wave decay on convex co compact hyperbolic manifolds for convex co compact hyperbolic quotients x gamma backslash mathbb h n 1 we analyze the long time asymptotic of the solution of the wave equation u t with smooth compactly supported initial data f f 0 f 1 we show that if the hausdorff dimension of the limit set is less than n 2 then u t c delta f e delta frac n 2 t gamma delta n 2 1 e delta frac n 2 t r t where c delta f in c infty x and r t mathcal o t infty we explain in terms of conformal theory of the conformal infinity of x the special cases delta in n 2 mathbb n where the leading asymptotic term vanishes in a second part we show for all epsilon 0 the existence of an infinite number of resonances and thus zeros of selberg zeta function in the strip n delta epsilon rm re lambda delta as a byproduct we obtain a lower bound on the remainder r t for generic initial data f

potential integrals associated with quadratic distributions in a triangular domain exact expressions are presented for the potentials at an arbitrary point in space due to two quadratic distributions in a triangular disc these expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions it is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here together with an expression for the potential corresponding to a linear distribution this latter expression was presented in an earlier paper 1 numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures

a detailed analysis on local bifurcation from infinity for nonlinear elliptic problems in this paper we analyze the local side of the bifurcation from infinity at the first eigenvalue of several elliptic operators we underline that the key to decide the local behavior of the bifurcation lies in the sign of certain integral involving all the values of the nonlinearity

a new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method the purpose of this paper is to report on a new and efficient method for the evaluation of singular integrals in stress analysis of elastic and elasto plastic solids respectively by the direct boundary element method bem triangle polar co ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares the method was subsequently extended to the cubature of singular integrals over three dimensional internal cells as occur in applications of the bem to three dimensional elasto plasticity for this purpose so called tetrahedron polar co ordinates were introduced singular boundary integrals stretching over either linear triangular or quadratic quadilateral isoparametric boundry elements and singular volume integrals extending over either linear tetrahedral or quadratic hexahedral isoparametric internal cells are treated in case of higher order isoparametric boundary elements and internal cells division into a number of subelements and subcells respectively is necessary the analytical investigation is followed by a numerical study restricted to the use of quadratic quadrilateral isoparametric boundary elements this is justified by the fact that such elements as opposed to linear elements yield singular boundary integrals which cannot be integrated analytically the results of the numerical investigation demonstrate the potential of the developed concept

nonvanishing of l values and the weyl law this work is concerned with the validity of weyl law for hyperbolic surfaces on the asymptotic counting of the laplace eigenvalues following phillipssarnak we show that weyl law is false for generic hyperbolic surfaces under the standard multiplicity assumption by establishing that a positive proportion of certain critical values of rankin selberg l functions do not vanish

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

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

semiclassical wavefunctions in chaotic scattering systems we have computed quantum wavefunctions in the high energy semiclassical regime in a system the stadium billiard with leads allowing particles to enter and escape exemplifying chaotic scattering the results exhibit a structure associated with classical paths that is dramatically more pronounced than the scars due to periodic orbits seen in bound systems moreover this structure is seen at all energies our results differ significantly from those previously conjectured on the basis of computations in the low energy regime the dominant role played by short classical paths is explained by a semiclassical theory based on the analytic structure of the green function this is verified by a direct semiclassical computation of wavefunctions using classical scattering trajectories

quantum decay rates in chaotic scattering we study quantum scattering on manifolds equivalent to the euclidean space near infinity in the semiclassical regime we assume that the corresponding classical flow admits a non trivial trapped set and that the dynamics on this set is of axiom a type uniformly hyperbolic we are interested in the distribution of quantum resonances near the real axis in two dimensions we prove that if the trapped set is sufficiently thin then there exists a gap between the resonances and the real axis that is quantum decay rates are bounded from below in higher dimension the condition for this gap is given in terms of a certain topological pressure associated with the classical flow under the same assumption we also prove a resolvent estimate with a logarithmic loss compared to non trapping situations

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

scaling integration method for singular integrals and its application to bem abstract a new accurate and efficient algorithm is developed for the numerical evaluation of a class of singular integrals which arise in the bem boundary element method analyses the algorithm is based on an idea of scaling integration that utilizes a proportional relationship inherent in the numerical computation of the singular integrals over flat triangular elements the present algorithm scaling integration method avoids the direct numerical evaluation of the integrand in the neighborhood of singularities it is shown and demonstrated that the method is simpler faster and more accurate than standard gaussian integration algorithms an application of the method to the bem analysis is also described and the results are favorably compared with the exact solution

the second moment of gl 4 gl 2 l functions at special points abstract in this paper we obtain upper bounds for the second moment of l u j 1 2 i t j where is a hecke maass form for s l 4 z and u j is taken from an orthonormal basis of hecke maass forms on s l 2 z with eigenvalue 1 4 t j 2 the bounds are consistent with the lindelof hypothesis previously these types of upper bounds are available for only g l n g l 2 where n 3

taylor expansions for singular kernels in the boundary element method the problem treated is the integration of singular functions which arise in three dimensional isoparametric formulations of boundary integral equations a taylor expansion in the local parametric co ordinates is developed for the singular integrand so allowing singular terms to be integrated in closed form even for curved surface elements the remainder integral obtained by subtracting out the worst singularities is integrated by repeated gaussian quadrature two groups of tests are presented first the accuracy of the integrations has been checked for plane parallelograms for which exact solutions have been developed and for curved elements on a sphere secondly results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems zonal surface harmonics on a sphere and the capacitance of an ellipsoid the agreement obtained with few degrees of freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration

quadrature formulas obtained by variable transformation and the de rule abstract this paper gives a survey of the results known to date about quadrature formulas obtained by variable transformation followed by an application of the trapezoidal rule with an equal mesh size it has been shown that a formula obtained by an appropriate transformation is in general efficient and also robust against the end point singularity various kinds of useful transformations together with the asymptotic error behaviors of the resulting quadrature formulas are summarized in particular special emphasis is placed on an asymptotically optimal formula called the double exponential formula abbreviated as the de rule which is characterized by the double exponential decrease of its weights in the neighborhood of the end points of the transformed interval of integration

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

the potential integral for a polynomial distribution over a curved triangular domain an expression is derived for the potential at an arbitrary point due to a general polynomial distribution of source over a curved triangular domain the expression is important for the numerical solution of electromagnetic field problems and generalizes the cases of linear and uniform distributions solved previously

direct computation of cauchy principal value integrals in advanced boundary elements this paper presents a new method for the direct computation of strongly singular integrals existing in the cauchy principal value sense it can be usefully applied in the solution by the direct boundary element method of many different problems initially some considerations are provided in order to summarize the state of the art on this issue then the features of the proposed method are reported the procedure allows the direct calculation of cauchy principal value integrals with first order singularity and it is applicable even in advanced boundary element methods employing high order elements it requires only the use of standard gaussian quadrature formulae plus the computation of a logarithmic term some examples show the effectiveness and efficiency of the procedure

the laplace operator on a hyperbolic manifold ii eisenstein series and the scattering matrix on considere des varietes m isometriques au quotient de l espace hyperbolique a n dimensions h n par un groupe discret geometriquement fini t sans elements paraboliques et sans elements d ordre fini on demontre que la serie de eisenstein associee admet un prolongement mesomorphe au plan complexe et on etudie l operateur diffusion associe

evaluations of hypersingular integrals using gaussian quadrature a gaussian quadrature formula for hypersingular integrals with second order singularities is developed based on previous gaussian quadrature formulae for cauchy principal value integrals the formula uses classical orthonormal polynomials and the formula is then specialized to the case of legendre and chebyshev polynomials numerical experiments are carried out using the current formula and a previous formula developed by kutt it is found that the two methods generally give similar results and in some cases the current method works better it has also been shown that the current method allows the choice of an appropriate weight which can increase the convergence rate and the accuracy of the results copyright 1999 john wiley sons ltd

deformations of maass forms we describe numerical calculations which examine the phillips sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume riemann surface s under deformation of the surface our calculations indicate that if the teichmuller space of s is not trivial then each cusp form has a set of deformations under which either the cusp form remains a cusp form or else it dissolves into a resonance whose constant term is uniformly a factor of 10 8 smaller than a typical fourier coefficient of the form we give explicit examples of those deformations in several cases

hypersingular residuals a new approach for error estimation in the boundary element method summary this paper presents a new approach for a posteriori pointwise error estimation in the boundary element method the estimator relies upon evaluation of the residual of hypersingular integral equations and is therefore intrinsic to the boundary integral equation approach a methodology is developed for approximating the error on the boundary as well as in the interior of the domain extensive computational experiments have been performed for the two dimensional laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve moreover a reasonable estimate of the magnitude of the actual error is also predicted

ends of hyperbolic 3 manifolds let n h3 f be a hyperbolic 3 manifold which is homeomorphic to the interior of a compact 3 manifold we prove that n is geometrically tame as a consequence we prove that f s limit set l is either the entire sphere at infinity or has measure zero we also prove that n s geodesic flow is ergodic if and only if lf is the entire sphere at infinity department of mathematics stanford university stanford california 94305 current address department of mathematics university of michigan ann arbor michigan 48109 e mail address dick canary math lsa umich edu this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 06 utc all use subject to http about jstor org terms

analysis and evaluation of singular integrals by the invariant imbedding approach the invariant imbedding formulae for evaluating singular integrals on flat domains are used to analyse the singular integrals which arise in the boundary element method although all orders of singularity are considered the primary objective of the paper is the evaluation of cauchy principal value integrals cpv conditions for boundedness of the cpv are derived and evaluation techniques are presented for situations in which the singular point lies on or is in close proximity to an element boundary specific cases analysed include straight and curved element boundaries and corners other numerical aspects of the formulae are also discussed by way of example the analysis techniques are applied to the volume integrals which arise in continuum inelastic problems

the laplace operator on hyperbolic three manifolds with cusps of non maximal rank where f is a geometrically finite discrete group of orientation preserving isometries which may contain parabolic elements of non maximal rank we prove the existence of a continuum eigenfunction expansion and show that in the spectral parameter the eigenfun ctions have meromorphic continuations to 112 1 these eigenfunctions are eisen stein series for f the continuous spectrum of laplace operators on hyperbolic manifolds was first analysed by number theorists as a means of studying eisenstein series maass and roelke i m r considered the case of finite volume manifolds in two dimen sions increasingly more general hyperbolic manifolds were studied by faddeev if patterson pal lax and phillips lpi lp4 mandouvalos m1 m3 and others recently agmon l a mazzeo and melrose mm and perry p proved the meromorphic continuation of the eisenstein series for geometrically finite groups with fundamental domains of infinite volume provided the groups have no parabolic elements or all the parabolic elements have maximal rank in this case the boundary at infinity which roughly speaking labels the directions at infinity in which scattering can occur is a smooth compact manifold or in the presence of parabolic elements of maximal rank the union of a smooth compact manifold with a finite number of points in fact the work of mazzeo and melrose and recent work of agmon applies to more general manifolds which have a similar structure near infinity however none of the proofs of meromorphic continuation of eigenfun ctions apply when the group has parabolic elements of non maximal rank we will study the laplace operator on a three dimensional hyperbolic manifold when parabolic elements of non maximal rank are present in this case the research supported by the national science and engineering research council of canada research supported in part by n s f grant dms 8911242 research supported in part by n s f grant dms 8802668

on the distribution of eigenvalues of maass forms on certain moonshine groups in this paper we study both analytically and numerically questions involving the distribution of eigen values of maass forms on the moonshine groups 0 n where n 1 is a square free integer after we prove that 0 n has one cusp we compute the constant term of the associated non holomorphic eisenstein series we then derive an average weyl s law for the distribution of eigenvalues of maass forms from which we prove the classical weyl s law as a special case the groups corresponding to n 5 and n 6 have the same signature however our analysis shows that asymptotically there are infinitely more cusp forms for 0 5 than for 0 6 we view this result as being consistent with the phillips sarnak philosophy since we have shown unconditionally the existence of two groups which have different weyl s laws in addition we employ hejhal s algorithm together with recently developed refinements from 32 and numerically determine the first 3557 of 0 5 and the first 12474 eigenvalues of 0 6 with this information we empirically verify some conjectured distributional properties of the eigenvalues

bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity this paper deals with existence results for the following nonlinear problem with the dirichlet p laplacian p in a bounded domain rn pu u p 2u h x u in u 0on here pu defdiv u p 2 u where p 1 is a fixed number h h x s is a given function from r into r and r stands for a spectral parameter we focus on close to 1 including the resonant case 1 the nonlinearity h is assumed to be of landesman lazer type but we can deal with vanishing nonlinearities as well our asymptotic method substitutes the lyapunov schmidt method in some sense unlike in the semilinear case p 2 our method can treat more general nonlinearities if p 2 vanishing nonlinearities with very fast decay

advanced boundary element analysis of two and three dimensional problems of elasto plasticity an advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach the iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment in the present analysis the geometry and functions are represented by higher order quadratic shape functions to model complex geometries and rapid functional variations accurately the methods of numerical integration of the kernels particularly the singular type are substantially improved by devising suitable automatic sub segmentation routines that incorporate the recent developments in mapping procedures the formulations have been implemented for two dimensional plane stress plane strain and three dimensional elasto plasticity problems

the spectrum of kleinian manifolds abstract we obtain the plancherel theorem for l 2 g where g is a classical simple lie group of real rank one and g is convex cocompact discrete subgroup and deduce its consequences for the spectrum of locally invariant differential operators on bundles over kleinian manifolds as the main tool we develop a geometric version of scattering theory which in particular contains the meromorphic continuation of the eisenstein series for this situation the central role played by invariant distribution sections supported on the limit set is emphasized

gauss quadrature rules for finite part integrals we construct a set of polynomials n x which are orthogonal with respect to w x x 2 where wx is a weight function these polynomials can be used for the definition of a gauss quadrature formula for the finite part integral the process is exactly the same as the one used for the extraction of the classical gauss formula for the riemann integrals three different methods are derived the first and most accurate quadrature formula is successfully tested in some numerical examples the proposed quadrature formulas have many applications in problems of mathematical physics mechanics etc

scattering poles for asymptotically hyperbolic manifolds for a class of manifolds x that includes quotients of real hyperbolic n 1 dimensional space by a convex co compact discrete group we show that the resonances of the meromorphically continued resolvent kernel for the laplacian on x coincide with multiplicities with the poles of the meromorphically continued scattering operator for x in order to carry out the proof we use shmuel agmon s perturbation theory of resonances to show that both resolvent resonances and scattering poles are simple for generic potential perturbations

deformation of compact clifford klein forms of indefinite riemannian homogeneous manifolds 1 1 let g be a lie group and h a closed subgroup of g if a discrete subgroup of g acts properly discontinuously and freely on g h then the double coset space g h carries naturally a manifold structure such that the quotient map g h g h is locally diffeomorphic the manifold g h is said to be a clifford klein form of g h if it is compact then is said to be a uniform lattice for g h a typical example is a compact riemann surface mg with genus g 2 which is biholomorphic to a compact clifford klein form of the poincare disk g h sl 2 r so 2 by the uniformization theorem it is important from geometric view point that a clifford klein form g h inherits any g invariant local geometric structure on g h such as indefinite riemannian metric complex structure symplectic structure causal structure and so on

computations of eisenstein series on fuchsian groups we present numerical investigations of the value distribution and distribution of fourier coefficients of the eisenstein series e z s on arithmetic and non arithmetic fuchsian groups our numer

scattering theory for conformally compact metrics with variable curvature at infinity abstract we develop the scattering theory of a general conformally compact metric by treating the laplacian as a degenerate elliptic operator with non constant indicial roots on a compact manifold with boundary variability of the roots implies that the resolvent admits only a partial meromorphic continuation and the bulk of the paper is devoted to studying the structure of the resolvent poisson and scattering kernels for frequencies outside the region of meromorphy for low frequencies the scattering matrix is shown to be a pseudodifferential operator with frequency dependent domain in particular generalized eigenfunctions exhibit l 2 decay in directions where the asymptotic curvature is sufficiently negative we explicitly construct the resolvent kernel for generic frequency in this part of the continuous spectrum

an invariant imbedding method for singular integral evaluation on finite domains the invariant imbedding technique is used to develop versatile and powerful integration formulae for the evaluation of singular integrals on finite domains encountered in continuum problems in engineering and applied science this method is considerably simpler than the several ad hoc integral evaluation methods presented in the recent literature moreover the method provides new insight into the central role played by the residue in the evaluation of principal value integrals this relationship is embodied as a gauge condition the main emphasis of the paper is on developing a general approach from which specific cases follow several examples chosen from different areas of engineering computation are provided in order to show the advantage of this approach

evaluation of hypersingular integrals in the boundary element method by complex variable techniques strongly singular and hypersingular integrals that occur in many two dimensional applications of the boundary element method e g potential theory and liner elasticity can be treated in a unified manner by complex analysis this paper presents an elegant approach for the evaluation of such hypersingular integrals the limit to the boundary method where a source point is moved from the inside or outside of a body to its boundary is carried out using complex variables the connection of this limit with the hadamard finite part of hypersingular integrals and principal value integrals is established many examples are worked out throughout the paper to illustrate the theory

equidistribution of eisenstein series on convex co compact hyperbolic manifolds the quantum ergodic theorem due to schnirelman 4 colin de verdiere 1 and zelditch 5 says that on any compact riemannian manifold x whose geodesic flow isergodic one can find a full density sequence j of eigenvalues of the laplacian delta x such that the corresponding normalized eigenfunctions j are equidistributed i e for all f l 2 x we have lim j rightarrow infty int limits x f z vert psi j z vert 2 dv z int limits x f z dv z where dv is the normalized volume measure

hypersingular integrals in boundary element fracture analysis a new general purpose boundary element method for domains with cracks has been recently developed this technique avoids the use of a multi domain decomposition by including an additional integral equation expressing the boundary condition on the crack the principal requirement of this technique is the analytic determination of certain hypersingular integrals of the green s function which arise from this equation in order to establish the applicability of this method for fracture these integrals are evaluated herein for the kelvin solution of the three dimensional navier equations of linear elasticity numerical results for fracture problems using the single domain boundary element analysis are also presented

two trigonometric quadrature formulae for evaluating hypersingular integrals two trigonometric quadrature formulae one of non interpolatory type and one of interpolatory type for computing the hypersingular integral are developed on the basis of trigonometric quadrature formulae for cauchy principal value integrals the formulae use the cosine change of variables and trigonometric polynomial interpolation at the practical abscissae fast three term recurrence relations for evaluating the quadrature weights are derived numerical tests are carried out using the current formula as applications two simple crack problems are considered one is a semi infinite plane containing an internal crack perpendicular to its boundary and the other is a centre cracked panel subjected to both normal and shear tractions it is found that the present method generally gives superior results copyright 2002 john wiley sons ltd

a mourre estimate and related bounds for hyperbolic manifolds with cusps of non maximal rank we consider the laplace operator on quotients of hyperbolic n dimensional space by a geometrically finite discrete group of hyperbolic isometries with parabolic subgroups of non maximal rank using methods developed by the first two authors we prove a mourre estimate and commutator estimates on the laplacian which imply absolute continuity of the spectrum and quantitative resolvent estimates these estimates will be used elsewhere to study the scattering matrix and eisenstein series and their meromorphic continuations and should be useful in studying trace formulas for these discrete groups

deformation of γ0 5 cusp forms we develop an algorithm for numerical computation of the eisenstein series on a riemann surface of constant negative curvature we focus in particular on the computation of the poles of the eisenst

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

singular and near singular integrals in the bem a global approach a unified approach for analyzing and evaluating singular and near singular integrals relevant to the boundary element method bem is obtained the original n dimensional integral is mapped to one that is performed exclusively on the boundary of the integration domain therefore the dimensionality of the integration is reduced by l and integrand evaluations close to the singularity are avoided the new formulae are obtained through a straightforward one dimensional analytical integration regardless of the dimensionality of the problem and can be used generally for numerical integration the formulae for evaluating near singular integrals are a generalization of those obtained by the invariant imbedding technique for singular integrals and reduce to the singular integral formulae in the limit in this sense the singular integrals are treated as limits or continuations of nonsingular ones this leads to a general interpretation that includes the singular integrals as a special case in particular t

scattering and inverse scattering on ach manifolds we study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds we show the existence of the scattering operator as a meromorphic family of operators in the heisenberg calculus on the boundary which is a contact manifold with a pseudohermitian structure then we define the radiation fields as in the real asymptotically hyperbolic case and reconstruct the scattering operator from those fields as an application we show that the manifold including its topology and the metric are determined up to invariants by the scattering matrix at all energies

landesman lazer type results for second order hamilton jacobi bellman equations we study the boundary value problem f d2u du u x u f x u in u 0on where the second order differential operator f is of hamilton jacobi bellman type f is sub linear in u at infinity and rn is a regular bounded domain we extend the well known landesman lazer conditions to study various bifurcation phenomena taking place near the two principal eigenvalues associated to the differential operator we provide conditions under which the solution branches extend globally along the eigenvalue gap we also present examples illustrating the results and hypotheses

on selberg s small eigenvalue conjecture and residual eigenvalues we show that selberg s eigenvalue conjecture concern ing small eigenvalues of the automorphic laplacian for congruence groups is equivalent to a conjecture about the non existence of residual eigenvalues for a perturbed system we prove this using a combination of methods from asymptotic perturbation theory and number theory

a new concept in near singular integral evaluation the continuation approach the functional homogeneity of green functions is exploited in the derivation of continuation formulae for the accurate evaluation of near singular integrals these formulae provide a means of systematically continuing such unconventional integrals as the principal value and finite part integrals of singular functions to conventional integrals of nonsingular functions a new concept the notion of continuum integral which is applicable to singular as well as to nonsingular integrals is introduced as a generalization of principal value and finite part integrals numerical examples are provided that illustrate the computational advantages of the continuation method and give a new perspective on the subtleties of singular and near singular integrals

the continuation approach a general framework for the analysis and evaluation of singular and near singular integrals the continuation approach presented in this paper is a simple and unified framework for analyzing and computing a large class of singular and near singular integrals such as those that arise in the boundary element method the analysis formulates singular and near singular integrals consistently as instances of a single phenomenon with all types of algebraic singularities treated in a similar way for domains of arbitrary dimension singular integrals are viewed merely as continuations of nonsingular but perhaps near singular ones by placing the singularity of the integrand outside the integration domain and taking the limit as it approaches the domain the technique exploits the functional homogeneity shared by the green s functions of many physical problems for flat surfaces this allows the integral to be mapped to the contour of the integration domain curved surfaces are handled by projecting the integration domain to a tangent hyperplane where the singular components of the integral can be

a bi cubic transformation for the numerical evaluation of the cauchy principal value integrals in boundary methods the numerical strategies employed in the evaluation of singular integrals existing in the cauchy principal value cpv sense are undoubtedly one of the key aspects which remarkably affect the performance and accuracy of the boundary element method bem thus a new procedure based upon a bi cubic co ordinate transformation and oriented towards the numerical evaluation of both the cpv integrals and some others which contain different types of singularity is developed both the ideas and some details involved in the proposed formulae are presented obtaining rather simple and attractive expressions for the numerical quadrature which are also easily embodied into existing bem codes some illustrative examples which assess the stability and accuracy of the new formulae are included