wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

analysis of locking and stress oscillations in a general curved beam element the exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force the functional re constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations the orthogonally correct field consistent interpolations are determined for the optimal form of the element and it is shown that the popular two point gaussian integrated13 version of the element is non orthogonal and has a cubic13 oscillation in the shear force that curiously vanishes at the barlow points

the n order iterative schemes for a nonlinear kirchhoff carrier wave equation associated with the mixed inhomogeneous conditions in this paper a high order iterative scheme is established in order to get a convergent sequence at a rate of order n n 1 to a local unique weak solution of a nonlinear kirchhoff carrier wave equation associated with mixed nonhomogeneous conditions the boundary conditions are dirichlet in one part and robin in other part of boundary on the other hand some numerical results were presented

existence blow up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two point type abstract this paper is devoted to studying a nonlinear wave equation with boundary conditions of two point type first we state two local existence theorems and under the suitable conditions we prove that any weak solutions with negative initial energy will blow up in finite time next we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions finally we present numerical results

high order iterative schemes for a nonlinear kirchhoff carrier wave equation associated with the mixed homogeneous conditions in this paper we consider the following nonlinear wave equation 1 utt t u t 2 ux t 2 uxx f x t u 0 x 1 0 t t ux 0 t h0u 0 t ux 1 t h1u 1 t 0 u x 0 u 0 x ut x 0 u 1 x where f u 0 u 1 are given functions and h0 0 h1 0 are given constants in eq 1 1 the nonlinear term t u t 2 ux t 2 depends on the integrals u t 2 01 u x t 2dx ux t 2 01 ux x t 2dx in this paper we associate with eq 1 1 a recurrent sequence um defined by 2 2um t2 t um t 2 umx t 2 umxx i 0n1i if ui x t um 1 um um 1 i 0 x 1 0 t t with um satisfying 1 2 3 the first term u0 is chosen as u0 0 if c1 r 3 and f cn 1 0 1 r r we prove that the sequence um converges at a rate of order n 1 to a unique weak solution of problem 1

a minimum distance estimator for long memory processes this paper considers a minimum distance estimator mde of the differencing para meter of the fractionally integrated white noise model the mde minimizes the differ ence between sample and population autocorrelations the paper presents calculations of asymptotic variances to examine the efficiency of the mde relative to that of the mle for values of the differencing parameter less than l 4 the mde is consistent and asymptotically normal and the asymptotic variance of the mde using the first n auto correlations approaches that of the mle as n increases however there is a substantial efficiency loss if low order autocorrelations are omitted this implies that a non parametric treatment of short run dynamics will involve a substantial loss of efficiency

existence and asymptotic expansion for a nonlinear wave equation associated with nonlinear boundary conditions consider the initial boundary value problem for the nonlinear wave equation 1 utt x x t ux f u ut f x t 0 x 1 0 t t 0 t ux 0 t p t 1 t ux 1 t k1 u 1 t p1 2u 1 t ut 1 t q1 2ut 1 t u x 0 u0 x ut x 0 u1 x where p1 q1 2 k1 0 are given constants and u0 u1 f f are given functions and the unknown function u x t and the unknown boundary value p t satisfy the following nonlinear integral equation 2 p t g t k0 u 0 t p0 2u 0 t ut 0 t q0 2ut 0 t 0tk t s u 0 s ds where p0 q0 2 k0 0 are given constants and g k are given functions in this paper we consider three main parts in part 1 under the conditions u0 u1 f g k h1 l2 l1 0 t l2 lq0 0 t l1 0 t c0 qt x t 0 0 t l1 0 t l t x t 0 a e x t qt k0 k1 0 p0 q0 p1 q1 2 q0 q0q0 1 the function f supposed to be continuous with respect to two variables and nondecreasing with respect to the second variable and some others we prove that the problem 1 and 2 has a weak solution u p if in addition k w1 1 0 t p0 p1 2 3 and some other conditions then the solution is unique the proof is based on the faedo galerkin method and the weak compact method associated with a monotone operator for the case of q0 q1 2 p0 p1 2 in part 2 we prove that the unique solution u p belongs to l 0 t h2 c0 0 t h1 c1 0 t l2 h1 0 t with ut l 0 t h1 utt l 0 t l2 u 0 u 1 h2 0 t if we assume u0 u1 h2 h1 f c1 r2 and some other conditions finally in part 3 with q0 q1 2 p0 p1 n 1 f cn 1 r2 n 2 we obtain an asymptotic expansion of the solution u p of the problem 1 and 2 up to order n 1 in two small parameters k0 k1

on a nonlinear wave equation associated with the boundary conditions involving convolution the paper deals with the initial boundary value problem for the linear wave equation 1 utt x x t ux ut f u 0 0 x 1 0 t t 0 t ux 0 t g0 t 0tk0 t s u 0 s ds 1 t ux 1 t g1 t 0tk1 t s u 1 s ds u x 0 u0 x ut x 0 u1 x where f g0 g1 k0 k1 u0 u1 are given functions and is a given constant the paper consists of four main parts in part 1 under conditions u0 u1 g0 g1 k0 k1 h1 l2 h1 0 t 2 w1 1 0 t 2 w1 qt t l1 0 t l x t 0 0 a e x t qt the function f continuous 0zf s ds c1z2 c1 for all z r with c1 c1 0 are given constants and some other conditions we prove that the problem 1 has a unique weak solution u the proof is based on the faedo galerkin method associated with the weak compact method in part 2 we prove that the unique solution u belongs to h2 qt l 0 t h2 c0 0 t h1 c1 0 t l2 with ut l 0 t h1 utt l 0 t l2 if we assume u0 u1 h2 h1 f c1 r and some other conditions in part 3 with f cn 1 r n 2 we obtain an asymptotic expansion of the solution u of the problem 1 up to order n 1 in a small parameter finally in part 4 we prove that the solution u of this problem is stable with respect to the data g0 g1 k0 k1

an additional stiffness parameter measure of error of the second kind in the finite element method conventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value in problems where two or more field variables are coupled it is possible that if the field interpolation functions do not consistently reproduce limiting situations of physical behaviour there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense the percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter even on a logarithmic plot errors due to these spurious constraints have recently been recognized as belonging to a special class described as errors of the second kind a new error norm called the additional stiffening parameter helps to recognize the manner in which errors of the second kind can be blown out of propprtion by a large variation in some structural parameter recent investigations in some multi field problems are summarized here to demonstrate the usefulness of this concept

the variance profile the variance profile is defined as the power mean of the spectral density function of a stationary stochastic process it is a continuous and nondecreasing function of the power parameter p which returns the minimum of the spectrum p the interpolation error variance harmonic mean p 1 the prediction error variance geometric mean p 0 the unconditional variance arithmetic mean p 1 and the maximum of the spectrum p the variance profile provides a useful characterization of a stochastic process we focus in particular on the class of fractionally integrated processes moreover it enables a direct and immediate derivation of the szego kolmogorov formula and the interpolation error variance formula the article proposes a nonparametric estimator of the variance profile based on the power mean of the smoothed sample spectrum and proves its consistency and its asymptotic normality from the empirical standpoint we propose and illustrate the use of the variance profile for estimating th

on the nonlinear wave equation utt b t ux 2 uxx f x t u ux ut associated with the mixed homogeneous conditions abstract in this paper we consider the following nonlinear wave equation 1 u tt b t u x 2 u xx f x t u u x u t x 0 1 0 2 u x 0 t h 0 u 0 t 0 u x 1 t h 1 u 1 t 0 3 u x 0 u 0 x u t x 0 u 1 x where h0 h1 are given nonnegative constants and b f u 0 u 1 are given functions in eq 1 the coefficient b t ux 2 containing an integral u x 2 0 1 u x x t 2 dx in this paper we associate with problem 1 3 a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument in case of b c 2 r 2 b b0 0 b 1 c 1 r 2 b1 0 f c 2 0 r 3 and f 1 c 1 0 r 3 we obtain from the following equation u tt b t u x 2 eb 1 t u x 2 u xx f x t u u x u t ef 1 x t u u x u t associated to 2 3 a weak solution ue x t having an asymptotic expansion of order 2 in e for e sufficiently small

nonstationary spectral analysis based on time frequency operator symbols and underspread approximations we present a unified framework for time varying or time frequency tf spectra of nonstationary random processes in terms of tf operator symbols we provide axiomatic definitions and tf operator symbol formulations for two broad classes of tf spectra one of which is new these classes contain all major existing tf spectra such as the wigner ville evolutionary instantaneous power and physical spectrum our subsequent analysis focuses on the practically important case of nonstationary processes with negligible high lag tf correlations so called underspread processes we demonstrate that for underspread processes all tf spectra yield effectively identical results and satisfy several desirable properties at least approximately we also show that gabor frames provide approximate karhunen loeve kl functions of underspread processes and tf spectra provide a corresponding approximate kl spectrum finally we formulate simple approximate input output relations for the tf spectra of underspread processes that are passed through underspread linear time varying systems all approximations are substantiated mathematically by upper bounds on the associated approximation errors our results establish a tf calculus for the second order analysis and time varying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes

on the nonlinear wave equation utt b t u 2 ux 2 uxx f x t u ux ut u 2 ux 2 associated with the mixed homogeneous conditions abstract in this paper we consider the following nonlinear wave equation 1 u tt b t u x 2 u xx f x t u u x u t u x 2 x 0 1 0 2 u x 0 t h 0 u 0 t g 0 t u 1 t g 1 t 3 u x 0 u 0 x u t x 0 u 1 x where b f g 0 g 1 u 0 u 1 are given functions in eq 1 the nonlinear terms b t u x 2 f x t u u x u t u x 2 depending on an integral u x 2 0 1 u x x t 2 dx in this paper we associate with problem 1 3 a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument in case of b c 3 r 2 b b 0 0 b 1 c 2 r 2 b 1 0 f c 3 0 1 r r 3 r and f 1 c 2 0 1 r r 3 r we obtain from the equation u tt b t u x 2 eb 1 t u x 2 u xx f x t u u x u t u x 2 ef 1 x t u u x u t u x 2 associated to 2 3 a weak solution u e x t having an asymptotic expansion of order 3 in e for e sufficiently small

an arima model based approach to seasonal adjustment abstract this article proposes a model based procedure to decompose a time series uniquely into mutually independent additive seasonal trend and irregular noise components the series is assumed to follow the gaussian arima model properties of the procedure are discussed and an actual example is given

a goodness of fit test for time series with long range dependence we propose a test statistic for goodness of fit in time series with slowly decaying serial correlations the asymptotic distribution of the test statistic originally proposed by milhoj for time series with smooth spectra turns out to be the same under the null hypothesis even if the spectrum has a pole at 0 in particular the test is suitable to detect lack of independence in the observations or estimated residuals if the first few correlations are small but the decay of the correlations is slow

linear recursive schemes and asymptotic expansion associated with the kirchoff carrier operator abstract in this paper we consider a nonlinear wave equation with the kirchoff carrier operator 1 u tt b 0 b u 2 u f x t u u x u t x 0 1 0 2 u 0 t u 1 t 0 3 u x 0 u 0 x u t x 0 u 1 x where b 0 0 is a given constant and b f are the given functions the above b u 2 depends on the integral u 2 u x t 2 dx in this paper we associate with the above problem a linear recursive scheme for which the existence of a local and unique solution is proved by using the standard compactness argument if b c 2 r b 1 c 1 r f c 2 formula 0 r 3 and f 1 c 1 formula 0 r 3 then an asymptotic expansion of order 2 in e is obtained with a right hand side of the form f x t u u x u t e f 1 x t u u x u t and b stands for b e b 1 for e sufficiently small

on the nonlinear wave equation utt b ux 2 uxx f x t u ux ut ux 2 associated with the mixed homogeneous conditions in this paper we consider the following nonlinear wave equation 1 utt b ux 2 uxx f x t u ux ut ux 2 x 0 1 0 t t 2 ux 0 t h0u 0 t u 1 t 0 3 u x 0 u0 x ut x 0 u1 x where b f u0 u1 are given functions in eq 1 the nonlinear terms b ux 2 f x t u ux ut ux 2 depending on an integral ux 2 01 ux x t 2dx in this paper we associate with problem 1 3 a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument in case of b cn 1 r b b0 0 b1 cn r b1 0 f cn 1 0 1 r r3 r and f1 cn 0 1 r r3 r we obtain from the following equation utt b ux 2 eb1 ux 2 uxx f x t u ux ut ux 2 ef1 x t u ux ut ux 2 associated to 2 3 a weak solution ue x t having an asymptotic expansion of order n 1 in e for e sufficiently small

a wave equation associated with mixed nonhomogeneous conditions global existence and asymptotic expansion of solutions abstract the paper deals with the initial boundary value problem for the linear wave equation 1 u t t u x x k u u t f x t 0 x 1 0 t t u x 0 t p t u 1 t 0 u x 0 u 0 x u t x 0 u 1 x where k are given constants and u 0 u 1 f are given functions and the unknown function u x t and the unknown boundary value p t satisfy the following nonlinear integral equation 2 p t g t k 1 u 0 t 2 u 0 t 1 u t 0 t 2 u t 0 t 0 t k t s u 0 s d s where k 1 1 are given constants and g k are given functions in this paper we consider three main parts in part 1 we prove a theorem of global existence and uniqueness of a weak solution u p of problem 1 1 1 5 the proof is based on a galerkin method associated with a priori estimates weak convergence and compactness techniques for the case of 2 part 2 is devoted the study of the asymptotic behavior of the solution u p as 1 0 finally in part 3 we obtain an asymptotic expansion of the solution u p of the problem 1 1 1 5 up to order n 1 2 in four small parameters k k 1 1

a unified view of multitaper multivariate spectral estimation summary the orthogonal multitaper framework for cross spectral estimators provides a simple unifying structure for determining the corresponding statistical properties here crossspectral estimators are represented by a weighted average of orthogonally tapered crossperiodograms with the weights corresponding to a set of rescaled eigenvalues such a structure not only encompasses the thomson estimators using slepian and sine tapers but also welch s weighted overlapped segment averaging estimator and lag window estimators including frequency averaged cross periodograms the means smoothing and leakage biases variances and asymptotic distributions of such estimators can all be formulated in a common way comparisons are made for a fixed number of degrees of freedom the common structure of the estimators also provides a necessary condition for the invertibility of an estimated cross spectral matrix namely that the weight matrix of the estimator written in bilinear form must have rank greater than or equal to the dimension of the cross spectral matrix an example is given showing the importance of small leakage and thus illustrating that the various estimators need not be equivalent in practice

on the nonlinear wave equation utt b t u 2 ux 2 ut 2 uxx f x t u ux ut u 2 ux 2 ut 2 associated with the mixed homogeneous conditions abstract in this paper we consider the following nonlinear wave equation 1 u tt b t u 2 u x 2 u t 2 u xx f x t u u x u t u 2 u x 2 u t 2 x 0 1 0 2 u x 0 t h 0 u 0 t u x 1 t h 1 u 1 t 0 3 u x 0 u 0 x u t x 0 u 1 x where h0 0 h1 0 are given constants and b f u 0 u 1 are given functions in eq 1 the nonlinear terms b t u 2 u x 2 u t 2 f x t u u x u t u 2 u x 2 u t 2 depending on the integrals u 2 u x t 2 d x u x 2 0 1 u x x t 2 d x and u t 2 u t x t 2 d x in this paper we associate with problem 1 3 a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument in case of b c n 1 r 4 b b 0 0 b 1 c n r 4 b 1 0 f c n 1 0 1 r r 3 r 3 and f1 cn 0 1 r r3 r 3 we obtain from the following equation utt b t u 2 ux 2 ut 2 eb1 t u 2 ux 2 ut 2 uxx f x t u ux ut u 2 ux 2 ut 2 ef1 x t u ux ut u 2 ux 2 ut 2 associated to 2 3 a weak solution ue x t having an asymptotic expansion of order n 1 in e for e sufficiently small

fitting time series models by minimizing multistep ahead errors a frequency domain approach this paper brings together two topics in the estimation of time series forecasting models the use of the multistep ahead error sum of squares as a criterion to be minimized and frequency domain methods for carrying out this minimization the methods are developed for the wide class of time series models having a spectrum which is linear in unknown coefficients this includes the ima 1 1 model for which the common exponentially weigh ted moving average predictor is optimal besides more general structural models for series exhibiting trends and seasonality the method is extended to include the box jenkins air line model the value of the multistep criterion is that it provides protection against using an incorrectly specified model the value of frequency domain estimation is that the iteratively reweighted least squares scheme for fitting generalized linear models is readily extended to construct the parameter estimates and their standard errors it also yields insight into the loss of efficiency when the model is correct and the robustness of the criterion against an incorrect model a simple example is used to illustrate the method and a real example demonstrates the extension to seasonal models the discussion considers a diagnostic test statistic for indicating an incorrect model

an improved state space representation for cyclical time series we consider a commonly used two state model for a cyclical time series and show how a particular specification of its observation vector allows maximum generality of the range of model spectra

on a nonlinear wave equation with boundary conditions of two point type abstract the paper is devoted to the study a nonlinear wave equation with boundary conditions of two point type existence of a weak solution is proved by using faedo galerkin method uniqueness regularity and decay properties of solutions are also discussed

existence and asymptotic expansion for a viscoelastic problem with a mixed nonhomogeneous condition abstract we study the initial boundary value problem for a nonlinear wave equation given by 1 u t t u x x 0 t k t s u x x s d s k u p 2 u u t q 2 u t f x t 0 x 1 0 t t u x 0 t u 0 t u x 1 t u 1 t g t u x 0 u 0 x u t x 0 u 1 x where 0 p 2 q 2 k are given constants and u 0 u 1 f g k are given functions in this paper we consider three main parts in part 1 we prove a theorem of existence and uniqueness of a weak solution u of problem 1 the proof is based on a faedo galerkin method associated with a priori estimates weak convergence and compactness techniques part 2 is devoted to the study of the asymptotic behavior of the solution u as 0 finally in part 3 we obtain an asymptotic expansion of the solution u of the problem 1 up to order n 1 in three small parameters k

a nonlinear wave equation associated with nonlinear boundary conditions existence and asymptotic expansion of solutions consider the initial boundary value problem for the nonlinear wave equation equation 1 utt uxx k u p 2u ut q 2ut f x t 0 x 1 0 t t ux 0 t p t ux 1 t u 1 t p1 2u 1 t ut 1 t q1 2ut 1 t u x 0 u0 x ut x 0 u1 x where pp p1p1 q1 2q1 2 q 1q 1 kk are given constants and u0u0 u1u1 ff are given functions and the unknown function u x t u x t and the unknown boundary value p t p t satisfy the following nonlinear integral equation equation 2 p t g t k0 u 0 t p0 2u 0 t ut 0 t q0 2ut 0 t 0tk t s u 0 s ds where p0p0 q0 2q0 2 k0k0 are given constants and gg kk are given functions in this paper we consider three main parts in part 1 under the conditions u0 u1 h1 l2 u0 u1 h1 l2 f l2 qt f l2 qt k w1 1 0 t k w1 1 0 t g lq0 0 t 1 1 kk k0 0k0 0 pp p0p0 q0q0 p1p1 q1 2q1 2 q 1q 1 q0 q0q0 1 we prove a theorem of existence and uniqueness of a weak solution u p u p of problem 1 and 2 the proof is based on the faedo galerkin method and the weak compact method associated with a monotone operator for the case of q0 q1 2q0 q1 2 pp qq p0p0 p1p1 2 2 in part 2 we prove that the unique solution u p u p belongs to l 0 t h2 c0 0 t h1 c1 0 t l2 h1 0 t l 0 t h2 c0 0 t h1 c1 0 t l2 h1 0 t with ut l 0 t h1 ut l 0 t h1 utt l 0 t l2 utt l 0 t l2 u 0 u 0 u 1 h2 0 t u 1 h2 0 t if we make the assumption that u0 u1 h2 h1 u0 u1 h2 h1 and some others finally in part 3 we obtain an asymptotic expansion of the solution u p u p of the problem 1 and 2 up to order n 1n 1 in three small parameters kk k0k0

on a shock problem involving a linear viscoelastic bar abstract the paper deals with the initial boundary value problem for the linear wave equation 1 u tt t u xx ku u t f x t 0 x 1 0 t t u 0 t 0 t u x 1 t q t u x 0 u 0 x u t x 0 u 1 x where k are given constants and u 0 u 1 f are given functions the unknown function u x t and the unknown boundary value q t satisfy the following linear integral equation 2 q t k 1 t u 1 t 1 t u t 1 t g t 0 t k t s u 1 s d s where g k k 1 1 are given functions the paper consists of four parts in part 1 we prove a theorem of global existence and uniqueness of a weak solution u q of problem 1 2 the proof is based on a galerkin type approximation associated to various energy estimates type bounds weak convergence and compactness arguments in part 2 it is devoted to the study of the regularity of the solution u q with respect to the functions 1 f g k k 1 in part 3 we prove that the solution u q of this problem is stable with respect to the data k 1 f g k k 1 finally in part 4 we obtain an asymptotic expansion of the solution u q of this problem up to order n 1 in k for k sufficiently small

mathematical framework for pseudo spectra of linear stochastic difference equations although spectral analysis of stationary stochastic processes has solid mathematical foundations this is not always so for some non stationary cases here we establish a rigorous mathematical extension of the classic fourier spectrum to the case in which there are ar roots in the unit circle i e the transfer function of the linear time invariant filter has poles on the unit circle to achieve it we embed the classical problem in a wider framework extend the discrete time fourier transform and defined a new extended fourier transform pair pseudo covariance function pseudo spectrum our approach is a proper extension of the classical spectral analysis within which the fourier transform pair auto covariance function spectrum is a particular case consequently spectrum and pseudo spectrum coincide when the first one is defined

reduced minimization in lagrangian mindlin plate element with arbitrary orientation under uniform isoparametric mapping for the displacement based lagrangian mindlin plate elements oriented arbitrarily under uniform isoparametric mapping without internal distortion a theoretical interpretation on the conventional shear reduced integration is presented by introducing the concept of reduced minimization it reveals that the conventional shear reduced integration such as uri and sri prevents the unmatched coefficients of shear strains from becoming spurious constraints thus the shear reduced integration eliminates spurious constraints and prevents locking

on the nonlinear wave equation with the mixed nonhomogeneous conditions linear approximation and asymptotic expansion of solutions in this paper we consider the following nonlinear wave equation equation 1 utt x u ux f x t u ux ut 0 x 1 0 t t ux 0 t g t u 1 t 0 u x 0 u 0 x ut x 0 u 1 x where u 0 u 1 ff gg are given functions to problem 1 we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the faedo galerkin method and the weak compact method in the case of cn 2 r cn 2 r 1 cn 1 r 1 cn 1 r z 0 0 z 0 0 1 z 0 1 z 0 for all z rz r and g c3 r g c3 r f cn 1 0 1 r r3 f cn 1 0 1 r r3 f1 cn 0 1 r r3 f1 cn 0 1 r r3 a weak solution ue1 e2 x t ue1 e2 x t having an asymptotic expansion of order n 1n 1 in two small parameters e1e1 e2e2 is established for the following equation associated to 1 2 3 equation 2 utt x u e1 1 u ux f x t u ux ut e2f1 x t u ux ut

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

consistency aspects of out of plane bending torsion and shear in a quadratic curved beam element curved beams in civil engineering applications call for out of plane bending and torsion under the action of out of plane transverse shear loads the design of a quadratic displacement type curved beam element capable of representing shear deformation as in the timoshenko beam theory will call for special attention to be paid to the manner in which the shear strain is to be represented field inconsistent representations of the out of plane transverse shear strain will result in a loss gf efficiency and introduce spuriou oscillations in the bending moment torsional moment and shear force the optimal field consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations

a linear wave equation with a nonlinear boundary condition of viscoelastic type abstract the paper is devoted to the study of a linear wave equation with a nonlinear boundary condition of viscoelastic type the existence of a weak solution is proved by using the faedo galerkin method the uniqueness regularity and asymptotic expansion of the solution are also discussed

reduced minimization theory in beam elements by using the field consistency and least squares fit concepts reduced minimization theory is proposed to show the effect of numerical integration on the behaviour of c0 continuous beam elements when the jacobian is constant within an element the theory provides a unified viewpoint on the relationship between spurious constraint the location of optimal sampling points and integration order the conventional uniformly reduced integration uri and selective reduced integration sri are redefined by using reduced minimization theory we also present numerical reduced minimization theory which explains the effects of more than two order lower reduced integration when gaussian quadrature is employed

reduced minimization of mindlin plate the use of inconsistent displacement fields for mindlin plate elements causes unmatched coefficients to appear in shear strain interpolations the role of the numerical integration order in relation to these unmatched coefficients and the existence of optimal stress points are explained through the use of the reduced minimization concept this concept makes it possible to test whether assumed displacement fields or shear strain fields result in inconsistent strain fields which contain spurious constraints we have included applications of reduced minimization to the conventional c0 continuous elements which employ reduced integration and to quadrilateral mindlin plate elements of hinton and huang to demonstrate how these elements alleviate shear locking

estimation error and the specification of unobserved component models abstract the paper deals with the problem of identifying stochastic unobserved two component models as in seasonal adjustment or trend cycle decompositions solutions based on the properties of the unobserved component estimation error are considered and analytical expressions for the variance of the errors in the final preliminary and concurrent estimators are obtained these expressions are straightforwardly derived from the arima model for the observed series the estimation error variance is always minimized at a canonical decomposition i e at a decomposition with one of the components noninvertible and a simple procedure to determine that decomposition is presented on occasion however the most precise final estimator may be obtained at a canonical decomposition different from the one that yields the most precise preliminary estimator two examples are presented first a simple trend plus cycle type model is used to illustrate the derivations the second example presents results for a class of models often encountered in actual time series

generalized evolutionary spectral analysis and the weyl spectrum of nonstationary random processes the evolutionary spectrum es is a time varying power spectrum of nonstationary random processes starting from an innovations system interpretation of the es we introduce the generalized evolutionary spectrum ges as a novel family of time varying power spectra the ges contains the es and the transitory evolutionary spectrum as special cases we consider the problem of finding an innovations system for a process characterized by its correlation function and we discuss the connection between ges analysis and the class of underspread processes furthermore we show that another special case of the ges a novel time varying power spectrum that we call the weyl spectrum has substantial advantages over all other members of the ges family the properties of the weyl spectrum are discussed and its superior performance is verified experimentally for synthetic and real data processes

blow up for solutions of some linear wave equations with mixed nonlinear boundary conditions this paper deals with the blow up in solutions of some linear wave equations with mixed nonlinear boundary conditions the finite time blow up in solutions are caused from the nonlinear boundary conditions even if the initial data are smooth and well defined for all times the pointwise blow up in exact solution and blow up in energy solution are investigated

reduced integration and the shear flexible beam element the timoshenko beam element is studied in an investigation of shear locking in the development of c 0 continuous elements using shear flexible or penalty function type formulations a penalty type argument is used to degenerate thick elements to thin elements and the various approximations of the shear related energy terms act as different types of constraints depending on the formulation two types of constraints may emerge which are classified as true or spurious formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation the argument is extended to a shallow curved timoshenko beam and another mechanism inplane locking arises if all energy terms corresponding to the membrane energy are exactly integrated