd

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12