algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

decentralized delayed feedback control of a one way coupled ring map lattice abstract this paper presents a decentralized delayed feedback control for a one way coupled ring map lattice the delayed feedback controller is used at each local site this paper gives a simple sufficient condition for the control system to be stable this condition does not depend on the system size hence it allows us to obtain a systematic simple procedure for designing the controller in order to confirm the theoretical results we show some numerical examples

resonant suppression of turing patterns by periodic illumination we study the resonant behavior of turing pattern suppression in a model of the chlorine dioxide iodine malonic acid reaction with periodic illumination the results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system the resonance in turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force square wave on off periodic forcing is more effective in suppressing turing patterns than sinusoidal forcing we compare the dynamics of periodically forced turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns

the borel conjecture for hyperbolic and cat 0 groups we prove the borel conjecture for a class of groups containing word hyperbolic groups and groups acting properly isometrically and cocompactly on a finite dimensional cat 0 space

ramanujan s theories of elliptic functions to alternative bases in his famous paper 3 10 pp 23 39 ramanujan offers several beautiful series representations for 1 pi he first states three formulas one of which is frac 4 pi sum limits mathbf n 0 infty frac left 6 mathbf n 1 right left frac 1 2 right 3 n left mathbf n right 3 4 n where a o 1 and for each positive integer n left mathbf a right n mathbf a left mathbf a 1 right left mathbf a 2 right left mathbf a mathbf n 1 right

controlling extended systems with spatially filtered time delayed feedback we investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time delay feedback the scheme is naturally suited to real time control of optical systems we apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable coherent traveling wave state exists but is a member of a nowhere stable family our scheme stabilizes this state and directs the system towards it from realistic distant and noisy initial conditions as confirmed by numerical simulation a linear stability analysis about the controlled state accurately predicts when the scheme is successful and illustrates some key features of the control including the individual merit of and interplay between the spatial and temporal degrees of freedom in the control

spatially periodic modulated rayleigh benard convection two dimensional thermal convection in a fluid layer between two rigid walls at different mean temperatures is investigated the top container boundary is undulated and the temperatures at the top and bottom boundaries are spatially periodic modulated with modulation wavelengths large compared to the thickness of the fluid layer the continuous translational invariance in the fluid layer is broken by these spatial modulations consequently phase differences between two periodic modulations give rise to an interesting drifting pattern with the drift direction depending on the sign of the relative phase between the modulations at distinguished ratios between the modulation wave numbers and relative phases the onset of convection changes as function of the modulation amplitudes from a stationary into an oscillatory one we call this phenomenon hopf bifurcation by frustrated drifts possible experiments are described in detail where this phenomenon can be expected textcopyright 1996 the american physical society

spatial synchronization of regular optical patterns we investigate an extended nonlinear optical experiment exhibiting the spontaneous formation of hexagonal patterns out of a stationary bifurcation the system is exposed to a two dimensional spatially periodic forcing namely static hexagonal patterns under variation of their spatial periodicity parameters are the strength of the forcing and the distance to pattern forming threshold the system response is quantitatively characterized with different methods we observe several locking regimes where the system is entrained by the forcing most of the locking regimes can be related to resonances between the different critical wave numbers and the forcing wave number or its spatial harmonics one particular locking appears to result from two of these simple resonances in a kind of generalized order m n synchronization the width of the locking regimes increases with forcing strength apparently representing a spatial analog of arnold tongues

the integral k theoretic novikov conjecture for groups with finite asymptotic dimension the integral assembly map in algebraic k theory is split injective for any geometrically finite discrete group with finite asymptotic dimension

feedback control of the kuramoto sivashinsky equation abstract this work focuses on linear finite dimensional output feedback control of the kuramoto sivashinsky equation kse with periodic boundary conditions under the assumption that the linearization of the kse around the zero solution is controllable and observable linear finite dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution for any value of the instability parameter the controllers are synthesized on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the performance of the controllers is successfully tested through computer simulations

sidewall forcing of hexagonal turing patterns rhombic patterns abstract rhombic arrays were obtained by sidewall forcing during turing pattern formation in numerical simulations locking between the frequency of forcing and the wave length between blobs was obtained in accordance with the farey sequence this locking appears as a perfect rhombic array oriented in the direction of the imposed forcing for a constant forcing in duration and amplitude the following scheme of bifurcation was observed parallel stripes rhombic array domains of hexagons and rhombi separated by penta hepta defects symmetry considerations based on a non uniform stretching along the x axis were used to describe these transitions unstable varicose vein stripes were observed to evolve during the temporal evolution arrays

algebraic hypergeometric transformations of modular origin it is shown that ramanujan s cubic transformation of the gauss hypergeometric function 2 f 1 arises from a relation between modular curves namely the covering of x 0 3 by x 0 9 in general when 2 n 7 the n fold cover of x 0 n by x 0 n 2 gives rise to an algebraic hypergeometric transformation the n 2 3 4 transformations are arithmetic geometric mean iterations but the n 5 6 7 transformations are new in the final two cases the change of variables is not parametrized by rational functions since x 0 6 x 0 7 are of genus 1 since their quotients x 0 6 x 0 7 under the fricke involution an atkin lehner involution are of genus 0 the parametrization is by two valued algebraic functions the resulting hypergeometric transformations are closely related to the two valued modular equations of fricke and h cohn

the homotopy theory of cyclic sets the aim of this note is to show that the homotopy theory of the cyclic sets of connes 3 is equivalent to that of s0 2 spaces i e spaces with a circle action and hence to that of spaces over k z 2

the iwasawa conjecture for totally real fields let f be a totally real number field let p be a prime number and for any integer n let fun denote the group of nth roots of unity let 41 be a p adic valued artin character for f and let f be the extension of f attached to 4 i e so that 4 is the character of a faithful representation of gal f f we will assume that f is also totally real for a number field k let k denote the cyclotomic zp extension of k following greenberg we say that 4 is of type s if f n fc f and of type w if 4 is one dimensional with f p c fcc deligne and ribet in dr following kubota and leopoldt for the case f q have proved the existence of a p adic l function associated to a one dimensional artin character 4 with f totally real this function lp s 4 is continuous for s e zp 1 and even at s 1 if 4 is not trivial and satisfies the following interpolation property

detecting k theory by cyclic homology we discuss which part of the rationalized algebraic k theory of a group ring is detected via trace maps to hochschild homology cyclic homology periodic cyclic or negative cyclic homology

space periodically driven codimension two bifurcations an amplitude equation is derived for a one dimensional extended dynamical system undergoing a codimension two bifurcation subjected to a weak near resonant spatially periodic forcing it is proved that in some appropriate limit the dynamics is of the propagative phase type and it is governed by the time dependent sine gordon equation with weak dissipation

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

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

stabilizing the absolutely or convectively unstable homogeneous solutions of reaction convection diffusion systems we study the problem of stabilization of a homogeneous solution in a two variable reaction convection diffusion one dimensional system with oscillatory kinetics in which moving or stationary patterns emerge in the absence of control we propose to use a formal spatially weighted feedback control to suppress patterns in an absolutely or convectively unstable system and pinning control for a convectively unstable system the latter approach is very effective and may require only one actuator to adjust feed conditions in the former approach the positive diagonal elements of the appropriate dynamics matrix are shifted to the left hand part of the complex plane to ensure linear asymptotic stability of the system according to gershgorin criterion moreover we construct a controller that with many actuators will approach the global stability of the solution according to liapunov s direct method we apply two alternative approaches to reveal the unstable modes an approximate one that is based on linear stability analysis of an unbounded system and an exact one that uses a traditional eigenstructure analysis of bounded systems the number of required actuators increases dramatically with system size and with the distance from the bifurcation point the methodology is developed for a system with learning cubic kinetics and is tested on a more realistic cross flow reactor model

pattern formation capacity of spatially extended systems we analyze a class of spatially extended systems which are capable of generating many complicated patterns these systems are given by the ginzburg landau equation coupled with a system of two linear equations and describe nonlinear media with localized defects we find a connection between these systems and spin glass systems we show that the system is capable to produce many patterns and describe patterning algorithms

chern characters for proper equivariant homology theories and applications to k and l theory we construct for an equivariant homology theory for proper equiv ariant cw complexes an equivariant chern character provided that certain conditions are satisfied this applies for instance to the sources of the assembly maps in the farrell jones conjecture with respect to the family f of finite subgroups and in the baum connes conjecture thus we get an explicit calculation in terms of group homology of qn z knorgu and qn z lnorgu for a commutative ring r with qh r provided the farrell jones conjecture with respect to f is true and of qnz k top n c r og fu for fa r c provided the baum connes conjecture is true

spatial forcing of spontaneous optical patterns a nonlinear optical system which spontaneously forms hexagonal patterns is exposed to a weak spatially modulated forcing as forcing stationary hexagonal patterns are used under variation of their transverse wave number in the experiment we observe a locking when the forcing wave number is close to one of the critical wave numbers of the unforced system outside the locking regimes forcing provokes spatiotemporal disorder the system response is characterized quantitatively with respect to its dynamics and to its spatial order

coefficients for the farrell jones conjecture abstract we introduce the farrell jones conjecture with coefficients in an additive category with g action this is a variant of the farrell jones conjecture about the algebraic k or l theory of a group ring rg it allows to treat twisted group rings and crossed product rings the conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties since known proofs using controlled algebra carry over to the set up with coefficients we obtain new results about the original farrell jones conjecture the conjecture with coefficients implies the fibered version of the farrell jones conjecture

effects of parametric disorder on a stationary bifurcation abstract effects of a frozen random contribution to the control parameter are investigated in terms of the complex ginzburg landau equation with real coefficients the threshold of the bifurcation from the homogeneous basic state is reduced by a random contribution even with a vanishing spatial mean value as shown by three different approaches by a perturbation calculation by a self consistent iteration method and by a fully numerical solution of the linear part of the ginzburg landau equation for arbitrary random contributions the nonlinear stationary solutions are numerically determined and in the limit of small random amplitudes analytical expressions are derived in terms of two different perturbation expansions which cover already several related trends beyond threshold for instance the spatial modulations of the solutions increase with the noise amplitude but decrease with increasing distance from threshold

two frequency forced faraday waves weakly damped modes and pattern selection abstract recent experiments a kudrolli b pier j p gollub physica d 123 1998 99 111 on two frequency parametrically excited surface waves produced an intriguing superlattice wave pattern near a codimension two bifurcation point where both subharmonic and harmonic waves onset simultaneously but with different spatial wave numbers the superlattice pattern is synchronous with the forcing spatially periodic on a large hexagonal lattice and exhibits small scale triangular structure similar patterns have been shown to exist as primary solution branches of a generic 12 dimensional d 6 t 2 equivariant bifurcation problem and may be stable if the nonlinear coefficients of the bifurcation problem satisfy certain inequalities m silber m r e proctor phys rev lett 81 1998 2450 2453 here we use the spatial and temporal symmetries of the problem to argue that weakly damped harmonic waves may be critical to understanding the stabilization of this pattern in the faraday system we illustrate this mechanism by considering the equations developed by zhang and vinals j fluid mech 336 1997 301 330 for small amplitude weakly damped surface waves on a semi infinite fluid layer we compute the relevant nonlinear coefficients in the bifurcation equations describing the onset of patterns for excitation frequency ratios of 2 3 and 6 7 for the 2 3 case we show that there is a fundamental difference in the pattern selection problems for subharmonic and harmonic instabilities near the codimension two point also we find that the 6 7 case is significantly different from the 2 3 case due to the presence of additional weakly damped harmonic modes these additional harmonic modes can result in a stabilization of the superpatterns

two primary algebraic k theory of two regular number fields we explicitly calculate all the 2 primary higher algebraic k groups of the rings of integers of all 2 regular quadratic number fields cyclotomic number fields or maximal real subfields of such here 2 regular means that 2 does not split in the number field and its narrow picard group is of odd order

effects of an almost resonant spatial thermal modulation in the rayleigh benard problem quasiperiodic behaviour the authors consider the effect of prescribed spatially periodic temperatures at the bounding walls of a 2d boussinesq fluid on 1d pattern forming transitions they determine the normal form equation for the slowly varying pattern amplitude quasiperiodic behaviour is found when one takes into account the deviation of the external wavelength modulation from the critical value for the onset of classical rayleigh benard convection

the farrell jones conjecture for the solvable baumslag solitar groups in this paper we prove the farrell jones conjecture for the solvable baumslag solitar groups with coefficients in an additive category we also extend our results to groups of the form z 1 p semidirect product with any virtually cyclic group where p is a prime number

finite decomposition complexity and the integral novikov conjecture for higher algebraic k theory decomposition complexity for metric spaces was recently introduced by guentner tessera and yu as a natural generalization of asymptotic dimension we prove a vanishing result for the continuously controlled algebraic k theory of bounded geometry metric spaces with finite decomposition complexity this leads to a proof of the integral k theoretic novikov conjecture regarding split injectivity of the k theoretic assembly map for groups with finite decomposition complexity and finite cw models for their classifying spaces by work of guentner tessera and yu this includes all geometrically finite linear groups

direct measurement of multiple instability regions via a fourier filtering method in an optical pattern forming system we determine the limits of stability of the homogeneous state of a pattern forming optical system in dependency on the wave number by experimental means the measurement becomes feasible by adopting a scheme based on a fourier filtering technique the system under study is a single mirror feedback arrangement using sodium vapor as the nonlinear medium the experiment confirms the existence of multiple instability regions of the homogeneous state expected by theory the measurements do not agree quantitatively with the marginal stability curve determined by a linear stability analysis of an infinitely extended homogeneous system we study the system numerically and demonstrate that the results of the simulations for the case of a gaussian beam can be reproduced by a simple modification of the linear stability analysis which accounts for the finite diameter of the input beam this explains the wave number dependent systematic deviations between the experiment and the linear stability analysis of the infinitely extended system

basic representations for eisenstein series from their differential equations abstract in this paper we provide a new approach for the derivation of parameterizations for the eisenstein series we demonstrate that a variety of classical formulas may be derived in an elementary way without knowledge of the inversion formulae for the corresponding schwarzian triangle functions in particular we provide a new derivation for the parametric representations of the eisenstein series in terms of the complete elliptic integral of the first kind the proof given here is distinguished from existing elementary proofs in that we do not employ the jacobi ramanujan inversion formula relating theta functions and hypergeometric series our alternative approach is based on a lie symmetry group for the differential equations satisfied by certain eisenstein series we employ similar arguments to obtain parameterizations from ramanujan s alternative signatures and those associated with the inversion formula for the modular j function moreover we show that these parameterizations represent the only possible signatures under a certain assumed form for the lie group parameters

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

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

k theory and dynamics i un theoreme de h cobordisme avec commande feuillettee la variete associee le transfert asymptotique dynamique du flot geodesique completion de la demonstration du theoreme principal revue de la theorie de la commande structures de longues cellules minces

synchronization and control of coupled ginzburg landau equations using local coupling in this paper we discuss the properties of a recently introduced coupling scheme for spatially extended systems based on local spatially averaged coupling signals see z tasev et al int j bifurcation chaos appl sci eng to be published and l junge et al int j bifurcation chaos appl sci eng 9 2265 1999 using the ginzburg landau model we performed an extensive numerical examination of this coupling scheme i e a complete scan through the relevant coupling parameters furthermore we demonstrate suppression and control of spatiotemporal chaos e g stabilizing the homogeneous steady state and spatially localized control as an application all model parameters of the ginzburg landau equation are estimated given only the local information of the system

control of pattern formation by time delay feedback with global and local contributions we consider the suppression of spatiotemporal chaos in the complex ginzburglandau equation by a combined global and local time delay feedback feedback terms are implemented as a control scheme i e they are proportional to the difference between the time delayed state of the system and its current state we perform a linear stability analysis of uniform oscillations with respect to space dependent perturbations and compare with numerical simulations similarly for the fixed point solution that corresponds to amplitude death in the spatially extended system a linear stability analysis with respect to space dependent perturbations is performed and complemented by numerical simulations

on the k theory of local fields in this paper we establish a connection between the quillen k theory of certain local fields and the de rham witt complex of their rings of integers with logarithmic poles at the maximal ideal the fieldsk we consider are complete discrete valuation fields of characteristic zero with perfect residue field k of characteristic p 2 when k contains the pth roots of unity the relationship between the k theory with z p coefficients and the de rham witt complex can be described by a sequence

cyclic homology and equivariant homology the purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of connes 9 11 see also loday and quillen 20 and if equivariant homology and cohomology theories here ii is the circle group the most general results involve the definitions of the cyclic homology of cyclic chain complexes and the notions of cyclic and cocyclic spaces so precise statements will be postponed until w 3 in this introduction we explain some of the formal similarities between the cyclic theory and the equivariant theory and give two examples where the general results apply let a be an associative algebra over a commutative ring k then one can form the cyclic homology hc a and cohomology hc a of a these groups have periodicity operators

pattern formation in diffusive advective coupled map lattices we investigate pattern formation and evolution in coupled map lattices when advection is incorporated inaddition to the usual diffusive term all patterns may be suitably grouped into ve classes three periodic supporting static patterns and traveling waves and two nonperiodic relative frequencies are determined as afunction of all model parameters diffusion advection local nonlinearity and lattice size advection plays animportant role in coupled map lattices being capable of considerably altering pattern evolution for instance advection may induce synchronization making chaotic patterns evolve periodically as a byproduct we de scribe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of travelingwaves doi 10 1103 physreve 69 066206 pacs number s 89 75 kd 05 45 xt 05 45 rai introduction

a cubic counterpart of jacobi s identity and the agm we produce exact cubic analogues of jacobi s celebrated theta function identity and of the arithmetic geometric mean iteration of gauss and legendre the iteration in question is a n 1 a n 2b n 3 and b n 1 formula cannot be replicated the limit of this iteration is identified in terms of the hypergeometric function f 1 3 2 3 1 which supports a particularly simple cubic transformation

empirical bifurcation analysis of optical pattern formation the experimental characterization of pattern forming bifurcations is difficult since the unstable solutions are generally not accessible in experiments in nonlinear optics a novel control scheme allows one to select and stabilize generic patterns and thus to track these solutions in parameter space this fourier space scheme is applied to a single feedback system and the amplitudes of roll square and hexagon patterns are determined experimentally even though the bifurcation is imperfect the coefficients of a prototype amplitude equation are recovered the coefficients show satisfactory agreement with theory and with numerical simulations which are performed for comparison the simulations also clarify the origin of the imperfect bifurcation in the experiment boundaries and speckles appear to have an unexpected strong influence

comparison of time delayed feedback schemes for spatiotemporal control of chaos in a reaction diffusion system with global coupling time delayed feedback control for stabilizing time periodic spatial patterns is investigated in a generic reaction diffusion system with global coupling we focus on the case of low dimensional chaos where unstable patterns admit only a single unstable mode spatial degrees of freedom are taken into account to define different control schemes the efficiency of these schemes is discussed where control forces are motivated by physical requirements as well as by the possibility of obtaining analytically exact results we find that control schemes that contain the full feedback of the inhibitor variable may finally destroy the control performance thus schemes that omit the inhibitor might be more efficient our numerical findings are explained in terms of floquet spectra and compared with analytical solutions of particular coupling schemes

controlling and synchronizing space time chaos control and synchronization of continuous space extended systems is realized by means of a finite number of local tiny perturbations the perturbations are selected by an adaptive technique and they are able to restore each of the independent unstable patterns present within a space time chaotic regime as well as to synchronize two space time chaotic states the effectiveness of the method and the robustness against external noise is demonstrated for the amplitude and phase turbulent regimes of the one dimensional complex ginzburg landau equation the problem of the minimum number of local perturbations necessary to achieve control is discussed as compared with the number of independent spatial correlation lengths s1063 651x 99 00806 5 pacs number s 05 45 2a in the last decade control and synchronization of chaos have attracted the attention of the scientific community in both cases a chaotic dynamics is conveniently disturbed by means of an external perturbation usually small as compared with the unperturbed dynamics in order to force the appearence of a goal behavior g t compatible with the natural evolution of the system in the former case the goal dynamics corresponds to one unstable periodic orbit embedded within the chaotic attractor 1 in the latter case it corresponds to compensating for the difference of the same system due to different initial conditions since the first proposals for control 2 and synchronization 3 of chaos many other approaches have been sug

generalized synchronization of spatiotemporal chemical chaos we report the synchronization of two spatially extended chemical systems in one spatial dimension under appropriate parameter conditions the model systems exhibit a transition to turbulence via backfiring of pulses by implementing continuous control to the underlying partial differential equations synchronization is achieved not only for identical systems but also for systems operating under unequal parameter values exhibiting different dynamical behavior using this technique spatiotemporal chaos turbulence can be suppressed maintained or even enhanced depending on the dynamical behavior of the drive system this could possibly be of relevance to biological systems where in certain situations the emergence of chaos is undesirable while under different circumstances the loss of the chaotic dynamics is undesirable epileptic seizures

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

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

on the nonexistence of elements of kervaire invariant one we show that the kervaire invariant one elements j 2j 1 2s exist only for j 6 by browder s theorem this means that smooth framed manifolds of kervaire invariant one exist only in dimensions 2 6 14 30 62 and possibly 126 except for dimension 126 this resolves a longstanding problem in algebraic topology