kernel density estimation for linear processes in this paper we provide a detailed characterization of the asymptotic behavior of kernel density estimators for one sided linear processes the conjecture that asymptotic normality for the kernel density estimator holds under short range dependence is proved under minimal assumptions on bandwidths we also depict the dichotomous and trichotomous phenomena for various choices of bandwidths when the process is long range dependent

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane this paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance the solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary and the discussion of the paper is motivated by this application the paper starts by deriving representations as laplace type integrals of the solution and its first partial derivatives the evaluation of these integral representations by gauss laguerre quadrature is discussed and theoretical bounds on the truncation error are obtained specific approximations are proposed which are shown to be accurate except in the very near field for all angles of incidence and a wide range of values of surface impedance the paper finishes with derivations of partial results and analogous laplace type integral representations for the case of a point source

density estimation under long range dependence dehling and taqqu established the weak convergence of the empirical process for a long range dependent stationary sequence under gaussian subordination we show that the corresponding density process based on kernel estimators of the marginal density converges weakly with the same normalization to the derivative of their limiting process the phenomenon which carries on for higher derivatives and for functional laws of the iterated logarithm is in contrast with independent or weakly dependent situations where the density process cannot be tight in the usual function spaces with supremum distances

the periodicity in stable equivariant surgery the classical surgery theory see 5 and 23 computes the structure set sm m rel of manifolds homotopy equivalent to m relative to the boundary siebenmann showed that in topological category the structure set is 4 periodic sm m rel sm 4 m d4 rel up to a copy of see 12 cappell and weinberger gave a geometric interpretation of this periodicity in 8 by using weinberger s stratified surgery theory see 24 we extend this to an equivariant periodicity result for topological manifolds with homotopically stratified actions by compact lie groups with d4 replaced by the unit ball of certain group representations in particular if g is an odd order group acting on a topological manifold m then the equivariant stable structure sets satisfy s m rel s m d 4 g rel up to copies of 1993 john wiley sons inc

hybrid fourier pseudospectral discontinuous galerkin time domain method for wave propagation the fourier pseudospectral time domain fourier pstd method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized euler equations lee but is limited to real valued frequency independent boundary conditions and predominantly staircase like boundary shapes this paper presents a hybrid approach to solve the lee coupling fourier pstd with a nodal discontinuous galerkin dg method dg exhibits almost no restrictions with respect to geometrical complexity or boundary conditions the aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of dg at the boundaries while keeping the efficient fourier pstd in the bulk of the domain the hybridization approach is based on conformal meshes to avoid spatial interpolation of the dg solutions when transferring values from dg to fourier pstd while the data transfer from fourier pstd to dg is done utilizing spectral interpolation of the fourier pstd solutions the accuracy of the hybrid approach is presented for one and two dimensional acoustic problems and the main sources of error are investigated it is concluded that the hybrid methodology does not introduce significant errors compared to the fourier pstd stand alone solver an example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach finally no instabilities were found during long time calculation using the current hybrid methodology on a two dimensional domain a method for wave propagation in fluid domains with complex geometries is presented the method combines fourier pstd in the bulk of the domain and dg at boundaries the main application of interest is atmospheric sound propagation in cities the method shows no significant additional error compare with a fourier pstd solver no indication of instability in long time calculations has been detected

simple conformal methods for finite difference time domain modeling of pressure release surfaces the finite difference time domain fdtd method provides a simple and accurate means of simulating a wide range of acoustic wave propagation problems unfortunately the method has a voracious appetite for computational resources for example to accurately model scattering from a continuously varying pressure release boundary an fdtd grid is typically required that has a much finer discretization than is necessary to model propagation in a homogeneous space such a fine discretization can become prohibitive when considering large scale problems two simple conformal techniques are presented for acoustic fdtd simulations of problems involving pressure release boundaries these techniques which rely upon splitting velocity cells adjacent to the pressure release boundary significantly improve the accuracy of the results over those of the standard staircase representation of the boundary these methods permit the use of a coarser fdtd grid than would otherwise be practical and yet add negligible computa

stratified path spaces and fibrations the main objects of study are the homotopically stratified metric spaces introduced by quinn closed unions of strata are shown to be stratified forward tame stratified fibrations between spaces with stratifications are introduced paths which lie in a single stratum except possibly at their initial points form a space with a natural stratification and the evaluation map from that space of paths is shown to be a stratified fibration applications to mapping cylinders and to the geometry of manifold stratified spaces are expected in future papers

constructing approximate fibrations in this paper two results concerning the construction of approximate fibrations are established the first shows that there are approximate fibrations p m s2 which are homotopic to bundle maps but which cannot be approximated by bundle maps here m can be a compact q manifold or some topological n manifold n 5 the second shows how to construct approximate fibrations p m b whose fibers do not have finite homotopy type for any b of euler characteristic zero here m can be a compact q manifold and b only has to be an anr or m can be an n manifold n 6 and b must then also be a topological manifold

regularity of skorohod integral processes based on integrands in a finite wiener chaos letf be a square integrable kernel on them dimensional unit cube u the skorohod integral process in themth wiener chaos associated with it isoperimetric inequalities for functions on wiener space yield the exponential integrability of the increments ofu to this result we apply the majorizing measure technique to show thatu possesses a continuous version and give an upper bound of its modulus of continuity

the k theoretic farrell jones conjecture for hyperbolic groups we prove the k theoretic farrell jones conjecture for hyperbolic groups with twisted coefficients in any associative ring with unit

rigidity and crystallographic groups i this is the first in a series of articles about rigidity theorems for crystallographic groups the main theorem is 1 1 it is an h cobordism rigidity statement it implies see 1 6 that any crystallographic manifold with odd order holonomy which is h cobordant and simply homotopically equivalent to the standard one is actually homeomorphic to it in the second part of this work 9 we will exploit this result to prove that one can remove the word h cobordant from the previous sentence the main theorem concerns an involution on the group wh p mr this is the group of g h cobordisms of the flat torus mr of a crystallographic group f with holonomy group g definitions of these terms appear in 1 4 we prove a vanishing result of the tate cohomology

approximation by equivariant homeomorphisms i locally linear locally smoothable actions of finite groups on finite dimensional manifolds are considered in which two incident components of fixed point sets of subgroups either coincide or one has codimension at least three in the other for these actions an equivariant o approximation theorem is proved using engulfing techniques as corollaries are obtained equivariant fibrations are bundles and controlled h cobordism theorems as well as an equivariant version of edwards cell like mapping theorem and the vanishing of the set of transfer invariant g homotopy topological structures rel bound ary on tn x dp when tn is the n torus with trivial g action and dp is a representation disc here we consider locally linear locally smooth br pl and topological actions of a finite group g on n manifolds in addition we require that a g manifold m have gaps of codimension 3 i e for h c g if mh is a component of the h fixed point set mh and m h c mh is the subspace of points x for which the isotropy subgroup gx strictly contains h then either m h mh or m h has codimension 3 in mh we shall use the term not necessarily locally linear g manifold when we wish to drop the local linearity hypothesis but retain the property that if mh c m but mh m then mh is a locally flat inequivariantly submanifold of mk of codimension at least three this while self contained is the second in a series of papers sw2 8 s in which we analyze the extent of failure of the topological invariance of equivari ant whitehead torsion and the consequent failure of subgroups of the equivariant whitehead group whgl m of illman ill cf rothenberg r to classify pl or smooth g h cobordisms up to topological equivalence under our gap hypotheses the arguments of browder and quinn bq and rothenberg r show that g h cobordisms are classified up to pl or smooth equivalence by such subgroups we eventually conclude in sw7 s cf sw2 that the topological equivalence classes of g h cobordisms on a g manifold m that are products over the union of fixed point components of m having dimension 5 are classised by a group whg p m to which whgl m maps homomorphically the image in whg p m of the per tinent subgroup of whgl m classifies up to equivariant homeomorphism rel m those g h cobordisms on m that admit equivariant handlebody decompositions relative to m this homomorphism is not generally surjective and there are g h cobordisms that do not admit such handle decompositions cf sw5 s in order

stratified fiber bundles quinn homology and brane stability of hyperbolic orbifolds we revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and k homology we propose a definition of type ii string theory on such backgrounds that further carry stratified systems of fiber bundles which generalize the more conventional orbifold and symmetric string backgrounds together with a classification of wrapped branes by a suitable generalized homology theory for spaces stratified fibered over hyperbolic orbifolds we use the algebraic k theory of their fundamental groups and quinn homology to derive criteria for brane stability in terms of an atiyah hirzebruch type spectral sequence with its lift to k homology stable d branes in this setting carry stratified charges which induce new additive structures on the corresponding k homology groups we extend these considerations to backgrounds which support h flux where we use k groups of twisted group algebras of the fundamental groups to analyze stability of locally symmetric spaces with k amenable isometry groups and derive stability conditions for branes wrapping the fibers of an eilenberg maclane spectrum functor

the law of the iterated logarithm for self similar processes represented by multiple wiener integrals on etablit une loi du logarithme itere fonctionnelle pour certains processus autosimilaires qui sont des images applications continues du mouvement brownien et on obtient le resultat desire en utilisant l approximation par de tels processus

strong invariance principles for sequential bahadur kiefer and vervaat error processes of long range dependent sequences in this paper we study strong approximations invariance principles of the sequential uniform and general bahadur kiefer processes of long range dependent sequences we also investigate the strong and weak asymptotic behavior of the sequential vervaat process that is the integrated sequential bahadur kiefer process properly normalized as well as that of its deviation from its limiting process the so called vervaat error process it is well known that the bahadur kiefer and the vervaat error processes cannot converge weakly in the i i d case in contrast to this we conclude that the bahadur kiefer and vervaat error processes as well as their sequential versions do converge weakly to a dehling taqqu type limit process for certain long range dependent sequences

the extended fourier pseudospectral time domain method for atmospheric sound propagation an extended fourier pseudospectral time domain pstd method is presented to model atmospheric sound propagation by solving the linearized euler equations in this method evaluation of spatial derivatives is based on an eigenfunction expansion evaluation on a spatial grid requires only two spatial points per wavelength time iteration is done using a low storage optimized six stage runge kutta method this method is applied to two dimensional non moving media models one with screens and one for an urban canyon with generally high accuracy in both amplitude and phase for a moving atmosphere accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen the method has also been validated for three dimensional sound propagation over a screen for that application the developed method is in the order of 100 times faster than the second order accurate fdtd solution to the linearized euler equations the method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated

an end theorem for stratified spaces we show that a manifold stratified space x is the interior of a compact manifold stratified space with boundary if and only if x is tame ended and a k theoretic obstruction x vanishes the obstruction x is a localization of quinn s mapping cylinder neighborhood obstruction the main results are theorem 1 6 and theorem 1 7 below in particular this explains when a g manifold is the interior of a compact g manifold with boundary one of our methods is a new transversality theorem theorem 1 16

whitehead groups and the bass conjecture this paper will be concerned with proving that certain whitehead groups of torsion free elementary amenable groups are torsion groups and related results and then applying these results to the bass conjecture in particular we shall establish the strong bass conjecture for an arbitrary elementary amenable group

geometric transfer and the homotopy type of the automorphism groups of a manifold introduction for m a compact manifold with or without boundary in one of the categories diff pl or top we denote by a m the semisimplicial ss group of automorphisms of m i e the group of diffeomorphisms pl homeomorphisms or homeomorphisms resp in this paper we describe in the stability range and localized away from two the homotopy structure of a m we do this in terms of a m the ss group of block automorphisms whose homotopy structure is a sophisticated formulation of surgery theory abk and some new homotopy functors 5 theorem c the functors 5 and 5 l here considered have already been studied in the pl category by hatcher h from a different point of view the present geometric description is appropriate to the description of the homotopy structure of a m and enables us to produce a natural map b sc x 5 x from the associative monoid of simple homotopy equivalence of x to 5 x which will be important for our study besides the geometric topology results blr two ideas partially developed in bli are basic the first is the transfer map and stability for concordances described in the pl context by hatcher and in the differentiable context in bli the second is the splitting of a z 1 weak commutative topological group with involution as a product up to homotopy of two pieces the symmetric respectively antisymmetric parts applied to our situation those parts manifest very different behavior the results of this paper have been sketched by the first author in the survey paper b there is an overlap between some but not all results of a and results of hatcher h2 published in the same volume as b the results of this paper are stated in the next section statement of results and the proofs are given in subsequent sections we continue this section with a description of the notations used

a multi domain fourier pseudospectral time domain method for the linearized euler equations the fourier pseudospectral time domain f pstd method is computationally one of the most cost efficient methods for solving the linearized euler equations for wave propagation through a medium with smoothly varying spatial inhomogeneities in the presence of rigid boundaries as the method utilizes an equidistant discretization local fine scale effects of geometry or medium inhomogeneities require a refinement of the whole grid which significantly reduces the computational efficiency for this reason a multi domain f pstd methodology is presented with a coarse grid covering the complete domain and fine grids acting as a subgrid resolution of the coarse grid near local fine scale effects data transfer between coarse and fine grids takes place utilizing spectral interpolation with super gaussian window functions to impose spatial periodicity local time stepping is employed without intermediate interpolation the errors introduced by the window functions and the multi domain implementation are quantified and compared to errors related to the initial conditions and from the time iteration scheme it is concluded that the multi domain methodology does not introduce significant errors compared to the single domain method examples of scattering from small scale density scatters sound reflecting from a slitted rigid object and sound propagation through a jet are accurately modelled by the proposed methodology for problems that can be solved by f pstd the presented methodology can lead to a significant gain in computational efficiency

algebraic k theory of virtually free groups we provide a general procedure for computing the algebraic k theory of finitely generated virtually free groups the procedure describes these groups in terms of the algebraic k theory of various finite subgroups and various farrell nil groups we illustrate this process by carrying out the computation for several interesting classes of examples the first two classes serve as a check on the method and show that our algorithm recovers results that already exist in the literature the last two classes of examples yield new computations

application of the fourier pseudospectral time domain method in orthogonal curvilinear coordinates for near rigid moderately curved surfaces the fourier pseudospectral time domain method is an efficient wave based method to model sound propagation in inhomogeneous media one of the limitations of the method for atmospheric sound propagation purposes is its restriction to a cartesian grid confining it to staircase like geometries a transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries for applicability of this method near the boundaries the acoustic velocity variables are solved for their curvilinear components the performance of the curvilinear fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain the applicability of the curvilinear fourier pseudospectral time domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer with the proposed method accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained

isomorphism conjectures in algebraic k theory duff in this paper we are concerned with the four functors y y3 if and which map from the category of topological spaces x to the category diff of q spectra the functor 3 or if maps the space x to the qspectrum of stable topological or smooth pseudoisotopies of x the spaces diff dif 3i x id9 x i 0 are hatcher s deloopings of 970 x yd x cf 29 the functor j maps a path connected space x to the algebraic ktheoretic s2 spectrum for the integral group ring z7r1x the spaces x x i 0 are the gersten wagoner deloopings of z o x cf 27 52 5 x is also defined on a nonpath connected space x to be x1 where xi i e i are the path components of x and ii xi indicates the direct limit of all finite products of the i xi i e i if x is path connected then the functor maps x to the l surgery classifying spaces for oriented surgery problems with fundamental group r i1x identified by their fourfold periodicity k 90 x k 4j x cf 35 39 44 47 in addition if x is not path connected then we set y77 x tiei5 fj xi where xi i e i are the path components of x results obtained by the authors over the past five years cf 15 25 and in particular 19 16 a 1 a 18 together with many earlier results and conjectures which are reviewed in 1 6 1 1 6 6 suggest that for any connected cwcomplex x and for 5 denoting any of the above functors the q spectrum x should be computable in a simple way from the values taken by 9 on covering spaces of x which have very simple fundamental groups in more detail we let 9 x denote the collection of all subgroups h c ir ix which are either finite or virtually infinite cyclic a group h is virtually infinite cyclic if there is a short exact sequence of groups 1 z h f 1 with f equal to a finite group and z equal to the infinite cyclic group for each such group we let xh x denote the covering space projection corresponding to h then the q spectrum 5 x should be computable in a simple way from the q spectra 5 xh h e 9 x the purpose of this paper is to formulate precisely a conjecture along these lines and to verify the conjecture for any x

the empirical process of some long range dependent sequences with an application to u statistics let x j infty j 1 be a stationary mean zero gaussian process with covariances r k ex k 1 x 1 satisfying r 0 1 and r k k d l k where d is small and l is slowly varying at infinity consider the two parameter empirical process for g x j bigg f n x t frac 1 n sum lbrack nt rbrack j 1 lbrack 1 g x j leq x p g x 1 leq x rbrack infty x infty 0 leq t leq 1 bigg where g is any measurable function noncentral limit theorems are obtained for f n x t and they are used to derive the asymptotic behavior of some suitably normalized von mises statistics and u statistics based on the g x j s the limiting processes are structurally different from those encountered in the i i d case

convergence rates in density estimation for data from infinite order moving average processes the effect of long range dependence in nonparametric probability density estimation is investigated under the assumption that the observed data are a sample from a stationary infinite order moving average process it is shown that to first order the mean integrated squared error mise of a kernel estimator for moving average data may be expanded as the sum of mise of the kernel estimator for a same sizerandom sample plus a term proportional to the variance of the moving average sample mean the latter term does not depend on bandwidth and so imposes a ceiling on the convergence rate of a kernel estimator regardless of how bandwidth is chosen this ceiling can be quite significant in the case of long range dependence we show thatall density estimators have the convergence rate ceiling possessed by kernel estimators

the functional iterated logarithm law for stochastic processes represented by multiple wiener integrals in a previous paper the authors obtained a functional law of the iterated logarithm for a class of self similar processes bar x with stationary increments which are represented by multiple wiener integrals this result is extended to a certain class of processes represented by multiple wiener integrals which converge to bar x with an appropriate normalization as an application a functional log log law for nonlinear functionals of some stationary gaussian processes is given

bounded homotopy equivalences of hilbert cube manifolds let m and f be hubert cube manifolds with f compact the purpose of this paper is to study homotopy equivalences m r x f which have bounded control in the redirection roughly these homotopy equivalences form a semi sim plicial complex 4 rm x f the controlled whitehead space using results about approximate fibrations rm x f is related to the semi simplicial complex of bounded concordances on r x f then the homotopy groups of rm x f are computed in terms of the lower algebraic at theoretic functors k i 1 introduction let f be a compact hilbert cube manifold we are interested in homotopy equivalences m rm x f which are controlled in the redirection where m is also a hilbert cube manifold to say is controlled in the redirection means that pf m rm is an approximate fibration where p rm x f rm is projection the collection of all such homotopy equivalences which are additionally given to be retractions onto the collared submanifold rm x f of m form the vertices of a semi simplicial complex ta rm x f see 2 for the precise definition the main result of this paper is the computation of the homotopy groups of wa rm x f see corollary 1 below in order to do this we relate wa rm x f to the semi simplicial complex h rm x f of bounded concordances on rm x f an simplex of eb rm x f is a homeomorphism

higher dimensional manifolds with s1 category 2 a closed topological n manifold mn is of s1 category 2 if it can be covered by two open subsets w1 w2 such that the inclusions wi mn factor homotopically through maps wi s1 we show that for n 3 if rm cat s 1 m n 2 then mn is homeomorphic to sn or sn 1 s1 or the non orientable sn 1 bundle over s1 we also obtain an unknotting theorem for locally flat knots of sn 2 in sn and a characterization of s1 sn 1

limit theorems for non linear functionals of gaussian sequences we prove limit theorems for sums of non linear functionals of gaussian sequences in certain cases we obtain a non gaussian limit with a norming factor n 0 1 2 the class of functionals we are investigating is a natural enlargement of the class investigated by m rosenblatt in 7 we prove our results by refining the method of the paper 3

group actions and equivariant lipschitz analysis the idea that one could prove by analytic methods the topological invariance of characteristic classes was suggested in an influential lecture by singer the concrete realization of this in the case of rational pontrjagin classes was the result of works by sullivan who showed that topological manifolds have essentially unique lipschitz structures and teleman who showed that lipschitz manifolds are the type of object for which one can analyze the signature operator a refinement of the same method proves the ko l 2 orientability of topological bundles much of this can be done for manifolds with group actions the main implication is that for certain sorts of topological group actions including all smooth and pl actions one can construct an equivariant signature operator whose class in equivariant if homology is a topological invariant this class satisfies the g signature theorem the topological method has implications for various precise classification problems e g semifree topological actions on the sphere but here we shall present only the consequences of these lipschitzian ideas a topologically locally linear g manifolds for odd order g have kog 1 2 orientations madsen rothenberg for all finite g there are lipschitz structures but the signature class is a zero divisor for even order groups the same method produces upon application of the localization theorem atiyah singer classes for some actions with nonmanifold fixed set weinberger extending earlier joint work with cappell b for odd order groups topological and linear conjugacy of linear representations are equivalent hsiang pardon madsen rothenberg this is a consequence of a alternatively one can return to the original argument of atiyah bott milnor for semifree representations a stronger result is true the atiyah bott local numbers associated to representations agree for elements that have discrete fixed sets in topologically equivalent representations this distinguishes many pairs of representations of even order groups c r top g r lip g for all finite g where r cat is the grothendieck group of representations up to cat conjugacy weinberger after inverting 2 this implies that there is no analytic definition of reidemeister torsion that works well in the lipschitz setting the reason is that following

on the farrell jones conjecture for higher algebraic k theory here b is the classifying space of the group and we denote by k r the non connective algebraic k theory spectrum of the ring r the homotopy groups of this spectrum are denoted kn r and coincide with quillen s algebraick groups of r qui73 in positive dimensions and with the negative k groups of bass bas68 in negative dimensions the homotopy groups of the spectrum x k r are denotedhn x k r they yield a generalized homology theory and in particular standard computational tools such as the atiyah hirzebruch spectral sequence apply to the left hand side of the assembly map above as a corollary of the main result of this paper we prove conjecture 1 1 in the case where is the fundamental group of a closed riemannian manifold with strictly negative sectional curvature in fact our result is more general and applies to group rings r where r is a completely arbitrary coefficient ring note that if one replaces in conjecture 1 1 the coefficient ring z by an arbitrary coefficient ringr the corresponding conjecture would be false already in the simplest non trivial case if c is the infinite cyclic group the bass heller swan formula bhs64 gra76 p 236 for kn rc kn r t 1 yields that kn rc kn 1 r kn r nkn r nkn r where nkn r is defined as the cokernel of the split inclusion kn r kn r t and does not vanish in general but since s is a model for bc one obtains on the left hand side of the assembly map only hn bc k r kn r kn 1 r

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

identifying assembly maps in k and l theory in this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in k and l theory and c theory

the farrell jones isomorphism conjecture for finite covolume hyperbolic actions and the algebraic theory of bianchi groups we prove the farrell jones isomorphism conjecture for groups acting properly discontinuously via isometries on real hyperbolic n space ihin with finite volume orbit space we then apply this result to show that for any bianchi group f wh f ko zr and ki zr vanish for i 1

fourier continuation methods for high fidelity simulation of nonlinear acoustic beams on the basis of recently developed fourier continuation fc methods and associated efficient parallelization techniques this text introduces numerical algorithms that due to very low dispersive errors can accurately and efficiently solve the types of nonlinear partial differential equation pde models of nonlinear acoustics in hundred wavelength domains as arise in the simulation of focused medical ultrasound as demonstrated in the examples presented in this text the fc approach can be used to produce solutions to nonlinear acoustics pdes models with significantly reduced discretization requirements over those associated with finite difference finite element and finite volume methods especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths in these examples the fc methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches a variety of one and two dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology including an example containing a number of scattering centers and nonlinear multiple scattering events

approximately fibering a manifold over an aspherical one the paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers i e is homotopic to manifold approximate fibration we define obstructions in algebraic k theory their vanishing is necessary and under certain conditions sufficient basic ingredients are quinn s thin h cobordism theorem and end theorem and knowledge about the farrell jones conjectures in algebraic k and l theory and the maf rigidity conjecture by hughes taylor williams

on the k theory of crystallographic groups for any crystallographic group f we show that the groups ki t are isomorphic via the forget control map to the controlled a groups ki r c for all 0