microlocal analysis of some isospectral deformations we study the microlocal structure of the examples of isospectral deformations of riemannian manifolds given by d deturck and c gordon in det gi the schwartz kernel of the intertwining operators considered by them may be written as an oscillatory integral with a singular phase function and product type amplitude in certain instances we identify them as belonging to the space of fourier integral operators associated with various pairwise intersecting lagrangians after formulating a class of operators incorporating the most relevant features of the operators above we establish a composition calculus for this class and show that is not necessary to introduce new lagrangians in the composition

fourier integral operators on lie groupoids abstract as announced in 36 we develop a calculus of fourier integral g operators on any lie groupoid g for that purpose we study lagrangian conic submanifolds of the symplectic groupoid t g this includes their product transposition and inversion we also study the relationship between these lagrangian submanifolds and the equivariant families of lagrangian submanifolds of t g x t g x parametrized by the units x g 0 of g this allows us to select a subclass of lagrangian distributions on any lie groupoid g that deserve the name of fourier integral g operators g fios by construction the class of g fios contains the class of equivariant families of ordinary fourier integral operators on the manifolds g x x g 0 we then develop for g fios the first stages of the calculus in the spirit of hormander s work finally we illustrate this calculus in the case of manifolds with boundary

transversal waves in beams via the network simulation method abstract in this paper the network simulation method nsm is proposed as a tool for solving the transverse motion of thin beams resulting from a bending action the reliability and robustness of the proposed technique is demonstrated with two examples in which a pinned pinned beam and a clamped mass load beam are respectively submitted to different flexural forces the nsm is a numerical technique for the solution of linear and non linear problems which are defined by a mathematical model assuming that the electrical variables of voltage and current are equivalent respectively to the displacement and the spatial variation of the displacement a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model the whole network model including the devices associated with the boundary conditions is solved by the numerical computer code pspice the numerical results have been compared with those obtained by the mode superposition method the agreement between them is impressive the temporal behaviour of each quantity involved in the problem is obtained without transform complications since the whole study has been conducted in the time domain with the possibility of obtaining the corresponding spectral content at the end of calculation the main contribution of the present paper therefore is to employ the nsm numerical method in order to arrive at solutions in the time domain of dynamic mechanical problems one must also emphasize that nsm has not previously been used by other authors to solve physical problems like the ones presented here

second microlocal ellipticity and propagation of conormality for semilinear wave equations we revisit three problems on the propagation of conormal singularities for semilinear wave equations the evolution of two simply tangent waves the interaction of three conormal waves and the evolution of one wave with a cusp singularity we use quasihomogeneous blow ups to reduce the geometries to normal crossing and show that the lift of the operator by these blow down maps is elliptic in some directions of the compressed cotangent bundle of the blown up manifold this leads to both a strengthening of the previously known results and to simplification of their proofs

a groupoid approach to pseudodifferential calculi we give an algebraic geometric characterization of the classical pseudodifferential operators on a smooth manifold in terms of the tangent groupoid and its natural r action specifically we show that a properly supported semiregular distribution on m m is the schwartz kernel of a classical pseudo differential operator if and only if it extends to a smooth family of distributions on the range fibres of the tangent groupoid which is homogeneous for the r action modulo smooth functions moreover we show that the basic properties of pseudo differential operators can be proven directly from this characterization finally we show that with the appropriate generalization of the tangent bundle the same definition applies without change to define pseudodifferential calculi on arbitrary filtered manifolds and in particular the heisenberg calculus

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

meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature abstract we give a detailed description of the schwartz kernel of the resolvent of the laplacian on a certain class of complete riemannian manifolds with negative sectional curvature near infinity these manifolds have compactifications as c manifolds with boundary on which the metric is conformai to a c metric up to the boundary with conformal factor 2 where is a defining function for the boundary the modified resolvent r s 2 n 1 defined and analytic in r n is shown to extend to be meromorphic in the whole complex plane when s 2 is equal to the sectional curvature at infinity for hyperbolic spaces obtained as quotients hn 1 where is a discrete group of fractional linear transformations having a geometrically finite fundamental domain without cusps at infinity s is constant we then deduce from the existence of this meromorphic extension of the resolvent the existence of a similar extension for the eisenstein series the basic method used to produce a parametrix for the laplacian is part of a more general construction by g mendoza and the second author but since this is not yet available the present paper has been made essentially self contained

the diffractive wave trace on manifolds with conic singularities abstract let x g be a compact manifold with conic singularities taking g to be the friedrichs extension of the laplace beltrami operator we examine the singularities of the trace of the half wave group e i t g arising from strictly diffractive closed geodesics under a generic nonconjugacy assumption we compute the principal amplitude of these singularities in terms of invariants associated to the geodesic and data from the cone point this generalizes the classical theorem of duistermaat guillemin on smooth manifolds and a theorem of hillairet on flat surfaces with cone points

analysis of periodic schrodinger operators regularity and approximation of eigenfunctions let v be a real valued potential that is smooth everywhere on r3 except at a periodic discrete set s of points where it has singularities of the coulomb type z r we assume that the potential v is periodic with period lattice l we study the spectrum of the schrodinger operator h v acting on the space of bloch waves with arbitrary but fixed wavevector k let t r3 l let u be an eigenfunction of h with eigenvalue and let 0 be arbitrarily small we show that the classical regularity of the eigenfunction u is u h5 2 t in the usual sobolev spaces and u k3 2 m t s in the weighted sobolev spaces the regularity index m can be as large as desired which is crucial for numerical methods for any choice of the bloch wavevector k we also show that h has compact resolvent and hence a complete eigenfunction expansion the case of the hydrogen atom suggests that our regularity results are optimal we present two applications to the numerical approximation of eigenvalues using wave functions and usi

adjoints of elliptic cone operators we study the adjointness problem for the closed extensions of a general b elliptic operator a x diff m b m e 0 initially defined as an unbounded operator a c c m e x l 2 b m e x l 2 b m e inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the case where a is a symmetric semibounded operator is of particular interest and we give a complete description of the domain of the friedrichs extension of such an operator

a note on the vibrations of restrained beams and rods with point masses abstract this paper is concerned with the approximate determination of the fundamental frequency and first mode shape of a beam or rod to which springs and point masses are attached after formulating the general eigenvalue problem which forms the basis of the analysis the theory is applied to three examples and it is shown that the results are quite satisfactory

on the existence and structure of ψ algebras of totally characteristic operators on compact manifolds with boundary as a contribution to the pseudodifferential analysis on manifolds with singularities we construct for each smooth compact manifold x with boundary a algebra a b x b 1 2 l bl2 x b 1 2 containing the algebra 0b cl x b 1 2 of totally characteristic pseudodifferential operators introduced by melrose 25 in 1981 as a dense subalgebra further there is a homomorphism b a a b x b 1 2 q b characterizing the fredholm property of a a b x b 1 2 by means of the invertibility of b a a q b where q b is an algebra of c symbols reflecting the smooth structure of the manifold x the fredholm inverses of fredholm operators in a b x b 1 2 are again in the algebra a b x r 1 2 and we have elliptic regularity corresponding to the scale bhmb x b 1 2 of b sobolev spaces naturally associated to x localized to the interior of x we recover the ordinary pseudodifferential calculus finally spectrum jacobson topology and the relationship of certain closed ideals in the algebra a b x b 1 2 are described explicitly

improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme new approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments specifically the exact eigendata i e the exact natural frequencies and mode shapes of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration this is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions once the updated matrices for the linear structure are found the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices numerical experiments show that for the same number of elements the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model alternatively the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model

frequency response of a combined structure using a modified finite element method a modified finite element method is proposed to analyze the frequency response of an arbitrarily supported linear structure carrying various lumped attachments this is accomplished by updating the finite element mass and stiffness matrices of the linear structure without any lumped attachments using its exact natural frequencies and mode shapes so that the eigensolutions of the updated linear structure coincide with the exact eigendata once the updated matrices for the linear structure are found the finite element assembling technique is then exploited to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices after assembling the global mass and stiffness matrices the frequency response of the combined system can be easily obtained numerical experiments show that using only a few finite elements the proposed scheme returns natural frequencies and frequency responses that are nearly identical to those obtained by using a finite element model with a very fine mesh the new method is easy to apply and efficient to use and it can be extended to determine the frequency response of any combined linear structure over any specified range of excitation frequencies

hopf bifurcation in an eco epidemic model abstract this paper deals with prey predator system where the prey population is infected with a microparasite predator functional response is assumed to be holling type i all the feasible equilibrium points of the system are obtained and the condition for the existence of positive interior equilibrium point is also determined the criteria for both local stability and instability involving system parameters are derived the criterion for existence of hopf type small periodic oscillation is shown the condition for survival of all the population is investigated we have developed a necessary and sufficient criteria for uniform persistence finally the numerical verifications of analytic results are done

double layer potentials on three dimensional wedges and pseudodifferential operators on lie groupoids abstract let w be a three dimensional wedge and k be the double layer potential operator associated to w and the laplacian we show that 1 2 k are isomorphisms between suitable weighted sobolev spaces which implies a solvability result in weighted sobolev spaces for the dirichlet problem on w furthermore we show that the double layer potential operator k is an element in c g m 2 c where g is the action transformation groupoid m g with g 1 0 a b a r b r which is a lie group and m is a kind of compactification of g this result can be used to prove the fredholmness of 1 2 k where is a domain with edge singularities and k the double layer potential operator associated to the laplacian and

the generation of semilinear singularities by a swallowtail caustic we construct examples of bounded solutions to a semilinear system p u f z u z inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i f smooth p p id with p a strictly hyperbolic differential operator of second order with smooth coefficients such that for a time function t of p the following properties are satisfied 1 u is conormal to a smooth characteristic hypersurface in t t 0 2 for t 0 u is singular not only at but also on the forward characteristic cone over the swallowtail tip

green s formulas for cone differential operators green s formulas for elliptic cone differential operators are established this is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint thereby utilizing the concept of a discrete asymptotic type from this description the singular coefficients replacing the boundary traces in classical green s formulas are deduced

on the regularity of solutions to the yamabe equation and the existence of smooth hyperboloidal initial data for einstein s field equations the regularity of the solutions to the yamabe problem is considered in the case of conformally compact manifolds and negative scalar curvature the existence of smooth hyperboloidal initial data for einstein s field equations is demonstrated

probleme de cauchy semi lineaire en 3 dimensions d espace un resultat de finitude soit x x 0 x le point courant de l espace temps r 4 x x 1 x 2 x 3 l operateur des ondes un ouvert de r 4 x 0 0 on suppose que est un domaine d influence pour soit u x 0 x un element de h s s 2 3 1 2 qui verifie l equation des ondes semi lineaire u p u dans u x 0 0 u 0 h loc s u x 0 x 0 0 u 1 h loc s 1 on suppose que p u j 0 d p j x u j ou les p j x sont des fonctions c sur et que les traces u 0 et u 1 sont des distributions integrales de fourier c sur ou ct est une lagrangienne analytique reelle lisse pour tout er il existe un ensemble sous analytique homogene isotrope l 6 dans t tel que wf u cl

dynamic behavior of an eco epidemic system with impulsive birth in the paper we investigate an eco epidemic system with impulsive birth the conditions for the stability of infection free periodic solution are given by applying floquet theory of linear periodic impulsive equation and we give the conditions of persistence by constructing a consequence of some abstract monotone iterative schemes by using the method of coincidence degree a set of sufficient conditions are derived for the existence of at least one strictly positive periodic solution finally numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level thus we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels

analytic k theory on manifolds with corners let y be a compact manifold in 1 atiyah proposed an analytic delinition of the k homology groups k y defined abstractly as the dual theory to the atiyah hirzebruch k cohomology theory these ideas were developed by kasparov 15 and brown douglas and fillmore lo cycles for this analytic k homology theory are abstract elliptic operators i e bounded linear operators between hilbert spaces satisfying additional conditions derived from the properties of elliptic pseudo differential operators in particular elliptic pseudodifferential operators between sections of vector bundles define such cycles the homology class of the cycle depends only on the principal symbol and indeed only on the k cohomology class it represents on the cotangent bundle in fact it had already been shown in essence by atiyah that the resulting map

singularities of solutions to semilinear boundary value problems soit p un operateur differentiel d ordre 2 strictement hyperbolique sur une region ouverte cr n a frontiere lisse non caracteristique etant donnee une solution u h s loc s n 1 2 de pu f x u on etudie la propagation des singularites microlocales h r pour s r 2n n 2 1 2 dans la situation generale ou le champ hamiltonien de p hp peut etre tangent a t o a un ordre infini ou fini arbitrairement eleve

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

interaction of nonlinear progressing waves for semilinear wave equations on etudie l interaction transversale de 3 ondes planes progressives pour une equation d onde semi lineaire a 3 dimensions

the wave equation on asymptotically de sitter like spaces in this paper we obtain the asymptotic behavior of solutions of the klein gordon equation on lorentzian manifolds x g which are de sitter like at infinity such manifolds are lorentzian analogues of the so called riemannian conformally compact or asymptotically hyperbolic spaces under global assumptions on the null bicharacteristic flow namely that the boundary of the compactification x is a union of two disjoint manifolds y and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to and to the other manifold as the parameter goes to we also define the scattering operator and show that it is a fourier integral operator associated to the bicharacteristic flow from y to y

normal solvability of elliptic boundary value problems on asymptotically flat manifolds abstract normal solvability is shown for a class of boundary value problems on riemannian manifolds with noncompact boundary using a concept of weighted pseudodifferential operators and weighted sobolev spaces together with lopatinski shapiro type boundary conditions an essential step is to show that the standard normal derivative defined in terms of the riemannian metric is in fact a weighted pseudodifferential operator of the considered class provided the metric is compatible with the symbols

fourier integral operators and the index of symplectomorphisms on manifolds with boundary given two compact manifolds with boundary x y and a boundary preserving symplectomorphism t y 0 t x 0 which is one homogeneous in the fibers and satisfies the transmission condition we introduce fourier integral operators of boutet de monvel type associated with we study their mapping properties between sobolev spaces develop a calculus and prove a egorov type theorem we also introduce a notion of ellipticity which implies the fredholm property finally we show how in the spirit of a classical construction by a weinstein a fredholm operator of this type can be associated with and a section of the maslov bundle if dim y 2 or the maslov bundle is trivial the index is independent of the section and thus an invariant of the symplectomorphism

equations des ondes semi lineaires ii controle des singularites et caustiques non lineaires nous etudions le phenomene d interaction des singularites pour les equations des ondes non lineaires nous traitons en particulier l apparition generique de caustiques en dimension 2 d espace

existence of periodic solutions for periodic eco epidemic models with disease in the prey abstract for an eco epidemic model with disease in the prey and periodic coefficients it is conjectured in niu et al 2011 5 that when the infected prey is permanent there is a positive periodic orbit that is globally asymptotically stable in the interior of r 3 in this paper we prove the existence part of the conjecture for a large family of periodic systems

singularities produced in conormal wave interactions three problems on the interactions of conormal waves are considered two are examples which demonstrate that nonlinear spreading of singularities can occur when the waves are conormal in one case two of the waves are tangential and the other wave is transversal to the first two the third result is a noninteraction theorem it is shown that under certain conditions no nonlinear spreading of the singularities will occur

singular parabolic equations of second order on manifolds with singularities abstract the main aim of this article is to establish an l p theory for elliptic operators on manifolds with singularities the particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the singular ends of the manifolds such a theory is of importance for the study of elliptic and parabolic equations on non compact or even incomplete manifolds with or without boundary

the hodge cohomology of a conformally compact metric on etudie le laplacien de hogde agissant sur des k formes differentielles pour une classe de varietes de riemann completes a courbure sectionnelle negative proche de l infini ces varietes ont des compactifications c sur lesquelles la metrique est conforme a une metrique lisse jusqu au bord avec un facteur conforme 2 une fonction definissante pour le bord

self spreading and strength of singularities for solutions to semilinear wave equations algebres microlocales propagation de la regularite solutions lineaires conduisant a l etalement auto etalement des singularites

a new analytical technique for vibration analysis of non proportionally damped beams abstract vibrating linear mechanical systems in particular continuous systems are often modelled considering proportional damping distributions only although in many real situations this simplified approach does not describe the dynamics of the system with sufficient accuracy in this paper an analytical method is given to take into account the effects of a more general viscous damping model referred to as non proportional damping on a class of vibrating continuous systems a state form expansion applied in conjunction with a transfer matrix technique is adopted to extract the eigenvalues and to express the eigenfunctions in analytical form i e complex modes corresponding to non synchronous motions numerical examples are included in order to show the efficiency of the proposed method non proportional damping distributions of different type such as internal and external lumped or distributed viscous damping are tested on non homogeneous euler bernoulli beams in bending vibration with different boundary conditions finally a discussion on root locus diagrams behaviour and on modal damping ratio significance for non proportionally damped systems is presented

a general approach to formulating the frequency equation for a beam carrying miscellaneous attachments beams carrying various lumped attachments have been studied extensively over the years in this paper a simple approach is proposed that can be used to readily determine the eigenvalues of an arbitrarily supported single span or multi span beam carrying any combination of lumped mass rotary inertia grounded translational or torsional spring grounded translational or torsional viscous damper an undamped or damped oscillator with or without a rigid body degree of freedom rather than solving a generalized eigenvalue problem to obtain the eigenvalues of the system a frequency equation is formulated instead whose solution can be easily solved either numerically or graphically the proposed scheme is easy to code and can be easily modified to accommodate beams with arbitrary supports and carrying any number of miscellaneous lumped attachments

global singularity structures of weak solutions to 4 d semilinear dispersive wave equations in this paper we are concerned with the global singularity structures of weak solutions to 4 d semilinear dispersive wave equations whose initial data are chosen to be discontinuous on the unit sphere combining strichartz s inequality with the commutator argument techniques we show that the weak solutions are c 2 regular away from the focusing cone surface x t 1 and the outgoing cone surface x t 1

interactions of conormal waves for fully semilinear wave equations an existence theorem is proved for the continuation form of the cauchy problem pu z u z u z where p is a second order strictly hyperbolic differential operator with initial data strongly conormal to three characteristic hypersurfaces intersecting at 0 and the light cone for p over 0 we assume that the hypersurfaces are either pairwisely transversal or two of them are tangent of finite order along the line of intersection by reduction to a model case conormal energy estimates are obtained for the linear equation with zero initial data the proof of the theorem follows from an extension lemma and a contraction mapping argument