spectral factorization using the delta operator abstract in recent years many papers have been published abouth the operator mostly caused by the better numerical properties and the rapprochement between continuous and discrete time a major problem within the lqg design of a based input output relation has been how to spectral factorize in an efficient way the discrete time method of kuccera will not be applied since numerical word length characteristics will be poor for fast sampling rates in this paper a new approach is considered a new operator tustin operator is introduced in order to make an iterative and numerical stable solution to the spectral factorization problem the key idea is to use the operator resembled by its behavior to the differential operator

context sensitive dependency pairs termination is one of the most interesting problems when dealing with context sensitive rewrite systems although a good number of techniques for proving termination of context sensitive rewriting csr have been proposed so far the adaptation to csr of the dependency pair approach one of the most powerful techniques for proving termination of rewriting took some time and was possible only after introducing some new notions like collapsing dependency pairs which are specific for csr in this paper we develop the notion of context sensitive dependency pair csdp and show how to use csdps in proofs of termination of csr the implementation and practical use of the developed techniques yield a novel and powerful framework which improves the current state of the art of methods for automatically proving termination of csr

a sampling theory approach for continuous arma identification the problem of estimating continuous domain autoregressive moving average processes from sampled data is considered the proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes we derive an exact evaluation of the discrete domain power spectrum using exponential b splines and further suggest an estimation approach that is based on digitally filtering the available data the proposed functional which is related to whittle s likelihood function exhibits several local minima that originate from aliasing the global minimum however corresponds to a maximum likelihood estimator regardless of the sampling step experimental results indicate that the proposed approach closely follows the cramer rao bound for various aliasing configurations

a levinson type algorithm for modeling fast sampled data the standard discrete time autoregressive model is poorly suited for modeling series obtained by sampling continuous time processes at fairly rapid rates large computational errors can occur when the levinson algorithm is used to estimate the parameters of this model because the toeplitz covariance matrix is ill suited for inversion an alternative model is developed based on an incremental difference operator rather than the shift operator it is shown that as the sampling period goes to zero unlike the standard autoregressive parameters the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous time process a levinson type algorithm for efficiently estimating the parameters of this model is derived numerical examples are given to show that when the sampling interval is small this algorithm is considerably less sensitivity to arithmetic roundoff errors than the levinson algorithm

travelling solitary waves in the discrete schrodinger equation with saturable nonlinearity existence stability and dynamics the present work examines in detail the existence stability and dynamics of travelling solitary waves in a schrodinger lattice with saturable nonlinearity after analysing the linear spectrum of the problem in the travelling wave frame a pseudo spectral numerical method is used to identify weakly nonlocal solitary waves by finding zeros of an appropriately crafted tail condition we can obtain the genuinely localized pulse like solutions subsequent use of continuation methods allows us to obtain the relevant branches of solutions as a function of the system parameters such as the frequency and intersite coupling strength we examine the stability of the solutions in two ways both by imposing numerical perturbations and observing the solution dynamics as well as by considering the solutions as fixed points of an appropriate map and computing the corresponding floquet matrix and its eigenvalues both methods indicate that our solutions are robustly localized finally the interactions of these solutions are examined in collision type phenomena observing that relevant collisions are near elastic although they may under appropriate conditions lead to the generation of an additional pulse

dynamics of circular arrays of josephson junctions and the discrete sine gordon equation abstract we analyze the damped driven discrete sine gordon equation with periodic boundary conditions and constant forcing analytical and numerical results are presented about the existence stability and bifurcations of traveling waves in this system these results are compared with experimental measurements of the current voltage i v characteristics of a ring of n 8 underdamped josephson junctions we find two types of traveling waves low velocity kinks and high velocity whirling modes the kinks excite small amplitude linear waves intheir wake at certain drive strengths the linear waves phase lock to the kink generating resonant steps in the i v curve steps also occur in the high velocity region due to parametric instabilities of the whirling mode we analyze the onset of these instabilities then numerically study the secondary bifurcations and complex spatiotemporal phenomena that occur past the onset in all cases the measured voltage locations of the resonant steps are in good agreement with the predictions

lattice filters for rls estimation of a delta operator based model a lattice filter algorithm is derived for the recursive least squares rls estimation of the parameters of the input output model of a plant based on the delta operator formulation the lattice derivation presented allows a numerically efficient implementation particularly for large orders the order recursive property of the lattices is ideally suited for order determination techniques and applications where the order of the plant may change during operation an example concerning parameter identification for a fourth order plant with measurement noise is given

dynamics and stability of a discrete breather in a harmonically excited chain with vibro impact on site potential abstract we investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro impact on site potentials the latter are comprised of harmonic springs and rigid constraints limiting the possible motion of the masses local dissipation is introduced through a non unit restitution coefficient characterizing the impacts the system is excited by uniform time periodic forcing the present work is aimed to study the existence and stability of similar breathers in the space of parameters if additional harmonic potentials are introduced existence stability patterns of the breathers in the parameter space and possible bifurcation scenarios are investigated analytically and numerically in particular it is shown that the addition of a harmonic on site potential can substantially extend the stability domain at least close to the anti continuum limit this result can be treated as an increase in the robustness of the breather from the perspective of possible practical applications

least squares parameter estimation of continuous time arx models from discrete time data when modeling a system from discrete time data a continuous time parameterization is desirable in some situations in a direct estimation approach the derivatives are approximated by appropriate differences for an arx model this lead to a linear regression the well known least squares method would then be very desirable since it can have good numerical properties and low computational burden in particular for fast or nonuniform sampling it is examined under what conditions a least squares fit for this linear regression will give adequate results for an arx model the choice of derivative approximation is crucial for this approach to be useful standard approximations like euler backward or euler forward cannot be used directly the precise conditions on the derivative approximation are derived and analyzed it is shown that if the highest order derivative is selected with care a least squares estimate will be accurate the theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation

on the unique identification of continuous time autoregressive models from sampled data in this work we investigate the relationship between continuous time autoregressive ar models and their sampled version we consider uniform sampling and derive criteria for uniquely determining the continuous time parameters from sampled data the model order is assumed to be known we achieve this by removing a set of measure zero from the collection of all ar models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions we provide necessary and sufficient conditions for uniqueness of general ar models and we demonstrate the usefulness of this result by considering particular examples we further exploit our theory and introduce an estimation algorithm that recovers continuous time ar parameters from sampled data regardless of the sampling interval we demonstrate the usefulness of our algorithm for various gaussian and non gaussian ar processes

discrete lattice solitons properties and stability the authors present a detailed numerical study of the dynamics of high energy kink excitations in monatomic chains with a simple description using a microscopic model of the narrow kink core they present velocity amplitude and energy momentum curves for the kink which fit well the numerical results kink kink collisions are slightly inelastic depending on the velocities and point of collision within a lattice spacing

kinks in chains with on site bistable nondegenerate potential beyond traveling waves this paper revisits the well known transition fronts kinks in chains of coupled oscillators with nondegenerate on site potentials usually such transition fronts are considered in terms of traveling wave solutions we explore the loss of stability of such traveling waves generically it corresponds to one of the common scenarios for fixed points of discrete maps for example one can encounter the quasiperiodic kink propagation due to hopf bifurcation or the feigenbaum cascade of period doublings leading to a chaoticlike propagation pattern the aforementioned scenarios show up for instance for triparabolic and 4 on site potentials numeric evidence suggests that the loss of stability occurs due to resonances between the frequency associated with the kink propagation and the linear band gaps of the chain particular resonance mechanisms are model dependent for the classical atkinson cabrera model with a biparabolic on site potential the stability threshold is estimated by the simple means of linear algebra the loss of stability in this model occurs through hopf bifurcation the results are in good agreement with numerical simulations

variational approximations to breather modes in the discrete sine gordon equation abstract long lived breather like modes have been observed in the numerical simulations of discrete sine gordon systems however little analytical work has been carried out on these systems we show how to use the variational form of nonlinear klein gordon equations to find corrections to breather modes caused by discreteness

a new barrier to the existence of moving kinks in frenkel kontorova lattices an explanation is offered for an observed lower bound on the wave speed of travelling kinks in frenkel kontorova lattices kinks exist at discrete wavespeeds within a parameter regime where there is a resonance with linear waves phonons however they fail to exist even in this codimension one sense whenever there is more than one phonon branch in the dispersion relation inside such bands only quasi kinks with nondecaying oscillatory tails are possible the results are presented for a discrete sine gordon lattice with an onsite potential that has a tunable amount of anharmonicity novel numerical methods are used to trace kinks with topological charge q 1 and 2 in three parameters representing the propagation speed lattice discreteness and anharmonicity although none of the analysis is presented as rigorous mathematics numerical results suggest that the bound on allowable wavespeeds is sharp the results also explain why the vanishing at discrete values of anharmonicity of the peierls nabarro barrier between stationary kinks as discovered by savin et al does not lead to bifurcation of kinks with small wave speed 2003 elsevier b v all rights reserved

the lorenz fermi pasta ulam experiment we consider a chain of lorenz 63 systems connected through a local nearest neighbour coupling we refer to the resulting system as the lorenz fermi pasta ulamlattice because of its similarity to the celebrated experiment conducted by fermi pasta and ulam at large coupling strengths the systems synchronize to a global chaotic orbit of the lorenz attractor for smaller coupling the synchronized state loses stability instead steady spatially structured equilibrium states are observed these steady states are related to the heteroclinic orbits of the system describing stationary solutions to the partial differential equation that emerges on taking the continuum limit of the lattice notably these orbits connect saddle foci suggesting the existence of a multitude of such equilibria in relatively wide systems on lowering the coupling strength yet further the steady states lose stability in what appear to be always subcritical hopf bifurcations this can lead to a variety of time dependent states with fixed time averaged spatial structure such solutions can be limit cycles tori or possibly chaotic attractors cluster states can also occur though with less regularity consisting of lattices in which the elements are partitioned into families of synchronized subsystems ultimately for very weak coupling the lattice loses its time averaged spatial structure at this stage the properties of the lattice are probably chaotic and approximately scale with the lattice size suggesting that the system is essentially an ensemble of elements that evolve largely independent of one another the weak interaction however is sufficient to induce widespread coherent phases these are ephemeral states in which the dynamics of one or more subsystems takes a more regular form we present measures of the complexity of these incoherent lattices and discuss the concept of a dynamical horizon that is the distance along the lattice that one subsystem can effectively influence another and error propagation how the introduction of a disturbance in one subsystem becomes spread throughout the lattice 2000 elsevier science b v all rights reserved

strict coherence of conditional rewriting modulo axioms conditional rewriting modulo axioms with rich types makes specifications and declarative programs very expressive and succinct and is used in all well known rule based languages however the current foundations of rewriting modulo axioms have focused for the most part on the unconditional and untyped case the main purpose of this work is to generalize the foundations of rewriting modulo axioms to the conditional order sorted case a related goal is to simplify such foundations in particular even in the unconditional case the notion of strict coherence proposed here makes rewriting modulo axioms simpler and easier to understand properties of strictly coherent conditional theories like operational equi termination of the r b and r b relations and general conditions for the conditional churchrosser property modulo b are also studied

specification and proof in membership equational logic this paper is part of a long term effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic basis on which efficient execution by rewriting and powerful theorem proving tools can be based in particular our rewriting techniques provide semantic foundations for maude s functional sublanguage where they have been efficiently implemented

modelling and identification of non linear deterministic systems in the delta domain this paper provides a formulation for using the delta operator in the modelling of non linear systems it is shown that a unique representation of a deterministic non linear auto regressive with exogenous input narx model can be obtained for polynomial basis functions using the delta operator and expressions are derived to convert between the shift and delta domain a delta narx model is applied to the identification of a test problem a van der pol oscillator a comparison is made with the standard shift operator non linear model and it is demonstrated that the delta domain approach improves the numerical properties of structure detection leads to a parsimonious description and provides a model that is closely linked to the continuous time non linear system in terms of both parameters and structure

atomic scale localization of high energy solitary waves on lattices one dimensional monatomic lattices with hamiltonian h p n2 z z 1 p 2 v qn 1 qn are known to carry localized travelling wave solutions for generic nonlinear potentials v fw94 in this paper we derive the asymptotic profile of these waves in the high energy limit h 1 for lennardjones type interactions the limit profile is proved to be a universal highly discrete piecewise linear wave concentrated on a single atomic spacing this shows that dispersionless energy transport in these systems is not confined to the long wave regime on which the theoretical literature has hitherto focused but also occurs at atomic scale localization

delta levinson and schur type rls algorithms for adaptive signal processing in this paper we develop delta operator based levinson and schur type on line rls algorithms such algorithms have the potential of improved numerical behavior for ill conditioned input data these new algorithms are obtained by a unified transformation on the existing q operator based ones we first show that the conventional lattice structure can be naturally derived when the backward delta operator is used with this operator levinson and schur algorithms for the stationary stochastic model in q domain can easily be transformed into the delta domain then same transformation will be applied to the q domain on line levinson and schur type rls algorithms to obtain the delta domain counterparts their normalized versions as well as a systolic array architecture implementing the new delta schur rls algorithm are proposed extension to the equal length multichannel case is also given computer simulations show the expected numerical advantages of the delta based algorithms for fast sampled data in real time over the q domain ones under finite precision implementation

semantic foundations for generalized rewrite theories rewriting logic rl is a logic of actions whose models are concurrent systems rewrite theories involve the specification of equational theories of data and state structures together with a set of rewrite rules that model the dynamics of concurrent systems since its introduction more than one decade ago rl has attracted the interest of both theorists and practitioners who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm the experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice these extensions may develop along several dimensions like the choice of the underlying equational logic the kind of side conditions allowed in rewrite rules and operational concerns for the execution of certain rewrites in particular the maude system now supports subsorting and conditional sentences in the equational logic for data and also frozen arguments to block undesired nested rewrites moreover it allows equality and membership assertions in rule conditions in this paper we give a detailed presentation of the inference rules model theory and completeness of such generalized rewrite theories our results provide a mathematical semantics for maude and a foundation for formal reasoning about maude specifications

moving kinks and nanopterons in the nonlinear klein gordon lattice we study moving topological solitons kinks and antikinks in the nonlinear klein gordon chain these solitons are shown to exist with both monotonic non oscillating and oscillating asymptotics tails using the pseudo spectral method the anti kink solutions with oscillating background so called nanopterons are found as travelling waves of permanent profile propagating with constant velocity each of these solutions may be considered as a bound state of an anti kink with a background nonlinear periodic wave so that the wave pushes the anti kink over the peierls nabarro barrier the stability of these bound states is confirmed numerically travelling wave solutions of permanent profile are shown to exist depending on the convexity of the on site substrate potential the set of velocities at which the anti kinks with monotonic asymptotics propagate freely is calculated we also find moving non oscillating anti kink profiles with higher topological charges each of which appears to be the bound state of anti kinks with lower topological charge jq jd 1 2000 elsevier science b v all rights reserved

long distance wave computation using nonlinear solitary waves a recently developed method is described to propagate short wave equation pulses over indefinite distances and through regions of varying indices of refraction including multiple reflections the method wave confinement utilizes a newly developed nonlinear partial differential equation pde that propagates basis functions according to the wave equation these basis functions are generated as stable solitary waves where the discretized equation can be solved without any numerical dissipation the method can also be used to solve for harmonic waves in the high frequency eikonal limit including multiple arrivals the solution involves discretizing the wave equation on a uniform eulerian grid and adding a simple nonlinear confinement term this term does not change the amplitude integrated through each point on the pulse surface or the propagation velocity or arrival time and yet results in capturing the waves as thin surfaces that propagate as thin nonlinear solitary waves and remain 2 3 grid cells in thickness indefinitely with no numerical spreading a new feature described in this paper involves computing scattering of short pulses from complex objects such as complete aircraft a simple immersed surface approach is used that utilizes the same uniform grid as the propagation and avoids complex body fitted or adaptive grid schemes the new method should be useful in areas of wave propagation from radar scattering and long distance communications to cell phone transmission

maximum likelihood estimation of delta domain model parameters from noisy output signals fast sampling is desirable to describe signal transmission through wide bandwidth systems the delta operator provides an ideal discrete time modeling description for such fast sampled systems however the estimation of delta domain model parameters is usually biased by directly applying the delta transformations to a sampled signal corrupted by additive measurement noise this problem is solved here by expectation maximization where the delta transformations of the true signal are estimated and then used to obtain the model parameters the method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

a new bias compensating ls method for continuous system identification in the presence of coloured noise a new bias compensating least squares ls method is presented for the parameter estimation of linear single input single output siso continuous time systems a discrete time model obtained by using the linear integral filter is augmented by introducing a pre filter on the input and then the parameters of the augmented model are estimated by the conventional ls method the distinct characteristic roots of the pre filter are used to estimate the bias in the ls estimate the pre filter should be chosen so that its frequency bandwidth is wider than those of the system and the input signals since the new method requires minimal information on the noise characteristics it is easily applicable to the case of coloured noise

nonlinear modes in coupled rotator models abstract we compare the properties of generalized nonlinear klein gordon equations with a sinusoidal coupling sine lattice equations to those of the usual nonlinear klein gordon equation with harmonic coupling for three equations leading to the same sine gordon equation in the continuum limit using hirota s bilinear method we find a strong analogy between the properties of nonlinear oscillatory modes in the three equations numerical simulations confirm this analogy even for very discrete cases however we point out a fundamental difference between the harmonic and sinusoidal coupling by exhibiting a new class of localized nonlinear excitations which are specific to the sinusoidal coupling the rotating modes they can be created thermally an approximate analytical solution is obtained for these modes which are intrinsically discrete and appear to be extremely stable even in collisions with breathers possible implications for physics are discussed

stability of solitary waves in finite ablowitz ladik lattices we discuss the effects of different types of boundary conditions b c on the linear stability of a solitary wave in a finite length dynamical lattice described by the ablowitz ladik al model types of b c considered are fixed dirichlet no flux neumann and free as well as periodic b c the behaviour of eigenvalues around a stationary nonlinear wave consistent with several types of b c is studied analytically and numerically the translational eigenvalues are found to move away from the origin it is shown that for b c of the fixed type these eigenvalues bifurcate into a neutrally stable oscillatory kind while the no flux and free b c lead to an exponentially weak instability the rotational eigenmodes those related to the gauge invariance of the lattice strictly remain at the origin as gauge invariance is not broken by the linear homogeneous b c these numerical results are compared to the analytical and semi analytical predictions obtained within the approximation of the images generated by the solitary wave beyond the lattice edges a potential effect of continuous spectrum band edge bifurcations on stability is also evaluated with the conclusion that that these bifurcations cannot destabilize the soliton for periodic b c the translational invariance is preserved and so is the lax pair structure sustaining the integrable nature of the problem the al model was chosen so that the effects of boundary conditions are monitored in the absence of non integrable discreteness finally the possibility of the generation of multipulse configurations due to the interplay of finiteness effects with the exponential tail tail interaction of the pulses is examined

modeling continuous time processes via input to state filters a direct algorithm to estimate continuous time arma carma models is proposed in this paper in this approach we first pass the observed data through an input to state filter and compute the state covariance matrix the properties of the state covariance matrix are then exploited to estimate the half spectrum of the observed data at a set of user defined points on the right half plane finally the continuous time parameters are obtained from the half spectrum estimates by solving an analytic interpolation problem with a positive real constraint as shown by simulations the proposed algorithm delivers much more reliable estimates than indirect modeling approaches which rely on estimating an intermediate discrete time model

sampled data models for nonlinear stochastic systems truncation errors and sampling zero dynamics in this paper we consider nonlinear stochastic systems and intersect ideas from nonlinear control theory and numerical analysis in particular we use the idea of relative degree this concept guarantees smoothness properties of the output and this in turn allows one to establish properties that are unique to the control theoretic perspective the contributions of the current paper are threefold firstly we define different error measures that extend the ideas of local and global approximation errors for nonlinear stochastic systems secondly we demonstrate that the concept of relative degree plays a key role in obtaining higher order of accuracy for integration procedures compared to euler maruyama integration we show that a particular state space model named stts model has an improved order of accuracy when compared to an euler maruyama approximation at no significant extra computational cost thirdly we show that a further approximation to the stts model named mstts model while retaining the order of local errors has explicit sampling zero dynamics associated with the noise processes that have no continuous time counterpart the extra zero dynamics are shown to be a function of the euler frobenius polynomials to the best of the authors knowledge this is the first reference to sampling zero dynamics for stochastic nonlinear systems

upper bound on the products of particle interactions in cellular automata abstract particle like objects are observed to propagate and interact in many spatially extended dynamical systems for one of the simplest classes of such systems one dimensional cellular automata we establish a rigorous upper bound on the number of distinct products that these interactions can generate the upper bound is controlled by the structural complexity of the interacting particles a quantity which is defined here and which measures the amount of spatio temporal information that a particle stores along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata thereby elucidating why that approach is of general utility the upper bound is tested against several relatively complex domain particle cellular automata and found to be tight

on a class of discretizations of hamiltonian nonlinear partial differential equations abstract we present a new class of discretizations of partial differential equations pdes that preserve a momentum like integral of the motion this results in an effective translational invariance for the dynamical problem and the absence of a peierls nabarro barrier that is usually present in discretizations of hamiltonian pdes a general method to construct such discretizations for any nonlinearity is given and the properties of the resulting differential difference equations are analyzed in a number of different cases for nonlinear klein gordon as well for nonlinear schrodinger type systems while for the former nonintegrability of the dynamical problem is evident in the latter case numerical evidence suggests that the behavior is close to the one of integrable systems we also show how static solutions of the equations can be constructed for these discretizations and discuss the similarities and differences of the method with previously reported ones

continuous time ar process parameter estimation in presence of additive white noise must existing work so far on continuous time ar car parameter estimation concentrates on the noiseless measurement case when measurement noise is present our previous results on car parameter estimation need to be revised accordingly here we model the additive measurement noise as continuous time white noise and consider some approaches including average sampling and the direct ls method which we developed previously their advantages and disadvantages in this application are discussed

oscillatory wave fronts in chains of coupled nonlinear oscillators wave front pinning and propagation in damped chains of coupled oscillators are studied there are two important thresholds for an applied constant stress f for f f cs static peierls stress there are only stable moving wave fronts for piecewise linear models extending an exact method of atkinson and cabrera s to chains with damped dynamics corroborates this description for smooth nonlinearities an approximate analytical description is found by means of the active point theory generically for small or zero damping stable wave front profiles are nonmonotone and become wavy oscillatory in one of their tails

travelling waves for a frenkel kontorova chain abstract in this article the frenkel kontorova model for dislocation dynamics is considered where the on site potential consists of quadratic wells joined by small arcs which can be spinodal concave as commonly assumed in physics the existence of heteroclinic waves making a transition from one well of the on site potential to another is proved by means of a schauder fixed point argument the setting developed here is general enough to treat such a frenkel kontorova chain with smooth c 2 on site potential it is shown that the method can also establish the existence of two transition waves for a piecewise quadratic on site potential

modulational and numerical solutions for the steady discrete sine gordon equation in two space dimensions abstract we develop a modulation theory based on a suitably averaged lagrangian for steady solutions of the sine gordon equation in a two dimensional lattice these lump solutions are nonzero in circular or polygonal regions and zero elsewhere the modulation theory gives approximate solutions away from small perturbations of the exact anti continuum solutions for both radial and polygonal solutions we show how the peierls nabarro potential determines the shape of the boundary between excited sites and the zero solution these solutions are compared with the corresponding numerical solutions and significant agreement is found moreover we show that solutions with a large radius more than sixteen lattice sites can be explained using a continuous trial function for the averaged lagrangian while smaller polygonal solutions can be constructed using a trial function which takes into account the angular variation of the boundary imposed by the lattice finally the ideas of equivariant bifurcation theory are used to obtain a full numerical description of the solution branches as functions of the coupling parameter between neighboring sites the results of this work can be used to study steady solutions for other types of lattice equations

box jenkins identification revisited part i theory in classical time domain box jenkins identification discrete time plant and noise models are estimated using sampled input output signals the frequency content of the input output samples covers uniformly the whole unit circle in a natural way even in case of prefiltering recently the classical time domain box jenkins framework has been extended to frequency domain data captured in open loop the proposed frequency domain maximum likelihood ml solution can handle i discrete time models using data that only covers a part of the unit circle and ii continuous time models part i of this series of two papers i generalizes the frequency domain ml solution to the closed loop case and ii proves the properties of the ml estimator under non standard conditions contrary to the classical time domain case it is shown that the controller should be either known or estimated the proposed ml estimators are applicable to frequency domain data as well as time domain data

properties of one dimensional anharmonic lattice solitons abstract the existence of bell and kink shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons a second order non linear differential equation involving advanced and retarded terms must be solved which is done by implementing a scheme based on the finite element and newton s methods if the potential has a harmonic limit the asymptotic time decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time inversely if the potential has no harmonic limit the asymptotic regime shows up either as a power law or faster than exponential excellent agreement is achieved with toda s model illustrative examples are also given for the fermi pasta ulam and sine gordon potentials owing to integrability an effective one body potential is worked out in each case lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior the relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned the reasons preventing solitons from arising in a diatomic lattice are discussed

conditional rewriting logic as a unified model of concurrency abstract rewriting with conditional rewrite rules modulo a set e of structural axioms provides a general framework for unifying a wide variety of models of concurrency concurrent rewriting coincides with logical deduction in conditional rewriting logic a logic of actions whose models are concurrent systems this logic is sound and complete and has initial models in addition to general models interpreted as concurrent systems which provide a more operational style of semantics more restricted semantics with an incresingly denotational flavor such as preorder poset cpo and standard algebraic models appear as special cases of the model theory this permits dealing with operational and denotational issues within the same model theory and logic a programming language called maude whose modules are rewriting logic theories is defined and given denotational and operational semantics maude provides a simple unification of concurrent programming with functional and object oriented programming and supports high level declarative programming of concurrent systems

kink dynamics in the highly discrete sine gordon system abstract we study kink dynamics in a very discrete sine gordon system where the kink width is of the order of the lattice spacing numerical simulations exhibit new properties of kinks in this case they lose the memory of their initial velocity and propagate preferentially at well defined velocities which correspond to quasi steady states while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations when a small external driving force is applied to the system the same velocities appear as plateus in the strongly nonlinear mobility of the kink the energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system and the preferential velocities for the kink are obtained to good accuracy similar results may be expected to be valid for other discrete systems manifesting topological solitons the numerical simulations reveal also new stable multiple kink excitations which can propagate almost freely in extremely discrete systems where ordinary simple kinks are pinned to the lattice by discreteness the stability of the multiple kinks is discussed

abstract data type systems abstract this paper is concerned with the foundations of an extension of pure type systems by abstract data types hence the name of abstract data type systems adts generalize inductive types as they are defined in the calculus of constructions by providing definitions of functions by pattern matching on the one hand and relations among constructors of the inductive type on the other it also generalizes the first order framework of abstract data types by providing function types and higher order equations the first half of the paper describes the framework of adts while the second half investigates cases where adts are strongly normalizing this is shown to be the case for the polymorphic lambda calculus with possibly subtypes enriched by higher order algebraic rules obeying a strong generalization of primitive recursion of higher type that we call the general schema this covers in particular the case of inductive types whose constructors do not have functional arguments we conjecture that this result holds true for all calculi of the so called barendregt s cube on the other hand the definition of a schema for the higher order rules allowing for more general inductive types is left open

estimation of continuous time ar process parameters from discrete time data the problem of estimating continuous time autoregressive process parameters from discrete time data is considered the basic approach used here is based on replacing the derivatives in the model by discrete time differences forming a linear regression and using the least squares method such a procedure is simple to apply computationally flexible and efficient and may have good numerical properties it is known however that all standard approximations of the highest order derivative such as repeated use of the delta operator gives a biased least squares estimate even as the sampling interval tends to zero some of our previous approaches to overcome this problem are reviewed then two new methods which avoid the shift in our previous results are presented one of them which is termed bias compensation is computationally very efficient finally the relationship of the above least squares approaches with an instrumental variable method is investigated comparative simulation results are also presented

chaos transition of soliton motion on a microstructured lattice abstract soliton motion on a damped driven one dimensional lattice is proposed the lattice model is made of a one dimensional chain equipped at each point with a rotatory molecule the set of coupled difference differential equations for the molecule rotation is obtained for the discrete system using a semi discrete kink solution for which its center of mass is considered as a collective variable we derive the equation of motion for the kink location we show that the kink location is then governed by the equation of the damped sinusoidally driven pendulum when the first order corrections are dropped by means of numerical simulations carried out directly on the lattice model the complex dynamics of the kink location is investigated and compared to that of the well known forced pendulum for some ranges of the control parameters the numerical simulations exhibit a cascade of odd subharmonic components as well as strange attractors which characterizes the chaotic behavior of the kink motion these results agree fairly well with the main features of the transition to chaos for the damped driven pendulum

estimation of continuous time autoregressive model from finely sampled data we extend our two earlier continuous time estimation methods for continuous time autoregressive car model to derive estimators using only finely sampled discrete time data the approach is based on the approximation of derivatives by divided differences coupled with some bias correction two types of estimators are provided having bias of the order o h or of o h sup 2 respectively for small sampling interval h the procedures are computationally efficient and always yield a stable autoregressive polynomial simulations show that their bias are quite low

bias compensating least squares method for identification of continuous time systems from sampled data abstract least squares ls techniques are applied to the identification problem of continuous time systems from sampled data of input output measurements the linear integral filter which solves the intial condition problem is employed for handling time derivatives the asymptotic bias in the ls estimator is derived and is compensated in a modified ls algorithm called a bias compensating ls method to obtain consistent estimates of the unknown parameters when it is unknown the variance of the noise can be estimated recursively together with the system parameters the bias compensating ls method not only has all merits of the ls method but also possesses good consistency properties it is applicable to both time invariant and time varying continuous time systems in the time varying case an adaptive ls algorithm with a variable forgetting factor is chosen to make the estimates track the changing parameters quickly and the bias is compensated as is done in the time invariant case representative nu

discrete klein gordon models with static kinks free of the peierls nabarro potential for the nonlinear klein gordon type models we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice these discrete models are therefore free of the peierls nabarro potential previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method a relevant physical consequence of our findings is the existence of a wide class of discrete klein gordon models where slow kinks practically do not experience the action of the peierls nabarro potential such kinks are not trapped by the lattice and they can be accelerated by even weak external fields