an explicit description of the global attractor of the damped and driven sine gordon equation we prove that the size of the finite dimensional attractor of the damped and driven sine gordon equation stays small as the damping and driving amplitude become small a decomposition of finite dimensional attractors in banach space is found into a part that attracts all of phase space except sets whose finitedimensional projections have lebesgue measure zero and a partc that only attracts sets whose finite dimensional projections have lebesgue measure zero we describe the components of the attractor andc which is called the hyperbolic structure for the damped and driven sine gordon equation is low dimensional but the dimension ofc which is associated with transients is much larger we verify numerically that this is a complete description of the attractor for small enough damping and driving parameters and describe the bifurcations of the attractor in this small parameter region

spectral theory for the periodic sine gordon equation a concrete viewpoint a summary of the spectral theory for quasiperiodic sine and sinh gordon equations is given analogies with whole line solitons and scattering theory motivates the discussion the relation between the ingredients in the inverse spectral solution of the periodic sine gordon equation and physical characteristics of sine gordon waves is emphasized the explicit topics covered are summarized in the table of contents in the introduction

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

phase pulling and breather instability in an ac driven damped one dimensional sine gordon system abstract an ac driven damped sine gordon system in the nonlinear schrodinger regime may converge into various nontrivial space time attractors one of them is breather riding on top of flat profile both locked to the driver frequency using collective coordinate ansatz for this attractor and a multiple scale perturbation technique we study the location and nature of its instability among the various characteristics this study includes understanding the role of the breather background coupling the structure of the associated unstable modes the scaling structure of the instability boundary etc most strikingly we find the instability mechanism and the above features to be strongly sensitive to the asymptotic phase difference between the spatially localized breather and the spatially extended uniform background we call this phenomenon phase pulling

frame theory based analysis and design of oversampled filter banks direct computational method this paper studies the frames corresponding to oversampled filter banks fbs for this class of fb frames we present a state space parameterization of perfect reconstruction fb frames and explicit and numerically efficient formulas to compute the tightest frame bounds to obtain the dual fb frame and to construct a tight paraunitary fb frame from a given untight nonparaunitary fb frame the derivation uses well developed techniques from modern control theory which results in the unified formulas for generic infinite impulse response iir and finite impulse response fir fbs these formulas involve only algebraic manipulations of real matrices and can be computed efficiently reliably and exactly without the approximation required in the existing methods for generic fbs the results provide a unified framework for frame theory based analysis and systematic design of oversampled filter banks

hereditarily hypercyclic operators and mixing abstract we show that hereditary transitivity respectively strongly hereditary transitivity is equivalent to weak mixing respectively strong mixing in a discrete dynamical system with polish phase space we also study the connection between local orbit structure and hypercyclicity and obtain a local hypercyclicity criterion

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

perturbations of hypercyclic vectors we show that a linear operator can have an orbit that comes within a bounded distance of every point yet is not dense we also prove that such an operator must be hypercyclic this gives a more general form of the hypercyclicity criterion we also show that a sufficiently small perturbation of a hypercyclic vector is still hypercyclic

picard potentials and hill s equation on a torus hill s equation has drawn an enormous amount of consideration due to its ubiquity in applications as well as its structural richness of particular importance in the last 20 years is its connection with the kdv hierarchy and hence with integrable systems we show in this paper that regarding the independent variable as a complex variable yields a breakthrough for the problem of an efficient characterization of all elliptic finitegap potentials a major open problem in the field specifically we show that elliptic finitegap potentials of hill s equation are precisely those for which all solutions for all spectral parameters are meromorphic functions in the independent variable complementing a classical theorem of picard the intimate connection between picard s theorem and elliptic finite gap solutions of completely integrable systems is established in this paper for the first time in addition we construct the hyperelliptic riemann surface associated with a finitegap potential not necessarily elliptic i e determine its branch and singular points from a comparison of the geometric and algebraic multiplicities of eigenvalues of certain auxiliary operators associated with hill s equation these multiplicities are intimately correlated with the pole structure of the diagonal green s function of the operator h d2 dx2 q x in l2 r our construction is new in the present general complex valued periodic finite gap case before describing our approach in some detail we shall give a brief account of the history of the problem involved this theme dates back to a 1940 paper of ince 43 who studied what is presently called the lam6 ince potential

explicit feature control in structural topology optimization via level set method abstract the present paper aims to address a long standing and challenging problem in structural topology optimization explicit feature control of the optimal topology the basic idea is to resort to the level set solution framework and impose constraints on the extreme values of the signed distance level set function used for describing the topology of the structure numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach

influence of solitons in the initial state on chaos in the driven damped sine gordon system abstract the appearance of chaos in the a c driven damped sine gordon equation is studied numerically several transitions from periodic to chaotic behaviour are investigated in detail for flat initial conditions spatial structures breather kink in the initial conditions smooth out many of these transitions and give rise to an interesting symbiosis of time and spatial intermittency this symbiosis appears to be due to the competition between the background tendency towards chaos and the system s preference to maintain a spatial pattern the way that this competition is relieved is also found to depend very strongly on symmetry in the initial conditions

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

frame analysis for biorthogonal cosine modulated filterbanks this paper addresses the efficient computation of frame bounds for cosine modulated filterbanks we derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype s polyphase components the number of channels and the downsampling factor may be even or odd and the oversampling factor is supposed to be an integer the analysis of low delay biorthogonal filterbanks shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and thus to an undesirable numerical behavior because the computational cost of determining the frame bounds with the proposed method is very low we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds various design examples are presented

travelling solitons in the externally driven nonlinear schrodinger equation we consider the undamped nonlinear schr dinger equation driven by a periodic external force in the absence of damping solitons do not have undulations on their tails yet we show that they can bind into stationary multisoliton complexes using two previously known stationary solitons and two newly found stationary complexes as starting points we obtain classes of localized travelling waves by the numerical continuation in the parameter space two families of stable solitons are identified one family is stable for sufficiently low velocities while solitons from the second family stabilize when travelling faster than a certain critical speed the stable solitons of the former family can also form stably travelling bound states

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

the relaxation of two well energies with possibly unequal moduli the elastic energy of a multiphase solid is a function of its microstructure determining the infimum of the energy of such a solid and characterizing the associated optimal microstructures is an important problem that arises in the modeling of the shape memory effect microstructure evolution and optimal design mathematically the problem is to determine the relaxation under fixed phase fraction of a multiwell energy this paper addresses two such problems in the geometrically linear setting first in two dimensions we compute the relaxation under fixed phase fraction for a two well elastic energy with arbitrary elastic moduli and transformation strains and provide a characterization of the optimal microstructures and the associated strain second in three dimensions we compute the relaxation under fixed phase fraction for a two well elastic energy when either 1 both elastic moduli are isotropic or 2 the elastic moduli are well ordered and the smaller elastic modulus is isotropic in both cases we impose no restrictions on the transformation strains we provide a characterization of the optimal microstructures and the associated strain we also compute a lower bound that is optimal except possibly in one regime when either 1 both elastic moduli are cubic or 2 the elastic moduli are well ordered and the smaller elastic modulus is cubic for moduli with arbitrary symmetry we obtain a lower bound that is sometimes optimal in all these cases we impose no restrictions on the transformation strains and whenever the bound is optimal we provide a characterization of the optimal microstructures and the associated strain in both two and three dimensions the quasiconvex envelope of the energy can be obtained by minimizing over the phase fraction we also characterize optimal microstructures under applied stress

isophasal isopolar and isospectral schrodinger operators and elementary complex analysis we explicitly construct super exponentially decaying potentials on d so that the associated schrodinger operators are isophasal and isopolar we use similar techniques to construct isospectral schrodinger operators with periodic potentials on and isospectral schrodinger operators on

frequency and phase locking of spatially periodic perturbed sine gordon breather trains this paper considers the damped driven sine gordon equation with even periodic boundary conditions on a finite length nearly integrable perturbation methods are applied to infer approximate solution branches of space and time periodic breather trains of order one amplitude these approximate solutions consist of coherent spatial structures either homogeneous or with one breather per period which lock in frequency and phase to the small time periodic perturbation in the presence of uniform weak damping the predicted resonant breather trains are then verified by overman via direct simulation of the perturbed sine gordon pde and shown to be accurate within the order of the perturbation theory

filters in topology optimization in this article a modified filtered version of the minimum compliance topology optimization problem is studied the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator in this setting it is possible to establish the existence of solutions moreover convergence of an approximation by means of finite elements can be obtained this is illustrated through some numerical experiments the filtering technique is also shown to cope with two important numerical problems in topology optimization checkerboards and mesh dependent designs copyright 2001 john wiley sons ltd

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

optimal design of oversampled synthesis fbs with lattice structure constraints oversampled filter banks fbs with lattice structure allow fast implementation and guarantee the linear phase and perfect reconstruction property for such fbs the synthesis fb is not unique this nonuniqueness provides extra design freedom for optimal reduction of subband noise required in many applications however the existing design methods of synthesis fb for optimal reduction of subband noise cannot guarantee the linear phase and lattice structure property this paper studies the design of oversampled synthesis fbs with guaranteed lattice structure for optimal reduction of subband noise based on a state space parameterization of all synthesis fbs with lattice structure the explicit formulae are derived to find the optimal solution for noise reduction numerical examples are presented to demonstrate the effectiveness of the new design methods obtained

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

complex hill s equation and the complex periodic korteweg de vries equations on etudie la classe spectrale des operateurs differentiels l d 2 dx 2 q avec un potentiel q de periode un on traite des potentiels complexes et des operateurs auto adjoints

coarse topological transitivity on open cones and coarsely j class and d class operators abstract we generalize the concept of coarse hypercyclicity introduced by feldman in 13 to that of coarse topological transitivity on open cones we show that a bounded linear operator acting on an infinite dimensional banach space with a coarsely dense orbit on an open cone is hypercyclic and a coarsely topologically transitive mixing operator on an open cone is topologically transitive mixing resp we also localize these concepts by introducing two new classes of operators called coarsely j class and coarsely d class operators and we establish some results that may make these classes of operators potentially interesting for further studying namely we show that if a backward unilateral weighted shift on l 2 n is coarsely j class or d class on an open cone then it is hypercyclic then we give an example of a bilateral weighted shift on l z which is coarsely j class hence it is coarsely d class and not j class note that concerning the previous result it is well known that the space l z does not support j class bilateral weighted shifts see 10 finally we show that there exists a non separable banach space which supports no coarsely d class operators on open cones some open problems are added

bifurcation and chaotic motion of a soliton in a long josephson junction oscillator the fluxon dynamics of a long josephson junction ljj is investigated numerically the effect of the surface resistance of the superconductor on the bifurcation phenomenon is examined in detail we show the occurrence of a period doubling route to chaos and the reappearance of low order periodic motions in the ljj by varying the magnitude of the external force the chaotic attractors of the ljj are characterized using maximal lyapunov exponents and a fractal correlation dimension we show the existence of noise induced oscillations in a force free ljj system finally the influence of noise on the periodic and chaotic dynamics is also presented

period doubling solitons yes or no we investigate the possibility of period doubling transition to temporal chaos of a coherent structure in a finite dimensional hamiltonian system with moderately small friction a solitary wave in a periodically driven chain of particles provides a typical example to this end the equations of motion are transformed to those of one driven dominant oscillator with one degree of freedom weakly coupled to a set of oscillators representing the other degrees of freedom the equations for the dominant oscillator alone confirm the possibility of such a transition to chaos for well chosen driving however taking into account coupling to the other degrees of freedom one must conclude that the supposed infinite period doubling sequence for small or no dampling survives only in a heavily damaged state in practice a reproducable completed sequence cannot be expected unless the damping is strong enough

topology design with optimized self adaptive materials significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems we study the optimal shape design of a two dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology relaxation of the optimization problem via quasiconvexification or homogenization methods is required the effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material

tight weyl heisenberg frames in l sup 2 z tight weyl heisenberg frames in l sup 2 z are the tool for short time fourier analysis in discrete time they are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory good resolution of short time fourier analysis in the joint time frequency plane is not attainable unless some redundancy is introduced that is the reason for considering overcomplete weyl heisenberg expansions the main result of this correspondence is a complete parameterization of finite length tight weyl heisenberg frames in l sup 2 z with arbitrary rational oversampling ratios this parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks which is introduced first

irregular vectors of hilbert space operators abstract a vector x in a hilbert space h is called irregular for an operator t h h provided that sup n t n x and inf n t n x 0 we establish some basic properties of operators having irregular vectors and present examples that highlight the relationship or lack thereof between irregularity and hypercyclicity

time domain oversampled lapped transforms theory structure and application in image coding this paper generalizes time domain lapped transforms tdlts proposed by tran et al to oversampled systems thus leading to time domain oversampled lapped transforms tdolts these new transforms correspond to a subclass of oversampled linear phase perfect reconstruction filterbanks olpprfbs which can be implemented by adding a prefilter before the discrete cosine transform dct and a post filter after the inverse discrete cosine transform idct structures of the pre and post filters are developed and the frame theoretic properties of tdolts are analyzed a new parameterization of lattice matrices through the givens qr factorization is proposed for unconstrained optimization comparisons with other parameterization methods are also included several design examples along with some image coding results are presented to demonstrate the validity of the theory and the potential of tdolts in image coding especially in error resilient coding

the center manifold and bifurcations of damped and driven sine gordon breathers abstract the generic bifurcations of breathers in the damped and driven sine gordon equation are investigated both numerically and analytically the linear stability analysis and information from periodic spectral theory suggest that three modes are relevant for the system they correspond to frequency and temporal phase changes and to the flat pendulum using these modes nonautonomous amplitude equations are derived and compared with numerical simulations of the perturbed sine gordon equation

mel nikov analysis of numerically induced chaos in the nonlinear schro dinger equation abstract certain hamiltonian discretizations of the periodic focusing nonlinear schrodinger equation nls have been shown to be responsible for the generation of numerical instabilities and chaos in this paper we undertake a dynamical systems type of approach to modeling the observed irregular behavior of a conservative discretization of the nls using heuristic mel nikov methods the existence of a pair of isolated homoclinic orbits is indicated for the perturbed system the structure of the persistent homoclinic orbits that are predicted by the mel nikov theory possesses the same features as the wave form observed numerically in the perturbed system after the onset of chaotic behavior and appears to be the main structurally stable feature of this type of chaos the mel nikov analysis implemented in the pde context appears to provide relevant qualitative information about the behavior of the pde in agreement with the numerical experiments in a neighborhood of the persistent homoclinic orbits the existence of a horseshoe is investigated and related with the onset of chaos in the numerical study

breather dynamics in the nonlinear schrodinger regime of perturbed sine gordon systems abstract a possible route to temporal chaos with coherent stable spatial structures is proposed for the driven damped sine gordon equation for near conservative perturbations the dynamics of a breather is investigated numerically and semi analytically in the presence of an ac driver and a simple damping term for moderate driver strengths a flat space independent attractor exists whereas above a threshold a phase locked breather co exists the latter can undergo a period doubling route to temporal chaos as is shown here for a certain parameter regime relations to other works which operate in a different parameter regime are discussed the near conservative perturbations and the low driver strengths allow to interpret the results within a simple model originating from the so called nonlinear schrodinger limit in fact within this limit small amplitude breather the chaotic or not transitions are dominated by interactions between breather like solutions and radiation mostly k 0 mode therefore three collective coordinates i e the amplitude of the phase locked breather its phase as well as the complex amplitude of the linear k 0 mode are sufficient to construct a system of four ordinary differential equations of first order which reveal the basic features of the partial differential equations in a satisfactory manner

existence threshold for the ac driven damped nonlinear schrodinger solitons abstractithasbeenknownforsometimethatsolitonsoftheexternallydriven dampednonlinearschrodingerequationcanonlyexistif the driver s strength h exceeds approximately 2 where is the dissipation coef cient although this perturbativeresultwasexpectedtobecorrectonlytotheleadingorderin recentstudieshavedemonstratedthattheformulah thr d 2 gives a remarkably accurate description of the soliton s existence threshold prompting suggestions that it is in fact exact in this note we evaluate the next order in the expansion of h thr showing that the actual reason for this phenomenon issimply that the next ordercoef cient is anomalously small h thr d 2 c0 002 3 our approach is based on a singularperturbation expansion of the soliton near the turning point it allows to evaluate h thr to all orders in and can be easilyreformulated for other perturbed soliton equations 1999 elsevier science b v all rights reserved pacs 03 40 kf 42 65 tg 42 81 dp 1 introductiontheexternallydriven dampednonlinearschrodinger nls equation i9

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

vortex blob methods applied to interfacial motion we develop a boundary integral method for computing the motion of an interface separating two incompressible inviscid fluids the velocity integral is regularized so that the vortex sheet on the interface is replaced by a sum of blobs of vorticity the regularization allows control of physical instabilities we design a class of high order blob methods and analyze the errors numerical tests suggest that the blob size should be scaled with the local spacing of the interfacial markers for a vortex sheet in one fluid with a first order kernel we obtain a spiral roll up similar to krasny j comput phys 65 1986 292 but the higher order kernels lead to more detailed structure we verify the accuracy of the new method by computing a liquid gas interface with rayleigh taylor instability we then apply the method to the more difficult case of rayleigh taylor flow separating two fluids of positive density a case for which the regularization appears to be essential as found by kerr and tryggvason both j comput phys 76 1988 48 75 1988 253 we use a blob regularization in certain local terms in the evolution equations as well as in the velocity integral we find strong evidence that improved spatial resolution with fixed blob size leads to a converged regularized solution without numerical instabilities however it is not clear that there is a weak limit as the regularization is decreased

stability of finite element models for distributed parameter optimization and topology design abstract we address a problem of numerical instability that is often encountered in finite element solutions of distributed parameter optimization and variable topology shape design problems we show that the cause of this problem is numerical rather than physical in nature we consider a two field distributed parameter optimization problem involving a design field and a response field and show that the optimization problem corresponds to a mixed variational problem an improper selection of the discrete function spaces for these two fields leads to grid scale anomalies in the numerical solutions to optimization problems similar to those that are sometimes encountered in mixed formulations of the stokes problem we present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models the general theoretical framework is specialized to analyze the stability of specific optimization problems and stability results for various mixed finite element models are presented we propose patch tests that are useful in identifying unstable elements

topological design for vibrating structures the topological optimization technique using micro scale voids with the homogenization method for stress analysis of perforated structures has been applied to solve stiffness maximization problem with success here the homogenization design technique is extended to design problems concerning vibrating structures an extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigenvalues to characterize forced vibration of a structure

on a theorem of hochstadt in fact hochstadt gives an explicit formula for the discriminant which will be reproduced below since hochstadt s work there has been a considerable interest in finite band potentials i e potentials q such that the spectrum of the operator associated with d2 dx 2 q consists of finitely many regular analytic arcs due to their close relationship with the korteweg de vries hierarchy and hence with integrable systems however the interest is not restricted to real valued potentials for instance

bound ratio minimization of filter bank frames this paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction pr filter banks fbs for a given analysis prfb a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel the redesign minimizes the frame bound ratio of the fb while maintaining its original properties and performance the obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing the optimal solution is applied to subband noise suppression and tree structured fb gain optimization resulting in deeper insights and novel solutions to these two general classes of problems and considerable performance improvement effectiveness of the optimal solution is demonstrated by extensive numerical examples

persistent homoclinic orbits for a perturbed nonlinear schrodinger equation the persistence of homoclinic orbits for certain perturbations of the integrable nonlinear schrodinger equation under even periodic boundary conditions is established more specifically the existence of a symmetric pair of homoclinic orbits is established for the perturbed nls equation through an argument that combines melnikov analysis with a geometric singular perturbation theory for the pde 1996 john wiley sons inc

a robust dual algorithm for topology design of structures in discrete variables dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since in topology design problems the number of constraints is small in comparison to the number of design variables good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint however when the perimeter constraint is relaxed the dual algorithm tends to give bad results even with the use of higher order finite element models as we demonstrate in this work since a priori one does not know what a good value of the perimeter to be specified is it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint we show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint in particular we show that the problem of checkerboarding which is frequently observed with the use of lower order finite elements is eliminated

stability and bifurcation of spatially coherent solutions of the damped driven nls equation an analytical study is conducted of the structure stability and bifurcation of the spatially dependent time periodic solutions of the damped driven sine gordon equation in the nonlinear schrodinger approximation locked states are found for which the spatial structure consists of coherent excitations localized about x 0 or l 2 a bifurcation analysis reveals the relationship of these spatially localized solutions to the spatially independent ones and provides a cutoff wavenumber above which there are no spatially dependent solutions this establishes an upper bound on the number of local excitations comprising the spatial pattern a linear stability analysis shows that the spatially localized solutions undergo a hopf bifurcation to temporal quasi periodicity as the driver amplitude gamma is increased for sufficiently high driver frequencies the temporally periodic solution regains its stability via another hopf bifurcation in a gamma window of finite width before undergoing a third hop

acceleration of the frame algorithm shows how polynomial acceleration techniques which have been developed for the solution of large linear systems can be employed to improve and accelerate the frame algorithm these methods permit a reduction in the number of necessary iterations by an order of magnitude when the frame algorithm is slow the author gives several examples from the theory of irregular sampling from wavelet theory and from gabor theory where these methods are probably mandatory for efficient reconstruction

low dimensional chaos in a driven damped nonlinear schro dinger equation abstract we study bifurcations of attractors in a driven damped nonlinear schrodinger equation which models nonlinear responses of a plasma driven by a rf field and a sequence of period doubling bifurcations is shown to lead to a chaotic attractor in a low dimensional subspace spanned by a soliton and long wavelength radiation

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

efficient computation of frame bounds using lmi based optimization this correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction pr filter banks fbs it first shows that computation of the optimal frame bounds for complex valued oversampled pr fbs can be formulated as a convex optimization subject to complex valued linear matrix inequality lmi constraints and solved by effective interior point algorithms it then deals with discrete time weyl heisenberg wh frames to compute bounds on the wh frames by real valued lmi optimization the wh frames are closely related to modulated fbs and have complex coefficients four examples are given to illustrate the generality and effectiveness of the proposed method

optimal two sided diagonal scaling for filter bank frames two sided diagonal scaling for transfer matrices is formulated an efficient algorithm is proposed to compute globally optimal solutions using the iterated bi section and linear matrix inequality lmi solver it is shown that the two sided scaling of filter bank fb frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal and that the frame bound ratio of fb frames can be effectively improved by such scaling explicit formulas are established for both uniform and nonuniform fb frames including detail formulas for discrete weyl heisenberg frames and tree structured fbs discrete wavelets different examples show the effectiveness of the obtained results

singularities of the complex korteweg de vries flows on etudie le probleme isospectral de l equation de hill complexe etant donne 2g 1 valeurs propres simples dans le plan complexe trouver la classe spectrale correspondante q on considere la caracterisation de la classe isospectrale et ses sections singulieres on construit q a l aide des flots non lineaires de korteweg de vries dans c 1 les fonctions regulieres de periode 1

coupled deformations of elastic curves and surfaces an equilibrium theory for the coupled finite deformations of elastic curves and surfaces is described possible wrinkling of the curve or surface is taken into account by using a relaxed version of the theory obtained from minimum energy considerations the relaxed theory admits a dual formulation leading to extremum principles and uniqueness of the equilibrium stress distribution a number of examples are treated using spatial finite differences together with a dynamic relaxation method in which equilibrium configurations are obtained in the long time limit of a damped dynamical problem

optimal noise reduction in oversampled pr filter banks this paper studies the optimal noise reduction problem for oversampled filter banks fbs with perfect reconstruction pr constraint both the optimal design and worst case design are considered where the former caters for the noise with known power spectral density psd and the latter for the noise with unknown psd state space based explicit formulae involving only algebraic riccati equation and matrix manipulations are provided for the general iir or fir oversampled pr fbs and the relations between different cases are analyzed and revealed extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness

a quasi periodic route to chaos in a near integrable pde abstract pattern formation and transitions to chaos are described for the damped ac driven one dimensional periodic sine gordon equation in a nonlinear schrodinger regime a generic quasi periodic route to intermittent chaos is exhibited in detail using a range of dynamical systems diagnostics in addition a nonlinear spectral transform is exploited i to identify and quantify coordinates of space time attractors in terms of a small number of soliton modes of the underlying integrable system ii to use these analytic coordinates to identify homoclinic orbits as possible sources of chaos and iii to demonstrate the significance of energy transfer between coherent and extended states in this chaotic system

hypercyclicity of the tensor products of multiplication operators on hardy spaces abstract in this paper we give a necessary and sufficient condition for the tensor product of two adjoints of multiplication hypercyclic operators to be mixing and chaotic these results partially answer a question posed by felix martinez gimenez and alfredo peris in 2003 we also prove that the tensor product of an operator satisfying the frequent hypercyclicity criterion with the identity is frequently hypercyclic thereby strengthening a previous result of martinez gimenez and peris

a study of two channel complex valued filterbanks and wavelets with orthogonality and symmetry properties we investigate two channel complex valued filterbanks and wavelets that simultaneously have orthogonality and symmetry properties first the conditions for the filterbank to be orthogonal symmetric and regular for generating smooth wavelets are presented then a complete and minimal lattice structure is developed which enables a general design approach for filterbanks and wavelets with arbitrary length and arbitrary order of regularity finally two integer implementation methods that preserve the perfect reconstruction property of the filterbank are proposed their performances are evaluated via experimental results