on the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents abstract the main goal of the present paper is establishing the existence and uniqueness of weak solutions for the nonlinear degenerate reaction diffusion system with variable exponents a model also is proposed to characterize the invasion of cancer cells towards healthy cells with acidification environment moreover the main results of this paper are obtained using regularization problem the faedo galerkin approximation method some apriori estimates compactness results and the gronwall lemma

weak and classical solutions to predator prey system with cross diffusion abstract in this paper we are concerned with a system of nonlinear partial differential equations modeling a predator prey system with cross diffusion in heterogeneous habitats predators are assumed to feed on preys with a holling type ii functional response to prey density and preys are assumed to follow a logistic growth in the absence of predation the mobility of each classes is assumed to be influenced by the gradient of other classes the existence result is proved by means of an approximation system the faedo galerkin method and the compactness method the global existence of classical solutions is proved under certain restrictions on the coefficients

bounds on complex eigenvalues and resonances we obtain bounds on the complex eigenvalues of non self adjoint schrodinger operators with complex potentials and also on the complex resonances of self adjoint schrodinger operators our bounds are compared with numerical results and are seen to provide useful information

analysis of a parabolic cross diffusion population model without self diffusion abstract the global existence of non negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown the cross diffusion terms are allowed to be arbitrarily large whereas the self diffusion terms are assumed to disappear the last assumption complicates the analysis since these terms usually provide h 1 estimates of the solutions the existence proof is based on a positivity preserving backward euler galerkin approximation discrete entropy estimates and l 1 weak compactness arguments furthermore employing the entropy entropy production method we show for special stationary solutions that the transient solution converges exponentially fast to its steady state as a by product we prove that only constant steady states exist if the inter specific competition parameters disappear no matter how strong the cross diffusion constants are

reducing stochasticity in the north atlantic oscillation index with coupled langevin equations we present a critical investigation of the functional relationship between the two pressure time series routinely used to define the index characterizing the north atlantic oscillation nao well known to regulate global climate variability and change first by a standard markov analysis we show that the standard nao index based on the pressure difference is not optimal in the sense of producing sufficiently reliable forecasts because it contains a dominating stochastic term in the corresponding langevin equation then we introduce a variationally optimized markov analysis involving two coupled langevin equations tailored to produce a nao quasi index having the desired minimum possible stochasticity the variationally optimized markov analysis is very general and can be applied in other physical situations involving two or more time series

comparison theorems for the gap of schrodinger operators on cherche des bornes inferieures aux decompositions de valeur propre en fonction des proprietes geometriques de l ensemble avec v x e ainsi que sur la taille de v sur cet ensemble

on a cross diffusion population model deduced from mutation and splitting of a single species we deduce a particular case of the population cross diffusion model introduced by shigesada et al 1979 1 by using the ideas of mutation and splitting from a single species as described by sanchez palencia for ode s systems sanchez palencia 2011 21 the resulting equations of the pde system only differ in the cross diffusion terms the corresponding diffusion matrix being self diffusion dominated which implies that the well known population segregation patterns of the shigesada et al model do not appear in this case we prove existence and uniqueness of solutions of the pde system and use a finite element approximation to discuss numerically stability properties of solutions with respect to the parameters in comparison with related models

stability for the multifrequency inverse medium problem abstract the solution of a multi frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies in this paper rigorous stability estimates are derived when the frequency takes value in a bounded interval it is showed that the ill posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger more precisely under certain regularity assumptions on the refractive index the estimates indicate that the power in holder stability is an increasing function of the largest value in the frequency band finally a lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula

stochastic heart rate model can reveal pathologic cardiac dynamics a simple one dimensional langevin type stochastic difference equation can simulate the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical of gaussian noise and both parts can be directly determined from measured heart rate data data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points studies of 15 congestive heart failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects results directly indicate that pathologic situations simplify the heart rate control system

a note on the gap between the first two eigenvalues for the schrodinger operator by means of a commutation formula the author gives a simple proof of the upper bound of wong et al on the gap between the first two eigenvalues in the schrodinger operator unfortunately this proof does not seem to generalise into higher dimensions

noise reduction in chaotic time series data a survey of common methods this paper surveys some of the methods that have been suggested for reducing noise in time series data whose underlying dynamical behavior can be characterized as low dimensional chaos although the procedures differ in details all of them must solve three basic problems how to reconstruct an attractor from the data how to approximate the dynamics in various regions on the attractor and how to adjust the observations to satisfy better the approximations to the dynamics all current noise reduction methods have similar limitations but the basic problems are reasonably well understood the methods are an important tool in the experimentalist s repertoire for data analysis in our view they should be used more widely particularly in studies of attractor dimension lyapunov exponents prediction and control

lower bounds for resonance widths in potential and obstacle scattering explicit lower bounds are given for the size of the imaginary parts of resonances for schrodinger operators with non trapping or trapping potentials and for the dirichlet laplacian in the exterior of a star shaped obstacle both acting in three dimensions

robust identification of harmonic oscillator parameters using the adjoint fokker planck equation we present a model based output only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators in this context suitable models of the oscillator s damping and stiffness properties are postulated guided by physical understanding of the oscillatory phenomena the temporal dynamics and the probability density function of the oscillation amplitude are described by a langevin equation and its associated fokker planck equation respectively one method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values obtained from data processing by taking the short time limit of the first two transition moments however this limit estimation loses robustness in some situations for instance when the data are band pass filtered to isolate the spectral contents of the oscillatory phenomena of interest in this paper we use a robust alternative where the adjoint fokker planck equation is solved to compute kramers moyal coefficients exactly and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales the method is illustrated with a stochastic van der pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors where system identification is highly relevant to control

computing the steady states for an asymptotic model of quantum transport in resonant heterostructures in this article we propose a rapid method to compute the steady states including bifurcation diagrams of resonant tunneling heterostructures in the far from equilibrium regime those calculations are made on a simplified model which takes into account the characteristic quantities which arise from an accurate asymptotic analysis of the nonlinear schrodinger poisson system after a summary of the existing theoretical results the asymptotic model is explicitly adapted to physically realistic situations and numerical results are shown in various cases

localization for a class of one dimensional quasi periodic schrodinger operators we prove for small and satisfying a certain diophantine condition the operator h varepsilon 2 delta frac 1 2 pi cos 2 pi j alpha theta j in mathbb z has pure point spectrum for almost all a similar result is established at low energy for h frac d 2 dx 2 k 2 cos 2 pi x cos 2 pi alpha x theta providedk is sufficiently large

distant perturbation asymptotics in window coupled waveguides i the nonthreshold case we consider a pair of straight adjacent quantum waveguides of constant and in general different widths these waveguides are coupled laterally by a pair of windows in the common boundary not necessarily of the same length at a distance 2l the hamiltonian is the respective dirichlet laplacian we analyze the asymptotic behavior of the discrete spectrum as the window distance tends to infinity for the generic case i e for eigenvalues of the corresponding one window problems separated from the threshold

analysis of stochastic time series in the presence of strong measurement noise an alternative approach for the analysis of langevin type stochastic processes in the presence of strong measurement noise is presented for the case of gaussian distributed exponentially correlated measurement noise it is possible to extract the strength and the correlation time of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying langevin equation

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

perturbation theory for shape resonances and large barrier potentials we develop a systematic perturbation and resonance theory for the one dimensional schrodinger equation of the form d 2 dx 2 u x lambda v x e psi x 0 0 leqq x infty where the barrier potentialv x is supported only wherex 1 and is non negative there and is a real parameter tending to infinity we prove that every eigenvalue turns into a resonance or an eigenvalue for finite

lower bounds for shape resonances widths of long range schrodinger operators in this article we give general lower bounds of shape resonance widths in the semi classical limit for schrodinger operators in the exterior of smooth compact obstacles with dirichlet or neuman boundary conditions and with long range dilation analytic potentials these lower bounds are exponentially small with respect to the planck constant

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

general lower bounds for resonances in one dimension lower bounds are derived for the magnitude of the imaginary parts of the resonance eigenvalues of a schrodinger operator frac d 2 dx 2 v x on the line depending only on the support and bounds ofv and on the real part of the resonance eigenvalue for example if the resonance eigenvalue is denotede i then there existc and l0 depending only on e ande such that if the support ofv is contained in an interval of length l l0 then left varepsilon right frac m 3 sqrt e m sqrt e 2 exp m ell 1 c ell 1 wherem v x e 1 2

on the semiclassical approximation to the eigenvalue gap of schrodinger operators abstract we consider two types of schrodinger operators h t d 2 d x 2 q x t cos x and h t d 2 d x 2 q x a cos t x defined on l 2 r where q is an even potential that is bounded from below a is a constant and t 0 is a parameter we assume that h t has at least two eigenvalues below its essential spectrum and we denote by 1 t and 2 t the lowest eigenvalue and the second one respectively the purpose of this paper is to study the asymptotics of the gap t 2 t 1 t in the limit as t

simple procedure for correcting equations of evolution application to markov processes a general procedure is proposed for correcting evolution equations arising in different branches of science its application to markov processes shows that the coefficients of the third and higher order derivatives in the kramers moyal expansion are in general not small nevertheless the macroscopic time evolution of the process is completely described by a differential equation of second order for brownian motion this equation is galilean invariant while the fokker planck equation is not finally a correction is derived for the master equation

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

extremal eigenvalue gaps for the schrodinger operator with dirichlet boundary conditions we consider the problems of minimizing and maximizing the gap between the two lowest dirichlet eigenvalues of the schrodinger operator v x on a bounded domain in rn when the potential v is subjected to a p norm constraint we give characterization theorems for extremizing potentials we prove in particular that a second eigenvalue corresponding to a minimizing potential is always single

improved estimation of fokker planck equations through optimization an improved method for the description of hierarchical complex systems by means of a fokker planck equation is presented in particular the limited memory broyden fletcher goldfarb shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the fokker planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the fokker planck equation the optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine

low lying spectral gaps induced by slowly varying magnetic fields abstract we consider a periodic schrodinger operator in two dimensions perturbed by a weak magnetic field whose intensity slowly varies around a positive mean we show in great generality that the bottom of the spectrum of the corresponding magnetic schrodinger operator develops spectral islands separated by gaps reminding of a landau level structure first we construct an effective hofstadter like magnetic matrix which accurately describes the low lying spectrum of the full operator the construction of this effective magnetic matrix does not require a gap in the spectrum of the non magnetic operator only that the first and the second bloch eigenvalues do not cross but their ranges might overlap the crossing case is more difficult and will be considered elsewhere second we perform a detailed spectral analysis of the effective matrix using a gauge covariant magnetic pseudo differential calculus adapted to slowly varying magnetic fields as an application we prove in the overlapping case the appearance of spectral islands separated by gaps

stochastic time series with strong correlated measurement noise markov analysis in n dimensions an extension and generalization of a recently presented approach for the analysis of langevin type stochastic processes in the presence of strong measurement noise is presented for a stochastic process in n dimensions which is superimposed with strong exponentially correlated gaussian distributed measurement noise it is possible to extract the strength and the correlation functions of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying process

estimation of drift and diffusion functions from time series data a maximum likelihood framework complex systems are characterized by a huge number of degrees of freedom often interacting in a nonlinear manner in many cases macroscopic states however can be characterized by a small number of order parameters that obey stochastic dynamics in time recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced this paper develops a framework for the estimation of the functions and their respective bayesian posterior confidence regions based on likelihood estimators in succession approximations are introduced that significantly improve the efficiency of the estimation procedure while being consistent with standard approaches to the problem this paper solves important problems concerning the applicability and the accuracy of estimated parameters

estimation of noise levels for models of chaotic dynamical systems we investigate how far it is possible to identify and separate dynamical noise from measurement noise in observed nonlinear time series using bayesian methods we derive estimates for the two noise levels and find that given a good model of the dynamics these can give accurate results even if the dynamical noise level is orders of magnitude smaller than the measurement noise level whereas a simple calculation of root mean square error badly understates the dynamical noise we argue that this allows better estimates of the underlying dynamical time series and so better predictions of its future and of its fundamental dynamical properties

bounds on scattering poles in one dimension for the class of super exponentially decaying potentials on the real line sharp upper bounds on the counting function of the poles in discs are derived and the density of the poles in strips is estimated in the case of nonnegative potentials explicit estimates for the width of a pole free strip are obtained

estimation of kramers moyal coefficients at low sampling rates an optimization procedure for the estimation of kramers moyal coefficients from stationary one dimensional markovian time series data is presented the method takes advantage of a recently reported approach that allows one to calculate exact finite sampling interval effects by solving the adjoint fokker planck equation therefore it is well suited for the analysis of sparsely sampled time series the optimization can be performed either by making a parametric ansatz for drift and diffusion functions or parameter free we demonstrate the power of the method in several numerical examples with synthetic time series

on eigenpairs of schrodinger equation with multiwell potential some monotonicity properties estimations and geometric features of the eigenpairs of schrodinger equation with multiwell potential are given through variational method

lower bounds on the width of stark wannier type resonances we prove that the schrodinger operator d2 dx2 fx w x onl2 r withw bounded and analytic in a strip has no resonances in a region ime exp c f

on the spectrum of schrodinger operators with a random potential we investigate the spectrum of schrodinger operatorsh of the type h qi f x xi i qi and i independent identically distributed random variables i d we establish a strong connection between the spectrum ofh and the spectra of deterministic periodic schrodinger operators from this we derive a condition for the existence of forbidden zones in the spectrum ofh for random one and three dimensional kronig penney potentials the spectrum is given explicitly

universal lower bounds on eigenvalue splittings for one dimensional schrodinger operators we provide lower bounds on the eigenvalue splitting for d2 dx2 v x depending only on qualitative properties ofv for example ifv is c on a b ande n en 1 are two successive eigenvalues of d2 dx2 v withu a u b 0 boundary conditions and if lambda mathop max limits e in e n 1 e n x in a b e v x 1 2 then e n e n 1 geqq pi lambda 2 exp left lambda b a right the exponential factor in such bounds are saturated precisely in tunneling examples our results arenot restricted tov s of compact support but only require e n mathop lim limits overline x to infty v x

pareto optimal structures producing resonances of minimal decay under l1 type constraints abstract resonances optimization is studied under the constraint b 1 m on the nonnegative function b l 1 0 l representing the resonator structure the problem is to design for a given frequency r a structure that generates a resonance on the line i r with minimal possible decay rate im we generalize the problem replacing b by a nonnegative measure and show that optimal measures consist of finite number of point masses this yields non existence of optimizers for the problem over absolutely continuous measures we derive restrictions on optimal masses and their positions this reduces the original infinitely dimensional problem to optimization over four real parameters for low frequencies we explicitly find optimizers the technique is based on the two parameter perturbation method and the notion of local boundary point which is introduced as a generalization of local extrema to vector optimization problems special attention is paid to multiple and non differentiable resonances

potentials producing maximally sharp resonances on considere des potentiels de mecanique quantique constitues d un fond fixe et un morceau additionnel contraint d avoir une hauteur finie et d etre a support dans une region finie donnee en dimension d 3 on caracterise les potentiels de cette classe qui produisent les resonances les plus etroites

semi discretization in time and numerical convergence of solutions of a nonlinear cross diffusion population model a positivity preserving numerical scheme for a strongly coupled cross diffusion model for two competing species is presented based on a semi discretization in time the variables are the population densities of the species existence of strictly positive weak solutions to the semidiscrete problem is proved moreover it is shown that the semidiscrete solutions converge to a non negative solution of the continuous system in one space dimension the proofs are based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional

almost periodic schrodinger operators iii the absolutely continuous spectrum in one dimension we studyh d2 dx2 v x withv x limit periodic e g v x ancos x 2n with an we prove that for a genericv and for generican in the explicit example h is a cantor nowhere dense perfect set for a dense set the spectrum is both cantor and purely absolutely continuous and therefore purely recurrent absolutely continuous

transient and recurrent spectrum abstract we deal primarily with spectral analysis of an abstract self adjoint operator h on a hilbert space h we propose a further refinement of the absolutely continuous subspace h ac into the transient absolutely continuous subspace h tac which is the closure of those with e ith o t n for all n and the recurrent absolutely continuous subspace h rac h ac h tac we discuss general features of this breakup in a subsequent paper we construct analytic almost periodic functions v on so that h d 2 dx 2 v x on l 2 has only recurrent absolutely continuous spectrum in the sense that h rac h

analysis of time series from stochastic processes analysis of time series from stochastic processes governed by a langevin equation is discussed several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the fokker planck equation the coefficients are estimated directly from a time series the applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting

extracting strong measurement noise from stochastic time series applications to empirical data it is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude our approach is based on a recently developed method for a nonparametric reconstruction of langevin processes minimizing a proper non negative function the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the langevin equation describing the evolution of the original uncorrupted signal as input the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals to demonstrate the power of the method we apply the algorithm to synthetic as well as climatological measurement data namely the daily north atlantic oscillation index shedding light on the discussion of the nature of its underlying physical processes