nonlinear prediction theory and the estimation of proportions in a finite population abstract the prediction approach to finite population inference is developed for a general nonlinear model an estimator of the finite population total and an estimator of its variance are derived and the asymptotic properties of both are obtained when the random variables in the model are independent the theory is applied to the problem of estimating the total number of units that have a specified characteristic an empirical study is presented which confirms that a nonlinear bernoulli model is potentially useful for that problem but also illustrates difficulties that may be encountered comparisons with the ratio and linear regression estimators are also included

energy pairs in the micropolar continuum in this paper the concept of energy pairs in the micropolar continuum is introduced a brief review of the micropolar continuum theory is presented for using in the subsequent derivations a mathematical lagrangian strain and a wryness tensor for the micropolar continuum are introduced using the first law of thermodynamics and for isothermal processes the power of deformation is obtained and the energy pairs in the eulerian and lagrangian descriptions are defined also the micropolar stress and couple stress tensors which are energy pairs to the micropolar lagrangian strain and wryness measures are determined

a novel approach to the solution of the tensor equation ax xa h a systematic approach to the solution of the tensor equation ax xa h where a is symmetric is presented it is based upon the reformulation of the original equation in the form ax h where a a 1 1 a is the fourth order tensor obtained from the square tensor product of the second order tensors a and 1 it is shown that the solution x which is known to be an isotropic function of a and h can be effectively obtained either by providing explicit formulas for a 1 or by reconverting to the format ax h the well known representation formulas for tensor valued isotropic functions the final form of the solution can thus be established a priori by suitably choosing a set of independent generators for a 1 the coefficients of the expansion of a 1 with respect to the assigned generators are then obtained by means of basic composition rules for square tensor products in this way it is possible to provide new expressions of the solution as well as to derive the existing ones in a simpler way both three dimensional and two dimensional cases are addressed in detail

phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution a nonlinear third order singular ordinary differential equation is a model for a viscous fluid which drains over a wet surface as a thin film down a vertical wall here we discuss the physical processes of a thin liquid film evolution the classical thin film equation is being derived and the series solution is obtained by employing the adomian decomposition method adm in this paper a new way for the phase planes analysis and traveling wave solution by adm is presented the proposed algorithm is implemented using mathematical software mathematica 6 0

bias robust estimation in finite populations using nonparametric calibration a standard problem in sample survey inference is that of predicting the finite population total h of a function h y of a random variable y the model based approach to this problem first defines a working model for y and then predicts h by estimating its expectation under conditional on the sample values of y this approach leads to biased predictions if is incorrect we explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust but inefficient predictor of h and then calibrates this predictor for its bias under an application to prediction of the finite population distribution function of a population of australian beef farms is presented

median estimation in the presence of auxiliary information summary this paper deals with the estimation under simple random sampling of a finite population median in the presence of an auxiliary variable an estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach these estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known on the basis of the asymptotic properties derived and some simulation results the efficiencies of these estimators are compared it is shown that the two estimators proposed unlike that obtained from modifying the ratio estimator always dominate the sample median in mean squared error and that their efficiencies depend directly on the probability of concordance rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable when the linearity assumption is approximately satisfied the three estimators are seen to have comparable efficiencies while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumnption

solution of the system of ordinary differential equations by adomian decomposition method in this article we use adomian decomposition method which is a well known method for solving functional equations now a days to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one theoretical considerations are being discussed and convergence of the method for theses systems is addressed some examples are presented to show the ability of the method for linear and non linear systems of differential equations

on the determination of the steady film profile for a non newtonian thin droplet abstract a shooting method is used to determine a solution to a third order ode modeling the steady profile of a non newtonian thin droplet we compare a direct approach to an iterative approach using a secant method we obtain a nonlinear relationship between the contact angle and the position of the contact line r from this nonlinear relationship we use curve fitting to obtain an empirical law of the form tan r f k where k is the power law coefficient and f is a nonlinear function of k

conjugate stresses of the seth hill strain tensors abstract in this paper conjugate stresses of the seth hill strain measures are treated by means of the definition of energy conjugacy and hill s principal axis method this approach results in relations between components of two different conjugate stress tensors the results are valid for distinct as well as coalescent principal stretches illustrative examples are solved to demonstrate the simplicity and usefulness of the derived relations between conjugate stress tensors

free vibration of size dependent mindlin microplates based on the modified couple stress theory this paper develops a mindlin microplate model based on the modified couple stress theory for the free vibration analysis of microplates this non classical plate model contains an internal material length scale parameter related to the material microstructures and is capable of interpreting the size effect that the classical mindlin plate model is unable to describe the higher order governing equations of motion and boundary conditions are derived using the hamilton principle the p version ritz method is employed to determine the natural frequencies of the microplate with different boundary conditions a detailed parametric study is conducted to study the influences of the length scale parameter side to thickness ratio and aspect ratio on the free vibration characteristics of the microplate it is found that the size effect is significant when the thickness of microplate is close to the material length scale parameter

the effect of sample design on principal component analysis abstract most sample surveys are multivariate and many lend themselves to multivariate methods of analysis the most usual mode of such analysis is a standard statistical package such as bmdp or spss in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution this assumption ignores the sample selection procedure involved in the survey which leads to the following basic questions what effects can the sample design have on methods of multivariate analysis how should such effects be taken into account this article considers the case of principal component analysis and in particular the point estimation of the eigenvalues and eigenvectors of a covariance matrix it is assumed that the selection of the sample depends on the population values of auxiliary variables as for example in stratified sampling the conventional estimators based on the assumption of simple random sampling are compar

balanced samples and robust bayesian inference in finite population sampling summary bayesian inference in finite populations uses probability models at two stages i to describe relationships among population units and ii to express uncertainty concerning the values of parameters appearing at stage i here we consider the bayes posterior distribution of the population total when a multivariate normal regression model is used at stage i with a diffuse prior distribution on the regression coefficients we study the situation where the stage i model is in error because an important regressor is omitted and we show that in balanced samples such errors do not affect the posterior distribution cases where the covariance matrix contains an unknown scale parameter or is itself misspecified are also considered

material symmetry group of the non linear polar elastic continuum we extend the material symmetry group of the non linear polar elastic continuum by taking into account microstructure curvature tensors as well as different transformation properties of polar and axial tensors the group consists of an ordered triple of tensors which makes the strain energy density of polar elastic continuum invariant under change of reference placement an analog of the noll rule is established four simple specific cases of the group with corresponding reduced forms of the strain energy density are discussed definitions of polar elastic fluids solids liquid crystals and subfluids are given in terms of members of the symmetry group within polar elastic solids we discuss in more detail isotropic hemitropic cubic symmetric transversely isotropic and orthotropic materials and give explicitly corresponding reduced representations of the strain energy density for physically linear polar elastic solids when the density becomes a quadratic function of strain measures reduced representations of the density are established for monoclinic orthotropic cubic symmetric hemitropic and isotropic materials in terms of appropriate joint scalar invariants of stretch wryness and undeformed structure curvature tensors

conditional coverage properties of finite population confidence intervals abstract standardized errors t v 1 2 were calculated for both ratio and regression estimators in each of 10 000 simple random samples of n 32 from each of six populations using four different variance estimators graphs show how the percentage of intervals t 1 96 v 1 2 that fail to contain t changes as a function of the average value of the auxiliary variable in the sample they reveal that a intervals using the variance estimators from standard linear regression theory were hopelessly unreliable b intervals using the conventional finite population variance estimators showed a striking excess of failures in badly balanced samples and c none of the four variance estimators produced satisfactory confidence intervals in populations arising from badly skewed prediction models

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

micropolar hyper elastoplasticity constitutive model consistent linearization and simulation of 3d scale effects summary a computational model for micropolar hyperelastic based finite elastoplasticity that incorporates isotropic hardening is developed the basic concepts of the non linear micropolar kinematic framework are reviewed and a thermodynamically consistent constitutive model that features neo hooke type elasticity and generalized von mises plasticity is described the integration of the constitutive initial value problem is carried out by means of an elastic predictor plastic corrector algorithm which retains plastic incompressibility the solution procedure is developed carefully and described in detail the consistent material tangent is derived the micropolar constitutive model is implemented in an implicit finite element framework the numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented the results of the finite element simulations demonstrate i that the methodology is capable of capturing the size effect in three dimensional elastoplastic solids in the finite strain regime ii that the formulation possesses a regularizing effect in the presence of strain localization and iii that asymptotically quadratic convergence rates of the newton raphson procedure are achieved throughout this paper effort is made to present the developments as a direct extension of standard finite deformation computational plasticity copyright 2012 john wiley sons ltd

the weighted residual technique for estimating the variance of the general regression estimator of the finite population total summary the paper deals with design based estimation of the variance of the general regression estimator of the finite population total the usual taylor linearization variance estimator is an expression in the design weighted regression residuals in many applications the resulting expression is counterintuitive from a model based standpoint the improved variance estimator in this paper attaches another simple weight called g weight to each individual residual this new variance estimator i gives valid design based confidence intervals ii is nearly unbiased uiider a suitably chosen regression model and iii works well for conditional inference examples are given

a note on variance estimation for the regression estimator in double sampling abstract double sampling of a finite population occurs when a sample from the population is itself sampled with the intent of measuring varites in the subsample not already available in the sample an important example is the regression estimator for means or totals which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample this article concerns estimation of the variance of the regression estimator the estimators of variance recommended by cochran rely solely on the subsample data at least to first order this article note proposes variance estimators that make better use of the entire sample

on vectorially parameterized natural strain measures of the non linear cosserat continuum the natural lagrangian stretch and wryness tensors of the non linear cosserat continuum are expressed in terms of the general finite rotation vector these expressions are then specialized for seven particular definitions of the rotation vectors known in the literature it is expected that some of the vectorially parameterized strain measures derived here may be more convenient than others in specific applications

conditioning ratio estimates under simple random sampling abstract the usual ratio estimates for a population mean use information on an auxiliary variable to improve the estimation the standard randomization analysis however does not take enough account of the observations on the auxiliary variable so estimates and estimated variates can be conditionally biased unless the sample is balanced with respect to the auxiliary variable i propose a method of adjustment for the bias of the estimate and its variance based only on the assumption of simple random sampling which uses an approximate conditional distribution of the estimate given the mean of the auxiliary variable roy all and cumberland 1981 illustrated empirically that the usual random sampling estimates and estimated variances could be badly conditionally biased when samples were obtained that were unbalanced in the auxiliary variate so if the sample mean and population mean both of which are known at the time of analysis are not close it is known that the results are biased but the usual rand

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

on the asymptotic distribution of ratio and regression estimators we give a formal derivation of the asymptotic normality of ratio and regression estimators of a finite population total for simple random sampling and for sampling with probability proportional to aggregate size the results are all well known and widely used of course but a rigorous development spelling out relatively simple sufficient conditions under which the standard results are valid does not seem to be available at present

analysis of adomian decomposition applied to a third order ordinary differential equation from thin film flow abstract the adomian decomposition method is applied to the third order ordinary differential equation y y k obtained by considering a travelling wave solution admitted by a generalized thin film equation or for thin film flow down a vertical wall the adomian decomposition method leads to a power series approximation to the solution of y y k we show that the domain of convergence of the adomian decomposition solution is dependent on k we truncate the adomian decomposition solution at a suitable order to ensure that the truncated solution satisfies the contact line condition y 0 at some point x x we then determine the contact angle where tan d y d x at x x and plot the variation of contact angle with increasing k

precision estimation in sample survey inference a criterion for choice between variance estimators summary we advocate the mean squared error of predicted squared error as a universal criterion for the choice between variance estimators in sample survey inference the predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample this makes the new measure more satisfactory than the simpler mean squared error of the variance estimator the criterion turns out to be the same for design based as for model based inference and may also be used for comparison between the design and model based theoretical variances the theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature these calculations are primarily made under a proportional regression model but consideration is also paid to model robustness three of the six estimators are shown to be inferior to the three others which are approximately equivalent

the stress conjugate to logarithmic strain abstract a stress s is said to be conjugate to a strain measure e if the inner product s e is the power per unit volume the logarithmic strain in u with u the right stretch tensor has been considered an interesting strain measure because of the relationship of its material time derivative ln u with the stretching tensor d in a previous article int j solids structures 22 1019 1032 1986 a formula for ln u was obtained in direct notation for the cases where the principal stretches are repeated as well as for the case where they are all distinct here the formula for ln u and the definition of conjugate stress are used to derive an explicit properly invariant expression for the stress conjugate to the logarithmic strain

conjugate stress and tensor equation r 1mum 1xur 1 c abstract in this paper we seek an explicit tensorial expression which for each integer m 0 gives the stress t m conjugate to the strain e m in the seth hill class the preceding problem leads us to find an intrinsic i e coordinate free representation of the solution of the tensor equation displayed in the title we obtain the requisite representation by using hill s principal axis method and the representation theorem of isotropic tensor functions we illustrate the general procedure to obtain an explicit lensorial expression for t m by working out the instance m 3 in detail

on conditioning for model based inference in survey sampling summary a discontinuity of sampling distribution inference between a prediction problem and an estimation problem in model based survey sampling is discussed the problem is resolved by conditioning on an appropriate ancillary within a curved exponential family framework the ignorability of the sampling design for inference is discussed

prediction models and unequal probability sampling summary prediction models are used to study the horvitz thompson estimator in probabilityproportional to size sampling and six estimators of its variance the variance estimators include the horvitz thompson yates grundy and jackknife statistics as well as two bias robust estimators from prediction theory an empirical study confirms prediction theory s implications about these estimators

variance estimation for the regression estimator in two phase sampling abstract many techniques in survey sampling depend on the possession of information about an auxiliary variable x or a vector of auxiliary variables available for the entire population regression estimates require the population mean if such information is unavailable then one can sometimes obtain a large preliminary sample of xi relatively cheaply and use this to obtain a good estimate say of a smaller subsample can then be taken and the characteristic of interest yi measured a regression estimator can then be used treating as if it were this is termed double sampling or two phase sampling this article focuses on variance estimators for the regression estimator in the aforementioned context and their use in constructing confidence intervals a design based linearization variance estimator that makes more complete use of the sample data than the standard one is considered for two phase sampling a jackknife variance estimator and its linearized version are obtained and shown to be design c

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

on natural strain measures of the non linear micropolar continuum we discuss three different ways of defining the strain measures in the non linear micropolar continuum a by a direct geometric approach b considering the strain measures as the fields required by the structure of local equilibrium conditions and c requiring the strain energy density of the polar elastic body to satisfy the principle of invariance under superposed rigid body deformations the geometric approach a generates several two point deformation measures as well as some lagrangian and eulerian strain measures the ways b and c allow one to choose those lagrangian strain measures which satisfy the additional mechanical requirements these uniquely selected relative strain measures are called the natural ones all the strain measures discussed here are formulated in the general coordinate free form they are valid for unrestricted translations stretches and changes of orientations of the micropolar body and are required to identically vanish in the absence of deformation the relation of the lagrangian stretch and wryness tensors derived here to the ones proposed in the literature is thoroughly discussed

distance sampling methodology we consider the method of distance sampling described by buckland anderson burnham and laake in 1993 we explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design and model based frameworks in particular we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator within each framework these results enable us to clarify aspects of the performance of the methodology which may be of interest to users and potential users of distance sampling

the decomposition method for ordinary differential equations with discontinuities in this paper the decomposition method is applied to the initial value problem ivp for ordinary differential equations with discontinuities for both linear and nonlinear cases

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

conditional properties of some estimators in stratified sampling abstract the prediction properties of the stratified expansion estimator the separate and combined ratio estimators and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable several estimators of variance for each total estimator are considered including standard ones from probability sampling theory alternative choices derived from a superpopulation model and the jackknife the theory is tested in an empirical study using a real population earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties whether similar results hold for stratified samples and estimators has been the subject of some debate this article illustrates both theoretically and empirically that the use of stratifi

estimating a finite population mean from unequal probability samples abstract two approaches to estimating a finite population mean from unequal probability samples are contrasted in the prediction approach a model is specified for the population values and is used to predict the nonsampled values in the generalized regression approach the horvitz thompson estimator of the population mean is modified to allow the introduction of covariate information sarndal 1980 generalized regression estimates have the desirable property of asymptotic design consistency which is not always enjoyed by estimates in the prediction class however it is suggested that the prediction approach is the more principled method of estimation if asymptotic design consistency is a desirable property in a given application then only models that yield asymptotically design consistent prediction estimates should be used two classes of models with this property are suggested namely fixed and random effects models that allow a separate intercept for subclasses of the population indexed by the pr

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

thin films with high surface tension this paper is a review of work on thin fluid films where surface tension is a driving mechanism its aim is to highlight the substantial amount of literature dealing with relevant physical models and also analytic work on the resultant equations in general the introduction of surface tension into standard lubrication theory leads to a fourth order nonlinear parabolic equation pad h t pad x left c frac h 3 3 frac partial 3 h partial x 3 f h h x h xx right 0 label abeq1 where h h x t is the fluid film height for steady situations this equation may be integrated once and a third order ordinary differential equation is obtained appropriate forms of this equation have been used to model fluid flows in physical situations such as coating draining of foams and the movement of contact lenses in the introduction a form of the above equation is derived for flow driven by surface tension surface tension gradients gravity and long range molecular forces modifications to the equation due to slip the effect of two free surfaces two phase fluids and higher dimensional forms are also discussed the second section of this paper describes physical situations where surface tension driven lubrication models apply and the governing equations are given the third section reviews analytical work on the model equations as well as the generalized lubrication equation pad h t pad x left h n h xxx right 0 in particular the discussion focusses on asymptotic results travelling waves stability and similarity solutions numerical work is also discussed while for analytical results the reader is directed to existing literature

design effects of two stage sampling abstract in sampe surveys the design effect of a statistic is usually defined as the ratio of its true variance under the given sample design to its variance had the sample been obtained by simple random sampling empirical work suggests certain patterns for design effects of different types of statistics under different designs but theoretical work explaining these patterns is limited this paper obtains general theoretical results on the sructure of design effects for a broad class of statistical inference under a two stage sampling design in particular it discusses the relation between design effects of multivariate and of univariate statistics this relation is of practical interest because it is of relevance to the imputation of standard errors for multivariate statistics such as correlation coefficients or regression coefficients using design effects of univariate statistics the latter quantities are often routinely derived on completion of the survey the former may be difficult to compute by standard procedures either because of the absence of the necessary design information or because of software or degrees of freedom limitations

the finite population linear regression estimator and estimators of its variance an empirical study abstract the usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction superpopulation models its bias is compared with that of the least squares variance estimator also described are three bias robust alternatives one of which is the jackknife variance estimator the theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive nonrandom samples are drawn from six real populations the results illustrate the need for prediction models and the inadequacy of randomization per se in providing a theoretical framework for robust inferences

poststratification and conditional variance estimation poststratification estimation is a technique used in sample surveys to improve efficiency of estimators survey weights are adjusted to force the estimated numbers of units in each of a set of estimation cells to be equal to known population totals the resulting weights are then used in forming estimates of means or totals of variables collected in the survey for example in a household survey the estimation cells may be based on age race sex categories of individuals and the known totals may come from the most recent population census although the variance of a poststratified estimator can be computed over all possible sample configurations inferences made conditionally on the achieved sample configuration are desirable theory and a simulation study using data from the u s current population survey are presented to study both the conditional bias and variance of the poststratified estimator of a total the linearization balanced repeated replication and jackknife variance estimators are also exa

non linear finite element implementation of micropolar hypo elastic materials in this paper updated lagrangian finite element formulations for large elastic deformation of micropolar hypo elastic materials are presented using representation theorems of tensor functions the general form of the constitutive equations for the micropolar hypo elastic materials model are presented the finite element formulations are based on the general form of the micropolar hypo elastic constitutive equations in conjunction with jaumann rate and a new rate called gyration rate gyration rate describes the deformation of the material in view of an observer attached to the micro structure an incrementally objective stress and couple stress update procedure is developed and its applicability is investigated based on the jaumann and gyration rates two planar examples based on the simplified forms of the proposed constitutive equations with jaumann and gyration rates are investigated in the first example a plate with a small circular hole is analyzed and it is shown that the results of non linear analysis converge to the linear micropolar elasticity for the case of infinitesimal deformations in another example 2d deformation of a cantilever beam which is modeled as a slender rectangle is investigated the results of jaumann and gyration rates are very close to each other but an increase in the micropolar material parameters particularly an increase in the length scale parameter results in the reduction of the deformation of the beam also it is shown that for a specimen with very small dimensions e g in a micro beam the effect of the length scale parameter is more sensible than that of a specimen with an ordinary or large dimensions this means that micropolar effects become important for deformations taking place at small scales

basis free relations for the conjugate stresses of the strains based on the right stretch tensor abstract in this paper general relations between two different stress tensors t f and t g respectively conjugate to strain measure tensors f u and g u are found the strain class f u is based on the right stretch tensor u which includes the seth hill strain tensors the method is based on the definition of energy conjugacy and hill s principal axis method the relations are derived for the cases of distinct as well as coalescent principal stretches as a special case conjugate stresses of the seth hill strain measures are then more investigated in their general form the relations are first obtained in the principal axes of the tensor u then they are used to obtain basis free tensorial equations between different conjugate stresses these basis free equations between two conjugate stresses are obtained through the comparison of the relations between their components in the principal axes with a possible tensor expansion relation between the stresses with unknown coefficients the unknown coefficients to be obtained in this regard some relations are also obtained for t 0 which is the stress conjugate to the logarithmic strain tensor ln u

does simple random sampling provide adequate balance une etude empirique montre que sous un echantillonnage aleatoire simple les intervalles de confiance du total peuvent avoir des probabilites de recouvrement conditionnelles qui sont imposantes de facon persistante lorsque la taille de l echantillon croit

some prediction properties of balanced half sample variance estimators in single stage sampling on introduit un modele de prediction et une classe d estimateurs qui inclut plusieurs estimateurs du ratio de la regression et autres on donne une approximation a l estimateur bhs balanced half sample

outlier resistant alternatives to the ratio estimator abstract many techniques have been suggested to lower the impact of outliers on sample survey estimates outliers can be downweighted by winsorization that is by replacing extreme data points by a data dependent or a predetermined value before calculating estimates another approach is to reduce the weight of outliers from the inverse sampling fraction to 1 in the estimation of population characteristics in this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered a resistant version of the ratio estimator is introduced it is constructed with a m or a gm estimator of the slope of the regression model through the origin which is implicitly called on when considering the ratio estimator the asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan the selection of a resistant estimator is seen to involve a trade off betwee

simultaneously model unbiased design unbiased estimation this paper proposes a class of inferential procedures incorporating both design and estimation elements that yield estimates of means that are simultaneously model unbiased and design unbiased classical regression procedures yield conditionally unbiased estimators for the mean conditioning on the model and choice of observation points in contrast design based methods yield estimators that are unconditionally unbiased on matter what the form of the underlying model variance properties of the proposed class are examined and applications to bioavailability water quality from mine run off and finite population regression estimation are considered the proposed procedures perform well especially in the typical case where a model is only approximately correct

estimating distribution functions from survey data summary a simple method for estimating population distribution functions and associated quantiles from sample survey data is described and some asymptotic theory for it presented the method assumes a model based approach to survey estimation and allows auxiliary population information to be directly incorporated into the estimation process monte carlo results comparing the proposed method with conventional design based methods are given these suggest that the model based approach offers significant gains when the auxiliary population information is linearly related to the survey variables of interest

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

the decomposition method for stiff systems of ordinary differential equations in this paper the decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases focusing our interest in stiff problems

a numerical and asymptotic study of some third order ordinary differential equations relevant to draining and coating flows some draining or coating fluid flow problems in which surface tension forces are important can be described by third order ordinary differential equations accurate computations are provided here

constitutive equations for micropolar hyper elastic materials in this paper the concept of hyper elasticity in the micropolar continuum theory is investigated the restrictions on the fourth order elasticity tensors are investigated using the representation theorems a general form of constitutive equations for micropolar hyper elastic isotropic materials is presented as some special cases generalizations of the neo hookean and mooney rivlin type materials to the micropolar continuum theory are presented the generalized constitutive equations reduce to those of the microplar linear elasticity theory when the deformations are infinitesimal also updated lagrangian finite element formulations for the micropolar hyper elastic materials are presented considering two planar examples it is shown that an increase in the micropolar parameter results in the reduction of the deformation of the bodies also it is shown that for a specimen with very small dimensions e g in the micron level the micropolar effects are more sensible furthermore it is shown that the influence of the micropolar parameters is dependent not only on the size of the body but also to its geometry and loading conditions for the problems in which the deformation is very close to a homogeneous state the micropolar effects are negligible