some finitely presented nilpotent by abelian groups this paper gives some sufficient conditions for the finite presentability of nilpotent by abelian groups the general question of deciding whether a particular soluble group admits a finite presentation has received considerable attention in recent years see the review article of strebel lo for a discussion of the work to 1984 in particular we want to draw attention to three papers particularly relevant to the topic of this paper firstly bieri and strebel have given in 4 a necessary and sufficient condition for the finite presentation of a metabelian group the present work is based on their methods the sufficient condition was extended by mcisaac in 7 to a condition for the finite presentation of a split extension of a group of nilpotency class 2 by an abelian group in a major work abels 2 deals with finite presentability of arithmetic groups his work shows for example that soluble arithmetic groups corresponding to connected algebraic groups are finitely presented if and only if the metabelian quotient is finitely presented and the multiplier the second homology with trivial coefficients of the derived group is finitely generated as a module for the group this therefore gives a superb answer to the question for arithmetic groups but it is not clear to what extent such results are available for general abstract groups we return briefly to this later in this introduction the aim of this paper is to carry the sufficient condition given by mcisaac considerably further we remove the restriction that the extension involved be split and widen the condition considerably in particular we make use of the jacobi identity which did not figure in mcisaac s treatment we also extend the results to the case where the nilpotent normal subgroup has arbitrary nilpotency class to describe our results we need to introduce some notation and to

breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps to identify and to explain coupling induced phase transitions in coupled map lattices cml has been a lingering enigma for about two decades in numerical simulations this phenomenon has always been observed preceded by a lowering of the lyapunov dimension suggesting that the transition might require changes of linear stability yet recent proofs of co existence of several phases in specially designed models work in the expanding regime where all lyapunov exponents remain positive in this paper we consider a family of cml composed by piecewise expanding individual map global interaction and finite number n of sites in the weak coupling regime where the cml is uniformly expanding we show mathematically for n 3 and numerically for n ge 3 that a transition in the asymptotic dynamics occurs as the coupling strength increases the transition breaks the milnor attractor into several chaotic pieces of positive lebesgue measure with distinct empiric averages it goes along with various symmetry breaking quantified by means of magnetization type characteristics despite that it only addresses finite dimensional systems to some extend this result reconciles the previous ones as it shows that loss of ergodicity symmetry breaking can occur in basic cml independently of any decay in the lyapunov dimension

birkhoff integral for multi valued functions abstract the aim of this paper is to study birkhoff integrability for multi valued maps f cwk x where is a complete finite measure space x is a banach space and cwk x is the family of all non empty convex weakly compact subsets of x it is shown that the birkhoff integral of f can be computed as the limit for the hausdorff distance in cwk x of a net of riemann sums n an f tn we link birkhoff integrability with debreu integrability a notion introduced to replace sums associated to correspondences when studying certain models in mathematical economics we show that each debreu integrable multi valued function is birkhoff integrable and that each birkhoff integrable multi valued function is pettis integrable the three previous notions coincide for finite dimensional banach spaces and they are different even for bounded multi valued functions when x is infinite dimensional and x is assumed to be separable we show that when f takes values in the family of all non empty convex norm compact sets of a separable banach space x then f is pettis integrable if and only if f is birkhoff integrable in particular these pettis integrable f s can be seen as single valued pettis integrable functions with values in some other adequate banach space incidentally to handle some of the constructions needed we prove that if x is an asplund banach space then cwk x is separable for the hausdorff distance if and only if x is finite dimensional

the mcshane integral in weakly compactly generated spaces abstract di piazza and preiss asked whether every pettis integrable function defined on 0 1 and taking values in a weakly compactly generated banach space is mcshane integrable in this paper we answer this question in the negative moreover we give a counterexample where the target banach space is reflexive

coupled map lattices one step forward and two steps back abstract we discuss the general notion of lattice dynamical systems and some recent progress in their studies we suggest also the approach that allows to extract some information on the dynamics of finitely extended real systems from the results obtained on the infinitely extended artificial ones

measurable selectors and set valued pettis integral in non separable banach spaces kuratowski and ryll nardzewski s theorem about the existence of measurable selectors for multi functions is one of the keystones for the study of set valued integration one of the drawbacks of this result is that separability is always required for the range space in this paper we study pettis integrability for multi functions and we obtain a kuratowski and ryll nardzewski s type selection theorem without the requirement of separability for the range space being more precise we show that any pettis integrable multi function f cwk x defined in a complete finite measure space with values in the family cwk x of all non empty convex weakly compact subsets of a general non necessarily separable banach space x always admits pettis integrable selectors and that moreover for each a the pettis integral afd coincides with the closure of the set of integrals over a of all pettis integrable selectors of f as a consequence we prove that if x is reflexive then every scalarly measurable multi function f cwk x admits scalarly measurable selectors the latter is also proved when x w is angelic and has density character at most 1 in each of these two situations the pettis integrability of a multi function f cwk x is equivalent to the uniform integrability of the family supx f x bx r results about norm borel measurable selectors for multi functions satisfying stronger measurability properties but without the classical requirement of the range banach space being separable are also obtained

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

gauge integrals and selections of weakly compact valued multifunctions abstract in the paper henstock mcshane birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general banach space x in particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered

non trivial collective behavior in coupled map lattices a transfer operator perspective abstract we discuss the link between the presence of non trivial collective behavior in coupled map lattices and the spectral properties of their transfer or perron frobenius operator in particular it is argued that non trivial collective behavior corresponds to a perron frobenius operator possessing a cyclical spectral decomposition known as asymptotic periodicity we also discuss to what extent changes in the spectral properties of the perron frobenius operator are related to the phase transitions observed between two types of non trivial collective behavior

chaos and diffusion in deterministic cellular automata abstract it is shown that some of the deterministic one dimensional cellular automata studied recently by wolfram exhibit a kind of spontaneous symmetry breaking the associated kinks bloch walls perform annihilating diffusive walks for infinite lattices and large times in addition close analogies between these automata and strange attractors are exhibited by mapping the automata onto dynamical systems defined by iterations of the unit square

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

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

phase transition and correlation decay in coupled map lattices for a coupled map lattice with a specific strong coupling emulating stavskaya s probabilistic cellular automata we prove the existence of a phase transition using a peierls argument and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling this implies the exponential decay in space and in time of the correlation functions of the invariant measures

liapunov exponents in high dimensional symplectic dynamics the existence of a thermodynamic limit of the distribution of liapunov exponents is numerically verified in a large class of symplectic models ranging from hamiltonian flows to maps and products of random matrices in the highly chaotic regime this distribution is approximately model independent near an integrable limit only a few exponents give a relevant contribution to the kolmogorov sinai entropy

realizing homology boundary links with arbitrary patterns hornology boundary links have become an increasingly important class of links largely due to their significance in the ongoing concordance classification of links tim cochran and jerome levine defined an algebraic object called a pattern associated to a homology boundary link which can be used to study the deviance of a homology boundary link from being a boundary link since a pattern is a set of nx elements which normally generates the free group of rank nxs any invariants which detect non trivial patterns can be applied to the purely algebraic question of when such a set is a set of conjugates of a generating set for the free group we will give a constructive geometric proof that all patterns are realized by some homology boundary link lrl in srl 2 we shall also prove an analogous existence theorem for calibrations of e links a more general and less understood class of links tha homology boundary links 1 1 ntroduction a lin1z of m components is a smooth oriented submanifold l x1 km of sn 2 that is an ordered disjoint union of m manifolds each of which is piecewiselinearly homeomorphic to sn if m 1 l is usually called a 1fnot l is a boundary lin1z if there exist m disjoint seifert surfaces i e oriented submanifolds v1 vm of sn 2 such that avi ki for i 1 m knots and links are of interest since they repeatedly arise in the classification of manifolds an especially significant equivalence relation on links is c oncordance two links lo and l1 are concordant if there exists a smooth oriented submanifold of m components c c1 cm of sn 2 x i such that i c is piecewise linearly homeomorphic to lo x i and ii ac n sn 2 x i lli for i c 0 1 the classification of knot concordance groups was obtained in the rnid 1960 s by m kervaire and j levine 12 14 among the things they prove is that the knot concordance group is trivial when n is even and is an infinitely generated group when n is odd the techniques used in the concordance classification of knots have been found to extend in a compatible manner to the class of bou ndary links 2 13 19 however the extension of these ideas to links in general has been a much more difficult and less successful task in the process another class of links called homology boundary links has arisen a hornology boundary link of m components is a link which admits m disjoint generalized seifelzt surfaces y1 ym such that received by the editors may 16 1995 and in revised form october 30 1995 1991 mathematics s lbject classification primary 57q45 57m07 57m15 a 1998 american mathematic 1l so iety 87 this content downloaded from 207 46 13 28 on tue 30 aug 2016 05 27 13 utc all use subject to http about jstor org terms

the emergence of coherent structures in coupled map lattices we show how increasing spatial interaction leads to the merging of coherent structures from chaos in some systems of coupled map lattices this phenomenon reflects the arising of new ground states in the corresponding model of statistical mechanics if we further increase the coupling then new ground states appear showing the coexistence of a large scale coherent structure with a small scale chaotic motion this allows us to propose a generalization of the notion of spatial intermittency

ising type and other transitions in one dimensional coupled map lattices with sign symmetry we consider a one dimensional lattice of expanding antisymmetric maps 1 1 1 1 with nearest neighbor diffusive coupling for such systems it is known that if the coupling parameter e is small there is unique stationary in time state which is chaotic in space time a disputed question is whether such systems can exhibit ising type phase transitions as e grows beyond some critical value ec we present results from computer experiments which give definite indication that such a transition takes place the mean square magnetization appears to diverge as e approaches some critical value with a critical exponent around 0 9 we also study other properties of the coupled map system

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

tensor powers of modules over finitely generated abelian groups in an earlier paper 11 the authors investigated as a major component of their final result a special case of the following question let r be a commutative ring with unity g a finitely generated abelian group and a4 a finitely generated rg module consider the tensor power m as an rg module via the diagonal action of g under what conditions is m a finitely generated rg module the answer obtained in 1 was for the case when r is a field and used an invariant z m introduced by the first author and strebel in 3 we briefly describe cl firstly if n is the torsion free rank of g we can identify hom g w with w defining two elements of hom g iw to be equivalent if they differ by a positive real multiple we obtain a natural projection of hom g w o onto the sphere s i denote the equivalence class of xe hom g 1w by x and define gcxi g ge g x g 30 then z is the subset of s consisting of all those x for which m is a finitely generated rg module and cl is the complement of c in s we say that m is k tame if there do not exist x i xk in zh such that x1 xk 0 then the partial answer referred to above theorem 3 4 of l is

seifert matrices and boundary link cobordisms to an m component boundary link of odd dimension a matrix is associated by taking the seifert pairing on a seifert surface of the link an algebraic description of the set of boundary link cobordism classes of boundary links is obtained by using this matrix invariant

l2 signatures homology localization and amenable groups aimed at geometric applications we prove the homology cobordism invariance of the l2 betti numbers and l2 signature defects associated to the class of amenable groups lying in strebel s class d r which includes some interesting infinite finite non torsion free groups this result includes the only prior known condition that is a poly torsion free abelian group or a finite p group we define a new commutator series that refines harvey s torsion free derived series of groups using the localizations of groups and rings of bousfield vogel and cohn the series called the local derived series has versions for homology with arbitrary coefficients and satisfies functoriality and an injectivity theorem we combine these two new tools to give some applications to distinct homology cobordism types within the same simple homotopy type in higher dimensions to concordance of knots in three manifolds and to spherical space forms in dimension 3 2012 wiley periodicals inc

injectivity theorems and algebraic closures of groups with coefficients abstractrecently cochran and harvey defined torsion free derived series of groups and proved an injectivity theorem on the associated torsion free quotients we show that there is a universal construction which extends such an injectivity theorem to an isomorphism theorem our result relates injectivity theorems to a certain homology localization of groups in order to give a concrete combinatorial description and existence proof of the necessary homology localization we introduce a new version of algebraic closures of groups with coefficients by considering certain types of equations

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

coupling induced statistical cycling in two diffusively coupled maps abstract this paper discusses the effects of diffusively coupling two identical one dimensional maps attention is focused on situations where the local isolated maps are statistically stable but where the coupled system is not a biologically motivated map and the quadratic map are numerically shown to display this behavior the piecewise linear tent map is then investigated analytically and we give a phase diagram of this system which displays the location of nonequilibrium phase transitions it is conjectured that the diffusive coupling of two chaotic but statistically stable maps i e with asymptotically stable perron frobenius operators can yield a two dimensional system which is not statistically stable whose associated perron frobenius operator is asymptotically periodic

correlations and spectra of an intermittent chaos near its onset point a one parameter family of piecewise linear discontinuous maps which bifurcates from a periodic state of periodm m 2 3 to an intermittent chaos is studied as a new model for the onset of turbulence via intermittency the onset of chaos of this model is due to the excitation of an infinite number of unstable periodic orbits and hence differs from pomeau manneville s mechanism which is a collapse of a pair of stable and unstable periodic orbits the invariant density the time correlation function and the power spectrum are analytically calculated for an infinite sequence of values of the bifurcation parameter which accumulate to the onset point c from the chaos side c 0 the power spectrum near 0 is found to consist of a large number of lorentzian lines with two dominant peaks the highest peak lies around frequency 2 m with the power law envelope l 2 m 4 the second highest peak lies around o 0 with the envelope l 2 the width of each line decreases as and the separation between lines decreases as lg3 1 it is also shown that the liapunov exponent takes the form m and the mean lifetime of the periodic state in the intermittent chaos is given bym 1 ln 1 1

analytical approach for piecewise linear coupled map lattices a simple construction is presented which generalizes piecewise linear one dimensional markov maps to an arbitrary number of dimensions the corresponding coupled map lattice known as a simplicial mapping in the mathematical literature allows for an analytical investigation in particular the spin hamiltonian which is generated by the symbolic dynamics is accessible as an example a formal relation between a globally coupled system and an ising mean field model is established the phase transition in the limit of infinite system size is analyzed and analytical results are compared with numerical simulations

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

ising type transitions in coupled map lattices we study by means of computer simulations some models of coupled map lattices cml with symmetry subject to diffusive nearest neighbor coupling with the purpose of providing a better understanding of the occurrence of isingtype transitions of the type found by miller and huse we argue on the basis of numerical evidence that such transitions are connected to the appearance of a minimum in the lyapunov dimension of the system as a function of the coupling parameter two dimensional cmls similar to the one in miller and huse but with no minimum in the lyapunov dimension plot have no ising transition the condition seems to be necessary though by no means sufficient we also argue relying on the analysis of bunimovich and sinai that coupled map lattices should behave differently with respect to dimension than ising models

coupled map lattices some topological and ergodic properties abstract lattice dynamical systems ldss form the class of extended systems that is the intermediate one between partial differential equations pdes and cellular automata the most popular class of ldss is formed by coupled map lattices cmls while being introduced rather recently ldss allowed already to clarify and to define exactly some notions that form the basis of the modern phenomenological theory of spatio temporal dynamics and to obtain some new and even rigorous results on space time chaos intermittency and pattern formation we discuss the rigorous results that were obtained in this area but eventually give also some applications

the pettis integral for multi valued functions via single valued ones abstract we study the pettis integral for multi functions f cwk x defined on a complete probability space with values into the family cwk x of all convex weakly compact non empty subsets of a separable banach space x from the notion of pettis integrability for such an f studied in the literature one readily infers that if we embed cwk x into l b x by means of the mapping j cwk x l b x defined by j c x sup x c then j f is integrable with respect to a norming subset of b l b x a natural question arises when is j f pettis integrable in this paper we answer this question by proving that the pettis integrability of any cwk x valued function f is equivalent to the pettis integrability of j f if and only if x has the schur property that is shown to be equivalent to the fact that cwk x is separable when endowed with the hausdorff distance we complete the paper with some sufficient conditions involving stability in talagrand s sense that ensure the pettis integrability of j f for a given pettis integrable cwk x valued function f

a cell dynamical system model of chemical turbulence a cellular automaton like caricature of chemical turbulence on an infinite one dimensional lattice is studied the model exhibits apparently turbulent space time patterns to make this statement precise the following problems or points are discussed 1 the infinite system size limit of such cell dynamical systems and its observability is defined 2 it is proved that the invariant state in the large system size limit of the turbulent phase exhibits spatial patterns governed by a gibbs random field 3 potential characteristics of turbulent space time patterns are critically surveyed and a working definition of weak turbulence is proposed 4 it is proved that the invariant state of the turbulent phase is actually weak turbulent furthermore we conjecture that the turbulent phase of our model is an example of a k system that is not bernoulli

on a problem of bousfield for metabelian groups abstract the homological properties of localizations and completions of metabelian groups are studied it is shown that for r q or r z n and a finitely presented metabelian group g the natural map from g to its r completion induces an epimorphism of homology groups h 2 r this answers a problem of a k bousfield for the class of metabelian groups

a new result on impulsive differential equations involving non absolutely convergent integrals in this paper we obtain as an application of a darbo type theorem global solutions for differential equations with impulse effects under the assumption that the function on the right hand side is integrable in the henstock sense we thus generalize several previously given results in literature for ordinary or impulsive equations

henstock kurzweil pettis integrability of compact valued multifunctions with values in an arbitrary banach space abstract the aim of this paper is to describe henstock kurzweil pettis hkp integrable compact valued multifunctions such characterizations are known in case of functions see di piazza and musial 2006 16 it is also known see di piazza and musial 2010 19 that each hkp integrable compact valued multifunction can be represented as a sum of a pettis integrable multifunction and of an hkp integrable function invoking to that decomposition we present a pure topological characterization of integrability having applied the above results we obtain two convergence theorems that generalize results known for hkp integrable functions we emphasize also the special role played in the theory by weakly sequentially complete banach spaces and by spaces possessing the schur property

cohomological finiteness conditions for elementary amenable groups it is proved that every elementary amenable group of type fp admits a cocompact classifying space for proper actions

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

link concordance invariants and homotopy theory we show that each of a sequence of concordance invariants for codimension two links of spheres ins n 2 defined by kent orr is identically zero forn 1 for classical links n 1 the same proof shows that these invariants vanish if and only if milnor s bar mu vanish a result obtained independently and earlier by orr himself we offer sufficient conditions for the vanishing of orr s invariant not covered by the above we discuss how this relates to positive results

cooperative behavior of a chain of synaptically coupled chaotic neurons abstract a coupled linear chain of hindmarsh rose model neurons with reciprocal inhibition between neighboring neurons exhibited synchronous oscillations in which neighboring neurons burst out of phase and next nearest neighbor neurons burst in phase the bifurcations observed inside this out of phase regime were qualitatively the same for all chains with an even number of neurons and were similar to those observed in a single isolated cell although the organization of the behavior of a chain of coupled neurons was more regular than that of an isolated cell when noise was added to the synaptic coupling strengths there was less hysteresis in the system and many of the bifurcations with smaller basins of attraction were eliminated making the system even more regular these results suggest that in populations of bursting neurons with reciprocal inhibition the chaotic behavior found in single cells is suppressed

noncharacteristic embeddings of the n dimensional torus in the n 2 dimensional torus we construct certain exotic embeddings of the n torus tn in tn 2 in the standard homotopy class we turn an embedding f tn tn 2 characteristic if there exists some map a tn 2 tn 2 in the standard homotopy class with the property that a o f tn tn 2 is the standard coordinate inclusion and a tn 2 f tn c tn 2 tn we find examples of noncharacteristic embeddings f in dimensions n 4k 1 n 5 and show that these examples are not even cobordant to characteristic embeddings we let g denote the fundamental group of the complement of the standard coordinate inclusion tn 2 tn then we can associate to f a real valued signature function on the set of j dimensional unitary representations of g where g denotes the fundamental group of the localization of tn 2 tn with respect to homology with local coefficients in z zn 2 this function is a cobordism invariant which has certain periodicity properties for characteristic embeddings we verify that this periodicity does not hold for our examples f implying that they are not characteristic additional results include a proof that the examples f become cobordant to characteristic embeddings upon taking the cartesian product with the identity map on a circle

a lusin type measurability property for vector valued functions abstract we study the class of riemann measurable vector valued functions based on a lusin type property this class contains all riemann integrable functions and is closely related to the restricted versions of the mcshane and henstock integrals the m and h integrals defined by means of lebesgue measurable gauges our developments are in the spirit of the riemann type integral theory for real valued functions in particular we prove that a bounded riemann measurable vector valued function is m integrable

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

on the comparison of aumann and bochner integrals we introduce the aumann integral in the finitely additive setting and we compare it with the bochner integral

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

notes on jordan fields based on an article by maharam abstract results of maharam on jordan fields associated with a finitely additive measure are extended to take into consideration the natural topology induced by an algebra of sets namely that induced by the stone space based on this the question of when the jordan field is a algebra and the question of the completeness of associated l 1 spaces are answered

on bousfield s problem for solvable groups of finite prufer rank abstract for a group g and r z z p q we denote by g r the r completion of g we study the map h n g k h n g r k where r k z z p z p z p q q we prove that h 2 g k h 2 g r k is an epimorphism for a finitely generated solvable group g of finite prufer rank in particular bousfield s hk localisation of such groups coincides with the k completion for k z p q moreover we prove that h n g k h n g r k is an epimorphism for any n if g is a finitely presented group of the form g m c where c is the infinite cyclic group and m is a c module

group localization and two problems of levine a k bousfield s h mathbb z localization of groups inverts homologically two connected homomorphisms of groups j p levine s algebraic closure of groups inverts homomorphisms between finitely generated and finitely presented groups which are homologically two connected and for which the image normally generates we resolve an old problem concerning bousfield h mathbb z localization of groups and answer two questions of levine regarding algebraic closure of groups in particular we show that the kernel of the natural homomorphism from a group g to its bousfield h mathbb z localization is not always a g perfect subgroup in the case of algebraic closure of groups we prove the analogous result that this kernel is not always a union of invisible subgroups