spectral shift function for trapping energies in the semiclassical limit semiclassical asymptotics of the spectral shift function ssf for schrodinger operator is studied at trapping energies it is shown that the ssf converges to sum of a smooth function and a step function which is essentially the counting function of resonances in particular the weyl asymptotics is proved

fine structure of zoll spectra this paper is concerned with the wave equation on a zoll manifold i e a compact riemannian manifold m g all of whose geodesics are closed by a result of v guillemin such metrics exist in abundance ons2 for any odd functionfons2there exists a one parameter deformation of the canonical metricgothru zoll metrics gt eftwithft tf and as has been known for a long time dg cv 1 hoiv w 1 2 the periodicity of the geodesic flow leads to a near periodicity in the wave grouput eit precisely there exists a unitary equivalence r q 1where r q 1 0 where the spectrum ofrlies on an arithmetic progression and whereq 1is a pseudodifferential operator of order 1 hence the eigenvalues fall into clusterckaround spec r with widthso k 1 the main result of this paper is to determine the limit distribution of the eigenvalues in the clusters it was long ago shown by weinsten loc cit that when properly normalized the limit distribution has the form q 1d whered is the liouville measure ons m we complete the calculation by determining q 1 it was conjectured w 2 ku that up to universal constants q 1 r whereris the radon transform of m g and is the scalar curvature w 2 ku but it turns out there is a second term involving the jacobi fields in addition we show that the cluster projections define almost isometric minimal immersions of m g into spheres and that in the case of maximally degenerate zoll metrics the errors are of rapid decay

analytic hypoellipticity for sums of squares and the treves conjecture abstract we are concerned with the problem of real analytic regularity of the solutions of sums of squares with real analytic coefficients treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the poisson treves stratification are symplectic we produce a model operator p 1 having a single symplectic stratum and prove that it is gevrey s 0 hypoelliptic and not better see theorem 2 1 for a definition of s 0 we also show that this phenomenon has a microlocal character we point out explicitly that this is a counterexample to the sufficient part of treves conjecture and not to the necessary part which is still an open problem

quantitative thermo acoustic imaging an exact reconstruction formula this paper aims to mathematically advance the field of quantitative thermo acoustic imaging given several electromagnetic data sets we establish for the first time an analytical formula for reconstructing the absorption coefficient from thermal energy measurements since the formula involves derivatives of the given data up to the third order it is unstable in the sense that small measurement noises may cause large errors however in the presence of measurement noise the obtained formula together with a noise regularization technique provides a good initial guess for the true absorption coefficient we finally correct the errors by deriving a reconstruction formula based on the least square solution of an optimal control problem and prove that this optimization step reduces the errors occurring and enhances the resolution

a probabilistic approach to semi classical approximations abstract we study in this paper the semi classical expansion of the schrodinger equation using a probabilistic approach based on the wiener measure using almost analytic extensions we exhibit a probabilistic ansatz for the wave function we show that this ansatz approximates very well the wave function in the semi classical regime and gives the semi classical expansion under mild hypothesis on the potential at infinity and no analyticity conditions in this paper the study takes place before the caustics

analytic and gevrey hypoellipticity for a class of pseudodifferential operators in one variable abstract we study the hypoellipticity of pseudo differential operators in one variable when a positivity assumption is made on a suitable principal part we prove that the found gevrey regularity is optimal

well posedness of systems of linear elasticity with dirichlet boundary control and observation an open loop system of linear elasticity with dirichlet boundary control and collocated observation is considered the main result we obtained states that this system is well posed in the sense of salamon the result deduces the exponential stability of the closed loop system under proportional output feedback hence it answers positively an open question proposed by liu and krstic ima j appl math 65 2000 pp 109 121 moreover the well posedness together with the regularity of the open loop system in the sense of weiss that was obtained in our separate paper s g chai and b z guo feedthrough operator for linear elasticity system with boundary control and observation preprint school of computational and applied mathematics university of the witwatersrand south africa 2008 makes this infinite dimensional system parallel in many ways to a linear finite dimensional system in the framework of well posed and regular linear infinite dimensional systems

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

decay rates for the three dimensional linear system of thermoelasticity we consider the two and three dimensional system of linear thermoelasticity in a bounded smooth domain with dirichlet boundary conditions we analyze whether the energy of solutions decays exponentially uniformly to zero as t to infty first of all by a decoupling method we reduce the problem to an observability inequality for the lame system in linear elasticity and more precisely to whether the total energy of the solutions can be estimated in terms of the energy concentrated on its longitudinal component we show that when the domain is convex the decay rate is never uniform in fact the lack of uniform decay holds in a more general class of domains in which there exist rays of geometric optics of arbitrarily large length that are always reflected perpendicularly or almost tangentially on the boundary we also show that in three space dimensions the lack of uniform decay may also be due to a critical polarization of the energy on the transversal component of the displacement in two space dimensions we prove a sufficient and almost necessary condition for the uniform decay to hold in terms of the propagation of the transversal characteristic rays under the further assumption that the boundary of the domain does not have contacts of infinite order with its tangents we also give an example due to d hulin in which these geometric properties hold in three space dimensions we indicate without proof how a careful analysis of the polarization of singularities may lead to sharp sufficient conditions for the uniform decay to hold in two space dimensions we prove that smooth solutions decay polynomially in the energy space to a finite dimensional subspace of solutions except when the domain is a ball or an annulus finally we discuss some closely related controllability and spectral issues

estimation risk for the var of portfolios driven by semi parametric multivariate models abstract joint estimation of market and estimation risks in portfolios is investigated when the individual returns follow a semi parametric multivariate dynamic model and the asset composition is time varying under ellipticity of the conditional distribution asymptotic theory for the estimation of the conditional value at risk var is developed an alternative method the filtered historical simulation which does not rely on ellipticity is also studied asymptotic confidence intervals for the conditional var which allow for simultaneous quantification of the market and estimation risks are derived the particular case of minimum variance portfolios is analyzed in more detail potential usefulness feasibility and drawbacks of the two approaches are illustrated via monte carlo experiments and an empirical study based on stock returns

schwinger terms and cohomology of pseudodifferential operators we study the cohomology of the schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra we prove that for all pseudodifferential operators in 3 1 dimensions of this type the schwinger term is equivalent to the twisted radul cocycle a modified version of the radul cocycle arising in non commutative differential geometry in the process we also show how the ordinary radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component

the magnetic weyl calculus in the presence of a variable magnetic field the weyl pseudodifferential calculus must be modified the usual modification based on the minimal coupling principle at the level of the classical symbols does not lead to gauge invariant formulas if the magnetic field is not constant we present a gauge covariant quantization relying on the magnetic canonical commutation relations the underlying symbolic calculus is a deformation defined in terms of the magnetic flux through triangles of the classical moyal product

estimating multivariate volatility models equation by equation summary the paper investigates the estimation of a wide class of multivariate volatility models instead of estimating an m multivariate volatility model a much simpler and numerically efficient method consists in estimating m univariate generalized auto regressive conditional heteroscedasticity type models equation by equation in the first step and a correlation matrix in the second step strong consistency and asymptotic normality of the equation by equation estimator are established in a very general framework including dynamic conditional correlation models the equation by equation estimator can be used to test the restrictions imposed by a particular multivariate generalized auto regressive conditional heteroscedasticity specification for general constant conditional correlation models we obtain the consistency and asymptotic normality of the two step estimator comparisons with the global method in which the model parameters are estimated in one step are provided monte carlo experiments and applications to financial series illustrate the interest of the approach

on the existence of euler lagrange orbits satisfying the conormal boundary conditions abstract let m g be a closed connected riemannian manifold l t m r be a tonelli lagrangian given two non empty closed submanifolds q 0 q 1 m and a real number k we study the existence of euler lagrange orbits with energy k connecting q 0 to q 1 and satisfying suitable boundary conditions known as conormal boundary conditions we introduce the mane critical value which is relevant for this problem and discuss existence results for supercritical and subcritical energies we also provide counterexamples showing that all the results are sharp

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

controllability of two coupled wave equations on a compact manifold we consider the exact controllability problem on a compact manifold for two coupled wave equations with a control function acting on one of them only action on the second wave equation is obtained through a coupling term first when the two waves propagate with the same speed we introduce the time t omega rightarrow mathcal o rightarrow omega for which all geodesics traveling in go through the control region then through the coupling region mathcal o and finally come back in we prove that the system is controllable if and only if both and mathcal o satisfy the geometric control condition and the control time is larger than t omega rightarrow mathcal o rightarrow omega second we prove that the associated hum control operator is a pseudodifferential operator and we exhibit its principal symbol finally if the two waves propagate with different speeds we give sharp sufficient controllability conditions on the functional spaces the geometry of the sets and mathcal o and the minimal time

stability of abstract thermo elastic semigroups abstract in this paper we characterize the stabilization for some thermo elastic type system with cattaneo law and we prove that the exponential or polynomial stability of this system implies a polynomial stability of the corresponding thermoelastic system with the fourier law the proof of the main results uses respectively the methodology introduced by haraux in 11 and generalized by ammari and tucsnak in 8 where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system and a characterization of the polynomial stability for a c 0 semigroup in a hilbert space by a polynomial estimation of the resolvent of its generator obtained by borichev and tomilov 9 illustrating examples are given

persistence of embedded eigenvalues we consider conditions under which an embedded eigenvalue of a self adjoint operator remains embedded under small perturbations in the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m infinity we show that in favorable situations the set of small perturbations of a suitable banach space which do not remove the eigenvalue form a smooth submanifold of codimension in we also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite

scattering theory in the energy space for a class of non linear wave equations we study the asymptotic behaviour in time of the solutions and the theory of scattering in the energy space for the non linear wave equation square varphi f varphi 0 in n n 3 we prove the existence of the wave operators asymptotic completeness for small initial data and forn 4 asymptotic completeness for arbitrarily large data the assumptions onf cover the case wheref behaves slightly better than a single powerp 1 4 n 2 both near zero and at infinity see 1 5 1 6 and 1 8

quantization of abelian varieties distributional sections and the transition from kahler to real polarizations abstract we study the dependence of geometric quantization of the standard symplectic torus on the choice of invariant polarization real and mixed polarizations are interpreted as degenerate complex structures using a weak version of the equations of covariant constancy and the weil brezin expansion to describe distributional sections we give a unified analytical description of the quantization spaces for all non negative polarizations the blattner kostant sternberg bks pairing maps between half form corrected quantization spaces for different polarizations are shown to be transitive and related to an action of sp 2 g r moreover these maps are shown to be unitary

the wave group on asymptotically hyperbolic manifolds abstract we show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of fourier integral operators then we use now standard techniques to analyze its regularized trace we prove that as in the case of compact manifolds without boundary the singularities of the regularized wave trace are contained in the set of periods of closed geodesics we also obtain an asymptotic expansion for the trace at zero

moyal planes are spectral triples axioms for nonunital spectral triples extending those introduced in the unital case by connes are proposed as a guide and for the sake of their importance in noncommutative quantum field theory the spaces r2n endowed with moyal products are intensively investigated some physical applications such as the construction of noncommutative wick monomials and the computation of the connes lott functional action are given for these noncommutative hyperplanes

on the theory of thermoelasticity with microtemperatures abstract this paper studies the linear theory of thermoelastic materials with inner structure whose particles in addition to the classical displacement and temperature fields possess microtemperatures we discuss uniqueness results within the context of the dynamic boundary value problems under very mild assumptions upon the thermoelastic profile we also establish the relations describing the partition of the total energy in terms of the cesaro means of various types of component energies

a unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi discretized vibrating damped systems the liapunov method is celebrated for its strength to establish strong decay of solutions of damped equations extensions to infinite dimensional settings have been studied by several authors see e g haraux 1991 11 and komornik and zuazua 1990 17 and references therein results on optimal energy decay rates under general conditions of the feedback is far from being complete the purpose of this paper is to show that general dissipative vibrating systems have structural properties due to dissipation we present a general approach based on convexity arguments to establish sharp optimal or quasi optimal upper energy decay rates for these systems and on comparison principles based on the dissipation property and interpolation inequalities in the infinite dimensional case for lower bounds of the energy we stress the fact that this method works for finite as well as infinite dimensional vibrating systems and as well as for applications to semi discretized nonlinear damped vibrating pde s a part of this approach has been introduced in alabau boussouira 2004 2005 1 2 in the present paper we identify a new simple and explicit criteria to select a class of nonlinear feedbacks for which we prove a simplified explicit energy decay formula comparatively to the more general but also more complex formula we give in alabau boussouira 2004 2005 1 2 moreover we prove optimality of the decay rates for this class in the finite dimensional case this class includes a wide range of feedbacks ranging from very weak nonlinear dissipation exponentially decaying in a neighborhood of zero to polynomial or polynomial logarithmic decaying feedbacks at the origin in the infinite dimensional case we establish a comparison principle on the energy of sufficiently smooth solutions through the dissipation relation this principle relies on suitable interpolation inequalities it allows us to give lower bounds for the energy of smooth initial data for the one dimensional wave equation with a distributed polynomial damping which improves haraux 1995 12 lower estimate of the energy for this case we also establish lower bounds in the multi dimensional case for sufficiently smooth solutions when such solutions exist we further mention applications of these various results to several classes of pde s namely the locally and boundary damped multi dimensional wave equation the locally damped plate equation and the globally damped coupled timoshenko beams system but it applies to several other examples furthermore we show that these optimal energy decay results apply to finite dimensional systems obtained from spatial discretization of infinite dimensional damped systems we illustrate these results on the one dimensional locally damped wave and plate equations discretized by finite differences and give the optimal energy decay rates for these two examples these optimal rates are not uniform with respect to the discretization parameter we also discuss and explain why optimality results have to be stated differently for feedbacks close to linear behavior at the origin

change of sign of the corrector s determinant for homogenization in three dimensional conductivity in this paper we study the positivity of the determinant of the local electric field in a conducting composite we know by 1 that the positivity holds true in two dimensions for any periodic structure using a different approach from 11 we prove that is also the case for a laminate microstructure in any dimension however and this is the main result of the paper we provide an example of a two phase three dimensional periodic composite for which the determinant changes sign

equivariant asymptotics for bohr sommerfeld lagrangian submanifolds suppose given a complex projective manifold m with a fixed hodge form the bohr sommerfeld lagrangian submanifolds of m are the geometric counterpart to semi classical physical states and their geometric quantization has been extensively studied here we revisit this theory in the equivariant context in the presence of a compatible hamiltonian action of a connected compact lie group

indirect boundary stabilization of weakly coupled hyperbolic systems this work is concerned with the boundary stabilization of an abstract system of two coupled second order evolution equations wherein only one of the equations is stabilized indirect damping see e g j math anal appl 173 1993 pp 339 358 we show that under a condition on the operators of each equation and on the boundary feedback operator the energy of smooth solutions of this system decays polynomially at infty we then apply this abstract result to several systems of partial differential equations wave wave systems kirchhoff petrowsky systems and wave petrowsky systems

tests for conditional ellipticity in multivariate garch models tests are proposed for the assumption that the conditional distribution of a multivariate garch process is elliptic these tests are of kolmogorov smirnov and cramer von mises type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution the asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions it is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the euclidean norm of the innovations therefore a conditional monte carlo procedure is used to actually carry out the tests the validity of this resampling scheme is formally justified results on the behavior of the new tests in finite samples are included along with comparisons with other tests

self weighted and local quasi maximum likelihood estimators for arma garch igarch models the limit distribution of the quasi maximum likelihood estimator qmle for parameters in the arma garch model remains an open problem when the process has infinite 4th moment we propose a self weighted qmle and show that it is consistent and asymptotically normal under only a fractional moment condition based on this estimator the asymptotic normality of the local qmle is established for the arma model with garch finite variance and igarch errors using the self weighted and the local qmles we construct wald statistics for testing linear restrictions on the parameters and their limiting distributions are given in addition we show that the tail index of the igarch process is always 2 which is independently of interest

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

the index of scattering operators of dirac equations ii abstract the index formula of scattering operators of the previous paper of the author t matsui the index of scattering operators of dirac equations commun math phys 110 1987 553 571 is shown to hold for a wider class of potentials which contains both gauge potentials with compactly supported energy and instantontype potentials

admittivity imaging from multi frequency micro electrical impedance tomography abstract the aim of this paper is to propose an optimal control optimization algorithm for reconstructing admittivity distributions i e both conductivity and permittivity from multi frequency micro electrical impedance tomography a convergent and stable optimal control scheme is shown to be obtainable from multi frequency data this opens a door for convergence analysis of optimal control type approaches in imaging from internal data the results of this paper have potential applicability in cancer imaging cell culturing and differentiation food sciences and biotechnology

blow up of solutions to the cauchy problem in nonlinear one dimensional thermoelasticity this paper is concerned with the blow up phenomena of solutions to the cauchy problem in non autonomous nonlinear one dimensional thermoelastic models obeying both fourier s law of heat flux and the theory due to gurtin and pipkin moreover some previously related results have been extended

the spectral action for moyal planes extending a result of vassilevich we obtain the asymptotic expansion for the trace of a spatially regularized heat operator l f e t where is a generalized laplacian defined with moyal products and l f is moyal left multiplication the moyal planes corresponding to any skewsymmetric matrix being spectral triples the spectral action introduced in noncommutative geometry by chamseddine and connes is computed this result generalizes the connes lott action previously computed by gayral for symplectic

quantum classical correspondence using projection operators classical properties associated with a large phase space domain with a smooth boundary as compared to the planck constant are shown to be expressed quantum mechanically by a family of quantum projection operators with the help of known theorems in microlocal analysis under the conditions of egorov s theorem the conservation of this correspondence under classical quantum dynamics is asserted

global carleman inequalities for parabolic systems and applications to controllability this paper has been conceived as an overview on the controllability properties of some relevant linear and nonlinear parabolic systems specifically we deal with the null controllability and the exact controllability to the trajectories we try to explain the role played by the observability inequalities in this context and the need of global carleman estimates we also recall the main ideas used to overcome the difficulties motivated by nonlinearities first we considered the classical heat equation with dirichlet conditions and distributed controls then we analyze recent extensions to other linear and semilinear parabolic systems and or boundary controls finally we review the controllability properties for the stokes and navier stokes equations that are known to date in this context we have paid special attention to obtaining the necessary carleman estimates some open questions are mentioned throughout the paper we hope that this unified presentation will be useful for those researchers interested in the field

regime switching for dynamic correlations we propose a new model for the variance between multiple time series the regime switching dynamic correlation we decompose the covariances into correlations and standard deviations and the correlation matrix follows a regime switching model it is constant within a regime but different across regimes the transitions between the regimes are governed by a markov chain this model does not suffer from a curse of dimensionality and it allows analytic computation of multi step ahead conditional expectations of the variance matrix when combined with the armach model taylor modelling financial time series wiley new york and schwert j finance 44 5 1989 1115 for the standard deviations we also present an empirical application which illustrates that our model can have a better fit of the data than the dynamic conditional correlation model proposed by engle j business econ statist 20 3 2002 339

bayesian linearized rock physics inversion abstractthe estimation of rock and fluid properties from seismic attributes is an inverse problem rock physics modeling provides physical relations to link elastic and petrophysical variables most of these models are nonlinear therefore the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties we have developed a new approach based on the linearization of the rock physics forward model using first order taylor series approximations the mathematical method adopted for the inversion is the bayesian approach previously applied successfully to amplitude variation with offset linearized inversion we developed the analytical formulation of the linearized rock physics relations for three different models empirical granular media and inclusion models and we derived the formulation of the bayesian rock physics inversion under gaussian assumptions for the prior distribution of the model the application of the inversion to real

a convergence analysis of the landweber iteration for nonlinear ill posed problems in this paper we prove that the landweber iteration is a stable method for solving nonlinear ill posed problems for perturbed data with noise level delta we propose a stopping rule that yields the convergence rate o delta 1 2 under appropriate conditions we illustrate these conditions for a few examples

existence of almost everywhere solution for nonlinear hyperbolic parabolic system in this paper the existence theorem for an almost everywhere solution of a mixed problem for more complicated nonlinear hyperbolic parabolic nonlinear thermoelasticity system was proved using galerkin s method and suitable a priori estimates were obtained

microwave imaging by elastic deformation in this paper we show that by using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by ammari et al in siam j appl math 68 2008 pp 1557 1573 to problems of the form nabla cdot a nabla u k 2 qu 0 in omega u varphi on partial omega and to reliably reconstruct both the real valued functions a and q from the internal energies a nabla u 2 and q u 2

picard lefschetz theory and characters of a semisimple lie group the paper applies picard lefschetz theory to the distribution characters of infinite dimensional representations of semisimple lie groups and analyzes their asymptotic behaviour at the identity

solvability for a class of doubly characteristic differential operators on 2 step nilpotent groups since h lewy s le discovery of a smooth linear partial differential operator without solution the problem of solvability of linear differential operators has been investigated intensively by various authors this has meanwhile led most notably through the work of hdrmander maslov egorov nirenberg erves and beals fefferman but with many important contributions also by others to a very satisfactory theory in the case of principal type operators see h6 much less is known about operators whose principal symbol vanishes of second order on part of its characteristic variety i e those which admit double characteristics even in the case of real principal symbols the main objective of this article is to present a model class of such operators for which we are able to discuss solvability in a complete way our class being composed of rather special operators will certainly not capture all phenomena which might arise in the study of general doubly characteristic operators with real symbol as the results in st already indicate but it is still rich enough to exhibit several new features if one compares with operators of principal type the operators that we shall consider will be left invariant differential operators on connected simply connected 2 step nilpotent lie groups g of the form m 0 1 le ajkvjvk u j k l

exponential stability of a mixture of two elastic solids with a degenerate weak damping mechanism abstract in this note we investigate stability issues for a mixture of two elastic solids the governing equations consist of two coupled systems of elastodynamic equations with a weak damping the damping involves the difference of velocities so that the damping operator is degenerate first we show that the underlying semigroup is strongly stable under a weaker parameters constraint thereby improving an earlier strong stability result of dafermos next we show that under extra appropriate constraints on the parameters of the coupled system the semigroup is exponentially stable our proof relies on the frequency domain method the multipliers technique and a seemingly new vector calculus identity lemma b our exponential stability result is new in the framework of mixtures involving elastodynamic equations with weak damping we also show that for some sets of parameters the system is asymptotically unstable in particular we use a concrete example to show that strong stability fails for a certain parameters constraint

optimal energy decay rate for partially damped systems by spectral compensation we study the stability of weakly coupled and partially damped systems by means of the riesz basis approach in higher dimensional spaces we propose a weaker structural damping that compensates for the behavior of the eigenvalues of the system therefore giving the optimal polynomial energy decay rate for smooth initial data

dixmier traces on noncompact isospectral deformations abstract we extend the isospectral deformations of connes landi and dubois violette to the case of riemannian spin manifolds carrying a proper action of the noncompact abelian group r l under deformation by a torus action a standard formula relates dixmier traces of measurable operators to integrals of functions on the manifold we show that this relation persists for actions of r l under mild restrictions on the geometry of the manifold which guarantee the dixmier traceability of those operators

on the fokker planck boltzmann equation we consider the boltzmann equation perturbed by fokker planck type operator to overcome the lack of strong a priori estimates and to define a meaningful collision operator we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the cauchy problem with large data the proof of stability and existence combines renormalization with an analysis of a defect measure

a higher order nonlocal operator method for solving partial differential equations abstract a higher order nonlocal operator method for the solution of boundary value problems is developed the proposed higher order nonlocal operator brings several advantages as compared to the original nonlocal operator method ren et al 2020 which only ensures first order convergence furthermore it can be applied to directly and efficiently obtain all partial derivatives of higher orders simultaneously without the need of using shape functions only the functionals based on the nonlocal operators termed as operator functional are needed to obtain the final discrete system of equations which significantly facilitates the implementation several numerical examples are presented to show the effectiveness and accuracy of the proposed higher order nonlocal operator method including the solution of the poisson equation in 2 5 dimensional space kirchhoff and von karman plate problems incompressible elastic materials as well as phase field modeling of fracture

stability analysis for magnetic resonance elastography we consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues the measurements are made on the entirety of a smooth domain since tissues can be modeled as quasi incompressible fluids we examine the stokes system and consider only the recovery of shear modulus distributions our main result is to establish lipschitz stable estimates on the shear modulus distributions from internal measurements of displacement fields these estimates imply convergence of a numerical scheme known as the landweber iteration scheme for reconstructing the shear modulus distributions

a two level energy method for indirect boundary observability and controllability of weakly coupled hyperbolic systems this work is concerned with the boundary observability of an abstract system of two coupled second order evolution equations the coupling operator being a compact perturbation of the uncoupled system we assume that only one of the two components of the unknown is observed this is indirect observability we prove that by observing only one component one can get back a full weakened energy of both components under a compatibility condition linking the operators of each equation and for small coupling using the hilbert uniqueness method we then establish an indirect exact controllability result we apply this abstract result to several coupled systems of partial differential equations wave wave coupled elastodynamic systems petrowsky petrowsky and wave petrowsky systems

foundational aspects of singular integrals abstract we investigate integration of classes of real valued continuous functions on 0 1 of course difficulties arise if there is a non l 1 element in the class and the hadamard finite part integral p f does not apply such singular integrals arise naturally in many contexts including pdes and singular odes the lebesgue integral as well as p f starting at zero obey two fundamental conditions i they act as antiderivatives and ii if f g on 0 a then their integrals from 0 to x coincide for any x 0 a we find that integrals from zero with the essential properties of p f plus positivity exist by virtue of the axiom of choice ac on all functions on 0 1 which are l 1 e 1 for all e 0 however this existence proof does not provide a satisfactory construction without some regularity at 0 the existence of general antiderivatives which satisfy only i and ii above on classes with a non l 1 element is independent of zf the usual zfc axioms for mathematics without ac and even of zfdc zf with the axiom of dependent choice moreover we show that there is no mathematical description that can be proved within zfc or even extensions of zfc with large cardinal hypotheses to uniquely define such an antiderivative operator such results are precisely formulated for a variety of sets of functions and proved using methods from mathematical logic descriptive set theory and analysis we also analyze p f on analytic functions in the punctured unit disk and make the connection to singular initial value problems

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

asymptotics of cholesky garch models and time varying conditional betas this paper proposes a new model with time varying slope coefficients our model called char is a cholesky garch model based on the cholesky decomposition of the conditional variance matrix introduced by pourahmadi 1999 in the context of longitudinal data we derive stationarity and invertibility conditions and prove consistency and asymptotic normality of the full and equation by equation qml estimators of this model we then show that this class of models is useful to estimate conditional betas and compare it to the approach proposed by engle 2016 finally we use real data in a portfolio and risk management exercise we find that the char model outperforms a model with constant betas as well as the dynamic conditional beta model of engle 2016

optimal decay rates and the selfadjoint property in overdamped systems abstract we deal with abstract linear strongly damped wave equations in the so called overdamped regime we show the occurrence of two interesting phenomena the first is the existence of an explicit special inner product which makes the problem selfadjoint the second is an improvement of the decay rate for more regular solutions that will be of an exponential polynomial type furthermore we prove the optimality of this decay rate

electrical impedance tomography by elastic deformation this paper presents a new algorithm for conductivity imaging our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations using asymptotics of the fields in the presence of small volume inclusions we relate the pointwise values of the energy density to the measured data through a nonlinear pde our algorithm is based on this pde and takes full advantage of the enriched data we give numerical examples that illustrate the performance and the accuracy of our approach

some new exact solutions for linear thermoelastic system the general analysis of transformation group method has been developed to study the linear thermoelastic system the application of one parameter group reduces the number of independent variables consequently the governing system of second order partial differential equations reduced into systems of ordinary differential equations in this paper some of these systems are solved analytically

asymptotic expansion of the trace of the heat kernel associated to the dirichlet to neumann operator abstract for a given bounded domain with smooth boundary in a smooth riemannian manifold m g by decomposing the dirichlet to neumann operator into a sum of the square root of the laplacian and a pseudodifferential operator and by applying grubb s method of symbolic calculus for the corresponding pseudodifferential heat kernel operators we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to dirichlet to neumann operator as t 0 in particular we explicitly give the first four coefficients of this asymptotic expansion these coefficients provide precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the steklov problem

gevrey regularity for a class of sums of squares of monomial vector fields abstract analytic or gevrey hypoellipticity is proved for a class of sums of squares of vector fields having a symplectic characteristic manifold of dimension 2 and arbitrary even codimension we note that this class contains examples for which the treves stratification seems to work as well as examples for which the treves stratification does not identify properly the non symplectic stratum

exponential decay of solutions in type ii porous thermo elasticity with quasi static microvoids abstract in this note we study the problem proposed by the one dimensional thermo porous elasticity of type ii with quasi static microvoids or in mathematical terms when the second time derivative of the volume fraction is so small that it can be negligible it is known that the isothermal deformations decay in a slow way here we prove that the introduction of a conservative mechanism as it is the type ii heat conduction makes the deformations damp generically in an exponential way which is a striking fact

the weyl type asymptotic formula for biharmonic steklov eigenvalues on riemannian manifolds abstract let be a bounded domain with c 2 smooth boundary in an n dimensional oriented riemannian manifold it is well known that for the biharmonic equation 2 u 0 in with the condition u 0 on there exists an infinite set u k of biharmonic functions in with positive eigenvalues k satisfying u k k u k 0 on in this paper by a new method we establish the weyl type asymptotic formula for the counting function of the biharmonic steklov eigenvalues k

complete determination of the singularity structure of zeta functions series of extended epstein type provide examples of non trivial zeta functions with important physical applications the regular part of their analytic continuation is seen to be a convergent or an asymptotic series their singularity structure is completely determined in terms of the wodzicki residue in its generalized form which is proven to yield the residua of all the poles of the zeta function and not just that of the rightmost pole obtainable from the dixmier trace the calculation is a very down to earth application of these powerful functional analytical methods in physics

on the propagation of polarization sets for systems of real principal type we define and study the polarization sets for vector valued distributions systems of real principal type are defined and we prove that for such systems of pseudodifferential operators we have a unique propagation of the polarization sets for the solutions

on asymptotic properties of biharmonic steklov eigenvalues abstract in this paper by explicitly calculating the principal symbols of pseudodifferential operators we establish two weyl type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic steklov eigenvalue problems of smooth bounded domains in a riemannian manifold

multidimensional extension of the generalized chowla selberg formula after recalling the precise existence conditions of the zeta function of a pseudodifferential operator and the concept of reflection formula an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous epstein type zeta function of the general form with a the p p matrix of a quadratic form a p vector and q a constant is obtained it is valid on the whole complex s plane is exponentially convergent and provides the residua at the poles explicitly it reduces to the famous formula of chowla and selberg in the particular case p 2 q 0 some variations of the formula and physical applications are considered

univalent σ harmonic mappings we study mappings from 2 into 2 whose components are weak solutions to the elliptic equation in divergence form div u 0 which we call harmonic mappings we prove sufficient conditions for the univalence i e injectivity of such mappings moreover we prove local bounds in bmo on the logarithm of the jacobian determinant of such univalent mappings thus obtaining the a e nonvanishing of their jacobian in particular our results apply to harmonic mapping associated with any periodic structure and therefore they play an important role in homogenization

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

on the impossibility of localization in linear thermoelasticity in the middle of the 1990s green naghdi proposed three theories of thermoelasticity that they labelled as types i ii and ii the type ii theory which is also called thermoelasticity without energy dissipation is conservative and the solutions cannot decay with respect to time it is well known that in general in the linear theories of thermoelasticity of types i and iii the solutions decay with respect to time in many situations this decay is at least exponential in this paper we study whether this decay can be fast enough to guarantee the solutions to be zero in a finite time we investigate the impossibility of the localization in time of the solutions of linear thermoelasticity for the theories of green naghdi this means that the only solution that vanishes after a finite time is the null solution the main idea is to show the uniqueness of solutions for the backward in time problem to be precise for type iii thermoelasticity we will prove the impossibility of localization of solutions in the case of bounded domains and for the type i thermoelasticity in the case of exterior domains even when the solutions can be unbounded whether the spatial variable goes to infinity

null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

the efficiency of the estimators of the parameters in garch processes we propose a class of estimators for the parameters of a garch p q sequence we show that our estimators are consistent and asymptotically normal under mild conditions the quasi maximum likelihood and the likelihood estimators are discussed in detail we show that the maximum likelihood estimator is optimal if the tail of the distribution of the innovations is polynomial even a quasi maximum likelihood estimator based on exponential density performs better than the standard normal density based quasi likelihood estimator of lee and hansen and lumsdaine

on asymptotic expansions of twisted products the series development of the quantum mechanical twisted product is studied the series is shown to make sense as a moment asymptotic expansion of the integral formula for the twisted product either pointwise or in the distributional sense depending on the nature of the factors a condition is given that ensures convergence and is stronger than previously known results possible applications are examined