some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

a fast and efficient cross validation method for smoothing parameter choice in spline regression abstract the spline smoothing approach to nonparametric regression is considered with particular reference to the problem of choosing how much to smooth both computational and statistical aspects of the method of cross validation are discussed an approximate cross validation method is proposed that requires a small linear amount of computer time a simulation study indicates that the method has very good statistical properties some mathematical justification and motivation are also provided

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

smoothing spline gaussian regression more scalable computation via efficient approximation summary smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with gaussian responses the computation of smoothing splines is generally of the order o n3 n being the sample size which severely limits its practical applicability we study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient a simple algorithm is presented and the bayes model that is associated with the approximations is derived with the latter guiding the porting of bayesian confidence intervals the practical choice of the dimension of the approximating space is determined through simulation studies and empirical comparisons of the approximations with the exact solution are presented also evaluated is a simple modification of the generalized cross validation method for smoothing parameter selection which to a large extent fixes the occasional undersmoothing problem that is suffered by generalized cross validation

global solutions to the equation of viscoelasticity with fading memory abstract we consider the initial history value problem for the one dimensional equation of thermoelasticity with fading memory it is proved that if the data are smooth and small then a unique smooth solution exists globally in time and converges to the constant equilibrium state as time goes to infinity our proof is based on a technical energy method which makes use of the strict convexity of the entropy function and the properties of strongly positive definite kernels

space time code design for correlated ricean mimo channels at finite snr space time code stc designs commonly rely on the assumptions of independent and identically distributed i i d rayleigh channels being either slow or fast fading and high signal to noise ratio snr however it has been shown that poor scattering conditions can have detrimental effects on the performance of stcs and that the behavior of codes at high snr is radically different from the finite snr behavior this calls for new design criteria that correctly predict the behavior of codes in correlated channels at finite snr in this paper we investigate how spatially and temporally correlated ricean fading affects the performance of stcs at finite snr we derive a code design criterion leading to robust stcs in a wide variety of propagation conditions and do not require any channel knowledge at the transmitter codes satisfying this criterion are shown to perform sensibly better in correlated channels than codes designed only for i i d slow or fast rayleigh fading channels examples of space time trellis codes and algebraic codes are proposed in order to illustrate the developed criterion

finite snr performance analysis of space time coding in correlated ricean mimo channels the performance analysis and the subsequent design of space time codes stc in multiantenna channels commonly assume an infinite signal to noise ratio snr this assumption has been shown to be justified in uncorrelated rayleigh fading channels by contrast this correspondence investigates stc in all snr regimes and in the broad class of space time correlated ricean fading multiple input multiple output mimo channels for rank deficient codes it is proven analytically that the error probability is significantly affected by spatial correlations and coherent components irrespective of the snr range and the temporal correlation for full rank codes the performance and the code design are shown to be affected by spatial correlations and or coherent paths only at finite snr in slow fading channels whereas in time varying channels they are affected in all snr regimes hence there is no guarantee that stc designed for independent and indentically distributed i i d rayleigh fading channels perform adequately in space time correlated rayleigh ricean channels simulation examples confirm the conclusions drawn from the analytical derivations they further illustrate that the use of a high snr assumption does not allow to accurately estimate the behavior of stc in practical scenarios and should thus be used with care

an optimal two transmit antenna space time code and its stacked extensions a space time code is proposed that exhibits the highest coding gain among competing full rate full transmit diversity space time codes for the two transmit and receive antenna coherent quasi static fading channel the proposed code is derived from a layered architecture with real rotation of quadrature amplitude modulation qam information symbols in two dimensions the existing codes of similar architecture concentrate on application of complex full modulation diversity rotations or asymmetric real rotations an analytic evaluation illustrates the significant improvement in coding gain achieved with the proposed code moreover the coding gain of the proposed code is independent of its rate this implies that the proposed code achieves the optimal diversity multiplexing tradeoff curve for the two transmit antenna system a stacked extension of the proposed code offers a reduced complexity capacity optimal alternative to the full diversity codes for larger number of transmit antennas performance enhancement in several scenarios is verified through simulations

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

on the control of a viscoelastic damped timoshenko type system abstract in this paper we consider the following timoshenko system tt x x 0 0 1 0 tt xx 0 t g t xx d x 0 0 1 0 with dirichlet boundary conditions where g is a positive nonincreasing function we establish an exponential and polynomial decay results with weaker conditions on g than those required in f ammar khodja a benabdallah j e munoz rivera r racke energy decay for timoshenko systems of memory type j differ equations 194 2003 82 115

on behaviour of solutions for a nonlinear viscoelastic equation with variable exponent nonlinearities abstract this paper deals with a viscoelastic wave equation with variable exponent nonlinearities subject to nonlinear boundary feedback under appropriate conditions a general decay result associated to solution energy is proved it is also shown that regarding arbitrary positive initial energy solutions blow up in a finite time

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

frictional versus viscoelastic damping in a semilinear wave equation in this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping the equation that models this problem is given by begin eqnarray u tt kappa 0 delta u int 0 t mbox div a x g t s nabla u s ds f u b x h u t 0 mbox in omega times bbb r quad end eqnarray where a b are nonnegative functions a in c 1 overline omega b in l infty omega satisfying the assumption begin eqnarray a x b x geq delta 0 quad forall x in omega end eqnarray and f and h are power like functions we observe that the assumption 0 2 gives us a wide assortment of possibilities from which to choose the functions a x and b x and the most interesting case occurs when one has simultaneous and complementary damping mechanisms taking this point of view into account a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily strategically localized dissipations as considered in the prior literature

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

mathematical model for a shock problem involving a linear viscoelastic bar are given constants problem 1 1 1 7 describes the shock between a solid body and a linear vis coelastic bar resting on a viscoelastic base with linear elastic constraints at the side constraints associated with a viscous frictional resistance in 1 an and trieu studied a special case of problem 1 1 1 2 1 4 1 7 associated with the following homogeneous boundary condition at x 1 u 1 t 0 1 8 with f u

confidence intervals for nonparametric curve estimates numerous nonparametric regression methods exist that yield consistent estimators of function curves often one is also interested in constructing confidence intervals for the unknown function when a function estimate is based on a single global smoothing parameter the resulting confidence intervals may hold their desired confidence level 1 on average but because bias in nonparametric estimation is not uniform they do not hold the desired level uniformly at all design points most research in this area has focused on mean squared error properties of the estimator for example mise itself a global measure in addition measures like mise are one step removed from the practical issue of coverage probability recent work that focuses on coverage probability has considered only coverage in an average sense ignoring the important issue of uniformity of coverage across the design space to deal with this problem a new estimator is developed which uses a local cross validation criterion lcv to determi

optimal g closure bounds via stability under lamination optimal bounds for a two dimensional g closure problem are proved they are obtained by combining together bounds derived using fine properties of quasiconformal mappings and a stability property of the g closure which is known as stability under lamination

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

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

spline smoothing and optimal rates of convergence in nonparametric regression models linear estimation is considered in nonparametric regression models of the form yi f xi ei xi e a b where the zero mean errors are uncorrelated with common variance a2 and the response function f is assumed only to have a bounded square integrable qth derivative the linear estimator which minimizes the maximum mean squared error summed over the observation points is derived and the exact minimax rate of convergence is obtained for practical problems where bounds on 11 f2q 11 and a2 may be unknown generalized cross validation is shown to give an adaptive estimator which achieves the minimax optimal rate under the additional assumption of normality 1 the model consider the nonparametric regression model

differentiation of matrix functionals using triangular factorization in various applications it is necessary to differentiate a matrix functional w a x where a x is a matrix depending on a parameter vector x usually the functional itself can be readily computed from a triangular factorization of a x this paper develops several methods that also use the triangular factorization to efficiently evaluate the first and second derivatives of the functional both the full and sparse matrix situations are considered there are similarities between these methods and algorithmic differentiation however the methodology developed here is explicit leading to new algorithms it is shown how the methods apply to several applications where the functional is a log determinant including spline smoothing covariance selection and restricted maximum likelihood

a comparison of the reinsch and speckman splines in the context of nonparametric regression spline smoothers can be used both for the estimation of the curve itself and for the estimation of the error variance we compare two approaches that have been suggested the reinsch spline i e roughness penalty and the speckman spline minimax the comparison is made on the basis of the summed mean squared error for curve estimation and on the basis of a closely related criterion for variance estimation we show in both asymptotic and small sample studies that the reinsch smoothing spline is close to optimal both as a curve and as a variance estimator

existence and decay of solutions of a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u tt u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove a local existence theorem and show for certain initial data and suitable conditions on g and that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g

efficient algorithms for robust generalized cross validation spline smoothing generalized cross validation gcv is a widely used parameter selection criterion for spline smoothing but it can give poor results if the sample size n is not sufficiently large an effective way to overcome this is to use the more stable criterion called robust gcv rgcv the main computational effort for the evaluation of the gcv score is the trace of the smoothing matrix tra while the rgcv score requires both tra and tra 2 since 1985 there has been an efficient o n algorithm to compute tra this paper develops two pairs of new o n algorithms to compute tra and tra 2 which allow the rgcv score to be calculated efficiently the algorithms involve the differentiation of certain matrix functionals using banded cholesky decomposition

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 the performance of space time codes over spatially correlated rayleigh fading channels we derive the exact pairwise error probability pep for space time coding over quasi static rayleigh fading channels in the presence of spatial fading correlation we show that receive correlation always degrades the pep for all signal to noise ratios snrs we quantify the effect of receive correlation by employing the notion of majorization we show that the stronger the receive correlation the worse the pep for all snrs we show that at low snr depending on the codes transmit correlation can either improve or degrade the pep performance we show that to guarantee robust performance for arbitrary transmit correlation the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs

diversity analysis for frequency selective mimo ofdm systems with general spatial and temporal correlation model in this paper the effect of a general spatial and temporal fading correlation structure on the performance of coded multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is studied the analysis handles an arbitrary joint transmit receive spatial correlation model including the non kronecker model an upper bound on the maximum achievable diversity order for frequency selective mimo ofdm systems with general temporal and spatial correlation is derived furthermore a space time frequency code design that can achieve the upper bound for any arbitrarily correlated channel scenario is provided the general framework of the analysis includes space frequency sf coded systems as a special case for the sf coded mimo ofdm system it is shown that any sf code designed to achieve full diversity in the independent fading channel can achieve full diversity in an arbitrary spatially correlated channel the derived analytical results are consistent with those in the existing literature for special correlation structures extensive simulation results are provided to confirm the theoretical analysis

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

improved decay rates for solutions to one dimensional linear and semilinear dissipative wave equations in all space abstract better decay estimates to the 1 dimensional cauchy problem on r to the linear equation u u t 0 can be discussed under rather restricted conditions on the initial data furthermore as applications we derive the small data global existence result to the equation u u t u p 1 u which has the odd functions as the initial data furthermore the new method see r ikehata t matsuyama sci math japon 55 2002 33 42 used in the first half will be applied to the problem coming from ehrenpreis sugaku 26 1974 168

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

an efficient method for calculating smoothing splines using orthogonal transformations a procedure for calculating the mean squared residual and the trace of the influence matrix associated with a polynomial smoothing spline of degree 2m 1 using an orthogonal factorization is presented the procedure substantially overcomes the problem of ill conditioning encountered by a recently developed method which employs a cholesky factorization but still requires only orderm 2 n operations and ordermn storage

systematic space time trellis code construction for correlated rayleigh fading channels the potential for capacity increase in multiple antenna wireless communication systems has drawn considerable attention to space time codes however most of the existing space time code construction methods have assumed ideal channel models either quasi static fading or fast fading in this work we propose a systematic space time trellis code construction method for correlated fading channels we derive the performance criteria that take into account both spatial and temporal channel correlation assuming that the space time correlation matrix is of full rank moreover we introduce a new design criterion and analyze the properties of the space time trellis codes satisfying the proposed criterion using the design criterion we develop a code construction procedure that jointly considers diversity advantage and coding advantage for an arbitrary number of transmit antennas and any memoryless modulation the flexibility of the proposed code construction method is demonstrated by designing space time trellis codes for two three and four transmit antennas with quaternary phase shift keying qpsk 8psk phase shift keying and 4ask amplitude shift keying modulations the simulation results demonstrate that not only can our method generate new codes for an arbitrary number of antennas but in some special cases where previously proposed codes exist our codes also perform very well

decay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving p laplacian in this paper we are concerned with the asymptotic behaviour of weak solutions to the initial boundary value problem for a class of quasilinear hyperbolic equations with damping terms involving p laplacian by using the multiplier methods we investigate the stability of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on strain caused stress term and damping terms

smoothing noisy data with spline functions a procedure for calculating the trace of the influence matrix associated with a polynomial smoothing spline of degree2m 1 fitted ton distinct not necessarily equally spaced or uniformly weighted data points is presented the procedure requires orderm 2 n operations and therefore permits efficient orderm 2 n calculation of statistics associated with a polynomial smoothing spline including the generalized cross validation the method is a significant improvement over an existing method which requires ordern 3 operations

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

design and performance of space time codes for spatially correlated mimo channels space time code stc designs classically rely on the assumption of independent and identically distributed i i d rayleigh channels however poor scattering conditions may have detrimental effects on the performance of stcs in this letter we derive code design criteria leading to robust stcs in a large variety of slow fading propagation conditions no channel knowledge is assumed at the transmitter codes satisfying these criteria are shown to perform much better on real world channels than codes designed only for i i d channels as examples the robustness of various spatial multiplexing schemes linear dispersion codes and space time trellis codes is discussed based on those criteria

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

a fast monte carlo cross validation procedure for large least squares problems with noisy data we propose a fast monte carlo algorithm for calculating reliable estimates of the trace of the influence matrixa involved in regularization of linear equations or data smoothing problems where is the regularization or smoothing parameter this general algorithm is simply as follows i generaten pseudo random valuesw 1 w n from the standard normal distribution wheren is the number of data points and letw w 1 w n t ii compute the residual vectorw a w iii take the normalized inner product w t w a w w t w as an approximation to 1 n tr i a we show both by theoretical bounds and by numerical simulations on some typical problems that the expected relative precision of these estimates is very good whenn is large enough and that they can be used in practice for the minimization with respect to of the well known generalized cross validation gcv function this permits the use of the gcv method for choosing in any particular large scale application with only a similar amount of work as the standard residual method numerical applications of this procedure to optimal spline smoothing in one or two dimensions show its efficiency

general decay of the solution for a viscoelastic wave equation with a time varying delay term in the internal feedback in this paper we consider a viscoelastic wave equation with a time varying delay term the coefficient of which is not necessarily positive by introducing suitable energy and lyapunov functionals under suitable assumptions we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases