natural vibration of pre twisted shear deformable beam systems subject to multiple kinds of initial stresses free vibration and buckling of pre twisted beams exhibit interesting coupling phenomena between compression moments and torque and have been the subject of extensive research due to their importance as models of wind turbines and helicopter rotor blades the paper investigates the influence of multiple kinds of initial stresses due to compression shears moments and torque on the natural vibration of pre twisted straight beam based on the timoshenko theory the derivation begins with the three dimensional green strain tensor the nonlinear part of the strain tensor is expressed as a product of displacement gradient to derive the strain energy due to initial stresses the frenet formulae in differential geometry are employed to treat the pre twist the strain energy due to elasticity and the linear kinetic energy are obtained in classical sense from the variational principle the governing equations and the associated natural boundary conditions are derived it is noted that the first mode increases together with the pre twisted angle but the second decreases seeming to close the first two modes together for natural frequencies and compressions the gaps close monotonically as the angle of twist increases for natural frequencies and buckling compressions however unlike natural frequencies and compressions the closeness is not monotonic for buckling shears moments and torques

a functional wavelet kernel approach for time series prediction summary we consider the prediction problem of a time series on a whole time interval in terms of its past the approach that we adopt is based on functional kernel nonparametric regression estimation techniques where observations are discrete recordings of segments of an underlying stochastic process considered as curves these curves are assumed to lie within the space of continuous functions and the discretized time series data set consists of a relatively small compared with the number of segments number of measurements made at regular times we estimate conditional expectations by using appropriate wavelet decompositions of the segmented sample paths a notion of similarity based on wavelet decompositions is used to calibrate the prediction asymptotic properties when the number of segments grows to 1 are investigated under mild conditions and a nonparametric resampling procedure is used to generate in a flexible way valid asymptotic pointwise prediction intervals for the trajectories predicted we illustrate the usefulness of the proposed functional wavelet kernel methodology in finite sample situations by means of a simulated example and two real life data sets and we compare the resulting predictions with those obtained by three other methods in the literature in particular with a smoothing spline method with an exponential smoothing procedure and with a seasonal autoregressive integrated moving average model

isothermic surfaces in sphere geometries as moutard nets we give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries projective mobius laguerre and lie we find the core of the theory to be a novel characterization of discrete isothermic nets as moutard nets the latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete moutard equation moutard nets admit also a projective geometric characterization as nets with planar faces with a five point property a vertex and its four diagonal neighbours span a three dimensional space restricting the projective theory to quadrics we obtain moutard nets in sphere geometries in particular moutard nets in mobius geometry are shown to coincide with discrete isothermic nets the five point property in this particular case states that a vertex and its four diagonal neighbours lie on a common sphere which is a novel characterization of discrete isothermic surfaces discrete laguerre isothermic surfaces are defined through the corresponding five plane property which requires that a plane and its four diagonal neighbours share a common touching sphere equivalently laguerre isothermic surfaces are characterized by having an isothermic gauss map s isothermic surfaces as an instance of moutard nets in lie geometry are also discussed

analytic trapezoidal fourier p element for vibrating plane problems a trapezoidal fourier p element for the in plane vibration analysis of two dimensional elastic solids is presented trigonometric functions are used as enriching functions instead of polynomials to avoid ill conditioning problems the element matrices are analytically integrated in closed form with the additional fourier degrees of freedom d o f s the accuracy of the computed natural frequencies is greatly increased one element can predict many modes accurately since a triangle can be divided into three trapezoidal elements the range of application is much wider than the previously derived rectangular fourier p element numerical examples show that convergence is very fast with respect to the number of trigonometric terms comparison of natural modes calculated by the trapezoidal fourier p element and the conventional finite elements is carried out the results show that the trapezoidal fourier p element produces much higher accurate modes than the conventional finite elements with the same number of d o f s for a benchmark problem the condition number of the mass matrix using legendre p element increases rapidly and it becomes non positive with 22 terms the condition numbers of the fourier p element matrices are consistently much lower than those of the legendre p element

soliton surfaces in the mechanical equilibrium of closed membranes for a closed material membrane in equilibrium in a force field we investigate whether the external observables membrane geometry and force field determine the internal membrane response the stress tensor t when the mean stress open image in new window tr t is known for membranes with boundary the indeterminacy of the response is classical for closed membranes the geometry decides the question we show uniqueness for all but a class of soliton surfaces the globally isothermic surfaces 1 2 the physical phenomenon exhibited by any closed globally isothermic membrane in equilibrium is that with all observables static there is in total a 1 parameter family of responses with the same mean stress all canonically determined by membrane geometry theorem 1 there exist closed embedded globally isothermic surfaces of every genus the recognition of the role of these soliton surfaces settles the old classification problem for the space of static shears in any closed membrane explicitly identifying all static shears where before only a genus dependent dimension bound was known theorem 2

a triangular fourier p element for the analysis of membrane vibrations abstract a triangular fourier p element for the analysis of membrane vibrations is presented the element s transverse displacement is written in terms of dimensionless area co ordinates and is described by three linear shape functions plus a variable number of trigonometric shape functions the three nodal displacements and the amplitudes of the trigonometric functions on the three edges and in the interior of the element respectively are used as generalized co ordinates inter element compatibility is achieved by matching the generalized co ordinates at the three nodes and the three edges results are obtained for a right isosceles triangular and a square membranes and comparisons are made with exact and linear triangular finite element solutions the results of both membranes confirm that the solutions converge very fast from above to the exact values as the number of trigonometric terms is increased and highly accurate values are obtained with the use of a very few terms the results also show that the triangular fourier p element produces a much higher accuracy than the linear triangular finite element with fewer system degrees of freedom

conditional quantile analysis when covariates are functions with application to growth data summary motivated by the conditional growth charts problem we develop a method for conditional quantile analysis when predictors take values in a functional space the method proposed aims at estimating conditional distribution functions under a generalized functional regression framework this approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors its good performance in comparison with other methods both for sparsely and for densely observed functional covariates is demonstrated through theory as well as in simulations and an application to growth curves where the method proposed can for example be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height

functional mixed effects models in this article a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced the linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects which are modeled as realizations of zero mean stochastic processes the fixed functional effects and the random functional effects are modeled in the same functional space which guarantee the population average and subject specific curves have the same smoothness property these models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures can include continuous covariates as well as dummy factors in both the fixed or random design matrices and include the nested curves models as special cases two estimation procedures are proposed the first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software the second procedure is a sequential estimation procedure using kalman filtering this algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets a generalized maximum likelihood gml ratio test is proposed for inference and model selection an application to comparison of cortisol profiles is used as an illustration

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

uniqueness of isometric immersions with the same mean curvature abstract motivated by the quasi local mass problem in general relativity we study the rigidity of isometric immersions with the same mean curvature into a warped product space as a corollary of our main result two star shaped hypersurfaces in a spatial schwarzschild or ads schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature we also prove similar results if the mean curvature condition is replaced by an 2 curvature condition

zero sets of solutions to semilinear elliptic systems of first order consider a nontrivial smooth solution to a semilinear elliptic system of first order with smooth coefficients defined over an n dimensional manifold assume the operator has the strong unique continuation property we show that the zero set of the solution is contained in a countable union of smooth n 2 dimensional submanifolds hence it is countably n 2 rectifiable and its hausdorff dimension is at most n 2 moreover it has locally finite n 2 dimensional hausdorff measure we show by example that every real number between 0 and n 2 actually occurs as the hausdorff dimension for a suitable choice of operator we also derive results for scalar elliptic equations of second order

estimating variance components in functional linear models with applications to genetic heritability quantifying heritability is the first step in understanding the contribution of genetic variation to the risk architecture of complex human diseases and traits heritability can be estimated for univariate phenotypes from nonfamily data using linear mixed effects models there is however no fully developed methodology for defining or estimating heritability from longitudinal studies by examining longitudinal studies researchers have the opportunity to better understand the genetic influence on the temporal development of diseases which can be vital for populations with rapidly changing phenotypes such as children or the elderly to define and estimate heritability for longitudinally measured phenotypes we present a framework based on functional data analysis fda while our procedures have important genetic consequences they also represent a substantial development for fda in particular we present a very general methodology for constructing optimal unbiased estimates of variance components in fu

hierarchical finite element analysis of the vibration of membranes abstract a hierachical finite element for the vibration of membranes is presented the element has the ability to be joined to neighbouring elements and the numbers of hierarchical terms are allowed to vary in both directions of the element co ordinate axes the element transverse displacement is described by four linear shape functions plus a variable number of hierarchical functions which are forms of legendre orthogonal polynomials the four nodal displacements and the amplitudes of the hierarchical functions on the edges and in the interior of the element are used as generalized co ordinates inter element compatibility is achieved by matching the generalized co ordinates at the nodes and edges shared by elements results are obtained for simply supported square and l shaped membranes comparisons are made with exact solutions for the square membrane and with highly accurate approximate and linear finite element solutions for the l shaped membrane the results for the square membrane confirm that the solutions always converge from above to the exact values as the numbers of hierarchical terms are increased and highly accurate answers are obtained depite the use of a very few hierarchical terms the results of the l shaped membrane show that the hierarchical finite element solutions are largely more accurate than the linear finite element solutions despite the use of fewer system degrees of freedom

deformation of hypersurfaces preserving the mobius metric and a reduction theorem abstract a hypersurface without umbilics in the n 1 dimensional euclidean space f m n r n 1 is known to be determined by the mobius metric g and the mobius second fundamental form b up to a mobius transformation when n 3 in this paper we consider mobius rigidity for hypersurfaces and deformations of a hypersurface preserving the mobius metric in the high dimensional case n 4 when the highest multiplicity of principal curvatures is less than n 2 the hypersurface is mobius rigid when the multiplicities of all principal curvatures are constant deformable hypersurfaces and the possible deformations are also classified completely in addition we establish a reduction theorem characterizing the classical construction of cylinders cones and rotational hypersurfaces which helps to find all the non trivial deformable examples in our classification with wider application in the future

wavelet based functional mixed models increasingly scientific studies yield functional data in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid we present new methodology that generalizes the linear mixed model to the functional mixed model framework with model fitting done by using a bayesian wavelet based approach this method is flexible allowing functions of arbitrary form and the full range of fixed effects structures and between curve covariance structures that are available in the mixed model framework it yields nonparametric estimates of the fixed and random effects functions as well as the various between curve and within curve covariance matrices the functional fixed effects are adaptively regularized as a result of the non linear shrinkage prior that is imposed on the fixed effects wavelet coefficients and the random effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient because we have posterior samples for all model quantities we can perform pointwise or joint bayesian inference or prediction on the quantities of the model the adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks

isothermic submanifolds of symmetric r spaces we extend the classical theory of isothermic surfaces in conformal 3 space due to bour christoffel darboux bianchi and others to the more general context of submanifolds of symmetric r spaces with essentially no loss of integrable structure

generalized functional linear models we propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function a linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function and the expected value of the response is related to this linear predictor via a link function if in addition a variance function is specified this leads to a functional estimating equation which corresponds to maximizing a functional quasi likelihood this general approach includes the special cases of the functional linear model as well as functional poisson regression and functional binomial regression the latter leads to procedures for classification and discrimination of stochastic processes and functional data we also consider the situation where the link and variance functions are unknown and are estimated nonparametrically from the data using a semiparametric quasi likelihood procedure an essential step in our proposal is dimension reduction by approximating the predictor processes with a truncated karhunen loeve expansion we develop asymptotic inference for the proposed class of generalized regression models in the proposed asymptotic approach the truncation parameter increases with sample size and a martingale central limit theorem is applied to establish the resulting increasing dimension asymptotics we establish asymptotic normality for a properly scaled distance between estimated and true functions that corresponds to a suitable l 2 metric and is defined through a generalized covariance operator as a consequence we obtain asymptotic tests and simultaneous confidence bands for the parameter function that determines the model the proposed estimation inference and classification procedures and variants with unknown link and variance functions are investigated in a simulation study we find that the practical selection of the number of components works well with the aic criterion and this finding is supported by theoretical considerations we include an application to the classification of medflies regarding their remaining longevity status based on the observed initial egg laying curve for each of 534 female medflies

3d hierarchical hp fem applied to elasto acoustic modelling of layered porous media this paper presents a 3 d hierarchical p version finite element description of the solid displacement fluid displacement form of biot s equation for elasto acoustic modelling of multiple layered isotropic porous media the convergence related to mesh refinement extensions for different orders of polynomial approximation is briefly discussed for a homogeneous foam the highest computational efficiency for reasonable levels of the error in the low frequency region was obtained for fourth order polynomial finite element interpolations the main focus is on coupling conditions and on the convergence of solutions to biot s equations in cases with multiple layers having different material properties simulations of a two layered porous material with low flow resistivity suggest slow convergence rate of the fluid displacement field close to the interface between the layers

inferring stochastic dynamics from functional data in most current data modelling for time dynamic systems one works with a prespecified differential equation and attempts to estimate its parameters in contrast we demonstrate that in the case of functional data the equation itself can be inferred assuming only that the dynamics are described by a first order nonlinear differential equation with a random component we obtain data adaptive dynamic equations from the observed data via a simple smoothing based procedure we prove consistency and introduce diagnostics to ascertain the fraction of variance that is explained by the deterministic part of the equation this approach is shown to yield useful insights into the time dynamic nature of human growth copyright 2012 oxford university press

generalized functional linear models with semiparametric single index interactions we introduce a new class of functional generalized linear models where the response is a scalar and some of the covariates are functional we assume that the response depends on multiple covariates a finite number of latent features in the functional predictor and interaction between the two to achieve parsimony the interaction between the multiple covariates and the functional predictor is modeled semiparametrically with a single index structure we propose a two step estimation procedure based on local estimating equations and investigate two situations a when the basis functions are predetermined e g fourier or wavelet basis functions and the functional features of interest are known and b when the basis functions are data driven such as with functional principal components asymptotic properties are developed notably we show that when the functional features are data driven the parameter estimates have an increased asymptotic variance due to the estimation error of the basis functio

conformal immersions of prescribed mean curvature in r 3 abstract we prove the existence of branched conformal immersions f s 2 r 3 with mean curvature h 0 arbitrarily prescribed up to a 3 dimensional affine indeterminacy a similar result is proved for the space forms s 3 h 3 and partial results for surfaces of higher genus

exact free vibration analysis for membrane assemblies with general classical boundary conditions abstract this paper proposes exact dynamic stiffness formulations for membranes and their assemblies under any arbitrary classical boundary conditions first by taking exact solutions in one direction satisfying all possible opposite edge supports we can derive exact general solutions of the helmholtz equation for membrane vibration then generic force and displacement boundary conditions in the other direction are expressed in terms of the general solutions finally the dynamic stiffness matrices of rectangular membrane elements are formulated which can be assembled directly and allows applications of arbitrary boundary conditions as an accurate and efficient modal solution technique the wittrick williams ww algorithm is applied onto the global dynamic stiffness matrix of the final structure the most important issue of the ww algorithm j 0 count has been resolved with the analytical expressions derived for all possible cases the proposed dynamic stiffness method dsm is then applied to several examples including individual membranes and their assemblies high accuracy and exactness of the proposed method within the whole frequency range is demonstrated by comparison with the finite element method besides interesting findings have been observed on repeated eigenvalues with distinct mode shapes corresponding to certain aspect ratio and tension ratio where physical and mathematical understanding has been provided

curved flats and isothermic surfaces we show how pairs of isothermic surfaces are given by curved flats in a pseudo riemannian symmetric space and vice versa calapso s fourth order partial differential equation is derived and using a solution of this equation a mobius invariant frame for an isothermic surface is built

isothermic triangulated surfaces we found a class of triangulated surfaces in euclidean space which have similar properties as isothermic surfaces in differential geometry we call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally we show that this class is mobius invariant isothermic triangulated surfaces can be characterized either in terms of circle patterns or based on conformal equivalence of triangle meshes this definition generalizes isothermic quadrilateral meshes a consequence is a discrete analog of minimal surfaces here the weierstrass data needed to construct a discrete minimal surface consist of a triangulated plane domain and a discrete harmonic function

functional principal component model for high dimensional brain imaging we explore a connection between the singular value decomposition svd and functional principal component analysis fpca models in high dimensional brain imaging applications we formally link right singular vectors to principal scores of fpca this combined with the fact that left singular vectors estimate principal components allows us to deploy the numerical efficiency of svd to fully estimate the components of fpca even for extremely high dimensional functional objects such as brain images as an example a fpca model is fit to high resolution morphometric ravens images the main directions of morphometric variation in brain volumes are identified and discussed

free vibration analysis of membranes using the h p version of the finite element method abstract the h p version of the finite element method is applied to the vibration of membranes this is accomplished using a polynomially enriched triangular element new simple expressions of hierarchical c 0 shape functions for triangles are given in terms of the shifted legendre orthogonal polynomials the h p version of the finite element method marries both the concepts of the conventional h version and the p version the accuracy of the solution is sought by simultaneously refining the mesh and increasing the polynomial order in each element results of frequency calculations are found for triangular and l shaped membranes using a number of meshes and polynomial orders it is shown that the h p version of the finite element method is always convergent from above and produces a high accuracy with few degrees of freedom

integrable equations arising from motions of plane curves the motion of plane curves in klein geometry is studied it is shown that the kdv harry dym sawada kotera burgers the defocusing mkdv hierarchies the camassa holm and the kaup kupershmidt equation naturally arise from the motions of plane curves in sl 2 sim 2 sa 2 and a 2 geometries these local and nonlocal dynamics conserve global geometric quantities of curves such as perimeter and enclosed area motions of curves in euclidean special linear and similarity geometries corresponding to the traveling wave solutions of the mkdv kdv and burgers equations are discussed