transverse shear modulus identification by an inverse method using measured flexural resonance frequencies from beams abstract many papers have already been presented about identification of 2d in plane elastic engineering constants e1 e2 v12 and g12 by inverse methods most of the described methods are based on measured resonance frequencies on plate specimens less attention has been paid to the identification of transverse shear moduli especially validation of the obtained results and error bound estimations are often lacking this paper presents an inverse method for the identification of the transverse moduli of test beams by measured flexural resonance frequencies the procedure is first illustrated with numerically generated test data and next applied on experimentally measured results the sensitivity of the flexural resonance frequencies for variations of the shear modulus is discussed as well as an estimation of the uncertainty intervals on the obtained moduli the results are validated by using the obtained shear moduli for the prediction of torsional resonance frequencies

single layer plate theories applied to the flexural vibration of completely free thick laminates two different refined single layer plate theories are used to analyze the flexural vibration of thick symmetrically laminated rectangular plates with all edges free both theories account for parabolic distribution of the transverse shear strains through the thickness of the plate the first theory includes the transverse normal effect and employs a three dimensional constitutive law whereas the second neglects this effect and employs plane stress reduced stiffnesses numerical results are obtained by using the ritz method characteristic orthogonal polynomials are used in the series representing the displacement functions convergence studies are shown to verify the accuracy of the approximate method the accuracy of the results is further assessed by comparison with results from three dimensional finite element analyses numerical results are presented for various plates including cross ply and angle ply laminated plates the effect of transverse shear and normal deformation on the plate natural frequencies is illustrated by comparing the frequencies of the two higher order theories and the classical plate theory for decreasing length to thickness ratio

direct identification of elastic constants of anisotropic plates by modal analysis theoretical and numerical aspects abstract a direct method of determining the six flexural stiffnesses of thin anisotropic plates is presented in this paper this technique is based on a relevant processing of natural frequencies and mode shapes of free free vibrating plates the unknown plate rigidities are the solution of an overdetermined linear system the equations of which are obtained with a set of relevant weighting functions associated with different natural modes of vibration numerical simulations indicate the accuracy and the sensitivity of this identification method

identification of elastic properties of laminates based on experiment design abstract a numerical experimental method for identification of elastic properties of laminated composites from the experimental results is developed it is proposed to use the method of experiment design and the response surface approach to solve the identification inverse problems the response surface approximations are obtained by using the information on the behavior of a structure in the reference points of the experiment design the finite element modeling of the structure is performed only in the reference points therefore a significant reduction about 50 100 times in calculations of the identification functional can be achieved in comparison with the conventional methods of minimization the functional to be minimized describes the difference between the measured and numerically calculated eigenfrequencies of structure by minimizing the functional the identification parameters are obtained it was shown that identification functional is convex if the stiffness matrix linearly depends on unknown parameters the method is employed to identify the elastic properties of cross ply laminates from the measured eigenfrequencies of composite plates

cluster sets for a generalized law of the iterated logarithm in banach spaces we identify the possible cluster sets for a general law of the iterated logarithm in the banach space setting and show that all the possible limit sets arise as cluster sets for some random vector in an arbitrary separable banach space this extends previous results obtained in finite dimensional euclidean spaces

small time two sided lil behavior for levy processes at zero we specify a function b0 t in terms of the levy triplet such that lim sup t 0xt b0 t 1 1 8 a s iff int 0 1 overline varpi b 0 t dt infty for any levy process x with unbounded variation and a brownian component 0 we show with an example that there are cases where lim sup t 0xt b t 1 a s but b t is not asymptotically equivalent to b0 t as t tends to 0 we achieve this by introducing an integral criterion which checks whether lim sup t 0xt b t is 0 infinity or a finite positive value for b t satisfying very mild conditions and any levy process

introduction to the bayesian approach applied to elastic constants identification the basic formulation of the least squares method based on the l2 norm of the residuals is still widely used today for identifying elastic constants of aerospace materials from experimental data while this method often works well methods that can benefit from statistical information such as the bayesian method may sometimes be more accurate we seek situations with significant difference between the material properties identified by the two methods for a simple three bar truss example we illustrate three situations in which the bayesian approach systematically leads to more accurate results different sensitivity of the measured response to the parameters to be identified different uncertainty in the measurements and correlation among response components when all three effects add up the bayesian approach can be much more accurate furthermore the bayesian approach has the additional advantage of providing the uncertainty in the identified parameters we also compare the two methods for a more realistic problem of identification of elastic constants from natural frequencies of a composite plate

asymptotics of toeplitz hankel and toeplitz hankel determinants with fisher hartwig singularities we study the asymptotics in n for n dimensional toeplitz determinants whose symbols possess fisher hartwig singularities on a smooth background we prove the general nondegenerate asymptotic behavior as conjectured by basor and tracy we also obtain asymptotics of hankel determinants on a nite interval as well as determinants of toeplitz hankel type our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the riemann hilbert approach

an asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle abstract we consider the system of biorthogonal polynomials p n q n n 0 with respect to a complex valued measure supported on the unit circle and give a uniform compound asymptotic expansion formula consisting of the sum of two inverse factorial series giving the explicit expression of the terms and including error bounds as a consequence we prove that the set of accumulation points of the zeros these polynomials is included in the unit circle some numerical experiments are included

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

some results on two sided lil behavior ni 1 xi n 1 we establish necessary and sufficient conditions for having with probability 1 0 1 and to h n log n r r 0 we obtain analogues of the hartman wintner lil in the infinite variance case our proof is based on a general result dealing with lil behavior of the normalized sums sn cn n 1 where cn is a sufficiently regular normalizing sequence

the small time chung wichura law for levy processes with non vanishing brownian component we give a small time functional version of chung s other law of the iterated logarithm for levy processes with non vanishing brownian component this is an analogue of the other law of the iterated logarithm at large times for levy processes and random walks with finite variance as extended to a functional version by wichura as one of many possible applications we mention a functional law for a two sided passage time process

weak convergence of positive self similar markov processes and overshoots of levy processes using lamperti s relationship between levy processes and positive self similar markov processes pssmp we study the weak convergence of the law x of a pssmp starting at x 0 in the skorohod space of cadlag paths when x tends to 0 to do so we first give conditions which allow us to construct a cadlag markov process x 0 starting from 0 which stays positive and verifies the scaling property then we establish necessary and sufficient conditions for the laws x to converge weakly to the law of x 0 as x goes to 0 in particular this answers a question raised by lamperti z wahrsch verw gebiete 22 1972 205 225 about the feller property for pssmp at x 0

an almost sure functional limit theorem at zero for a class of levy processes normed by the square root function and applications a recent result of bertoin doney and maller ann prob 2007 gives an integral condition to characterize the class of levy processes x t for which lim sup t downarrow 0 x t sqrt t in 0 infty occurs almost surely a s for such processes we have a kind of almost sure iterated logarithm result but without the logs in the present paper we prove a functional version of this result which then opens the way to various interesting applications obtained via a continuous mapping theorem we set these out in a rigorous framework including a characterisation of the existence of an a s cluster set for the interpolated process appropriate to the continuous time situation the applications relate to functional laws for the supremum reflected and a variety of other processes including a class of stochastic differential equations where we aim to give as informative a description as we can of the functional limit sets

stability of the overshoot for levy processes we give equivalences for conditions like x t r r rightarrow 1 and x t r allowbreak r rightarrow 1 where the convergence is in probability or almost sure both as r rightarrow 0 and r rightarrow infty where x is a l e vy process and t r and t r are the first exit times of x out of the strip t y t 0 y leq r and half plane t y t 0 y leq r respectively we also show using a result of kesten that x t r r rightarrow 1 a s as r to 0 is equivalent to x creeping across a level

on a class of biorthogonal polynomials on the unit circle abstract a system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by r askey for this system an electrostatic interpretation for the zeros of a class of para orthogonal polynomials associated with the biorthogonal system is also considered

on the existence of short trajectories of quadratic differentials related to generalized jacobi polynomials with non real varying parameters abstract the motivation of this paper is to analyze to a large degree the behavior of the jacobi p n n n polynomials when the parameters determining the polynomials are complex and depend on the degree n linearly we show that the cauchy transform of the limit weak of the root counting measures of these polynomials satisfies quadratic algebraic equation we investigate the existence of solutions to these equations as cauchy transform of compactly supported positive measures any connected curve of the support of these measures if exists coincides with a horizontal trajectory of some quadratic differential in this paper we describe the trajectories of the family of quadratic differentials 2 z a z b z 2 1 2 d z 2 and we give a necessary and sufficient condition on the complex numbers a b and for the existence of at least one finite critical trajectory

when is the cluster set of s_n a_n empty we investigate the relationship between the bounded law of the iterated logarithm and the compact law of the iterated logarithm for banach space valued random variables through the cluster set of s n a n some rate of escape questions are also examined

passage of levy processes across power law boundaries at small times we wish to characterise when a l e vy process x t crosses boundaries like t kappa kappa 0 in a one or two sided sense for small times t thus we enquire when limsup t downarrow 0 x t t kappa limsup t downarrow 0 x t t kappa and or liminf t downarrow 0 x t t kappa are almost surely a s finite or infinite necessary and sufficient conditions are given for these possibilities for all values of kappa 0 often for many values of kappa when the limsups are finite a s they are in fact zero as we show but the limsups may in some circumstances take finite nonzero values a s in general the process crosses one or two sided boundaries in quite different ways but surprisingly this is not so for the case kappa 1 2 an integral test is given to distinguish the possibilities in that case some results relating to other norming sequences for x and when x is centered at a nonstochastic function are also given

strong approximations for partial sums of i i d b valued r v s in the domain of attraction of a gaussian law we obtain a strong approximation theorem for partial sums of i i d d dimensional r v s with possibly infinite second moments using this result we can extend philipp s strong invariance principle for partial sums of i i d b valued r v s satisfying the central limit theorem tob valued r v s which are only in the domain of attraction of a gaussian law this new strong invariance principle implies a compact as well as a functional law of the iterated logarithm which improve some recent results of kuelbs 1985

small time compactness and convergence behavior of deterministically and self normalised levy processes the first author s research was partially supported by arc grant dp0664603 the second author s research was partially supported by nsf grant dms 0503908

the growth of random walks and levy processes let x i be a sequence of independent identically distributed non degenerate random variables taking values in mathbb r d and s n sum n i 1 x i m n max 1 leqq i leqq n s i define for x 0 g x p x 1 x k x x 2 e x 1 2 1 x 1 leq x m x x 1 e x 1 1 x 1 leq x and h x g x k x m x then if beta sup alpha lim sup x alpha h x 0 delta sup alpha lim inf x alpha h x 0 it is proved that n 1 alpha m n rightarrow 0 for alpha delta while the lim inf is 0 and the lim sup is infty for beta alpha delta some alternative characterizations of the indices beta delta are obtained as well as the analogous results for levy processes

determination of elastic constants of orthotropic plates by a modal analysis method of superposition abstract the aim of the work reported here is to provide a single non destructive test to determine the elastic constants of an orthotropic material by studying the free vibrations of a rectangular plate in completely free boundary conditions after the experimental impulse technique to measure the natural frequencies of the plate has been presented this paper deals with the development of an accurate numerical method to calculate these frequencies the method of superposition based on series expansions of the deformed plate shape and requiring the boundary conditions to be satisfied in contrast to the rayleigh ritz approximate technique the equations derived by the method of superposition are incorporated into a computer designed to determine the five elastic constants of the material from the measured experimental natural frequencies of the completely free rectangular plate in the following part of the paper a few results are reported first the study of a glass plate validates the methodology employed by showing the expected isotropy of this material second the very weak orthotropy found for a laminated steel plate shows the sensitivity of the method and finally the values of the two young s moduli the in plane shear modulus and the two poisson ratios calculated for a glass epoxy plate are reported