some remarks on the segal and sullivan conjectures introduction the recurrent theme of this paper is the concept of invariance introduced in 1 let g be a finite group and let hg q denote the homotopy category of g cw complexes given a set f of morphisms of our category a functor h defined on hg q is said to be g invariant if it carries each element of p to an isomorphism maps in hg q are determined by fixed point data accordingly we obtain interesting sets of morphisms by considering the so called sc equivalences here 3c is a collection of subgroups of g and a map f x y is an sc equivalence if h xh yh is a homotopy equivalence for each h e sc we then say that h is sc invariant if it inverts all the sc equivalences the smaller sc is the stronger the statement becomes since less and less data is required of a map to ensure that it is inverted by h the generalization of the segal conjecture proved in 1 produces the smallest class of subgroups sc such that the functor s i7r is sc invariant s 17r i denotes pro group valued equivariant stable cohomotopy localized at a multiplicatively closed subset s of the burnside ring a g and completed at an ideal i c a g the class sc admits a description given entirely in terms of s and i but does nonetheless depend on the cohomology theory 7 rg indeed while equivariant k theory enjoys a similar even stronger property 2 this is not so for an arbitrary a g module valued theory h g our first objective will be to produce a collection 3c s i of subgroups such that s h is 3c s i invariant for a large class of cohomology theories h namely those representable by g spectra families i e collections i of subgroups that are closed under taking subconjugates play a privileged role in our context this is due to the existence of a space el which is i equivalent to a point and yet is i isotropic namely ejk 0 unless k e i it follows that there exists a universal

correction to the sullivan conjecture on maps from classifying space on page 49 i assert that given an unstable coalgebra c over the mod p steenrod algebra a c e ca the module of primitives pc is the suspension of an unstable a module e pc e u this is true for p 2 but certainly false for p 2 consider for instance the a coalgebra h bzp which plays such a large role in this paper this error makes nonsense of the spectral sequence 2 5 ext m 1rp cp ext s e ma c which is central to the proof of the sullivan conjecture however we may proceed as follows consider instead of the category u the category v of a modules satisfying the modified unstable condition xpt ofor lxi 2pt

a simplified algorithm for the second order sound fields an analytical description for the second order field of the sum difference frequency and second harmonic components is derived this treatment is based on the fact that an arbitrary axially symmetric beam can be expressed as the linear superposition of a set of gaussian beams j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 so that the three dimensional integral for the second order components is typically expressed as a combination of a set of interaction terms of the gaussian beams correspondingly the evaluation of the field distribution is reduced to the summation of exponential integral functions from some examples the present approach provides the results for the second order field which are in good agreement with those obtained directly by numerical integration

lattice basis reduction improved practical algorithms and solving subset sum problems we report on improved practical algorithms for lattice basis reduction we present a variant of the l3 algorithm with deep insertions and a practical algorithm for blockwise korkine zolotarev reduction a concept extending l3 reduction that has been introduced by schnorr 1987 empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 58 random weights of arbitrary bit length within at most a few hours on a unisys 6000 70 or within a couple of minutes on a sparc 2 computer

towers and injective cohomology algebras since carlsson s paper 5 and the work of lannes and zarati 9 topo1ogists have learned to recognize many spaces y so h y is injective in u for example if g is a finite group with p sylow subgroup z p kn the h bg is injective further infinite examples include eb z p k and any of the many wedge summands of these spaces a complete classification of u injectives is given in 18 and from this it can be seen that the only such injectives which are not a unbounded are the brown gitler modules these have been adequately discussed elsewhere see 6 among many an immediate consequence of theorem a will be the following result suppose y satisfies the same hypotheses as in theorem a

deconstructing hopf spaces we characterize hopf spaces with finitely generated cohomology as an algebra over the steenrod algebra we deconstruct the original space into an h space y with finite mod p cohomology and a finite number of p torsion eilenberg mac lane spaces we give a precise description of homotopy commutative h spaces in this setting

low sidelobe limited diffraction beams in the nonlinear regime in linear propagation sidelobe levels of bessel limited diffraction beams are only about 8 db down relative to the mainlobe in the nonlinear regime these beams will have a region near the source where the side lobe level of the second harmonic is 16 db down but this region has usually been considered to be so small that it is of little practical interest in this paper it is shown that when there are only 1 to 3 sidelobes in a finite aperture bessel beam the second harmonic field will have low sidelobes for distances up to half of the depth of field this result is backed up by simulations in a medium with absorption previous theory has shown that the sidelobes of the bessel beam will also be reduced but only for absorption that was too high to be of practical use simulations presented here show that for breast tissue which only has about 10 of the absorption of previous criteria one will still get sidelobes which are comparable to that of a rectangular aperture even when the sidelobes would be high in a non absorbing medium

homotopy and homology of simplicial abelian hopf algebras let a be a simplicial bicommutative hopf algebra over the field mathbb f 2 with the property that pi 0a cong mathbb f 2 we show that pi ast a is a functor of the andre quillen homology of a where a is regarded as an mathbb f 2 algebra then we give a method for calculating that andre quillen homology independent of knowledge of pi ast a

the classification of p compact groups for p odd a p compact group as defined by dwyer and wilkerson is a purely homotopically defined p local analog of a compact lie group it has long been the hope and later the conjecture that these objects should have a classification similar to the classification of compact lie groups in this paper we finish the proof of this conjecture for p an odd prime proving that there is a one to one correspondence between connected p compact groups and finite reflection groups over the p adic integers we do this by providing the last and rather intricate piece namely that the exceptional compact lie groups are uniquely determined as p compact groups by their weyl groups seen as finite reflection groups over the p adic integers our approach in fact gives a largely self contained proof of the entire classification theorem for p odd

second harmonic generation of practical bessel beams a fast gaussian expansion approach is used to investigate fundamental and second harmonic generation in practical bessel beams of finite aperture the analysis is based on the integral solutions of the kzk equation under the quasilinear approximation the influence of the medium s attenuation on the beam profile is considered analysis results show that the absorption parameter has a significant effect on the far field beam profile of the second harmonic under certain circumstances the second harmonic of a practical bessel beam still has the main properties of an ideal bessel beam of infinite aperture when it propagates within its depth of field

low complexity sphere decoding algorithm for quasi orthogonal space time block codes space time codes can be decoded by the sphere decoding sd algorithm to reduce the complexity and retain maximum likelihood ml performance in this letter the ml metric of quasi orthogonal space time block codes is written into two independent euclidean norms thus sd can be applied to each function independently the new scheme reduces the complexity by at least 85 for systems with four or more transmit antennas compared with the conventional sd algorithm

nonlinear effects in the farfield of a directive sound source nonlinear propagation of a periodic sound beam in a dissipative fluid is considered using fourier series expansion and numerical methods to solve the governing equation of motion in the parabolic approximation the nearfield was considered in a previous paper aanonsen et al j acoust soc am 75 749 768 1984 the analysis is now extended to the farfield numerical and asymptotic results are derived and used to explain the development of the fundamental and harmonic components from the nearfield into the farfield a discussion is also given of some earlier models for the farfield of directional waves emphasis is put on the importance of imposing the proper matching conditions between the nearfield solution and the spherical solution in the farfield in order to obtain a good approximation propagation and saturation curves are calculated as well as beam patterns for various harmonic components the results are compared with available experimental observations nonlinear effects although generated

a gaussian finite element method for description of sound diffraction a new method for solving diffraction problems is presented it is based on the use of gaussian diffraction theory comparison of the gaussian beam expansion and fourier series expansion reveals that the gaussian expansion is a more general and more powerful technique the new method combines the gaussian beam superposition technique wen and breazeale j acoust soc am 83 1752 1756 1988 and the numerical finite element solution to the parabolic equation huang j acoust soc am 84 1405 1413 1988 the new method is capable of solving for the sound field even in an inhomogeneous medium or in the presence of reflection as shown by computer modeling the source may be a gaussian source or a distributed source calculated results are compared with experimental results in a laboratory water tank

localization and periodicity in unstable homotopy theory in this paper we develop a hierarchy of natural localizations of spaces called the vn periodizations for n 0 which may be used to expose and study periodic phenomena in unstable homotopy theory these vn periodizations act less radically than the corresponding homological localizations 2 and respect fibrations to a very considerable extent a major part of this paper is devoted to developing the general theory of periodizations of spaces thereby providing a foundation for the study of the vn periodization and many others some of this general theory has been developed independently by dror farjoun 13 14 and we refer the reader to his work for an alternative approach with other interesting general results during the past decade remarkable progress was made by ravenel hopkins devinatz and smith 12 16 17 33 toward a global understanding of stable periodic phenomena and we hope that the present paper will help to prepare the way for a similar understanding of unstable periodic phenomena an excellent exposition of localization and periodicity in stable homotopy theory is now available in ravenel s book 35 major features of stable homotopy are understood chromatically as manifestations of more basic periodic phenomena these phenomena belong to a hierarchy starting with those detected rationally followed by those detected in classical k theory and in the successive morava k theories most fundamentally each finite cw spectrum has an intrinsic periodicity given by a vn self map which becomes a selfequivalence after suitable localization for simplicity we describe our results in the pointed homotopy category hoo of connected cw complexes for spaces w y e hoo we call y w periodic or w local when the pointed mapping space map w y is contractible or equivalently when xt w y for t 0 as shown more generally in 3 corollary 7 2 10 or 13 there is a natural initial example x pwx of a map from x to a w periodic space pwx in hoo and we call this the w periodization or w localization of x our notation is derived from the classical example where w sn l and pwx is the n th postnikov section

on maximum likelihood detection and the search for the closest lattice point maximum likelihood ml decoding algorithms for gaussian multiple input multiple output mimo linear channels are considered linearity over the field of real numbers facilitates the design of ml decoders using number theoretic tools for searching the closest lattice point these decoders are collectively referred to as sphere decoders in the literature in this paper a fresh look at this class of decoding algorithms is taken in particular two novel algorithms are developed the first algorithm is inspired by the pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the viterbo boutros sphere decoder the connection between the proposed algorithm and the stack sequential decoding algorithm is then established this connection is utilized to construct the second algorithm which can also be viewed as an application of the schnorr euchner strategy to ml decoding aided with a detailed study of preprocessing algorithms a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near ml detection performance this claim is supported by intuitive arguments and simulation results in many relevant scenarios

the bar complex of an e infinity algebra the standard reduced bar complex b a of a differential graded algebra a inherits a natural commutative algebra structure if a is a commutative algebra we address an extension of this construction in the context of e infinity algebras we prove that the bar complex of any e infinity algebra can be equipped with the structure of an e infinity algebra so that the bar construction defines a functor from e infinity algebras to e infinity algebras we prove the homotopy uniqueness of such natural e infinity structures on the bar construction we apply our construction to cochain complexes of topological spaces which are instances of e infinity algebras we prove that the n th iterated bar complexes of the cochain algebra of a space x is equivalent to the cochain complex of the n fold iterated loop space of x under reasonable connectedness completeness and finiteness assumptions on x

postnikov pieces and bz p homotopy theory we present a constructive method to compute the cellularization with respect to b m z p for any integer m 1 of a large class of h spaces namely all those which have a finite number of non trivial b m z p homotopy groups the pointed mapping space map b m z p x is a postnikov piece we prove in particular that the b m z p cellularization of an h space having a finite number of b m z p homotopy groups is ap torsion postnikov piece along the way we characterize the bz p r cellular classifying spaces of nilpotent groups

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

vector bundles over classifying spaces of compact lie groups the completion theorem of atiyah and segal as says that the complex k theory group k bg of the classifying space of any compact lie group g is isomorphic to r g the representation ring completed with respect to its augmentation ideal however the group k bg bg z bu does not directly contain information about vector bundles over the infinite dimensional complex bg itself the purpose of this paper is to compare the grothendieck group of vector bundles over bg which we denote k bg with both k bg and r g the main result is an algebraic description of k bg in terms of the representation rings of certain subgroups of g as one consequence we show that of the natural maps

2 nilpotent real section conjecture we show a 2 nilpotent section conjecture over mathbb r for a geometrically connected curve x over mathbb r such that each irreducible component of its normalization has mathbb r points pi 0 x mathbb r is determined by the maximal 2 nilpotent quotient of the fundamental group with its galois action as the kernel of an obstruction of jordan ellenberg this implies that for x smooth and proper x mathbb r pm is determined by the maximal 2 nilpotent quotient of mathrm gal mathbb c x with its mathrm gal mathbb r action where x mathbb r pm denotes the set of real points equipped with a real tangent direction showing a 2 nilpotent birational real section conjecture

fibrations of classifying spaces we investigate fibrations of the form z y x where two of the three spaces are classifying spaces of compact connected lie groups we obtain certain finiteness conditions on the third space which make it also a classifying space our results allow to express some of the basic notions in group theory in terms of homotopy theory i e in terms of classifying spaces as an application we prove that every retract of the classifying space of a compact connected lie group is again a classifying space

higher comparison maps for the spectrum of a tensor triangulated category abstract for each object in a tensor triangulated category we construct a natural continuous map from the object s support a closed subset of the category s triangular spectrum to the zariski spectrum of a certain commutative ring of endomorphisms when applied to the unit object this recovers a construction of p balmer these maps provide an iterative approach for understanding the spectrum of a tensor triangulated category by starting with the comparison map for the unit object and iteratively analyzing the fibers of this map via higher comparison maps we illustrate this approach for the stable homotopy category of finite spectra in fact the same underlying construction produces a whole collection of new comparison maps including maps associated to and defined on each closed subset of the triangular spectrum these latter maps provide an alternative strategy for analyzing the spectrum by iteratively building a filtration of closed subsets by pulling back filtrations of affine schemes

equivariant stable homotopy and sullivan s conjecture let g be a p group and let x be a g complex let eg denote a contractible space on which g acts freely by the homotopy fixed point set of x we mean the fixed point set f eg x g where f eg x denotes the function space of all maps eg x equipped with a g action by 9f 9f9 1 if we let denote the one point space with trivial g action we may also consider the g space f x it is canonically g homeomorphic to x the g map e g induces a map x g f x g in 19 d sullivan proposed the following

supplementary notes on the gaussian beam expansion the letter provides alternatively a simple way of computing the fresnel field integral a further extension to the gaussian beam expansion the zeroth order bessel function of the first kind is expanded into an approximate sum of gaussian functions the field integral is then expressible in terms of these simple functions the approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics as examples the calculation results for the uniform and the simply supported piston sources are presented in a good agreement with those evaluated by numerical integration

space time power optimization of variable rate space time block codes based on successive interference cancellation based on a zero forcing with successive interference cancellation zfsic method we construct variable rate space time block codes stbcs for two three and four transmit antennas in rayleigh fading channels considering the error propagation effect in the zfsic scheme we analyze the bit error rate ber and optimize the transmit power so that the average ber is minimized unlike the approach based on zero forcing zf the method adopted in this paper can construct variable rate stbcs even when the receive antennas are fewer than the transmit antennas in addition to improve the bers further we propose space time power optimization numerical results show that the codes presented in this paper provide much lower bers compared with the codes developed by kim and tarokh

on simplicial commutative algebras with vanishing andre quillen homology in this paper we study the andre quillen homology of simplicial commutative l algebras l a field having certain vanishing properties when l has non zero characteristic we obtain an algebraic version of a theorem of j p serre and y umeda that characterizes such simplicial algebras having bounded homotopy groups we further discuss how this theorem fails in the rational case and as an application indicate how the algebraic serre theorem can be used to resolve a conjecture of d quillen for algebras of finite type over noetherian rings having non zero characteristic

homotopy groups of highly connected manifolds abstract in this paper we give a formula for the homotopy groups of n 1 connected 2n manifolds as a direct sum of homotopy groups of spheres in the case the n th betti number is larger than 1 we demonstrate that when the n th betti number is 1 the homotopy groups might not have such a decomposition the techniques used in this computation also yield formulas for homotopy groups of connected sums of sphere products and cw complexes of a similar type in all the families of spaces considered here we establish a conjecture of j c moore

some extensions of the gaussian beam expansion radiation fields of the rectangular and the elliptical transducer a straightforward extension of gaussian beam expansion is presented for calculation of the fresnel field integral j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 the source distribution function is expanded into the superposition of a series of two dimensional gaussian functions the corresponding radiation field is expressed as the superposition of these two dimensional gaussian beams and is then reduced to the computation of these simple functions this treatment overcomes the limit that the shape of source is of circular axial symmetry the numerical examples are presented for the field of the uniform elliptical and the rectangular piston transducers and agree well with the results given by complicated computation

characterizations of spectra with injective cohomology which satisfy the brown gitler property we work in the stable homotopy category ofp complete connective spectra having mod p homology of nite type h x means cohomology with z p coecients and is a left module over the steenrod algebraa a spectrum z is called spacelike if it is a wedge summand of a suspension spectrum and a spectrum x satises the brown gitler property if the natural map x z homa h z h x is onto for all spacelike z it is known that there exist spectra t n satisfying the brown gitler prop erty and with h t n isomorphic to the injective envelope of h s n i n the categoryu of unstablea modules call a spectrum x standard if it is a wedge of spectra of the form l t n where l is a stable wedge summand of the classifying space of some elementary abelian p group such spectra haveu injective cohomology and allu injectives appear in this way working directly with the two properties of t n stated above we clarify and extend earlier work by many people on brown gitler spectra our main theorem is that if x is a spectrum withu injective cohomology the following conditions are equivalent a there exists a spectrum y whose cohomology is a reducedu injective and a map x y that is epic in cohomology b there exists a spacelike spectrum z a nd am apx z that is epic in cohomology c 11 x x is monic in cohomology d x satises the brown gitler property e x is spacelike f x is standard m2uis reduced if it has no nontrivial submodule which is a suspension as an application we prove that the snaith summands of 2 s 3 are brown gitler spectra a new result for the most interesting summands at odd primes another application combines the theorem with the second author s work on the whitehead conjecture of independent interest enroute to proving that b implies c we prove that the homology suspension has the following property if an n connected space x admits a map to an n fold suspension that is monic in mod p homol ogy then nn x x is onto in mod p homology

autour de la cohomologie de maclane des corps finis nous decrivons une nouvelle methode de calcul de la cohomologie de maclane des corps finis cette theorie est intimement reliee aux extensions du groupe additif deja etudiees par l breen et a l homologie de hochschild topologique de m bokstedt et donc a la k theorie stable notre approche utilise de maniere cruciale l annulation de la cohomologie de maclane du corpsf p avec pour coefficients l algebre symetrique ou l on a inverse le frobenius nous recourons alors a l analyse des complexes de koszul et de de rham en caracteristique non nulle

indecomposablea module summands inh v which are unstable algebras letp be a prime and denote bya the modp steenrod algebra we determine the indecomposablea module summands ofh p d f p which admit the structure of an unstablea algebra in fact it turns out that this is equivalent to the problem of determining those indecomposablea module summands which arise as the modp cohomology of a space or even a classifying space of a finite group we reduce this problem to one in modular representation theory namely for whichd andp is the projective cover of the trivial one dimensional gl d f p representationf p a permutation module our solution of this latter problem makes use of the classification of subgroups of gl d f p acting transitively on f p d 0 and hence depends on the classification of finite simple groups on feit thompson s odd order theorem ifp 2

lannes t functor on summands of h b z p s let h be the mod p cohomology of the classifying space b z p thought of as an object in the category u of unstable modules over the steenrod algebra lannes constructed a functor t u u which is left adjoint to the functor a a h in this paper we evaluate t on the indecomposable u summands of h s the tensor product of s copies of h our formula involves the composition factors of certain tensor products of irreducible representations of the semigroup ring f p m s s z p

nullification and cellularization of classifying spaces of finite groups in this note we discuss the effect of the bz p nullification p bz p and the bz p cellularization cw bz p over classifying spaces of finite groups and we relate them with the corresponding functors with respect to moore spaces that have been intensively studied in the last years we describe p bz p bg by means of a covering fibration and we classify all finite groups g for which bg is bz p cellular we also carefully study the analogous functors in the category of groups and their relationship with the fundamental groups of p bz p bg and cw bz p bg

notes on the gaussian beam expansion a powerful gaussian beam expansion technique j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 is widely used in calculating the fresnel field integral a basic ideal of this treatment is to expand the source distribution function into the superposition of a series of gaussian functions the evaluation of the radiation field is then greatly simplified as a supplement this paper presents a simple approach to determine the expansion coefficients for the sound source the results for the ultrasonic field radiated by piston transducers are typically given in a fairly good agreement with those calculated by numerical integration and breazeale s the limits of the present method are also discussed

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

rational equivalences between classifying spaces the paper contains a homotopy classification of rational equivalences between classifying spaces of compact connected lie groups with an application to genus sets of such spaces

a simple calculation approach for the second harmonic sound field generated by an arbitrary axial symmetric source in a linear approximation an arbitrary axial symmetric source can be expressed as the linear superposition of a set of gaussian sources and the corresponding radiated sound field can be represented as the superposition of this set of gaussian beams the analysis is extended to the second harmonic generation due to nonlinear effects under a quasilinear approximation then the second harmonic sound field could be considered as a sum of self and cross interaction terms produced by a series of gaussian beams therefore the calculation of the second harmonic sound field of an axial symmetric source can be reduced to a simple linear combination of a set of exponential integral functions instead of a complicated triple integral in order to verify this calculation approach the second harmonic generation of a focused and a simple piston source is examined and the result is in good agreement with that in earlier paper by complicated computation

homotopy fixed point methods for lie groups and finite loop spaces a loop space x is by definition a triple x bx e in which x is a space bx is a connected pointed space and e x qbx is a homotopy equivalence from x to the space qbx of based loops in bx we will say that a loop space x is finite if the integral homology h x z is finitely generated as a graded abelian group i e if x appears at least homologically to be a finite complex in this paper we prove the following theorem

degenerate fibres in the stone cech compactification of the universal bundle of a finite group applied to a continuous surjection e b of completely regular hausdorff spaces e and b the stone cech compactification functor yields a surjection e b for an n fold covering map we show that the fibres of while never containing more than n points may degenerate to sets of cardinality properly dividing n in the special case of the universal bundle eg bg of a p group g we show more precisely that every possible type of g orbit occurs among the fibres of to prove this we use a weak form of the so called generalized sullivan conjecture

homotopy classification of self maps of bg via g actions to complete the classification of self maps of bg theorem 4 2 it remains to prove theorem 4 1 i e to show that the higher limits of certain functors n 1h 2 f p g z p wall vanish and that h0 mp g f i has the expected value in this section these limits h mp g hi will be calculated in the easy cases when g is a simply connected classical group i e one of the groups su n sp n or spin n or when i 2 the computation of h mp g hi for the simply connected exceptional lie groups will be put off until section 6 we begin with some general properties of higher limits let 6 be any small discrete category it is convenient when dealing with higher limits of functors on to let 4 moldenote the category of contravariant functors from v to ad then for any f e w muok we can identify

group cohomology and control of p fusion we show that if an inclusion of finite groups h g of index prime to p induces a homeomorphism of mod p cohomology varieties or equivalently an f isomorphism in mod p cohomology then h controls p fusion in g if p is odd this generalizes classical results of quillen who proved this when h is a sylow p subgroup and furthermore implies a hitherto difficult result of mislin about cohomology isomorphisms for p 2 we give analogous results at the cost of replacing mod p cohomology with higher chromatic cohomology theories

derived representation theory of lie algebras and stable homotopy categorification of slk abstract we set up foundations of representation theory over s the sphere spectrum which is the initial ring of stable homotopy theory in particular we treat s lie algebras and their representations characters g l n s verma modules and their duals harish chandra pairs and zuckermann functors as an application we construct a khovanov s l k stable homotopy type with a large prime hypothesis which is a new link invariant using a stable homotopy analogue of the method of j sussan

on the homotopy type of p completions of infra nilmanifolds infra nilmanifolds are compact k g 1 manifolds with g a torsion free finitely generated virtually nilpotent group motivated by previous results of various authors on p completions of k g 1 spaces with g a finite or a nilpotent group we study the homotopy type of p completions of infra nilmanifolds for any prime p we prove that the p completion of an infra nilmanifold is a virtually nilpotent space which is either aspherical or has infinitely many nonzero homotopy groups the same is true for p localization moreover we show by means of examples that rationalizations of infra nilmanifolds may be elliptic or hyperbolic

acoustic bullets transient bessel beams generated by planar apertures acoustic bullets are defined to be waves which maintain their peak amplitude and or general shape as they propagate in free space a general theoretical approach is presented to investigate the space time properties of a new class of acoustic bullets which are defined here as acoustic transient bessel beams the approach encompasses both baseband and modulated carrier signal wave fields closed form space time expressions are developed using fourier and hilbert transform methods for several special cases of transient bessel beams the space time source distributions for generating such wave fields from planar apertures are developed from the free space wave fields via the use of the rayleigh surface integral solution for time dependent fields finally numerical results are presented to illustrate the general space time characteristics of the acoustic transient bessel beams

a simplified algorithm for second order sound beams with arbitrary source distribution and geometry l an earlier investigation j acoust soc am 108 2759 2764 2000 of the simplified algorithm for the second order sound fields with circular axial symmetry is extended to a more general case of the sound sources with an arbitrary distribution this extension is based on the fact that the source function is expanded into the sum of a series of two dimensional gaussian ones the two and five dimensional integral expressions for the primary and second order fields are respectively reduced in terms of gaussian functions and simple one dimensional integrals numerical calculations are then greatly simplified

on the p adic completions of nonnilpotent spaces this paper deals with the p adic completion f p x developed by bousfield kan for a space x and prime p a space x is called f p good when the map x f p x is a mod p homology equivalence and called f p bad otherwise general examples of f p good spaces are established beyond the usual nilpotent or virtually nilpotent ones these include the polycyclic by finite spaces however the wedge of a circle with a sphere of positive dimension is shown to be f p bad this provides the first example of an f p bad space of finite type and implies that the p profinite completion of a free group on two generators must have nontrivial higher mod p homology as a discrete group

rational homotopy of the homotopy fixed point sets of circle actions in this paper when g is the circle s 1 and m is a g space we study the rational homotopy type of the fixed point set m g the homotopy fixed point set m hg and the natural injection m g m hg c 2009 elsevier inc all rights reserved

on the cohomology of highly connected covers of finite hopf spaces relying on the computation of the andre quillen homology groups for unstable hopf algebras we prove that if the mod p cohomology of both the fiber and the base in an h fibration is finitely generated as algebra over the steenrod algebra then so is the mod p cohomology of the total space in particular the mod p cohomology of the n connected cover of a finite h space is always finitely generated as algebra over the steenrod algebra

homology decompositions for p compact groups we construct a homotopy theoretic setup for homology decompositions of classifying spaces of p compact groups this setup is then used to obtain a subgroup decomposition for p compact groups which generalizes the subgroup decomposition with respect to p stubborn subgroups for a compact lie group constructed by jackowski mcclure and oliver

systems of fixed point sets let g be a compact lie group a canonical method is given for constructing a c space from homotopy theoretic information about its fixed point sets the construction is a special case of the categorical bar construction applications include easy constructions of certain classifying spaces as well as c eilenbergmac lane spaces and postnikov towers 0 introduction let g be a compact lie group and x a g space the equivariant homotopy theory of x is reflected to a remarkable extent in its system of fixed point sets defined as a functor from a certain category 0g to top the category of topological spaces our spaces will be compactly generated weak hausdorff they may or may not be equipped with a basepoint depending on the context these functors or systems have considerable technical advantages over g spaces it is easy to apply most homotopy theoretic constructions to them whereas in many cases it is unclear how to proceed for g spaces it is the purpose of this paper to present a canonical way of recovering from any system a g space which preserves all the homotopy theoretic structure of the system this allows us to give easy equivariant versions of some standard topological constructions such as eilenberg mac lane spaces and postnikov towers and to simplify other equivariant constructions 1 1 statements of the main theorems throughout g is a fixed compact lie group definitions the category of canonical orbits written 0g is a topological category with discrete object space 0g g 77 77 a closed subgroup of g and morphisms the g maps topologized by requiring the natural bijection hoxn0cig h g k g k h to be a homeomorphism by an oc space we shall mean a continuous contravariant functor from 0g to top these functors form the objects of a topological category in the usual manner we will also consider gg rings oc groups etc defined similarly definition let a1 be a g space the fixed point set system of x written x is an gg space defined as follows g 77 x received by the editors october 30 1981 and in revised form april 26 1982 1980 mathematics subject classification primary 57s10 55n25

a propos de conjectures de serre et sullivan we first give a new proof of a conjecture of j p serre on the homotopy of finite complexes which was recently proved by c mcgibbon and j neisendorfer the emphasis is on a property of the mod 2 homology of certain spaces their quasi boundedness as right modules over the steenrod algebra this property is preserved when one goes from a simply connected space to its loop space and also when one takes a covering of anh space then we show that this notion of quasi boundedness simplifies h miller s proof of d sullivan s conjecture on the contractibility of the space of pointed maps from the classifying space of the groupe 2 into a finite complex

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

fast ml detection for quasi orthogonal stbcs of rate 2 in under determined systems transactions papers a fast maximum likelihood ml detection scheme is proposed for the important quasi orthogonal space time block codes stbcs of symbol rate 2 for three and four transmission antennas in particular the proposed scheme is applicable even to the under determined system where the number of transmission antennas is larger than that of the receive antennas the half of the symbols of the transmission matrix are detected by two dependent double layer sphere decoders which are referred to as dual double layer sphere decoding in this paper the remaining half of the symbols are detected by single symbol detection of which complexity is extremely low numerical results demonstrate that the proposed new detection method improves the detection speed up to ten times depending on the signal to noise ratio snr compared to the state of the art scheme