tutorial on seismic interferometry part 2 underlying theory and new advances in the 1990s the method of time reversed acoustics was developed this method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal when ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers they focus at the position of the original source even when the medium is very complex in seismic interferometry the time reversed responses are not physically sent into the earth but they are convolved with other measured responses the effect is essentially the same the time reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers a mathematical derivation based on reciprocity theory formalizes this principle the crosscorrelation of responses at two receivers integrated over different sources gives the green s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver this green s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving recent developments circumventing these assumptions include interferometric representations for attenuating and or moving media as well as unified representations for waves and diffusion phenomena bending waves quantum mechanical scattering potential fields elastodynamic electromagnetic poroelastic and electroseismic waves significant improvements in the quality of the retrieved green s functions have been obtained with interferometry by deconvolution a trace by trace deconvolution process compensates for complex source functions and the attenuation of the medium interferometry by multidimensional deconvolution also compensates for the effects of one sided and or irregular illumination

the resolving power of seismic amplitude data an anisotropic inversion migration approach a description of the theory and numerical implementation of a 3 d linearized asymptotic anisotropic inversion method based on the generalized radon transform is given we discuss implementation aspects including 1 the use of various coordinate systems 2 regularization by both spectral and bayesian statistical techniques and 3 the effects of limited acquisition apertures on inversion we give applications of the theory in which well resolved parameter combinations are determined for particular experimental geometries and illustrate the interdependence of parameter and spatial resolutions procedures for evaluating uncertainties in the parameter estimates that result from the inversion are derived and demonstrated

compactness of conformally compact einstein manifolds in dimension 4 abstract in this paper we establish some compactness results of conformally compact einstein metrics on 4 dimensional manifolds our results were proved under assumptions on the behavior of some local and non local conformal invariants on the compactness of the boundary metrics at the conformal infinity and on the topology of the manifolds

a characterization of strongly measurable kurzweil henstock integrable functions and weakly continuous operators abstract we give necessary and sufficient conditions for the kurzweil henstock integrability of functions given by f n 1 x n e n where x n belong to a banach space and the sets e n n are measurable and pairwise disjoint also weakly completely continuous operators between banach spaces are characterized by means of scalarly kurzweil henstock integrable functions

asymptotic curvature decay and removal of singularities of bach flat metrics we prove a removal of singularities result for bach flat metrics in dimension 4 under the assumption of bounded l 2 norm of curvature bounded sobolev constant and a volume growth bound this result extends the removal of singularities result for special classes of bach flat metrics obtained by tian and viaclovsby for the proof we emulate cheeger and tian and analyze the decay rates of solutions to the bach flat equation linearized around a flat metric this classification is used to prove that bach flat cones are in fact ale of order 2 this result is then used to prove the removal of singularities theorem

the stable topology of self dual moduli spaces soit m une 4 variete de riemann compacte connexe orientee et soit g un groupe de lie connexe simple on fixe un entier q m q alors l application inclusion i induit un epimorphisme sur les groupes respectifs d homologie et d homotopie a toutes les dimensions inferieures ou egales a q

on p dunford integrable functions with values in banach spaces abstract let be a complete probability space x a banach space and 1 p in this paper we discuss several aspects of p dunford integrable functions f x special attention is paid to the compactness of the dunford operator of f we also study the p bochner integrability of the composition u f y where u is a p summing operator from x to another banach space y finally we also provide some tests of p dunford integrability by using w thick subsets of x

retrieving the green s function in an open system by cross correlation a comparison of approaches l we compare two approaches for deriving the fact that the green s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions one approach is based on physical arguments exploiting the principle of time reversal invariance of the acoustic wave equation the other approach is based on rayleigh s reciprocity theorem using a unified notation we show that the result of the time reversal approach can be obtained as an approximation of the result of the reciprocity approach

multidimensional born velocity inversion single wideband point source the inverse scattering problem for an acoustic medium is considered within the approximate direct inversion framework as opposed to iterative methods the direct inversion approach gives an estimate of the medium velocities by operating on the observed scattered field without repeated solutions of the forward problem previous solutions to the multidimensional born velocity inversion problem require either coincident source and receiver arrays or plane wave sources in both cases an array of point sources is required to collect the proper data for inversion in this paper the solution to the single point source problem is derived it is shown that by extrapolating and imaging the observed scattered field appropriately the projections of the velocity function at all angles can be obtained the velocities are then reconstructed by the inverse radon transform method of tomography

reverse time wave field extrapolation imaging and inversion the scattered wave field propagated backward in time into an arbitrary background medium is related via a volume integral to perturbations in velocity about the background which are expressed as a scattering potential in general there is no closed form expression for the kernel of this integral representation although it can be expressed asymptotically as a superposition of plane waves backpropagated from the receiver array when the receiver array completely surrounds the scatterer the kernel reduces to the imaginary part of the green s function for the background medium this integral representation is used to relate the images obtained by imaging algorithms to the actual scattering potential two such relations are given 1 for the migrated image obtained by deconvolving the extrapolated field with the incident field and 2 for the reconstructed image obtained by applying a one way wave operator to the extrapolated field and then deconvolving by the incident field the migrated image highlig

the birkhoff integral and the property of bourgain in this paper we study the birkhoff integral of functions f x defined on a complete probability space with values in a banach space x we prove that if f is bounded then its birkhoff integrability is equivalent to the fact that the set of compositions of f with elements of the dual unit ball zf x f x bx has the bourgain property a non necessarily bounded function f is shown to be birkhoff integrable if and only if zf is uniformly integrable and has the bourgain property as a consequence it turns out that the range of the indefinite integral of a birkhoff integrable function is relatively norm compact we characterize the weak radon nikod m property in dual banach spaces via birkhoff integrable radon nikod m derivatives we also point out that a recently introduced notion of unconditional riemann lebesgue integrability coincides with the notion of birkhoff integrability some other applications are given

moduli spaces of critical riemannian metrics with l n 2 norm curvature bounds abstract we consider the moduli space of a class of critical metrics on compact manifolds that includes extremal kahler metrics we show that under the conditions of volume and diameter bounds l n 2 curvature bounds and sobolev constant bounds this moduli space can be compactified by including orbifolds with finitely many orbifold points in dimension 4 these orbifold points are c riemannian orbifold points and in the 4 dimensional extremal kahler case they are also of class c

a brief comparison of some kirchhoff integral formulas for migration and inversion kirchhoff migration has traditionally been viewed as an imaging procedure usually few claims are made regarding the amplitudes in the imaged section in recent years a number of inversion formulas similar in form to those of kirchhoff migration have been proposed a kirchhoff type inversion produces not only an image but also an estimate of velocity variations or perhaps reflection coefficients the estimate is obtained from the peak amplitudes in the image in this paper prestack kirchhoff migration and inversion formulas for the one parameter acoustic wave equation are compared following a heuristic approach based on the imaging principle a migration formula is derived which turns out to be identical to one proposed by bleistein for inversion prestack kirchhoff migration and inversion are thus seen to be the same both in terms of the image produced and the peak amplitudes of the output

the gradient flow of the l 2 curvature energy near the round sphere abstract we investigate the low energy behavior of the gradient flow of the l 2 norm of the riemannian curvature on four manifolds we show long time existence and exponential convergence to a metric of constant sectional curvature when the initial metric has positive yamabe constant and small initial energy

moduli spaces of critical riemannian metrics in dimension four abstract we obtain a compactness result for various classes of riemannian metrics in dimension four in particular our method applies to anti self dual metrics kahler metrics with constant scalar curvature and metrics with harmonic curvature with certain geometric non collapsing assumptions the moduli space can be compactified by adding metrics with orbifold like singularities similar results were obtained for einstein metrics in j amer math soc 2 3 1989 455 invent math 97 2 1989 313 invent math 101 1 1990 101 but our analysis differs substantially from the einstein case in that we do not assume any pointwise ricci curvature bound

bach flat asymptotically locally euclidean metrics we obtain a volume growth and curvature decay result for various classes of complete noncompact riemannian metrics in dimension 4 in particular our method applies to anti self dual or kahler metrics with zero scalar curvature and metrics with harmonic curvature similar results were obtained for einstein metrics in and89 bkn89 tia90 but our analysis differs from the einstein case in that 1 we consider more generally a fourth order system in the metric and 2 we do not assume any pointwise ricci curvature bound

on a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth on etudie le comportement asymptotique de varietes de riemann on construit des coordonnees a l infini sous certaines conditions intrinseques

a concentration collapse decomposition for l2 flow singularities we exhibit a concentration collapse decomposition of singularities of fourth order curvature flows including the l2 curvature flow and calabi flow in dimensions n 4 the proof requires the development of several new a priori estimates first we develop a smoothing result for initial metrics with small energy and a volume growth lower bound in the vein of perelman s pseudolocality result next we generalize our technique from prior work to exhibit local smoothing estimates for the l2 flow in the presence of a curvature related bound a final key ingredient is a new local regularity result for l2 critical metrics with possibly nonconstant scalar curvature applications of these results include new compactness and diffeomorphism finiteness theorems for smooth compact 4 manifolds satisfying the necessary and effectively minimal hypotheses of l2 curvature pinching and a volume noncollapsing condition 2014 wiley periodicals inc

nonlinear extended images via image domain interferometry wave equation finite frequency imaging and inversion still face many challenges in addressing the inversion of highly complexvelocitymodelsaswellasindealingwithnonlinearimaging e g migration of multiples amplitude preserving migration extended images eis are particularly important for designing image domain objective functions aimed at addressing standing issues in seismic imaging such as two way migration velocity inversion or imaging inversion using multiples general oneand two way representations for scattered wavefields can describe and analyze eis obtained in wave equation imaging we have developed a formulation that explicitly connects the wavefield correlations done in seismic imaging with the theory and practiceofseismicinterferometry inlightofthisconnection we define eis as locally scattered fields reconstructed by model dependent image domain interferometry because they incorporate the same one and two way scattering representations used for seismic interferometry the reciprocity based eis can in principle account for all possible nonlinear effects in the imaging process i e migrationofmultiplesandamplitudecorrections in this case the practice of two way imaging departs considerably from the one way approach we have studied the differences betweentheseapproachesinthecontextofnonlinearimaging analyzingthedifferencesinthewavefieldextrapolationstepsaswell as in imposing the extended imaging conditions when invoking single scatteringeffectsandignoringamplitudeeffectsingenerating eis the one and two way approaches become essentially the same as those used in today s migration practice with the straightforwardadditionofspaceandtimelagsinthecorrelationbased imaging condition our formal description of the eis and theinsightthattheyarescatteredfieldsintheimagedomainmay beusefulinfurtherdevelopmentofimagingandinversionmethodsinthecontextoflinear migration basedvelocityinversionor inmoresophisticatedimage domainnonlinearinversescattering approaches

compact self dual manifolds with positive scalar curvature on etudie l existence d une metrique auto duale a courbure scalaire positive sur une variete compacte simplement connexe qui n est pas conformement equivalente a ces metriques standard sur s 4 ou cp 2

counter examples to the generalized positive action conjecture we give examples of complete locally asymptotically flat riemannian 4 manifolds with zero scalar curvature and negative mass the generalized positive action conjecture of hawking and pope 5 is therefore false

on conformally kahler einstein manifolds we prove that any compact complex surface with c1 0 admits an einstein metric which is conformally related to a kahler metric the key new ingredient is the existence of such a metric on the blow up cp2 2cp2 of the complex projective plane at two distinct points

a compactness result for kahler ricci solitons abstract in this paper we prove a compactness result for compact kahler ricci gradient shrinking solitons if m i g i is a sequence of kahler ricci solitons of real dimension n 4 whose curvatures have uniformly bounded l n 2 norms whose ricci curvatures are uniformly bounded from below and g i 1 2 a where is perelman s functional there is a subsequence m i g i converging to a compact orbifold m g with finitely many isolated singularities where g is a kahler ricci soliton metric in an orbifold sense satisfies a soliton equation away from singular points and smoothly extends in some gauge to a metric satisfying kahler ricci soliton equation in a lifting around singular points

riemannian manifolds with flat ends soit m une variete de riemann complete non compacte de dimension n 2 une extremite de m est une application e qui affecte a chaque sousensemble compact de m une composante connexe e de m telle que e e si une extremite e est dite plate si e est plate pour un sousensemble de m on determine le type d isometrie de e pour un bon ensemble

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

on the equivalence of mcshane and pettis integrability in non separable banach spaces abstract we show that mcshane and pettis integrability coincide for functions f 0 1 l 1 where is any finite measure on the other hand assuming the continuum hypothesis we prove that there exist a weakly lindelof determined banach space x a scalarly null hence pettis integrable function h 0 1 x and an absolutely summing operator u from x to another banach space y such that the composition u h 0 1 y is not bochner integrable in particular h is not mcshane integrable

a wide class of ultrabornological spaces of measurable functions abstract our main result states that a bornological locally convex space having a suitable boolean algebra of projections is ultrabornological this general theorem whose proof is a variation of the sliding hump techniques used in diaz et al arch math basel 60 1993 73 78 diaz et al resultate math 23 1993 242 250 drewnowski el al proc amer math sec 114 1992 687 694 drewnowski et al atti sem mat fis univ modena41 1993 317 329 is applied to prove that some non complete normed spaces such as the spaces of dunford pettis or mcshane integrable functions as well as other interesting spaces of weakly or strongly measurable functions are ultrabornological we also give applications to vector valued sequence spaces in particular we prove that lp x 1 p

critical metrics on connected sums of einstein four manifolds abstract we develop a gluing procedure designed to obtain canonical metrics on connected sums of einstein four manifolds the main application is an existence result using two well known einstein manifolds as building blocks the fubini study metric on cp 2 and the product metric on s 2 s 2 using these metrics in various gluing configurations toric invariant critical metrics are found on connected sums for a specific riemannian functional which depends on the global geometry of the factors furthermore using certain quotients of s 2 s 2 as one of the gluing factors critical metrics on several non simply connected manifolds are also obtained

variable background born inversion by wavefield backpropagation the inverse scattering problem for an acoustic medium is formulated by using the variable background born approximation a constant density acoustic medium is probed by a wide band point source and the scattered field is observed along a curved receiver array located outside the region where the medium velocity is different from the assumed background velocity function the solution proposed relies on the introduction of a backpropagated field this field is obtained by using a finite difference scheme backward in time to backpropagate into the medium the scattered field observed along the receiver array the backpropagated field is imaged at the source travel times giving an image of the same type as obtained by reverse time finite difference migration techniques the gradient of this image is then taken along rays linking the source to points in the medium and after scaling this gives the reconstructed potential to relate the reconstructed potential to the true scattering potential high frequency

source receiver reverse time imaging of dual source vector acoustic seismic data abstractnovel technologies in seismic data acquisition allow for recording full vector acoustic va data pointwise recordings of pressure and its multicomponent gradient excited by pressure only as well as dipole gradient sources building on recent connections between imaging and seismic interferometry we present a wave equation based nonlinear reverse time imaging approach that takes full advantage of dual source multicomponent data the method s formulation relies on source receiver scattering reciprocity thus making proper use of va fields in the wavefield extrapolation and imaging condition steps in a self consistent manner the va imaging method is capable of simultaneously focusing energy from all in and outgoing waves the receiver side up and downgoing receiver ghosts fields are handled by the va receiver extrapolation whereas source side in and outgoing source ghosts arrivals are accounted for when combining dual source data at the imaging condition additionally va imaging handl

ricci curvature bounds and einstein metrics on compact manifolds where f mo m1 is a homeomorphism and dil f is the dilatation of f given by dil f supx x2 dist f x f x2 dist x1 x2 if mo and m1 are not homeomorphic define dl mo mi oo gromov 20 proves the remarkable result that the space of compact riemannian manifolds f a 3 d of sectional curvature iki 3 0 and diameter dm v and diameter dm c iki dm vm1 in particular gromov s compactness theorem may be strengthened to the statement that f a v d is c1 l compact in the lipschitz topology in this paper we study the question of lipschitz convergence of compact riemannian manifolds with bounds imposed on the ricci curvature ric in

gap phenomena and curvature estimates for conformally compact einstein manifolds author s li gang qing jie shi yuguang abstract in this paper we first use the result in 12 to remove the assumption of the l 2 boundedness of weyl curvature in the gap theorem in 9 and then obtain a gap theorem for a class of conformally compact einstein manifolds with very large renormalized volume we also uses the blow up method to derive curvature estimates for conformally compact einstein manifolds with large renormalized volume the second part of this paper is on conformally compact einstein manifolds with conformal infinities of large yamabe constants based on the idea in 15 we manage to give the complete proof of the relative volume inequality 1 9 on conformally compact einstein manifolds therefore we obtain the complete proof of the rigidity theorem for conformally compact einstein manifolds in general dimensions with no spin structure assumption cf 29 15 as well as the new curvature pinch estimates for conformally compact einstein manifolds with conformal infinities of very large yamabe constant we also derive the curvature estimates for conformally compact einstein manifolds with conformal infinities of large yamabe constant

proof of the positive mass theorem ii the positive mass theorem states that for a nontrivial isolated physical system the total energy which includes contributions from both matter and gravitation is positive this assertion was demonstrated in our previous paper in the important case when the space time admits a maximal slice here this assumption is removed and the general theorem is demonstrated abstracts of the results of this paper appeared in 11 and 13

removable singularities in yang mills fields we show that a field satisfying the yang mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite we obtain the result that every yang mills field overr4 with bounded functional l2 norm may be obtained from a field ons4 r4 hodge or coulomb gauges are constructed for general small fields in arbitrary dimensions including 4

on closed manifolds with harmonic weyl curvature abstract we derive point wise and integral rigidity gap results for a closed manifold with harmonic weyl curvature in any dimension in particular there is a generalization of tachibana s theorem for non negative curvature operator the key ingredients are new bochner weitzenbock lichnerowicz type formulas for the weyl tensor which are generalizations of identities in dimension four

critical riemannian 4 manifolds of m g and d is the volume element measured by g a critical point of sr g is called a critical metric on m that is the ricci tensor satisfies the critical equations grad srg 0 in particular for a compact 4 manifold m every einstein metric is a critical metric for sr on m recently gao g1 proved that the space of einstein metrics on a compact 4 manifold m has a certain compactness property in this paper we propose an extension of the compactness property for einstein metrics to critical metrics on a compact smooth riemannian 4 manifold m first we consider the subspace i m of all critical metrics on m with the injectivity radius bounded from below by a constant io 0 and diameter bounded from above by d then we are able to prove that i m is compact as a subset of moduli space of critical metrics in the ca topology more precisely we have the following theorem theorem a theorem 5 1 let i m be the subspace of all critical metrics on a compact 4 manifold m such that

wave field reciprocity and optimization in remote sensing a unified approach to local optimization techniques and wave field reciprocity as applied to constructing solutions to remote sensing imaging and inversion problems in acoustic elastic and electromagnetic wave theory is presented the starting point is a system of linear first order partial differential equations in space time of the class to which the indicated wave phenomena gives rise for this system three types of remote sensing problems the inverse source the inverse scattering and the inverse transducted wave field problems are formulated and the construction of their solutions via local optimization techniques is discussed emphasis is placed on iterative algorithms that are based on a guaranteed decrease in the mismatch between modelled and observed data at each update of the medium subsequently the wave field reciprocity theorems of the time convolution and the time correlation types are derived and their occurrence in the optimization procedures is discussed also attention is paid to approximate methods in particular to the rayleigh gans born approximation approximations of this sort provide the means to invoke the method of preconditioning in the process of inverting the operator equations exotic media for example chiral media in electromagnetics are included in the analysis

a critical appraisal of asymptotic 3d to 2d data transformation in full waveform seismic crosshole tomography abstractseismic full waveform inversion fwi is often based on forward modeling in the computationally attractive 2d domain this implies the assumption of a line source extended in the out of plane medium invariant direction with far field amplitudes decaying inversely with the square root of distance realistic point sources however generate amplitudes that decay approximately with the inverse of distance conventionally practitioners correct for this amplitude difference and the associated phase shift by transforming the recorded 3d field data to the approximate 2d equivalent by using simplistic asymptotic filter algorithms such filters assume straight raypaths a constant velocity medium and far field recordings we have assessed the validity of 3d to 2d data transformation in the context of crosshole seismic full waveform tomography by propagating 3d and 2d wavefields through 2d media and comparing 2d reference synthetics with their filtered 3d equivalent the filter performs well in simple si

the glivenko cantelli problem we give a new type of characterization of the glivenko cantelli classes in the case of a class mathscr l of sets the characterization is closely related to the configuration that the sets of mathscr l can have it allows one to decide simply whether a given class is a glivenko cantelli class the characterization is based on a new measure theoretic analysis of sets of measurable functions this analysis also gives an approximation theorem for glivenko cantelli classes sharpenings of the vapnik cervonenkis criteria and the value of the asymptotic discrepancy for classes that are not glivenko cantelli an application is given to the law of large numbers in a banach space for functions that need not be random variables

space of ricci flows i based on the compactness of the moduli of non collapsed calabi yau spaces with mild singularities we set up a structure theory for polarized kahler ricci flows with proper geo metric bounds our theory is a generalization of the structure theory of non collapsed kahler einstein manifolds as applications we prove the hamilton tian conjecture and the partial c 0 conjecture of tian

unified double and single sided homogeneous green s function representations in wave theory the homogeneous green s function consists of the impulse response to a point source minus its time reversal it can be represented by a closed boundary integral in many practical situations the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only the inherent approximations are acceptable as long as the effects of multiple scattering are negligible however in case of strongly inhomogeneous media the effects of multiple scattering can be severe we derive double and single sided homogeneous green s function representations the single sided representation applies to situations where the medium can be accessed from one side only it correctly handles multiple scattering it employs a focusing function instead of the backward propagating green s function in the classical double sided representation when reflection measurements are available at the accessible boundary of the medium the focusing function can be retrieved from these measurements throughout the paper we use a unified notation which applies to acoustic quantum mechanical electromagnetic and elastodynamic waves we foresee many interesting applications of the unified single sided homogeneous green s function representation in holographic imaging and inverse scattering time reversed wave field propagation and interferometric green s function retrieval

compact subsets of the first baire class perhaps the earliest results about pointwise compact sets of baire class 1 functions are the two selection theorems of e helly found in most of the standard texts on real variable see e g lo n these two theorems are really theorems about a particular example of a compact set of baire class 1 functions known today as helly space the space of all nondecreasing functions from the unit interval i 0 1 into itself more recently the notion of baire class 1 function turned out to also be important in some areas of functional analysis see r3 for example odell and rosenthal or showed that the double dual of a separable banach space e with the weak topology consists only of baire class 1 functions defined on the unit ball of e if and only if the space e contains no subspace isomorphic to 1 this resulted in a renewed interest in this class of spaces for example building on the work of rosenthal r2 bourgain fyemlin and talagrand bft proved analogues of the two theorems of helly for the whole first baire class using their results godefroy go showed that this class of spaces enjoys some interesting permanence properties for example if a compact space k is representable as a compact set of baire class 1 functions then so is p k the space of all radon probability measures on k with the weak topology some further permanence properties of this class of spaces were obtained by marciszewski ml m2 and an excellent survey of the early results is given by r pol po2 our paper is an attempt towards a fine structure theory of compact subsets of first baire class the first result that we give is a positive answer to a natural question one usually asks in such a context

a characterization of absolutely summing operators by means of mcshane integrable functions absolutely summing operators between banach spaces are characterized by means of mcshane integrable functions

regularity and compactness of harmonic einstein equations let m x g be pointed riemannian manifold with mathrm vol b 1 x ge mathrm v 0 and satisfy harmonic einstein equation mathrm ric g nabla u otimes nabla u lambda g with lambda le n 1 where u m g rightarrow n h is a harmonic map to a fixed compact riemannian manifold n h then for any p 1 we prove the l p curvature estimate open image in new window as a consequence if n h has nonpositive sectional curvature we have mathrm ric le c n mathrm v n that means harmonic einstein equation automatically implies bounded ricci curvature provided nonpositive sectional curvature of n h let x x infty d u infty be the limit of a sequence of harmonic einstein manifolds m i x i g i u i we show that the singular set of x is closed and the convergence is smooth on the regular part we also prove an orbifold type compactness theorem of harmonic einstein equations with bounded int m mathrm rm n 2 without assuming nonpositive sectional curvature of n h which generalizes xu s compactness result in yiyan adv math 231 2 680 708 2012

the construction of ale spaces as hyper kahler quotients on decrit la construction d une famille particuliere de 4 varietes hyper kahler les espaces asymptotiquement localement euclidiens ale on decrit une 4 variete de riemann avec juste une extremite qui a l infini ressemble au quotient r 4 de l espace euclidien r 4 par un groupe fini d identifications

absolutely summing operators and integration of vector valued functions abstract let be a complete probability space and u x y an absolutely summing operator between banach spaces we prove that for each dunford integrable i e scalarly integrable function f x the composition u f is scalarly equivalent to a bochner integrable function such a composition is shown to be bochner integrable in several cases for instance when f is properly measurable birkhoff integrable or mcshane integrable as well as when x is a subspace of an asplund generated space or a subspace of a weakly lindelof space of the form c k we also study the continuity of the composition operator f u f some other applications are given

a mass for alf manifolds we prove a positive mass theorem on alf manifolds i e complete noncompact manifolds that are asymptotic to a circle fibration over a euclidean base with fibers of asymptotically constant length

linear complementarity problem a novel approach to design finite impulse response wavefield extrapolation filters abstractin this paper the problem of complex valued finite impulse response fir wavefield extrapolation filter design was considered as a linear complementarity problem lcp lcp is not an optimization technique because there is no objective function to optimize however quadratic programming one of the applications of lcp can be used to find an optimal solution for the 1d fir wavefield extrapolation filter quadratic programs are an extremely important source of applications of lcp in fact several algorithms for quadratic programs are based on lcp we found that fir wavefield extrapolation filter design problem can be written as a quadratic program and then finally to an equivalent lcp there are two families of algorithms available to solve for lcp 1 direct pivoting based algorithms and 2 indirect iterative algorithms in this study the lcp has been solved using direct and indirect algorithms to show the effectiveness of the proposed method the seg eage salt velocity model data ha

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

einstein metrics and complex singularities this paper is concerned with the construction of special metrics on non compact 4 manifolds which arise as resolutions of complex orbifold singularities our study is close in spirit to the construction of the hyperkahler gravitational instantons but we focus on a different class of singularities we show that any resolution x of an isolated cyclic quotient singularity admits a complete scalar flat kahler metric which is hyperkahler if and only if k x is trivial and that if k x is strictly nef then x also admits a complete non kahler self dual einstein metric of negative scalar curvature in particular complete self dual einstein metrics are constructed on simply connected non compact 4 manifolds with arbitrary second betti number

regularity for the harmonic einstein equation abstract we establish a regularity theorem for the harmonic einstein equation as a byproduct of the local regularity we also have a compactness theorem on the harmonic einstein equation the method is mainly the moser iteration technique which has been used and developed by bando et al 1989 4 tian 1990 22 tian and viaclovsky 2005 23 and others

refined kato inequalities and conformal weights in riemannian geometry abstract we establish refinements of the classical kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first order linear differential operator our main result is a general expression which gives the value of the constants appearing in the refined inequalities these constants are shown to be optimal and are computed explicitly in most practical cases

virtual reflector representation theorem acoustic medium the virtual reflector method simulates new seismic signals by processing traces recorded by a plurality of sources and receivers the approach is based on the crossconvolution of the recorded signals and makes it possible to obtain the green s function of virtual reflected signals as if in the position of the receivers or sources there were a reflector even if said reflector is not present this letter presents the virtual reflector theory based on the kirchhoff integral representation theorem for wave propagation in an acoustic medium with and without boundary and a generalization to variable reflection coefficients for scattered wavefields