invariant ergodic measures and the classification of crossed product c algebras abstract let g x be a minimal free continuous action of an infinite countable amenable group on an infinite compact metrizable space in this paper under the hypothesis that the invariant ergodic probability borel measure space e g x is compact and zero dimensional we show that the action has the small boundary property this partially answers an open problem in dynamical systems that asks whether a minimal free action of an amenable group has the small boundary property if its space m g x of invariant borel probability measures forms a bauer simplex in addition under the same hypothesis we show that dynamical comparison implies almost finiteness which was shown by kerr to imply that the crossed product is z stable finally we discuss some rank properties and provide two classifiability results for crossed products one of which is based on the work of elliott and niu

strongly self absorbing c algebras say that a separable unital c algebra v c is strongly self absorbing if there exists an isomorphism v such that lx ai e approximately unitarily equivalent homomorphisms we study this class of algebras which includes the cuntz algebras 2 ooo the uhf algebras of infinite type the jiang su algebra z and tensor products of 00 with uhf algebras of infinite type given a strongly self absorbing c algebra v we characterise when a separable c algebra absorbs v tensorially i e is p stable and prove closure properties for the class of separable testable c algebras finally we compute the possible if groups and prove a number of classification results which suggest that the examples listed above are the only strongly self absorbing c algebras

organizing the arithmetic of elliptic curves abstract suppose that e is an elliptic curve defined over a number field k p is a rational prime and k is the maximal z p power extension of k in previous work b mazur k rubin elliptic curves and class field theory in ta tsien li ed proceedings of the international congress of mathematicians icm 2002 vol ii higher education press beijing 2002 pp 185 195 b mazur k rubin pairings in the arithmetic of elliptic curves in j cremona et al eds modular curves and abelian varieties progress in mathematics vol 224 2004 pp 151 163 we discussed the possibility that much of the arithmetic of e over k i e the mordell weil groups and their p adic height pairings the shafarevich tate groups and their cassels pairings over all finite extensions of k in k can be described efficiently in terms of a single skew hermitian matrix with entries drawn from the iwasawa algebra of k k in this paper using work of nekovar j nekovar selmer complexes preprint available at http www math jussieu fr nekovar pu we show that under not too stringent conditions such an organizing matrix does in fact exist we also work out an assortment of numerical instances in which we can describe the organizing matrix explicitly

computations in non commutative iwasawa theory we study special values of l functions of elliptic curves over mathbb q twisted by artin representations that factor through a false tate curve extension mathbb q mu p infty sqrt p infty m mathbb q in this setting we explain how to compute l functions and the corresponding iwasawa theoretic invariants of non abelian twists of elliptic curves our results provide both theoretical and computational evidence for the main conjecture of non commutative iwasawa theory

cartan subalgebras in c algebras existence and uniqueness we initiate the study of cartan subalgebras in c algebras with a particular focus on existence and uniqueness questions for homogeneous c algebras these questions can be analyzed systematically using the theory of fiber bundles for group c algebras while we are able to find cartan subalgebras in c algebras of many connected lie groups there are classes of discrete groups for instance non abelian free groups whose reduced group c algebras do not have any cartan subalgebras moreover we show that uniqueness of cartan subalgebras usually fails for classifiable c algebras however distinguished cartan subalgebras exist in some cases for instance in nuclear uniform roe algebras

stereoscopic ranging by matching image modulations we apply an am fm surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system this is used to support the use of modulation based stereo matching where local image phase is used to compute stereo disparities the local image phase is an advantageous feature for image matching since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data local phase shifts however are problematic at high frequencies due to phase wrapping when disparities exceed spl plusmn spl pi we meld powerful multichannel gabor image demodulation techniques for multiscale coarse to fine computation of local image phase with a disparity channel model for depth computation the resulting framework unifies phase based matching approaches with am fm surface image models we demonstrate the concepts in a stereo algorithm that generates a dense accurate disparity map without the problems associated with phase wrapping

decomposition rank and z stability we show that separable simple nonelementary unital c algebras with finite decomposition rank absorb the jiang su algebra mathcal z tensorially this has a number of consequences for elliott s program to classify nuclear c algebras by their k theory data in particular it completes the classification of c algebras associated to uniquely ergodic smooth minimal dynamical systems by their ordered k groups

convection patterns in large aspect ratio systems abstract a theory which should have widespread application is developed to treat the statics and slow dynamics of patterns of convective rolls encountered in large aspect ratio rayleigh benard boxes for case of presentation the theory is developed using model equations wavenumber selection the shape of patterns stability and the time dependence resulting from long wavelength instabilities are discussed the effects of adding the local mean drift important in low prandtl number situations are investigated our theory includes the notion of the busse stability balloon reduces near critical values of the stress parameter to the newell whitehead segel equations and contains the pomeau manneville phase equation it also gives a detailed description of the way in which the field amplitude which is slaved to the phase gradient away from threshold becomes an independent order parameter near the critical point

nuclear dimension and mathcal z stability simple separable unital monotracial and nuclear mathrm c algebras are shown to have finite nuclear dimension whenever they absorb the jiang su algebra mathcal z tensorially this completes the proof of the toms winter conjecture in the unique trace case

defects are weak and self dual solutions of the cross newell phase diffusion equation for natural patterns abstract we show that defects are weak solutions of the phase diffusion equation for the macroscopic order parameter for natural patterns further by exploring a new class of nontrivial solutions for which the graph of the phase function has vanishing gaussian curvature in 3d all sectional curvatures excetp at points we are able to derive explicit expressions which capture the anatomies of point and line and surface defects in two and three dimensional patterns together with their topological characters and energetic constraints

unitary orbits of self adjoint operators in simple z stable c algebras abstract we prove that in a simple unital exact z stable c algebra the distance between the unitary orbits of self adjoint elements with connected spectrum is completely determined by spectral data this fails without the assumption of z stability

the spatio temporal structure of spiral defect chaos abstract we present a study of the recently discovered spatially extended chaotic state known as spiral defect chaos which occurs in low prandtl number large aspect ratio rayleigh benard convection we employ the modulus squared of the space time fourier transform of time series of two dimensional shadowgraph images to construct the structure factor s k this analysis is used to characterize the average spatial and temporal scales of the chaotic state we find that the correlation length and time can be described by power law dependences on the reduced rayleigh number these power laws have as yet no theoretical explanation

on equivariant global epsilon constants for certain dihedral extensions we consider a conjecture of bley and burns which relates the epsilon constant of the equivariant artin l function of a galois extension of number fields to certain natural algebraic invariants for an odd prime number p we describe an algorithm which either proves the conjecture for all degree 2p dihedral extensions of the rational numbers or finds a counterexample we apply this to show the conjecture for all degree 6 dihedral extensions of q the correctness of the algorithm follows from a finiteness property of the conjecture which we prove in full generality

on a simple unital projectionless c algebra we construct a unital separable c algebra z as an analog of the hyperfinite type ii 1 factor besides being nuclear simple projectionless and infinite dimensional z has a unique tracial state and is kk equivalent to inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the algebra of complex numbers it is shown that unital endomorphisms on z are approximately inner and that z is isomorphic to the infinite tensor product of its replicas it is also shown that a z a for certain interesting classes of unital simple nuclear c algebras a of real rank zero

the cuntz toeplitz algebras have nuclear dimension one abstract we prove that unital extensions of kirchberg algebras by separable stable af algebras have nuclear dimension one the title follows

nuclear dimension mathcal z stability and algebraic simplicity for stably projectionless c algebras the main result here is that a simple separable c algebra is mathcal z stable where mathcal z denotes the jiang su algebra if i it has finite nuclear dimension or ii it is approximately subhomogeneous with slow dimension growth this generalizes the main results of toms invent math 183 2 225 244 2011 and winter invent math 187 2 259 342 2012 to the nonunital setting as a consequence finite nuclear dimension implies mathcal z stability even in the case of a separable c algebra with finitely many ideals algebraic simplicity is established as a fruitful weakening of being simple and unital and the proof of the main result makes heavy use of this concept

on mordell weil groups and congruences between derivatives of twisted hasse weil l functions let a be an abelian variety defined over a number field k and let f be a finite galois extension of k let p be a prime number then under certain not too stringent conditions on a and f we compute explicitly the algebraic part of the p component of the equivariant tamagawa number of the pair h1 a f 1 z gal f k by comparing the result of this computation with the theorem of gross and zagier we are able to give the first verification of the p component of the equivariant tamagawa number conjecture for an abelian variety in the technically most demanding case in which the relevant mordell weil group has strictly positive rank and the relevant field extension is both non abelian and of degree divisible by p more generally our approach leads us to the formulation of certain precise families of conjectural p adic congruences between the values at s 1 of derivatives of the hasse weil l functions associated to twists of a normalised by a product of explicit equivariant regulators and periods and to explicit predictions concerning the galois structure of tate shafarevich groups in several interesting cases we provide theoretical and numerical evidence in support of these more general predictions

localized measurement of emergent image frequencies by gabor wavelets the authors derive implement and demonstrate a computational approach for the measurement of emergent image frequencies measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space conflicting requirements that are shown to be balanced by a generalized uncertainty relationship such spectral measurements can be obtained from the responses of multiple wavelet like channel filters that sample the signal spectrum and that yield a locus of possible solutions for each locally emergent frequency it is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are gabor wavelets a constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal the measurement of frequencies is then cast as an ill posed extremum problem regularized by the stabilizing term leading to an iterative constraint propagation algorithm the technique is demonstrated by application to a variety of 2 d textured images

on the structure of simple c algebras tensored with a uhf algebra ii let d be a simple unital c algebra let b be a uhf algebra and put a b d it is proved that if p q a are projections and p q for all quasitraces on a then p q in the sense of murray and von neumann a more general result involving positive operators in a is also proved if d has finitely many extremal quasi traces and the projections in d k separate these then it is proved that a has real rank zero finally it is proved that provided d is stably finite then each positive state on k0 d lifts to a quasi trace

on the equivariant tamagawa number conjecture for tate motives and unconditional annihilation results dfg collaborative research center 701 spectral structures and topological methods in mathematics

on the classification problem for nuclear c algebras we exhibit a counterexample to elliott s classification conjecture for simple separable and nuclear c algebras whose construction is elementary and demonstrate the necessity of extremely fine invariants in distinguishing both approximate unitary equivalence classes of automorphisms of such algebras and isomorphism classes of the algebras themselves the consequences for the program to classify nuclear c algebras are far reaching one has among other things that existing results on the classification of simple unital ah algebras via the elliott invariant of k theoretic data are the best possible and that these cannot be improved by the addition of continuous homotopy invariant functors to the elliott invariant

towards a universal theory for natural patterns abstract our goal is to find a macroscopic description of patterns that both unifies and simplifies classes of externally stressed dissipative pattern forming systems such as convecting fluids liquid crystals wideband lasers that are seemingly unrelated at the microscopic level we construct an order parameter equation which provides a controlled approximation of the original microscopic field in the limit of large aspect ratios it is built from and is a regularization of the cross newell phase diffusion equation obtained by averaging over the local periodicity of the pattern unlike the latter it is valid for all wavenumbers and can correctly capture the nucleation shape and nontrivial properties of the far fields of disclinations dislocations and grain boundaries it reduces to the cross newell equation away from pattern singularities and to the newell whitehead segel equation near onset as a consequence it correctly determines all the long wave instability boundaries zig zag eckhaus skew varicose of the busse balloon far from onset the order parameter is a real variable but its equation involves a functional corresponding to its local amplitude the local amplitude and phase required for the order parameter equation and the reconstruction of the approximation to the original field respectively are extracted from the order parameter field by wavelet analysis numerical comparisons between solutions of the original equation and the regularized equation are carried out we also explore a new class of singular and weak solutions of the cross newell equation which take account of the energetics of defects as well as their topologies these solutions correspond to convex and concave disclinations and their composites including saddles vortices targets dislocations and two new objects handles and bridges finally we show that phase grain boundaries lines across which the wavevector is discontinuous but the phase is continuous are captured by shock solutions of the phase diffusion equation

rokhlin dimension for flows we introduce a notion of rokhlin dimension for one parameter automorphism groups of c algebras this generalizes kishimoto s rokhlin property for flows and is analogous to the notion of rokhlin dimension for actions of the integers and other discrete groups introduced by the authors and zacharias in previous papers we show that finite nuclear dimension and absorption of a strongly self absorbing c algebra are preserved under forming crossed products by flows with finite rokhlin dimension and that these crossed products are stable furthermore we show that a flow on a commutative c algebra arising from a free topological flow has finite rokhlin dimension whenever the spectrum is a locally compact metrizable space with finite covering dimension for flows that are both free and minimal this has strong consequences for the associated crossed product c algebras those containing a non zero projection are classified by the elliott invariant for compact manifolds this consists of topological k theory together with the space of invariant probability measures and a natural pairing given by the ruelle sullivan map

minimal dynamics and the classification of c algebras let x be an infinite compact metrizable space of finite covering dimension and x x a minimal homeomorphism we prove that the crossed product c x absorbs the jiang su algebra tensorially and has finite nuclear dimension as a consequence these algebras are determined up to isomorphism by their graded ordered k theory under the necessary condition that their projections separate traces this result applies in particular to those crossed products arising from uniquely ergodic homeomorphisms

on the analytic signal the teager kaiser energy algorithm and other methods for defining amplitude and frequency this paper compares the teager kaiser algorithm tka and other similar local methods to the analytic signal as procedure the general concepts of the instantaneous amplitude and frequency are discussed it is shown that only as meets certain physical conditions for the amplitude phase and frequency apf the advantage of accuracy and simplicity of the as is also demonstrated

decomposable approximations of nuclear c algebras abstract we show that nuclear c algebras have a refined version of the completely positive approximation property in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps we use this to show that a separable nuclear c algebra a which is closely contained in a c algebra b embeds into b

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

quasidiagonal traces on exact c algebras abstract recently it was proved by tikuisis white and winter that any faithful trace on a separable nuclear c algebra in the uct class is quasidiagonal building on their work we generalise the result and show that any faithful amenable trace on a separable exact c algebra in the uct class is quasidiagonal we also prove that any amenable trace on a separable exact quasidiagonal c algebra in the uct class is quasidiagonal

strict comparison and z absorption of nuclear c algebras for any unital separable simple infinite dimensional nuclear c algebra with finitely many extremal traces we prove that mathcal z absorption strict comparison and property si are equivalent we also show that any unital separable simple nuclear c algebra with tracial rank zero is approximately divisible and hence is mathcal z absorbing

the jiang su algebra revisited we give a number of new characterizations of the jiang su algebra z both intrinsic and extrinsic in terms of c algebraic dynamical topological and k theoretic conditions along the way we study divisibility properties of c algebras we give a precise characterization of those unital c algebras of stable rank one that admit a unital embedding of the dimensiondrop c algebra zn n 1 and we prove a cancellation theorem for the cuntz semigroup of c algebras of stable rank one

computing fitting ideals of iwasawa modules this paper determines in an equivariant sense the fitting ideals of several iwasawa modules including the most canonical one the connection between the modules themselves which are usually not of finite projective dimension and the required auxiliary modules of finite projective dimension is made rather explicit the resulting fitting ideals look like stickelberger ideals and there is a close relation with recent work of kurihara as an application we obtain new evidence in favor of the brumer stark conjecture

computation of stark tamagawa units let k be a totally real number field and let l denote an odd prime number we design an algorithm which computes strong numerical evidence for the validity of the equivariant tamagawa number conjecture for the q g equivariant motive h0 spec l where l k is a cyclic extension of degree l and group g this conjecture is a very deep refinement of the classical analytic class number formula in the course of the algorithm we compute a set of special units which must be considered as a generalization of the conjecturally existing stark units associated to first order vanishing dirichlet l functions

constructing minimal homeomorphisms on point like spaces and a dynamical presentation of the jiang su algebra the principal aim of this paper is to give a dynamical presentation of the jiang su algebra originally constructed as an inductive limit of prime dimension drop algebras the jiang su algebra has gone from being a poorly understood oddity to having a prominent positive role in george elliott s classification programme for separable nuclear c algebras here we exhibit an etale equivalence relation whose groupoid c algebra is isomorphic to the jiang su algebra the main ingredient is the construction of minimal homeomorphisms on infinite compact metric spaces each having the same cohomology as a point this construction is also of interest in dynamical systems any self map of an infinite compact space with the same cohomology as a point has lefschetz number one thus if such a space were also to satisfy some regularity hypothesis which our examples do not then the lefschetz hopf theorem would imply that it does not admit a minimal homeomorphism

patterns defects and integrability abstract in this paper recent results on the behavior of roll patterns in a class of problems typified by high prandtl number convection are presented a key finding is that the gaussian curvature of the crumpled phase surface which consists of patches with an almost constant wave number line defects on which most of the free energy is stored and point defects with nontrivial topologies condenses onto line and point defects this property allows considerable mathematical simplification in that the fourth order nonlinear diffusion equation governing stationary states can be effectively reduced to the linear helmholtz equation the observed patterns have much is common with the deformation of thin elastic sheets

quasidiagonality of nuclear c algebras we prove that faithful traces on separable and nuclear c algebras in the uct class are quasidiagonal this has a number of consequences firstly by results of many hands the classification of unital separable simple and nuclear c algebras of finite nuclear dimension which satisfy the uct is now complete secondly our result links the finite to the general version of the toms winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension finally we confirm the rosenberg conjecture discrete amenable groups have quasidiagonal c algebras

the equivariant tamagawa number conjecture and modular symbols we show that for each elliptic curve e mathbb q with l e mathbb q 1 ne 0 there are infinitely many odd primes l and for each such l infinitely many abelian l extensions k mathbb q such that the l part of the equivariant tamagawa number conjecture holds for the pair h 1 e k 1 mathbb z text gal k mathbb q

equivariant epsilon constant conjectures for weakly ramified extensions we study the local epsilon constant conjecture as formulated by breuning in breuning j london math soc 70 2 289 306 2004 this conjecture fits into the general framework of the equivariant tamagawa number conjecture etnc and should be interpreted as a consequence of the expected compatibility of the etnc with the functional equation of artin l functions let k mathbb q p be unramified under some mild technical assumption we prove breuning s conjecture for weakly ramified abelian extensions n k with cyclic ramification group as a consequence of breuning s local global principle we obtain the validity of the global epsilon constant conjecture as formulated in bley and burns proc lond math soc 87 3 545 590 2003 and of chinburg s omega 2 conjecture as stated in chinburg ann math 121 2 351 376 1985 for certain infinite families f e of weakly and wildly ramified extensions of number fields

finding large selmer rank via an arithmetic theory of local constants we obtain lower bounds for selmer ranks of elliptic curves over dihedral extensions of number fields suppose k k is a quadratic extension of number fields e is an elliptic curve defined over k and p is an odd prime let denote the maximal abelian p extension of k that is unramified at all primes where e has bad reduction and that is galois over k with dihedral galois group i e the generator c of gal k k acts on gal k by inversion we prove under mild hypotheses on p that if the zp rank of the pro p selmer group sp e k is odd then rank zp s p e f f k for every finite extension f of k in

non commutative fitting invariants and annihilation of class groups abstract one can associate to each finitely presented module m over a commutative ring r an r ideal fitt r m which is called the zeroth fitting ideal of m over r and which is an important natural invariant of m we generalize this notion to o orders in separable algebras where o is a complete commutative noetherian local ring as an application we construct annihilators of class groups assuming the validity of the equivariant tamagawa number conjecture for a certain motive attached to a galois cm extension of number fields

a new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable hilbert space abstract in 1975 a connes proved the fundamental result that injective factors on a separable hilbert space are hyperfinite in this paper a new proof of this result is presented in which the most technical parts of connes proof are avoided particularly the proof does not rely on automorphism group theory the starting point in this approach is wassermann s simple proof of injective semidiscrete together with choi and effros characterization of semidiscrete von neumann algebras as those von neumann algebras n for which the identity map on n has an approximate completely positive factorization through n n matrices

nuclear dimension and mathcal z stability of pure c algebras in this article i study a number of topological and algebraic dimension type properties of simple c algebras and their interplay in particular a simple c algebra is defined to be tracially m bar m pure if it has strong tracial m comparison and is tracially bar m almost divisible these notions are related to each other and to nuclear dimension

on the non abelian brumer stark conjecture and the equivariant iwasawa main conjecture we show that for an odd prime p the p primary parts of refinements of the imprimitive non abelian brumer and brumer stark conjectures are implied by the equivariant iwasawa main conjecture eimc for totally real fields crucially this result does not depend on the vanishing of the relevant iwasawa mu invariant in combination with the authors previous work on the eimc this leads to unconditional proofs of the non abelian brumer and brumer stark conjectures in many new cases

classification of inductive limits of 1 dimensional nccw complexes abstract a classification result is obtained for the c algebras that are stably isomorphic to inductive limits of 1 dimensional noncommutative cw complexes with trivial k 1 group the classifying functor cu is defined in terms of the cuntz semigroup of the unitization of the algebra for the simple c algebras covered by the classification cu reduces to the ordered k 0 group the cone of traces and the pairing between them as an application of the classification it is shown that the crossed products by a quasi free action o 2 r are all isomorphic for a dense set of positive irrational numbers

classifying crossed product c algebras i combine recent results in the structure theory of nuclear rm c algebras and in topological dynamics to classify certain types of crossed products in terms of their elliott invariants in particular transformation group rm c algebras associated to free minimal bbb z d actions on the cantor set with compact space of ergodic measures are classified by their ordered rm k theory in fact the respective statement holds for finite dimensional compact metrizable spaces provided that projections of the crossed products separate tracial states moreover rm c algebras associated to certain minimal homeomorphisms of spheres s 2n 1 are only determined by their spaces of invariant borel probability measures without a condition on the space of ergodic measures finally i show that for a large collection of classifiable rm c algebras crossed products by bbb z d actions are generically again classifiable

on the equivariant tamagawa number conjecture in tame cm extensions let l k be a finite galois cm extension with galois group g the equivariant tamagawa number conjecture etnc for the pair h 0 rm spec l 0 mathbb z g naturally decomposes into p parts where p runs over all rational primes if p is odd these p parts in turn decompose into a plus and a minus part let l k be tame above p we show that a certain ray class group of l defines an element in k 0 mathbb z p g mathbb q p which is determined by a corresponding stickelberger element if and only if the minus part of the etnc at p holds for this we use the lifted root number conjecture for small sets of places which is equivalent to the etnc in the number field case for abelian g we show that the minus part of the etnc at p implies the strong brumer stark conjecture at p we prove the minus part of the etnc at p for almost all primes p

equivariant epsilon constants discriminants and etale cohomology let l k be a finite galois extension of number fields we formulate and study a conjectural equality between an element of the relative algebraic k group k 0 mathbb z mathrm gal l k mathbb r which is constructed from the equivariant artin epsilon constant of l k and a sum of structural invariants associated to l k the precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the tamagawa number conjecture of bloch and kato as formulated by flach and the second named author should be compatible with the functional equation of the associated l function we show that more concretely our conjecture also suggests a completely systematic refinement of the central approach and results of classical galois module theory in particular the evidence for our conjecture that we present here already strongly refines many of the main results of galois module theory

ranks of operators in simple c algebras with stable rank one let a be a simple c algebra with stable rank one we show that every strictly positive lower semicontinuous affine function on the simplex of normalized quasitraces of a is realized as the rank of an operator in the stabilization of a assuming moreover that a has locally finite nuclear dimension we deduce that a is mathcal z stable if and only if it has strict comparison of positive elements in particular the toms winter conjecture holds for simple approximately subhomogeneous c algebras with stable rank one

integrality of stickelberger elements and the equivariant tamagawa number conjecture let l k be a nite galois cm extension of number elds with galois group g in an earlier paper the author has de ned a module sku l k over the center of the group ring zg which coincides with the sinnott kurihara ideal if g is abelian and in particular contains many stickelberger elements it was shown that a certain conjecture on the integrality of sku l k implies the minus part of the equivariant tamagawa number conjecture at an odd prime p for an in nite class of non abelian galois cm extensions of number elds which are at most tamely rami ed above p provided that iwasawa s invariant vanishes here we prove a relevant part of this integrality conjecture which enables us to deduce the equivariant tamagawa number conjecture from the vanishing of for the same class of extensions

central sequence c algebras and tensorial absorption of the jiang su algebra we study properties of the central sequence algebra a a 0 of a c algebra a and we present an alternative approach to a recent result of matui and sato they prove that every unital separable simple nuclear c algebra whose trace simplex is nite dimensional tensorially absorbs the jiang su algebra if and only if it has the strict comparison property we extend their result to the case where the extreme boundary of the trace simplex is closed and of nite topological dimension we are also able to relax the assumption on the c algebra of having the strict com parison property to a weaker property that we call local weak comparison namely we prove that a unital separable simple nuclear c algebra whose trace simplex has nite dimensional closed extreme boundary tensorially absorbs the jiang su algebra if and only if it has the local weak comparison property we can also eliminate the nuclearity assumption if instead we assume the si property of matui and sato and moreover that each ii1 factor representation of the c algebra is a mcdu factor

a wavelet based algorithm for pattern analysis abstract patterns with a local roll structure arise in many diverse physical systems which have little in common at the microscopic level in this paper we construct an algorithm based on the wavelet transform that can be used as a diagnostic tool to extract from such patterns macroscopic information like the local director field the local amplitude away from defects and slowly varying fields such as mean drift which may be soft modes of pattern it allows a precise detection of phase grain boundaries and point defects several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm finally the algorithm is applied to actual experimental convection patterns allowing us to draw several conclusions about the nature of the wave director field in such patterns