a bloch decomposition based split step pseudospectral method for quantum dynamics with periodic potentials we present a new numerical method for accurate computations of solutions to linear one dimensional schro dinger equations with periodic potentials this is a prominent model in solid state physics where we also allow for perturbations by nonperiodic potentials describing external electric fields our approach is based on the classical bloch decomposition method which allows us to diagonalize the periodic part of the hamiltonian operator hence the dominant effects from dispersion and periodic lattice potential are computed together while the nonperiodic potential acts only as a perturbation because the split step communicator error between the periodic and nonperiodic parts is relatively small the step size can be chosen substantially larger than for the traditional splitting of the dispersion and potential operators indeed it is shown by the given examples that our method is unconditionally stable and more efficient than the traditional split step pseudospectral schemes to this end a particular focus is on the semiclassical regime where the new algorithm naturally incorporates the adiabatic splitting of slow and fast degrees of freedom

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

stochastic mean square performance analysis of an adaptive hammerstein filter this paper presents an almost sure mean square performance analysis of an adaptive hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence the system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter a bound for the long term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment this bound consists of two terms one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system one consequence of this result is that the long term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time invariant

coupled mode equations and gap solitons in higher dimensions abstract we study wave packets in nonlinear periodic media in arbitrary d spatial dimension modeled by the cubic gross pitaevskii equation in the asymptotic setting of small and broad wave packets with n n carrier bloch waves the effective equations for the envelopes are first order coupled mode equations cmes we provide a rigorous justification of the effective equations the estimate of the asymptotic error is carried out in an l 1 norm in the bloch variables this translates to a supremum norm estimate in the physical variables in order to investigate the existence of gap solitons of the d dimensional cmes we discuss spectral gaps of the cmes for n 4 and d 2 a family of time harmonic gap solitons is constructed formally asymptotically and numerically moving gap solitons have not been found for d 1 and for the considered values of n due to the absence of a spectral gap in the standard moving frame variables

recursive identification for nonlinear arx systems based on stochastic approximation algorithm the nonparametric identification for nonlinear autoregressive systems with exogenous inputs narx described by yk 1 f yk yk 1 n0 uk uk 1 n0 ek 1 is considered first a condition on f is introduced to guarantee ergodicity and stationarity of yk then the kernel function based stochastic approximation algorithm with expanding truncations saawet is proposed to recursively estimate the value of f at any given y 1 y n0 u 1 u n0 r2n0 it is shown that the estimate converges to the true value with probability one in establishing the strong consistency of the estimate the properties of the markov chain associated with the narx system play an important role numerical examples are given which show that the simulation results are consistent with the theoretical analysis the intention of the paper is not only to present a concrete solution to the problem under consideration but also to profile a new analysis method for nonlinear systems the proposed method consisting in combining the markov chain properties with stochastic approximation algorithms may be of future potential although a restrictive condition has to be imposed on f that is the growth rate of f x should not be faster than linear with coefficient less than 1 as x tends to infinity

accuracy and cut off point selection in three class classification problems using a generalization of the youden index we study properties of the index j 3 defined as the accuracy or the maximum correct classification for a given three class classification problem specifically using j 3 one can assess the discrimination between the three distributions and obtain an optimal pair of cut off points c 1 c 2 in the sense that the sum of the correct classification proportions will be maximized it also serves as the generalization of the youden index in three class problems parametric and non parametric approaches for estimation and testing are considered and methods are applied to data from an mrs study on human immunodeficiency virus hiv patients

adaptive tracking and recursive identification for hammerstein systems a weighted least squares wls based adaptive tracker is designed for a class of hammerstein systems it is proved that the tracking error is asymptotically minimized incorporating with the diminishing excitation technique the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved numerical examples are given and the simulation results are consistent with the theoretical analysis

identification of a class of nonlinear systems under stationary non gaussian excitation this paper provides new solutions to the nonlinear system identification problem when the input to the system is a stationary non gaussian process we propose the use of a model called the hammerstein series which leads to significant reductions in both the computational requirements and the mathematical tractability of the nonlinear system identification problem we show that unlike the volterra series one can obtain closed form expressions for the hammerstein series kernels and the quadratic coherence function in the non gaussian case estimation of the kernels and quadratic coherence function is discussed a comparison with a nonlinear system identification approach that uses the volterra series is provided an automotive engineering application illustrates the usefulness of the proposed method

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

a nonparametric polynomial identification algorithm for the hammerstein system almost all existing hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable to overcome this defect in this paper a new nonparametric polynomial identification algorithm for the hammerstein system is proposed which extends the idea in the author s previous work 1993 1994 on the hammerstein system identification to a more general and practical case where no functional value of the system nonlinearity is known a priori convergence and convergence rates in both uniform and global senses are established and simulation studies demonstrate the effectiveness and advantage of the new algorithm

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

strong consistency of recursive identification for hammerstein systems with discontinuous piecewise linear memoryless block this note deals with identification of hammerstein systems with discontinuous piecewise linear memoryless block followed by a linear subsystem recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block by taking a sequence of iid random variables with uniform distribution to serve as the system input strong consistency is proved for all estimates given in the note the theoretical results are verified by computer simulation

identifying mimo hammerstein systems in the context of subspace model identification methods in this paper we outline the extension of the moesp family of subspace model identification schemes to the hammerstein type of nonlinear system two types of identification problem are considered the first type assumes the polynomial structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para metrization of the static nonlinearity the second type addresses the identification of both the linear dynamic part and the static nonlinearity where only limited a priori information regarding the structure of the nonlinearity is available the improved robustness properties of the algorithms developed for this second type of hammerstein identification problem over existing correlation based schemes is illustrated by a numerical example

controller design oriented model identification method for hammerstein system abstract the paper proposes a new polynomial identification method for the hammerstein system by combining the results of parameter estimation theory and functions approximation theory the method circumvents many disadvantages of the earlier methods it is suitable for producing the controller design oriented model of hammerstein system consistency and convergency analysis are given for the obtained parameter estimates of the system s linear dynamics and approximating polynomial of its nonlinear memoryless element respectively simulation study verifies the effectiveness of the method

semi classical asymptotics in solid state physics this article studies the schrodinger equation for an electron in a lattice of ions with an external magnetic field in a suitable physical scaling the ionic potential becomes rapidly oscillating and one can build asymptotic solutions for the limit of zero magnetic field by multiple scale methods from homogenization for the time dependent schrodinger equation this construction yields wave packets which follow the trajectories of the semiclassical model for the time independent equation one gets asymptotic eigenfunctions or quasimodes for the energy levels predicted by onsager s relation

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed

a recursive local linear estimator for identification of nonlinear arx systems asymptotical convergence and applications in this paper we propose a recursive local linear estimator rlle for nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx first the rlle is introduced next the strong consistency as well as the asymptotical mean square error properties of the rlle are established and then an application of the rlle to an additive nonlinear system is discussed the rlle provides recursive estimates not only for the function values but also their gradients at fixed points a simulation example is provided to confirm the theoretical analysis

stochastic approximation in nonparametric identification of hammerstein systems derived from the idea of stochastic approximation recursive algorithms to identify a hammerstein system are presented two of them recover the characteristic of the nonlinear memoryless subsystem while the third one estimates the impulse response of the linear dynamic part the a priori information about both subsystems is nonparametric consistency in quadratic mean is shown and the convergence rate is examined results of numerical simulation are also presented

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

pathwise convergence of recursive identification algorithms for hammerstein systems this paper gives estimates for 1 coefficients contained in the linear part of the hammerstein system 2 the value of the nonlinear function f u in the hammerstein system at any u 3 ef u sub k and eu sub k f u sub k with u sub k denoting the system input no assumption is made on structure of f spl middot the estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one two numerical examples are given

split step methods for the solution of the nonlinear schro dinger equation a split step method is used to discretize the time variable for the numerical solution of the nonlinear schrodinger equation the space variable is discretized by means of a finite difference and a fourier method these methods are analyzed with respect to various physical properties represented in the nls in particular it is shown how a conservation law dispersion and instability are reflected in the numerical schemes analytical and numerical instabilities of wave train solutions are identified and conditions which avoid the latter are derived these results are demonstrated by numerical examples

recursive identification of multi input multi output errors in variables hammerstein systems the note considers the identification of multi input multi output errors in variables hammerstein systems in which both the input and output can be observed but with additive noises being arma processes with unknown coefficients with the help of stochastic approximation combined with the deconvolution kernel function the recursive algorithms are proposed for estimating coefficients of the linear subsystem and for the values of the nonlinear function under some reasonable conditions all the estimates are proved to converge to the true values with probability one these results include identification of the errors in variables linear systems as a special case a simulation example is given justifying the theoretical analysis

a general framework for nonparametric identification of nonlinear stochastic systems in this paper nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx is considered a general criterion function is introduced for estimating the value of the nonlinear function within the system at any fixed point the criterion function is constructed using a kernel together with a convex objective function not only does this framework include the classical kernel based weighted least squares estimator but also the kernel based l q q geq1 criteria as special cases first we prove that the minimizer of the general criterion function converges to the true function value with probability one second recursive algorithms are proposed to find the estimates which minimize the criterion function and it is shown that these estimates also converge to the true function value with probability one numerical examples are given justifying that the framework guarantees the strong consistency of the estimates and exhibits the robustness against outliers in the observations

justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear schrodinger equation abstract we consider wavepackets composed of two modulated carrier bloch waves with opposite group velocities in the one dimensional periodic nonlinear schrodinger gross pitaevskii equation these can be approximated by first order coupled mode equations cmes for the two slowly varying envelopes under a suitably selected periodic perturbation of the periodic structure the cmes possess a spectral gap of the corresponding spatial operator and allow families of exponentially localized solitary waves parametrized by velocity this leads to a family of approximate solitary waves in the periodic nonlinear schrodinger equation besides a formal derivation of the cmes a rigorous justification of the approximation and an error estimate in the supremum norm are provided several numerical tests corroborate the analysis

almost everywhere convergence of a recursive regression function estimate and classification corresp it is shown that the recursive kernel estimate of the regression function e y x x is consistent at almost every x mu regardless of the distribution mu of x thus the result is distribution free from this we show that the risk for a suitable classification rule derived from the estimate converges to bayes risk no matter what the class distributions are

perfectly matched layers in photonics computations 1d and 2d nonlinear coupled mode equations extending the general approach for first order hyperbolic systems developed in d appelo t hagstrom g kreiss perfectly matched layers for hyperbolic systems general formulation well posedness and stability siam j appl math 2006 to appear we construct pml equations for the mixed type system governing propagation of optical wave packets in both 1d and 2d bragg resonant photonic waveguides with a cubic nonlinearity i e the coupled mode equations we prove that in the linear case the layer equations are absorbing and perfectly matched we also prove they are stable for constant parameters a number of numerical experiments are performed to assess the layer s performance in both the linear and nonlinear regimes

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

matching in studies of classification accuracy implications for analysis efficiency and assessment of incremental value in case control studies evaluating the classification accuracy of a marker controls are often matched to cases with respect to factors associated with the marker and disease status in contrast with matching in epidemiologic etiology studies matching in the classification setting has not been rigorously studied in this article we consider the implications of matching in terms of the choice of statistical analysis efficiency and assessment of the incremental value of the marker over the matching covariates we find that adjustment for the matching covariates is essential as unadjusted summaries of classification accuracy can be biased in many settings matching is the most efficient covariate dependent sampling scheme and we provide an expression for the optimal matching ratio however we also show that matching greatly complicates estimation of the incremental value of the marker we recommend that matching be carefully considered in the context of these findings

on estimation of a class of nonlinear systems by the kernel regression estimate the estimation of a multiple input single output discrete hammerstein system is studied such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem the impulse response of the dynamic linear subsystem is obtained by the correlation method the main results concern the estimation of the nonlinear memoryless subsystem no conditions are imposed on the functional form of the nonlinear subsystem and the nonlinearity is recovered using the kernel regression estimate the distribution free pointwise and global convergence of the estimate is demonstrated that is no conditions are imposed on the input distribution and convergence is proven for virtually all nonlinearities the rates of pointwise as well as global convergence are obtained for all input distributions and for lipschitz type nonlinearities

recursive identification for wiener model with discontinuous piece wise linear function this paper deals with identification of wiener systems with nonlinearity being a discontinuous piece wise linear function recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid gaussian inputs the estimates are proved to converge to the corresponding true values with probability one a numerical example is given to justify the obtained theoretical results

on identification of the controlled plants described by the hammerstein system a new polynomial identification method for the hammerstein system is proposed the method employs the results of nonparametric statistics and best approximation theory obtaining a polynomial form estimate of the nonlinearity in the system except continuity no conditions are imposed on the nonlinearity the uniform as well as global convergence of the method is established the rates of convergence in both cases are derived under mild conditions on the smoothness of the nonlinearity the method is especially suitable for identifying the controlled plants with the description of hammerstein systems

evaluation of confounding effects in roc studies summary diagnosis of disease it is often true that the result of the test although dichotomous is based on the dichotomization of a continuous variable say x herein referred to as the separator variable let us assume without loss of generality that smaller values of x are associated with the diseased population often called the population of the cases conversely larger values of the separator are assumed to be associated with the control or nondiseased population a test result is classified by choosing a cut off x x against which the observation of the separator is compared a test result is positive if the value of the separator does not exceed the cut off otherwise the result is classified as negative most diagnostic tests are imperfect instruments in the sense that healthy individuals will occasionally be classified wrongly as being ill while some individuals who are really ill may fail to be detected as such therefore there is the ensuing conditional probability of the correct classification of a randomly selected case called the sensitivity of the test

nonparametric estimation of nonlinear dynamic systems using semirecursive regression estimates abstract in the paper we apply semirecursive nonparametric estimation techniques for the estimation of dynamic systems we investigate in detail the estimation of hammerstein dynamic systems using kernel and partitioning regression estimates in particular we propose estimation algorithms and study their convergence for all distributions of the data

parametric identification of hammerstein systems with consistency results using stochastic inputs the extended least squares algorithm is applied to identify the hammerstein system where the nonlinear static function f is expressed as a linear combination of basic functions with unknown coefficients strong consistency of the estimates is established and their convergent rates are obtained as well

recursive identification of hammerstein systems convergence rate and asymptotic normality in this work recursive identification algorithms are developed for hammerstein systems under the conditions considerably weaker than those in the existing literature for example orders of linear subsystems may be unknown and no specific conditions are imposed on their moving average part the recursive algorithms for estimating both linear and nonlinear parts are based on stochastic approximation and kernel functions almost sure convergence and strong convergence rates are derived for all estimates in addition the asymptotic normality of the estimates for the nonlinear part is also established the nonlinearity considered in the paper is more general than those discussed in the previous papers a numerical example verifies the theoretical analysis with simulation results

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

coupled mode equations and gap solitons for the 2d gross pitaevskii equation with a non separable periodic potential abstract gap solitons near a band edge of a spatially periodic nonlinear pde can be formally approximated by solutions of coupled mode equations cmes here we study this approximation for the case of the 2d periodic nonlinear schrodinger gross pitaevskii equation with a non separable potential of finite contrast we show that unlike in the case of separable potentials t dohnal d pelinovsky g schneider coupled mode equations and gap solitons in a two dimensional nonlinear elliptic problem with a separable periodic potential j nonlinear sci 19 2009 95 131 the cme derivation has to be carried out in bloch rather than physical coordinates using the lyapunov schmidt reduction we then give a rigorous justification of the cmes as an asymptotic model for reversible non degenerate gap solitons and provide h s estimates for this approximation the results are confirmed by numerical examples including some new families of cmes and gap solitons absent for separable potentials

self tuning control based on multi innovation stochastic gradient parameter estimation abstract this paper uses the multi innovation stochastic gradient misg algorithm to estimate the parameters of discrete time systems and presents an misg based self tuning control scheme furthermore we prove that the parameter estimation error converges to zero under persistent excitation and the parameter estimation based control algorithm can asymptotically achieve virtually optimal control and ensure that the closed loop systems are stable and globally convergent the simulation example is included

adaptive regulator for hammerstein and wiener systems with noisy observations for hammerstein and wiener systems observed with additive noises the adaptive regulation control is produced by a truncated stochastic approximation sa algorithm with truncation regions expanding with a prescribed rate it is proved that the stochastic adaptive control given in this note is optimal in the sense that it minimizes the long run average of regulation errors a s

an interpretation for the roc curve and inference using glm procedures the accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic roc curve this paper puts forth an interpretation for each point on the roc curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject this interpretation gives rise to new methods for making inference about roc curves it is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results one component of the pair being from a diseased subject and the other from a nondiseased subject within the generalized linear model glm binary regression framework roc curves can be estimated and we highlight a new semiparametric estimator covariate effects can also be evaluated with the glm models the methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters

global identification of nonlinear hammerstein systems by recursive kernel approach abstract in this paper we discuss identification of hammerstein systems by the recursive kernel regression estimate we propose the identification algorithm and study its global convergence and the rate of convergence

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

analysis and identification of hammerstein model non linear delay systems using block pulse function expansions algorithms for the analysis and identification of non linear delay systems described by a hammerstein model which consists of a single value non linearity followed by a linear time delayed plant are presented by using the finite dimensional block pulse expansion the solution of a hammerstein model non linear dynamic system with time delay is reduced to the solution of a set of linear algebraic equations in addition through the block pulse expansions of the measured input output data parameters of both the linear time delayed plant and the polynomial approximation of the non linear gain are estimated using the least squares method examples are given to illustrate the utility of this method

effective dynamics for bloch electrons peierls substitution and beyond we consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential x and vector potential a x with x d and 1 we prove that associated to an isolated family of bloch bands there exists an almost invariant subspace of l 2 d and an effective hamiltonian governing the evolution inside this subspace to all orders in to leading order the effective hamiltonian is given through the peierls substitution we explicitly compute the first order correction from a semiclassical analysis of this effective quantum hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics

brief paper parameter identification of hammerstein systems containing backlash operators with arbitrary shape parametric borders a two stage parameter identification method is developed for hammerstein systems containing backlash nonlinearities bordered by parametric arbitrary shape lines in the first stage a persistently exciting input is designed so that the linear subsystem can be made decoupled from the nonlinear element therefore linear subsystem identification is coped with using a least squares estimator enjoying consistency due to input persistent excitation then the backlash parameters are estimated using appropriate periodic exciting signals and consistent parameter estimators

interaction of modulated pulses in the nonlinear schrodinger equation with periodic potential abstract we consider a cubic nonlinear schrodinger equation with periodic potential in a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several bloch bands is studied the notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic interaction of these pulses

traveling solitary waves in the periodic nonlinear schrodinger equation with finite band potentials this paper studies asymptotics of moving gap solitons in nonlinear periodic structures of finite contrast deep grating within the one dimensional periodic nonlinear schrodinger equation pnls periodic structures described by a finite band potential feature transversal crossings of band functions in the linear band structure and a periodic perturbation of the potential yields new small gaps novel gap solitons with o 1 velocity despite the deep grating are presented in these gaps an approximation of gap solitons is given by slowly varying envelopes which satisfy a system of generalized coupled mode equations gcme and by bloch waves at the crossing point the eigenspace at the crossing point is two dimensional and it is necessary to select bloch waves belonging to the two band functions this is achieved by an optimization algorithm traveling solitary wave solutions of the gcme then result in nearly solitary wave solutions of the pnls moving at an o 1 velocity across the periodic structure

global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation an improved exponential bound on the l sub 1 error for the recursive kernel regression estimates is derived it is shown using the martingale device that weak strong and complete l sub 1 consistencies are equivalent consequently the conditions on a certain smoothing sequence are necessary and sufficient for strong l sub 1 consistency of the recursive kernel regression estimate the rates of global convergence are also given obtained results are applied to recursive classification rules and to nonlinear time series estimation

recursive identification for hammerstein system with arx subsystem identification is considered for the hammerstein system consisting of a static nonlinear block f middot followed by an arx subsystem when the system output is observed with noise no assumption is made on the structure of f middot recursive estimates are given for coefficients of the arx subsystem and for the value of f u at any u all estimates are proved to converge to the true values with probability one numerical examples are provided justifying the theoretical analysis

identification scheme for hammerstein output error models with bounded noise this technical note presents a method for the identification of hammerstein output error hoe models corrupted by bounded noise the method is based on an iterative scheme using two optimal bounding ellipsoid obe type algorithms the proposed approach allows the joint estimation of the linear part and of the nonlinear part with a low computational burden a numerical example is given so as to show the efficiency of the method