k theory of log schemes ii log syntomic k theory abstract we prove that suitably truncated topological log syntomic etale homotopy k theory of proper semistable schemes in mixed characteristic surjects onto the kummer log etale p adic k theory of the generic fiber as a corollary we get that the log syntomic etale cohomology is a direct factor of the log syntomic etale cohomology of homotopy k theory sheaves the proofs use p adic hodge theory computations of p adic nearby cycles

artin tate motivic sheaves with finite coefficients over an algebraic variety we propose a construction of a tensor exact category fxm of artin tate motivic sheaves with finite coefficients z m over an algebraic variety x over a field k of characteristic prime to m in terms of etale sheaves of z m modules over x among the objects of fxm in addition to the tate motives z m j there are the cohomological relative motives with compact support mccm y x of varieties y quasi finite over x exact functors of inverse image with respect to morphisms of algebraic varieties and direct image with compact supports with respect to quasi finite morphisms of varieties y x act on the exact categories fxm assuming the existence of triangulated categories of motivic sheaves dm x z m over algebraic varieties x over k and a weak version of the six operations in these categories we identify fxm with the exact subcategory in dm x z m consisting of all the iterated extensions of the tate twists mccm y x j of the motives mccm y x an isomorphism of the z m modules ext between the tate motives z m j in the exact category fxm with the motivic cohomology modules predicted by the beilinson lichtenbaum etale descent conjecture recently proved by voevodsky rost et al holds for smooth varieties x over k if and only if the similar isomorphism holds for artin tate motives over fields containing k when k contains a primitive m root of unity the latter condition is equivalent to a certain koszulity hypothesis as shown in our previous paper positselski mixed artin tate motives with finite coefficients mosc math j 11 2011 317 402

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

on the kernel of the reciprocity map of varieties over local fields this thesis is about higher dimensional class field theory of varieties over local and finite fields their abelianized etale fundamental group is compared with an attached class group via the reciprocity map like in the classical case of a local or global field the main results in this thesis are about the structure of the kernel of their reciprocity maps and criteria for the vanishing of it resp

zeta functions of regular arithmetic schemes at s 0 lichtenbaum conjectured in 22 the existence of a weil etale cohomology in order to describe the vanishing order and the special value of the zeta function of an arithmetic scheme x at s 0 in terms of euler poincare characteristics assuming the conjectured finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over spec z in particular we compute uncon ditionally the right weil etale cohomology of number rings and projective spaces over number rings we state a precise version of lichtenbaum s con jecture which expresses the vanishing order resp the special value of the zeta function x s at s 0 as the rank resp the determinant of a single perfect complex of abelian groups r w c x z then we relate this conjecture to soule s conjecture and to the tamagawa number conjecture lichtenbaum s conjecture for projective spaces over the ring of integers of an abelian number field follows

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

on case control sampling of clustered data summary we derive the relationship between the population model and the sample model in the case of case control sampling of clustered responses the derived formulae provide insight into why methods that ignore the sampling scheme fail to provide consistent estimators in this case the differences between clustered and independent responses in the context of the case control design are discussed the case control design is known for its efficiency at a fixed sample size when the disease under study is rare it is also potentially useful in clustered data set ups where the interest is in covariate effects or in dependence within clusters neuhaus jewell 1990 showed that sampling clusters instead of individuals can bias the estimation of population parameters if standard logistic regression techniques are used even if the individuals within a cluster are independent they investigated the estimation problem under marginal conditional and random effect models for marginal models they presented expressions for the distribution of disease in the sampled observations in the case of within cluster independence we restrict attention to marginal also called population averaged models zeger liang albert 1988 for these models we extend the results of neuhaus jewell 1990 by presenting expressions for the sample mean and dependence structure in the general case allowing dependence among members of a cluster we envisage a population consisting of a large number of clusters observations within a cluster are dependent but clusters are independent of each other let yij be a binary random variable denoting the jth response in the ith cluster xij a p x 1 covariate vector i 1 2 k j 1 2 ni furthermore let y and xi be the response vector and covariate matrix for the ith cluster respectively suppose that the response is coded so that yj 1 indicates the presence of disease and yij 0 its absence we consider designs in which clusters rather than individual observations are the sampling units specifically let si 1 and si 0 indicate whether the ith cluster was sampled or not respectively the sampling probabilities are defined as oi pr si 1i1 y xi we consider only the case in which oi depends on yi only through t n i 1 and xi neuhaus jewell 1990 refer to this case as sampling with probability dependent on the number of responses in that case oi g t7 xi ni for a known function g we shall write gi ti for brevity a special case is one in which clusters with one or more affected members are sampled with probability rc and clusters with no affected member are sampled with probability co

motivic periods and grothendieck arithmetic invariants abstract we construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers for the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective showing that a suitable betti de rham realization of 1 motives is fully faithful we can verify this period conjecture in several cases the divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical grothendieck period conjecture for algebraic cycles on smooth and proper schemes these divisibility properties are treated in an appendix by b kahn extending previous work of bloch and colliot thelene raskind

motivic cohomology over dedekind rings we study properties of bloch s higher chow groups on smooth varieties over dedekind rings we prove the vanishing of open image in new window for i n and the existence of a gersten resolution for open image in new window if the residue characteristic is p we also show that the bloch kato conjecture implies the beilinson lichtenbaum conjecture open image in new window an identification open image in new window for m invertible and a gersten resolution with arbitrary finite coefficients over a complete discrete valuation ring of mixed characteristic 0 p we construct a map from motivic cohomology to syntomic cohomology which is a quasi isomorphism provided the bloch kato conjecture holds

longitudinal studies of binary response data following case control and stratified case control sampling design and analysis we discuss design and analysis of longitudinal studies after case control sampling wherein interest is in the relationship between a longitudinal binary response that is related to the sampling case control variable and a set of covariates we propose a semiparametric modeling framework based on a marginal longitudinal binary response model and an ancillary model for subjects case control status in this approach the analyst must posit the population prevalence of being a case which is then used to compute an offset term in the ancillary model parameter estimates from this model are used to compute offsets for the longitudinal response model examining the impact of population prevalence and ancillary model misspecification we show that time invariant covariate parameter estimates other than the intercept are reasonably robust but intercept and time varying covariate parameter estimates can be sensitive to such misspecification we study design and analysis issues impacting study efficiency namely choice of sampling variable and the strength of its relationship to the response sample stratification choice of working covariance weighting and degree of flexibility of the ancillary model the research is motivated by a longitudinal study following case control sampling of the time course of attention deficit hyperactivity disorder adhd symptoms

on the rational derivation of a hierarchy of dynamic equations for a homogeneous isotropic elastic plate abstract flexural equations of motion for a homogeneous isotropic elastic plate are derived by an antisymmetric expansion in the thickness coordinate of the displacement components all but the lowest order expansion functions are eliminated with the help of the three dimensional equations of motion and are plugged into the boundary conditions eliminating between these an equation is obtained for the mean plane vertical displacement which also includes arbitrary loading on the plate surface this equation can be truncated to any order in the thickness and it is in particular noted that the corresponding dispersion relation seems to correspond to a power series expansion of the exact rayleigh lamb dispersion relation to all orders various truncations of the equation are discussed and are compared numerically with each other the exact three dimensional solution and mindlin s plate equation both the dispersion relation and the corresponding displacement components as well as an excitation problem are used for the comparisons the theories are reasonably close to each other and in order to be on the safe side none of them should in fact be used for frequencies above the cutoff of the second flexural mode

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

theoremes de dualite pour les corps de fonctions sur des corps locaux superieurs let k be the function field of a smooth projective curve x over a higher dimensional local field k we define tate shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of k coming from a closed point of x we establish duality theorems between tate shafarevich groups for finite groups schemes and for tori

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

modelling of finite piezoelectric patches comparing an approximate power series expansion theory with exact theory plate equations for a plate consisting of one elastic layer and one piezoelectric layer with an applied electric voltage have previously been derived by use of power series expansions of the field variables in the thickness coordinate these plate equations are here evaluated by the consideration of a time harmonic 2d vibration problem with finite layers the boundary conditions at the sides of the layers then have to be considered numerical comparisons of the displacement field are made with solutions from two other theories a solution with equivalent boundary conditions for a thin piezoelectric layer applied on an elastic plate and an exact solution based on fourier series expansions the two approximate theories are shown to be equally good and they both yield accurate results for low frequencies and thin plates

approximate dynamic boundary conditions for a thin piezoelectric layer abstract approximate dynamic boundary conditions of different orders are derived for the case of a thin piezoelectric coating layer bonded to an elastic material the approximate boundary conditions are derived using series expansions of the elastic displacements and the electric potential in the thickness coordinate of the layer all the expansion functions are then eliminated with the aid of the equations of motion and boundary interface conditions of the layer this results in boundary conditions on the elastic material that may be truncated to different orders in the thickness of the layer to obtain approximate boundary conditions the approximate boundary conditions may be used as a replacement for the piezoelectric layer and thus simplify the analysis significantly numerical examples show that the approximate boundary conditions give good results for low frequencies and or thin piezoelectric layers

realisation l adique des motifs triangules geometriques ii for geometrical triangulated motives with rational coefficients over a ground field of characteristic zero which is embeddable into mathbb c huber j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 has constructed a realization functor with values in the category of mixed realization of huber mixed motives and their realization in derived categories lecture notes in mathematics vol 1604 springer berlin 1995 in this sequel to ivorra doc math 12 607 671 2007 we prove that the l adic realization functor obtained in theorem 4 3 of ivorra doc math 12 607 671 2007 is the same up to a canonical isomorphism as the l adic component of a huber s construction in this way ivorra in doc math 12 607 671 2007 might be viewed as an integral generalization to all noetherian separed schemes of the work huber in j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 as far as the l adic setting is concerned we also prove a comparison theorem with the classical l adic cycle class map over a perfect field using a naive motivic cycle class map

factorization of p adic rankin l series we prove that the p adic l series of the tensor square of a p ordinary modular form factors as the product of the symmetric square p adic l series of the form and a kubota leopoldt p adic l series this establishes a generalization of a conjecture of citro greenberg s exceptional zero conjecture for the adjoint follows as a corollary of our theorem our method of proof follows that of gross who proved a factorization result for the katz p adic l series associated to the restriction of a dirichlet character whereas gross s method is based on comparing circular units with elliptic units our method is based on comparing these same circular units with a new family of units called beilinson flach units that we construct the beilinson flach units are constructed using bloch s intersection theory of higher chow groups applied to products of modular curves we relate these units to special values of classical and p adic l functions using work of beilinson as generalized by lei loeffler zerbes in the archimedean case and bertolini darmon rotger as generalized by kings loeffler zerbes in the p adic case central to our method are two compatibility theorems regarding bloch s intersection pairing and the classical and p adic beilinson regulators defined on higher chow groups

the order of higher brauer groups let x be a smooth projective variety of dimension 2r over a finite field mathbb f we prove that for every prime ell ne mathrm char mathbb f the order of the non divisible quotient of the ell primary torsion group of the higher brauer group mathrm br r x ell mathrm nd is a square number

rost nilpotence and etale motivic cohomology abstract a smooth projective scheme x over a field k is said to satisfy the rost nilpotence principle if any endomorphism of x in the category of chow motives that vanishes on an extension of the base field k is nilpotent we show that an etale motivic analogue of the rost nilpotence principle holds for all smooth projective schemes over a perfect field this provides a new approach to the question of rost nilpotence and allows us to obtain an elegant proof of rost nilpotence for surfaces as well as for birationally ruled threefolds over a field of characteristic 0

mindlin plate theory best shear coefficient and higher spectra validity mindlin plate theory predicts three frequency spectra or equivalently three branches to a phase velocity dispersion diagram the lowest of which thew1mode provides rotatory inertia and shear deformation corrections to classical thin plate theory employing consistent truncation procedures to both the mindlin and the exact rayleigh lamb frequency equations valid for long wavelength and low phase velocity one finds thatw1mode agreement is achieved when the shear coefficient takes the valuek 5 6 v the mindlin prediction is then less than 0 5 in error when the wavelength is equal to the plate thickness and less than 1 in error as wavelength approaches zero the previously dismissed mindlinhmode is seen to be in exact frequency or phase velocity agreement with the second slowestshwave in the infinite plate as long as the shear coefficient for this mode takes the valuek 2 12 however thew2mode as with the second frequency spectrum of timoshenko beams should be regarded as the inevitable but meaningless consequence of an otherwise remarkable approximate engineering theory

asymptotic splitting in the three dimensional problem of elasticity for non homogeneous piezoelectric plates a novel asymptotic approach to the theory of non homogeneous anisotropic plates is suggested for the problem of linear static deformations we consider solutions which are slowly varying in the plane of the plate in comparison to the thickness direction a small parameter is introduced in the general equations of the theory of elasticity according to the procedure of asymptotic splitting the principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms three dimensional conditions of compatibility make the analysis more efficient and straightforward we obtain the system of equations of classical kirchhoff s plate theory including the balance equations compatibility conditions elastic relations and kinematic relations between the displacements and strain measures subsequent analysis of the edge layer near the contour of the plate is required in order to satisfy the remaining boundary conditions of the three dimensional problem matching of the asymptotic expansions of the solution in the edge layer and inside the domain provides four classical plate boundary conditions additional effects like electromechanical coupling for piezoelectric plates can easily be incorporated into the model due to the modular structure of the analysis the results of the paper constitute a sound basis to the equations of the theory of classical plates with piezoelectric effects and provide a trustworthy algorithm for computation of the stressed state in the three dimensional problem numerical and analytical studies of a sample electromechanical problem demonstrate the asymptotic nature of the present theory

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

fitting logistic models under case control or choice based sampling on compare deux approches dans le cas important de l ajustement des modeles de regression logistique

the effect of retrospective sampling on binary regression models for clustered data recently a great deal of attention has been given to binary regression models for clustered or correlated observations the data of interest are of the form of a binary dependent or response variable together with independent variables x1 xk where sets of observations are grouped together into clusters a number of models and methods of analysis have been suggested to study such data many of these are extensions in some way of the familiar logistic regression model for binary data that are not grouped i e each cluster is of size 1 in general the analyses of these clustered data models proceed by assuming that the observed clusters are a simple random sample of clusters selected from a population of clusters in this paper we consider the application of these procedures to the case where the clusters are selected randomly in a manner that depends on the pattern of responses in the cluster for example we show that ignoring the retrospective nature of the sample design by fitting standard logistic regression models for clustered binary data may result in misleading estimates of the effects of covariates and the precision of estimated regression coefficients

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

addendum to values of zeta functions of varieties over finite fields the original article it amer j math bf 108 1986 no 2 297 360 expressed the special values of the zeta function of a variety over a finite field in terms of the widehat bbb z cohomology of the variety as the article was being completed september 1983 lichtenbaum conjectured the existence of complexes of sheaves bbb z r extending the sequence bbb z bbb g m 1 ldots the complexes given by bloch s higher chow groups are known to satisfy most of the axioms for bbb z r using lichtenbaum s weil e tale topology we can now give a beautiful restatement of the main theorem of the original article in terms of bbb z cohomology groups

comparison of dualizing complexes we prove that there is a map from bloch s cycle complex to kato s complex of milnor k theory which induces a quasi isomorphism from etale sheafified cycle complex to the gersten complex of logarithmic de rham witt sheaves next we show that the truncation of bloch s cycle complex at 3 is quasi isomorphic to spiess dualizing complex

on asymptotically correct linear laminated plate theory abstract the focus of this paper is the development of asymptotically correct theories for laminated plates the material properties of which vary through the thickness and for which each lamina is orthotropic this work is based on the variational asymptotical method a mathematical technique by which the three dimensional analysis of plate deformation can be split into two separate analyses a one dimensional through the thickness analysis and a two dimensional plate analysis the through the thickness analysis includes elastic constants for use in the plate theory and approximate closed form recovering relations for all three dimensional field variables expressed in terms of plate variables in general the specific type of plate theory that results from this procedure is determined by the procedure itself however in this paper only reissner like plate theories are considered often called first order shear deformation theories this paper makes three main contributions first it is shown that construction of an asymptotically correct reissner like theory for laminated plates of the type considered is not possible in general second a new point of view on the variational asymptotical method is presented leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible third numerical results from such an optimum reissner like theory are presented these results include comparisons of plate displacement as well as of three dimensional field variables and are the best of all extant reissner like theories indeed they even surpass results from theories that carry many more generalized displacement variables

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

evaluation of higher order theories of piezoelectric plates in bending and in stretching many models for the flexural and membranal behaviour of piezoelectric plates are available in the literature they are based on different assumptions concerning the strain stress electric and electric displacement fields inside the plate a critical comparison among such models is presented here in a completely analytic way in order to assess the accuracy of the results they provide and determine their range of applicability the comparison is made by using a class of case study problems whose analytical solutions in the framework of the linear theory of piezoelectricity are available as benchmarks for the solutions supplied by the plate models the evaluated models are also here rationally derived from the three dimensional theory of piezoelectricity and a consistent treatment of the stress and electric displacement relaxation conditions is proposed

a hierarchy of dynamic equations for micropolar plates this work considers homogeneous isotropic micropolar plates adopting a power series expansion method in the thickness coordinate variationally consistent equations of motion and end boundary conditions are derived in a systematic fashion up to arbitrary order for extensional and flexural displacement cases the plate equations are asymptotically correct to all studied orders numerical results are presented for various orders of the present method other approximate theories as well as the exact three dimensional theory the results illustrate that the present approach may render benchmark solutions provided higher order truncations are used and act as engineering plate equations using low order truncation

dynamic equations for an isotropic spherical shell using the power series method and surface differential operators dynamic equations for an isotropic spherical shell are derived by using a series expansion technique the displacement field is split into a scalar radial part and a vector tangential part surface differential operators are introduced to decrease the length of the shell equations the starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid surface of the shell by using the expansions of the displacement components the three dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of these of lowest orders applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness after lengthy manipulations the final four shell equations are obtained in a more compact form which can be represented explicitly in terms of the surface differential operators the method is believed to be asymptotically correct to any order the eigenfrequencies are compared to exact three dimensional theory and membrane theory

a hierarchy of dynamic equations for solid isotropic micropolar circular cylinders this work considers the derivation procedure and evaluation of dynamic equations for isotropic micropolar circular cylinders by adopting a power series expansion method in the radial coordinate variationally consistent equations of motion together with pertinent sets of boundary conditions are expressed in a systematic fashion up to arbitrary order the numerical results cover eigenfrequencies mode shapes and field distributions over cross sections for axisymmetric and flexural motion adopting different sets of end boundary conditions for equations of different truncation orders of the present method the results illustrate that the present approach may render benchmark solutions provided that higher order equations are used and act as accurate approximate engineering solution for lower order equations

dynamic equations for fluid loaded porous plates using approximate boundary conditions systematically derived equations for fluid loaded thin poroelastic layers are presented for time harmonic conditions the layer is modeled according to biot theory for both open and closed pores series expansion techniques in the thickness variable are used resulting in separate symmetric and antisymmetric plate equations these equations which are believed to be asymptotically correct are expressed in terms of approximate boundary conditions and can be truncated to arbitrary order analytical and numerical results are presented and compared to the exact three dimensional theory and a flexural plate theory numerical comparisons are made for two material configurations and two thicknesses the results show that the presented theory predicts the plate behavior accurately

a hierarchy of high order theories for symmetric modes in an elastic layer abstract a hierarchy of high order theories for symmetric modes in an infinitely long elastic layer of the constant thickness is derived by means of the inertia corrected polynomial approximations for each member of the hierarchy boundary conditions for layers of the finite length are formulated the forcing problems at several approximation levels are solved with the use of the bi orthogonality conditions accuracy of these approximations is assessed by comparison of results with the exact solution of the rayleigh lamb problem special attention is paid to the power flow analysis in alternative modal excitation cases and to the applicability of the saint venant s principle in stationary elasto dynamics

an exact three dimensional solution for normal loading of inhomogeneous and laminated anisotropic elastic plates of moderate thickness an exact three dimensional solution is presented for the deformation and stress distribution in an elliptical plate under uniform normal loading of the lateral surfaces and clamped along its edge the plate is assumed to be of constant moderate thickness and composed of anisotropic elastic material which is inhomogeneous in the through thickness direction but symmetric about the mid plane the only material symmetry assumed is that of reflectional symmetry in planes parallel to the mid plane a transfer matrix method is used which without making any further assumptions gives the exact solution at each point in the plate in terms of the stress and displacement at the mid plane the two dimensional differential equations governing these mid plane values are found to be the same as those for an equivalent homogeneous plate whose constant elastic moduli are determined by appropriate through thickness weighted averages of the inhomogeneous moduli the solution of the two dimensional problem is known for such a plate when subject to the specified surface and edge conditions and yields a closed form analytical solution that satisfies all the governing equations and surface conditions of the full three dimensional elasticity problem with edge displacement conditions satisfied on the mid plane the important special case of an anisotropic laminated plate is given by assuming piecewise constant properties through the thickness

on webster s horn equation and some generalizations sound waves along a rigid axisymmetric tube with a variable cross section are considered the governing helmholtz equation is solved using power series expansions in a stretched radial coordinate leading to a hierarchy of one dimensional ordinary differential equations in the longitudinal direction the lowest approximation for axisymmetric motion turns out to be webster s horn equation fourth order differential equations are obtained at the next level of approximation comparisons with existing asymptotic theories for waves in slender tubes are made

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

on the so called variational consistency of plate models i indefinite plates evaluation of dispersive behaviour abstract four groups of refined shear deformation plate theories are examined including the so called variationally inconsistent theories of schmidt levinson and touratier whose inconsistence is in fact weak after a unified presentation of these two dimensional theories all are deduced from the three dimensional theory of elasticity through a suitable variation procedure which disconnects the choice of the so called virtual motions from the choice of an approximation for the small displacement field this procedure makes obvious in a natural way the importance of the stress boundary conditions on the faces of the pate for any two dimensional theory as a test comparison a wave dispersion evaluation of these theories is performed for the propagation of flexural waves in an indefinite plate a detailed comparison leads to the conclusion that the inconsistent theories may offer some advantages in the domain of short waves

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions wave propagation through a layer of a material that is inhomogeneous in the thickness direction typically a functionally graded material fgm is investigated the material parameters and the displacement components are expanded in power series in the thickness coordinate leading to recursion relations among the displacement expansion functions these can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions and this can be done even if the layer is not thin this gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties for thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer thus completely replacing the layer by these effective boundary conditions numerical examples illustrate the convergence properties of the scheme for fg layers and the influence of different variations of the material parameters in the fg layer