lyapunov exponents and control sets near singular points abstract we consider control affine systems of the form x f 0 x i 1 m u i t f i x u u u r u loc integrable on r d with compact control range u and a singular point x r d i e f i x 0 i 0 m control sets are maximal subsets of r d with nonvoid interior where the system is approximately controllable we suppose that there is a periodic control functions u h such that linearized the system has positive and negative lyapunov exponents for u h and a periodic control function u s such that the linearized system has only negative lyapunov exponents for u s under an inner pair condition we show the existence of control sets near the singular point by using local stable and unstable manifolds of the system corresponding to u h and its asymptotic phase

time reversal based imaging and inverse scattering of multiply scattering point targets the treatment of time reversal imaging of multiply scattering point targets developed by the present authors in gruber et al time reversal imaging with multiple signal classification considering multiple scattering between the targets j acoust soc am 115 3042 3047 2004 is reformulated and extended to the estimation of the target scattering strengths using the foldy lax multiple scattering model it is shown that the time reversal multiple signal classification music pseudospectrum computed using the background green function as the steering vector yields accurate estimates of the target locations even in the presence of strong multiple scattering between the targets and that the target scattering strengths are readily computed from the so determined target locations using a nonlinear iterative algorithm the paper includes computer simulations illustrating the theory and algorithms presented in the paper

certain properties of a music type imaging functional in inverse scattering from an open sound hard arc abstract this paper concerns a mathematical formulation of the well known multiple signal classification music type imaging functional in the inverse scattering problem by an open sound hard arc based on the physical factorization of the so called multi static response msr matrix and the structure of left singular vectors linked to the non zero singular values of the msr matrix we construct a relationship between the imaging functional and the bessel functions of order 0 1 and 2 of the first kind we then expound certain properties of music and present numerical results for several differently chosen smooth arcs

stability and resolution analysis for a topological derivative based imaging functional the aim of this paper is to study a topological derivative based anomaly detection algorithm we compare its performance with other imaging approaches such as multiple signal classification backpropagation and kirchhoff migration we also investigate its stability with respect to medium and measurement noises as well as its resolution a simple postprocessing of the data set is introduced and shown to be essential in order to obtain an efficient topological based imaging functional both in terms of resolution and stability

a music type algorithm for detecting internal corrosion from electrostatic boundary measurements we establish an asymptotic representation formula for the steady state current perturbations caused by internal corrosive boundary parts of small surface measure based on this formula we design a non iterative method of music multiple signal classification type for localizing the corrosive parts from voltage to current observations we perform numerical experiments to test the viability of the algorithm and the results clearly demonstrate that the algorithm works well even in the presence of relatively high noise ratios

music imaging and electromagnetic inverse scattering of multiple scattering small anisotropic spheres the foldy lax equation is used to derive a multiple scattering model for the multiple scattering small anisotropic spheres by this model if the number of the non zero singular values of the multistatic response msr matrix is smaller than the number of the antennas the range space of the msr matrix is found to be spanned by the background green s function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer which indicates that the multiple signal classification music method could be implemented to obtain the locations of the scatterers after estimating the positions of the scatterers a non iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer two numerical simulations show that the music method and the non iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple scattering small anisotropic spheres such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres

admissibility and exponential trichotomy of dynamical systems described by skew product flows abstract the aim of this paper is to present a new and very general method for the detection of the uniform exponential trichotomy of dynamical systems the investigation is done in several constructive stages that correspond to three admissibility properties that are progressively introduced with respect to an associated input output system we prove that the uniform admissibility of the pair c b r x l 1 r x for the associated system is a sufficient condition for the existence of a uniform trichotomic behavior of the initial dynamical system if p 1 and the pair c b r x l 1 r x is uniformly p admissible then we obtain the uniform exponential trichotomy next we study whether the admissibility conditions are also necessary for the uniform exponential trichotomy supposing that a dynamical system has a uniform exponential trichotomy we prove that the associated input output system has unique bounded solutions in certain subspaces finally we obtain that the uniform p admissibility of the pair c b r x l 1 r x is a necessary and sufficient condition for uniform exponential trichotomy

multi frequency topological derivative for approximate shape acquisition of curve like thin electromagnetic inhomogeneities abstract in this paper we investigate a non iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and or magnetic permeability differ from those in the embedding homogeneous space the main objective is the imaging of crack like thin inclusions but the algorithm can be applied to arbitrarily shaped inclusions for this purpose we apply multiple time harmonic frequencies and normalize the topological derivative imaging function by its maximum value in order to verify its validity we apply it for the imaging of two dimensional crack like thin electromagnetic inhomogeneities completely hidden in a homogeneous material corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm

topological derivative strategy for one step iteration imaging of arbitrary shaped thin curve like electromagnetic inclusions in this manuscript a fast imaging of thin curve like electromagnetic inclusions completely hidden in the homogeneous domain with smooth boundaries is considered by creating an electromagnetic inclusion of a small diameter and applying the asymptotic expansion formula in the existence of such an inclusion the topological derivative is successfully derived based on this derivative a one step iteration imaging algorithm is designed by solving an adjoint problem various numerical experiments of single and multiple inclusions demonstrate the viability and limitation of the designed algorithm

electromagnetic music type imaging of perfectly conducting arc like cracks at single frequency we propose a non iterative music multiple signal classification type algorithm for the time harmonic electromagnetic imaging of one or more perfectly conducting arc like cracks found within a homogeneous space r 2 the algorithm is based on a factorization of the multi static response msr matrix collected in the far field at a single nonzero frequency in either transverse magnetic tm mode dirichlet boundary condition or transverse electric te mode neumann boundary condition followed by the calculation of a music cost functional expected to exhibit peaks along the crack curves each half a wavelength numerical experimentation from exact noiseless and noisy data shows that this is indeed the case and that the proposed algorithm behaves in robust manner with better results in the tm mode than in the te mode for which one would have to estimate the normal to the crack to get the most optimal results

analysis of music type imaging functional for single thin electromagnetic inhomogeneity in limited view inverse scattering problem this study analyzes the well known multiple signal classification music algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so called multi static response matrix in limited view inverse scattering problems the mathematical theories of music are partially discovered e g in the full view problem for an unknown target of dielectric contrast or a perfectly conducting crack with the dirichlet boundary condition transverse magnetic tm polarization and so on hence we perform further research to analyze the music type imaging functional and to certify some well known but theoretically unexplained phenomena for this purpose we establish a relationship between the music imaging functional and an infinite series of bessel functions of integer order of the first kind this relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve various results of numerical simulation are presented in order to support the identified structure of music although a priori information of the target is needed we suggest a least condition of range of incident and observation directions to apply music in the limited view problem

convergence to equilibrium in the classical model of population genetics abstract in the classical model of population genetics for continuous time fisher s equation for n alleles a stationary point is called regular if the viability of each of the absent alleles is distinct from the average viability of the population it is shown that if the limit set of a trajectory contains a regular point then it contains only one point

crack reconstruction using a level set strategy we present a level set based technique to recover key characteristics of a defect or crack e g location length and shape in a two dimensional material from boundary electrical measurements the key feature of this work is to extend the usual level set technique for modeling volumetric objects to very thin objects two level set functions are employed the first one models the location and form of the crack and the second one models its length and connectivity an efficient gradient based method is derived in order to define evolution laws for these two level set functions which minimize the least squares data misfit numerical experiments show the utility of this method even in the presence of a significant noise level in the measurements a finite element method is used to simulate the electric field behavior in the presence of very thin objects

optimal monodomain approximations of the bidomain equations abstract the bidomain equations are widely accepted to model the spatial distribution of the electrical potential in the heart although order optimal methods have been devised for discrete versions of these equations it is still very cpu demanding to solve the equations numerically on a sufficiently fine mesh in 3d furthermore the equations are hard to analyze from a mathematical point of view very little is known about the qualitative behavior of the solutions generated by these equations it is well known that upon appealing to a certain relation between the extracellular and intracellular conductivities the bidomain model can be rewritten in terms of a scalar reaction diffusion equation referred to as the monodomain model this model is of course much easier to solve and also the qualitative properties of the solutions are well known such equations have been studied intensively for decades it is the purpose of the present paper to show how the bidomain equations can be approximated in an optimal manner by the solution of a monodomain model the key feature here is that this optimal solution can be computed without solving the bidomain model itself the solution is obtained by putting the problem into a framework of parameter identification problems our results are illuminated by a series of numerical experiments

an investigation of stability of a control surface with structural nonlinearities in supersonic flow using zubov s method it is well known that the presence of nonlinearities may significantly affect the aeroelastic response of an aerospace vehicle structure in this paper the aeroelastic behaviour at high mach numbers of an all moving control surface with a nonlinearity in the root support is investigated very often under certain flight conditions a stable equilibrium point corresponding to zero displacement of the structure together with an unstable limit cycle arising from a sub critical hopf bifurcation results from the presence of the nonlinearity the dynamic aeroelastic response to external excitation is also of interest and when sinusoidal forcing is applied the stable equilibrium point may then be replaced by a periodic attractor and the limit cycle by an unstable multi periodic solution with or without this forcing there is an attractor which will possess a domain of attraction in this paper the problem of estimating these domains of attraction is tackled using zubov s method in the absence of forcing the method is applied directly to the aeroelastic equations while for the forced system the method of averaging is applied to approximate the aeroelastic equations by an autonomous system the behaviour of the system with forcing is also investigated for flight speeds below a threshold which may occur where the unstable limit cycle of the unforced system disappears in this regime the nonlinear system may nevertheless still possess multiple attractors and their domains of attraction are investigated again using an averaged form of the aeroelastic equations in this study the nonlinearity in the root support was assumed to be due to a cubic hardening restoring moment the zubov approach which always yields conservative estimates was shown to be capable of rapidly giving a good indication of stability domain boundaries under many conditions although this investigation focuses on an aeroelastic system the general form of equations considered arises in many other settings so that the approach would be relevant to a whole range of engineering applications

imaging schemes for perfectly conducting cracks we consider the problem of locating perfectly conducting cracks and estimating their geometric features from multistatic response matrix measurements at a single or multiple frequencies a main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal to noise ratios in this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength to crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks a central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multistatic response matrix measurements we present numerical experiments to illustrate some of our main findings

direct sampling method for identifying magnetic inhomogeneities in limited aperture inverse scattering problem abstract the direct sampling method dsm in limited aperture inverse scattering problems for transverse electric te polarization is considered based on the asymptotic expansion formula in the presence of small targets we demonstrate that the indicator function of dsm can be represented by an infinite series of bessel functions of integer order and correspondingly examine various properties of dsm simulation results with noisy data are created to support theoretical results based on the identified structure of the indicator function we design a new indicator function of dsm analyze its mathematical structure and generate simulation results to demonstrate its effectiveness and improvement

h k trichotomies and asymptotics of nonautonomous difference systems abstract discrete nonautonomous nonlinear systems possessing h k trichotomies are considered we specialize to the case of solutions moving inside and in a neighborhood of an invariant manifold of a special kind which we call h k hyperbolic the aulbach coppel knobloch transformation is then developed and used to state conditions for granting asymptotic equivalence of solutions our results generalize some of aulbach s results in which the manifold considered was made of stationary points and the system taken was autonomous

behavior of solutions near manifolds of periodic solutions abstract consider an autonomous differential system x f x of dimension n that admits a k dimensional invariant manifold in x space represented by a k parameter family of periodic solutions then k characteristic multipliers of the corresponding variational equation are equal to 1 under the hypothesis that none of the remaining n k characteristic multipliers has modulus 1 the behavior of the solutions of x f x near is investigated the main results are the description of a neighborhood of in terms of stable and unstable manifolds and the statement that whenever a solution of x f x approaches the invariant manifold as t it tends to with asymptotic amplitude and phase

music algorithm for location searching of dielectric anomalies from s parameters using microwave imaging abstract motivated by the biomedical engineering used in early stage breast cancer detection we investigated the use of multiple signal classification music algorithm for location searching of small anomalies using s parameters we considered the application of music to functional imaging where a small number of dipole antennas are used our approach is based on the application of born approximation or physical factorization we analyzed cases in which the anomaly is respectively small and large in relation to the wavelength and the structure of the left singular vectors is linked to the nonzero singular values of a multi static response msr matrix whose elements are the s parameters using simulations we demonstrated the strengths and weaknesses of the music algorithm in detecting both small and extended anomalies

a model based block triangular preconditioner for the bidomain system in electrocardiology we introduce a preconditioner for the solution of the bidomain system governing the propagation of action potentials in the myocardial tissue the bidomain model is a degenerate parabolic set of nonlinear reaction diffusion equations the nonlinear term describes the ion flux at the cellular level the degenerate nature of the problem results in a severe ill conditioning of its discretization our preconditioning strategy is based on a suitable adaptation of the monodomain model a simplified version of the bidomain one which is by far simpler to solve nevertheless is unable to capture significant features of the action potential propagation the monodomain preconditioner application to a non symmetric formulation of the bidomain system results at the algebraic level in a lower block triangular preconditioner we prove optimality of the preconditioner with respect to the mesh size and corroborate our theoretical results with 3d numerical simulations both on idealized and real ventricle geometries

nonlinear criteria for the existence of the exponential trichotomy in infinite dimensional spaces abstract in this paper we obtain for the first time nonlinear conditions for the existence of the exponential trichotomy of skew product flows in infinite dimensional spaces we treat the most general case without any additional assumptions concerning the cocycle and without assuming a priori the existence of the projection families we show that an inedit assembly of integral conditions imply the existence of the exponential trichotomy with all of its properties and we prove that the imposed conditions are also necessary our results generalize the previous studies on this topic and provide as particular cases many interesting situations among which we mention the detection of the exponential trichotomy of general non autonomous systems

asymptotic phase revisited abstract we discuss the classical problem on asymptotic phase of periodic orbits of planar systems the existence of asymptotic phase for non hyperbolic periodic orbits is completely determined with hypotheses on the derivatives of a poincare map and a return time map smoothness of the vector field turns out to be crucial for existence of asymptotic phase for hyperbolic periodic orbits a new proof for the existence of invariant foliations is provided

preconditioning the bidomain model with almost linear complexity the bidomain model is widely used in electro cardiology to simulate spreading of excitation in the myocardium and electrocardiograms it consists of a system of two parabolic reaction diffusion equations coupled with an ode system its discretisation displays an ill conditioned system matrix to be inverted at each time step simulations based on the bidomain model therefore are associated with high computational costs in this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues the torso the preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi definite a block lu decomposition of the system together with a heuristic approximation referred to as the monodomain approximation are the key ingredients for the preconditioning definition numerical results are provided for two test cases a 2d test case on a realistic slice of the thorax based on a segmented heart medical image geometry a 3d test case involving a small cubic slab of tissue with orthotropic anisotropy the analysis of the resulting computational cost both in terms of cpu time and of iteration number shows an almost linear complexity with the problem size i e of type nlog a n for some constant a which is optimal complexity for such problems

input output admissibility and exponential trichotomy of difference equations abstract we propose a new method for the study of the asymptotic behavior of difference equations in infinite dimensional spaces providing characterizations for the property of uniform exponential trichotomy we deduce the structure of the stable unstable and bounded subspace and prove the uniqueness of the projection families we introduce a new admissibility concept with respect to a discrete input output system and prove that this is a necessary and sufficient condition for the existence of uniform exponential trichotomy throughout the paper there is no assumption on the coefficients and the obtained results are applicable to any class of difference equations

invariant manifolds with asymptotic phase for nonautonomous difference equations abstract for autonomous difference equations with an invariant manifold conditions are known which guarantee that a solution approaching this manifold eventually behaves like a solution on this manifold in this paper we extend the fundamental result in this context to difference equations which are nonautonomous and whose solutions are guaranteed only in forward time

invariant manifolds with asymptotic phase this paper is concerned with invariant manifolds allowing a generic approach to solutions of the underlying autonomous differential system only this means that any solution approaching such an invariant manifold m ultimately behaves like a particular solution on j4 in the sense that the difference n t i l of the two solutions tends to 0 as t cq in other words only solutions on the stable manifold of m can approach m as f cc invariant manifolds with that property are said to have an asymptotic phase the simplest nontrivial example of an invariant manifold with asymptotic phase is the orbit of an isolated periodic solution whose floquet multipliers lie all but one in the open unit disc of the complex plane malkin 12 proved a manifold of stationary solutions to have an asymptotic phase if each of these solutions has all eigenvalues with nonpositive real parts and if in addition the number of eigenvalues on the imaginary axis equals the dimension of the manifold more generally a k dimensional manifold generated by a family of periodic solutions has an asymptotic phase if all but k floquet multipliers have modulus less than 1 see hale stokes 9 conditions for a torus to be asymptotically stable with asymptotic phase are given by samoilenko 13 and coppel 5 invariant manifolds without any specified structure are considered by fenichel 6 7 and in kirchgraber s note 111 moreover each center manifold has an asymptotic phase if the corresponding equilibrium is stable see carr al amood 4 and henry lo in any case the condition guaranteeing the existence of an asymptotic phase amounts to the fact that the decay rate of solutions toward the manifold is greater than the decay rate of the solutions within the manifold in each of the cases quoted so far the invariant manifold is asymptotically stable and thus the question arises whether an asymptotic phase can exist only in connection with asymptotic stability a negative answer to this question is given by the author in l 21 where hyperbolic manifolds of periodic solutions are proved to have an asymptotic phase in l the manifold is supposed to be compact while the noncompact case is treated in 2 under the restriction that the generating family of periodic solutions has an amplitude independent period recently hale massatt 8 extended the corresponding result for manifolds of stationary solutions to a certain class of partial differential equations in this paper we drop the periodicity assumption of the flow on the given manifold and prove the following result a compact invariant manifold has an asymptotic phase if the manifold is hyperbolic assumption hl and carries a flow parallel in the sense of our assumption h2 this includes most of the aforementioned results

asymptotic imaging of perfectly conducting cracks in this paper we consider cracks with dirichlet boundary conditions we first derive an asymptotic expansion of the boundary perturbations that are due to the presence of a small crack based on this formula we design a noniterative approach for locating a collection of small cracks in order to do so we construct a response matrix from the boundary measurements the location and the length of the crack are estimated respectively from the projection onto the noise space and the first significant singular value of the response matrix indeed the direction of the crack is estimated from the second singular vector we then consider an extended crack with dirichlet boundary conditions we rigorously derive an asymptotic expansion for the boundary perturbations that are due to a shape deformation of the crack to reconstruct an extended crack from many boundary measurements we develop two methods for obtaining a good guess several numerical experiments show how the proposed techniques for imaging small cracks as well as those for obtaining good initial guesses toward reconstructing an extended crack behave

period function and normalizers of vector fields in rn with n 1 first integrals we extend the theory that relates period function normalizers and first integrals which has been widely developed in r2 to any dimension in particular we show how to find n 1 independent normalizers of vector fields in rn with n 1 independent first integrals a formula for the derivatives of the period function is obtained and a necessary and sufficient condition for isochronicity is also proved these results generalize previous works of freire gasull and guillamon sabatini and villarini

a phase and space coherent direct imaging method a direct imaging algorithm for point and extended targets is presented the algorithm is based on a physical factorization of the response matrix of a transducer array the factorization is used to transform a passive target problem to an active source problem and to extract principal components tones in a phase consistent way the multitone imaging function can superpose multiple tones spatial diversity aperture of the array and frequencies bandwidth of the probing signal based on phase coherence the method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed robustness of the algorithm with respect to noise is demonstrated via numerical examples

roughness of h k dichotomies abstract in this paper we prove a roughness theorem for a class of dichotomies of linear systems of differential equations the so called h k dichotomies these include a great variety of dichotomies among them the ordinary and exponential dichotomies exponential ordinary dichotomies levinson dichotomies for diagonal systems etc we prove that under general uniform conditions upon the functions h and k these dichotomies are not destroyed by integrable perturbations this result generalizes the property of roughness of ordinary dichotomies under integrable perturbations

asymptotic stability regions via extensions of zubov s method i on considere un systeme differentiel x f t x satisfaisant les hypotheses suivantes f r n 1 r n est analytique f t x est presque periodique en t pour chaque x r n f t 0 0 t r la matrice principale fondamentale t s de y f x t 0 y satisfait t s exp t s t s avec et des constantes positives f t x f x t o x 0 x uniformement en t quand x 0

asymptotic integration of a system resulting from the perturbation of an h system z systems were introduced in lo with the intention of obtaining results about stability for a weakly stable system at least weaker than those given by exponential stability under some perturbations in this paper we get asymptotic formulae for these systems which state new results about asymptotic integration for nonlinear systems under general hypotheses moreover the corresponding results for linear systems give new insight about levinson s theorem on asymptotic integration in this way using the h systems we get a uniform treatment for the concept of stability and we verify that several classical theorems of stability take a precise form by the asymptotic formulae in section 2 we recall the definition and some properties of an h system and we state two new theorems about asymptotic behavior of solutions of perturbed h systems in section 3 some general results about asymptotic integration are given these results extend those given in lo in section 4 we apply the technique to the linear case finally in section 5 we show examples and applications and we study the emden fowler equation which originally does not satisfy the general hypothesis but can be transformed into one where they are satisfied 2 h systems let us consider the differential system

on the linearization theorem of fenner and pinto this paper reports an improvement of the linearization theorem of fenner and pinto 1999 22 fenner and pinto presented a version of hartman s result they showed that there exists a one to one correspondence between solutions of the linear system and the nonlinear system moreover if h t x denotes the transformation then h t x x is uniformly bounded however no proof of the holder regularity of the transformation h t x appears in fenner and pinto 1999 22 the main objective in this paper is precisely to give a proof of the holder regularity of the transformation h t x namely we show that the conjugating function h t x in the hartman grobman theorem is always holder continuous and has holder continuous inverse moreover we weakened an important assumption in fenner and pinto 1999 22 fenner and pinto obtained the linearization theorem by setting that the whole linear system should satisfy is condition in this paper this assumption is reduced in fact it is enough to assume that the linear system partially satisfies is condition therefore we improve the linearization theorem of fenner and pinto

riccati based feedback control of the monodomain equations with the fitzhugh nagumo model feedback control for the monodomain equations is studied the dynamics of interest are governed by a coupled pde ode reaction diffusion system with nonmonotone nonlinearity of fitzhugh nagumo type a localized distributed control is used to locally stabilize the nonlinear system this is achieved by a riccati based feedback law determined by the linearized system it is shown that the riccati equation corresponding to the pde variable suffices for exponential stabilization of the linearized pde ode system the theoretical findings are underlined by several numerical examples

optimal controller tuning for nonlinear processes the present work proposes a systematic methodology for the optimal selection of controller parameters in the sense of minimizing a performance index which is a quadratic function of the tracking error and the control effort the performance index is calculated explicitly as an algebraic function of the controller parameters by solving zubov s partial differential equation pde standard optimization techniques are then employed for the calculation of the optimal values of the controller parameters the solution of zubov s pde is also used to estimate the closed loop stability region for the chosen values of the controller parameters the proposed approach is finally illustrated in a chemical reactor control problem

brief a new lyapunov design approach for nonlinear systems based on zubov s method the present research work proposes a new nonlinear controller synthesis approach that is based on the methodological principles of lyapunov design in particular it relies on a short horizon model based prediction and optimization of the rate of energy dissipation of the system as it is realized through the time derivative of an appropriately selected lyapunov function the latter is computed by solving zubov s partial differential equation based on the system s drift vector field a nonlinear state feedback control law with two adjustable parameters is derived as the solution of an optimization problem that is formulated on the basis of the aforementioned lyapunov function and closed loop performance characteristics a set of system theoretic properties of the proposed control law are examined as well finally the proposed lyapunov design method is evaluated in a chemical reactor example which exhibits nonminimum phase behaviour

error estimates for approximating non hyperbolic heteroclinic orbits of maps in this paper we consider heteroclinic orbits in discrete time dynamical systems that connect a hyperbolic fixed point to a non hyperbolic fixed point with a one dimensional center direction a numerical method for approximating the heteroclinic orbit by a finite orbit sequence is introduced and a detailed error analysis is presented the loss of hyperbolicity requires special tools for proving the error estimate the polynomial dichotomy of linear difference equations and a partial normal form transformation near the non hyperbolic fixed point this situation appears for example when one fixed point undergoes a flip bifurcation for this case the approximation method and the validity of the error estimate is illustrated by an example

music type imaging of perfectly conducting cracks in limited view inverse scattering problems abstract although standard multiple signal classification music algorithm has been considered a promising non iterative imaging technique for cracks its application is restricted to the full view inverse scattering problems many experimental results revealed that music can be applied to the imaging of perfectly conducting cracks with small length in limited view inverse scattering problem on the other hand music is not applicable for imaging of extended cracks in limited view problems but the reason behind this restricted application has not been theoretically investigated this gave an impetus for this study to attempt to identify the structure of music type algorithm that appears in the limited view inverse scattering problems by establishing a relationship between music and bessel functions of integer order of the first kind some numerical experiments are illustrated to support the identified structure of music

on the critical points of the flight return time function of perturbed closed orbits abstract we deal here with planar analytic systems x x x e which are small perturbations of a period annulus for each transversal section to the unperturbed orbits we denote by t q e the time needed by a perturbed orbit that starts from q to return to we call this the flight return time function we say that the closed orbit of x x x 0 is a continuable critical orbit in a family of the form x x x e if for any q and any that passes through q there exists q e a critical point of t e such that q e q as e 0 in this work we study this new problem of continuability in particular we prove that a simple critical periodic orbit of x x x 0 is a continuable critical orbit in any family of the form x x x e we also give sufficient conditions for the existence of a continuable critical orbit of an isochronous center x x x 0

music algorithm for two dimensional inverse problems with special characteristics of cylinders a multiple signal classification music algorithm is proposed to determine the positions of small cylinders which have some special characteristics that may lend traditional music unsuccessful the tm case is discussed in detail up to three independent currents are induced on each cylinder in the tm case however for a cylinder if the material property is the same as the background medium in one or two of the principal axes or if the geometry makes one or two of the induced currents very small with respect to the others so as to be negligible in noisy scenario the number of significant sources may be less than three and the traditional music may fail in locating the cylinder in such event knowledge of the direction of the induced source becomes mandatory to locate the cylinder the proposed method determines the direction of the induced source and uses the background green s function corresponding to it as music s test function the method uses minimization of the analytical expressions and gives good results in noise free as well as noisy scenarios

on h k manifolds with asymptotic phase abstract we introduce the notion of h k manifolds and give conditions under which the property of being a manifold with asymptotic phase holds these conditions allow the construction of a transformation of the variational equation of a nonlinear nonautonomous systems with h k dichotomies into an almost decoupled quasilinear system the class of admissiblehandkfunctions is also briefly analyzed