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

dynamics of complex interfaces complex interfacial dynamics is studied in an oscillatory medium described by a deterministic coupled map lattice this dynamical system supports only stable periodic attractors the interfaces that separate the stable homogeneous phases exhibit different types of behavior ranging from simple planar fronts with low periodicity to highly irregular fronts with complex spatiotemporal transients a dynamical analysis of the system is carried out for a small interface length l in which the probabilities of occurrence of given periodic orbits the velocities of the corresponding interfaces and lyapunov exponents are calculated the importance of transient dynamics for large l is demonstrated in the large l regime the interfacial evolution and structure are characterized in statistical terms and the simulation results are compared with phenomenological stochastic models such as edwards wilkinson and kardar parisi zhang equations in some parameter regions the deterministic transient interfacial dynamics of the coupled map model is described well by such models if finite size effects are taken into account nucleation and growth dynamics are also investigated the system provides a framework in which to study complex interfacial structures

k homology asymptotic representations and unsuspended e theory connes and higson defined a bivariant homology theory e a b for separable c algebras the elements of e a b are taken to be homotopy classes of asymptotic momorphisms from sa k to sb k in symbols e a b sa sb k if a is k nuclear then e theory agrees with kasparov s bivariant k theory we show that in many cases one need not take suspensions to calculate the e theory group e a b for many a we show e a b a b k for all b among the a for which this is true are c0 x pt for x with the homotopy type of a finite connected cw complex this gives a concrete realization of k homology related to the brown douglas fillmore description for example k0 x arises as asymptotic representations k0 x c0 x k other a for which our isomorphic holds include the nonunital dimension drop intervals in this case there is no distinction between homomorphisms and asymptotic morphisms so we have succeeded in classifying all homomorphisms from a dimension drop interval to a stable c algebra this was subsequently used by elliott j reine angew math 443 1993 179 219 in the classification of certain c algebras the dimension drop interval may also be used to describe k x z n in terms of paths of asymptotic representations of c0 x

phase transitions in 2d linearly stable coupled map lattices abstract interface dynamics separating homogeneous phases is shown to be the main mechanism underlying irregular evolution in 2d linearly stable coupled map lattices in a fully deterministic model belonging to this class we find evidence of at least two different regimes that we call weak and strong turbulence the transition between the two regimes is carefully investigated revealing a direct connection with the destabilization of the interfaces separating homogeneous phases the critical behaviour is analysed and compared with that of stochastic models like directed percolation

c algebras generated by stable relations abstract presentations of certain c algebras such as c0 0 1 mn by generators and relations are proven to be stable by the weakest definition of stability a set p1 pn of star polynomials is stable if operators a1 an which almost satisfy these relations meaning pi a1 an can be perturbed within c a1 an to satisfy these relations exactly homotopy and perturbation results for these c algebras are corollaries in particular we prove some new results about the dimension drop c algebras a n c 0 1 m n 0 1 c i we show that an is semiprojective answering a question of effros and kaminker also we show that whenever an b is a homomorphism approximately contained in a sub c algebra b0 b there is a nearby homomorphism of an into b0 this answers a question raised by elliott we prove technical results regarding mn c0 0 1 which should be useful elsewhere first we show this is projective meaning a star homomorphism mn c0 0 1 b j always lifts to a star homomorphism mn c0 0 1 b secondly we show that for a finitely generated m n a m n c 0 0 1 c 0 0 1 a if the amalgamation is done properly

perturbation of a hopf bifurcation by an external time periodic forcing contenrs i introduction ii the mathematical model iii dynamics of the poincark map in the non resonant and weakly resonant cases iv dynamics of the poincark map in the p l resonant case v dynamics of the poincart map in the p 2 resonant case vi dynamics of the poincark map in the p 3 resonant case

z stability of crossed products by strongly outer actions ii we consider a crossed product of a unital simple separable nuclear stably finite z stable c algebra a by a strongly outer cocycle action of a discrete countable amenable group under the assumption that a has finitely many extremal tracial states and is elementary amenable we show that the twisted crossed product c algebra is z stable as an application we also prove that all strongly outer cocycle actions of the klein bottle group on z are cocycle conjugate to each other this is the first classification result for actions of non abelian infinite groups on stably finite c algebras

the ext class of an approximately inner automorphism let a be a simple unital at algebra of real rank zero it is shown below that the range of the natural map from the approximately inner automorphism group to kk a a coincides with the kernel of the map kk a a l 1 0 hom ki a ki a 1 introduction and preliminaries 1 1 an automorphism of a unital c algebra a is said to be an approximately inner automorphism if there is a sequence of unitaries un 2 a such that a limadun a for all a 2 a it follows that the induced map on k a is the identity map there is however an invariant of k theoretical interest which can occur nontrivial extensions may arise in the six term periodic sequence for the k theory of the mapping torus we show below that every extension does arise if a is a simple unital at algebra of real rank zero as an immediate corollary we obtain a stronger form of elliott s classification theorem for such algebras an invertible kk element that preserves positivity and the class of the unit lifts to an isomorphism 1 2 recall that a unital c algebra a is said to be a unital at algebra if it is expressible as the inductive limit of finite direct sums of algebras of the form mn c t with unital embeddings let a be a unital at algebra and let be an approximately inner automorphism of a the mapping torus of is the c algebra

pattern formation in the strong resonant forcing of spatially distributed oscillators abstract this paper is devoted to the study of the strongly resonant forcing of the hopf bifurcation in the weak forcing limit pattern formation can be seen as the stabilization of the modulational instability applications to patterns in optics are considered

classification of homomorphisms and dynamical systems let a be a unital simple c algebra with tracial rank zero and let x be a compact metric space suppose that h 1 h 2 c x a are two unital monomorphisms we show that h 1 and h 2 are approximately unitarily equivalent if and only if h 1 h 2 in kl c x a and o h 1 f o h 2 f for every f c x and every trace r of a inspired by a theorem of tomiyama we introduce a notion of approximate conjugacy for minimal dynamical systems let x be a compact metric space and let x x be two minimal homeomorphisms using the above mentioned result we show that two dynamical systems are approximately conjugate in that sense if and only if a k theoretical condition is satisfied in the case that x is the cantor set this notion coincides with the strong orbit equivalence of giordano putnam and skau and the k theoretical condition is equivalent to saying that the associate crossed product c algebras are isomorphic another application of the above mentioned result is given for c dynamical systems related to a problem of kishimoto let a be a unital simple ah algebra with no dimension growth and with real rank zero and let a aut a we prove that if r fixes a large subgroup of k 0 a and has the tracial rokhlin property then ax z is again a unital simple ah algebra with no dimension growth and with real rank zero

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

on the second adjunction mapping the case of a 1 dimensional image let l be a very ample line bundle on an n dimensional projective manifold x i e assume that l i opn 1 for some embedding i x pn in this article a study is made of the meromorphic map x z associated to ik1 n 2 l in the case when the kodaira dimension of kx n 2 l is 3 and 9 has a 1 dimensional image assume for simplicity that n 3 the first main result of the paper shows that 9 is a morphism if either h0 kk l 7 or i x 0 the second main result of this paper shows that if i x 0 then the genus g f of a fiber f of the map induced by 9 on hyperplane sections is 21 then g f 5 a connected component f of a general fiber of 9 is either a k3 surface or the blowing up at one point of a k3 surface and h1 0k 1 finally the structure of the finite to one part of the remmert stein factorization of o is worked out

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

approximating macroscopic observables in quantum spin systems with commuting matrices abstract macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements 1 2 n 1 j n n j a i n n i 1 m in a uhf algebra one of their properties is that they commute asymptotically as n goes to infinity it is not true that any given set of asymptotically commuting matrices can be approximated by commuting ones in the norm topology in this paper we show that for macroscopic observables this is true

front explosion in a resonantly forced complex ginzburg landau system abstract periodically forced oscillatory reaction diffusion systems near the hopf bifurcation can be modeled by the resonantly forced complex ginzburg landau equation in the 3 1 resonant locking regime this equation has three stable fixed points corresponding to the phase locked states in the underlying reaction diffusion system phase fronts separate spatial domains containing the phase locked states when the ginzburg landau equation parameters lie in the benjamin feir unstable regime the phase fronts have a turbulent internal spatio temporal structure as the forcing intensity is changed the intrinsic width of a front grows until at a critical value the front explodes and the turbulent interfacial zone expands to fill the entire domain the scaling properties of this transition are explored and it is shown that front width and spatial and temporal correlations diverge as the critical forcing intensity is approached these results are compared with similar behavior seen in a coupled map model with period 3 local dynamics the prospects for observation of these phenomena in experiments on periodically forced reaction diffusion systems are discussed

projective manifolds with small pluridegrees let be a very ample line bundle on a connected complex pro jective manifold m of dimension n 3 except for a short list of degenerate pairs m k km n 2 c n and there exists a morphism 7r m m expressing m as the blowup of a projective manifold m at a finite set b with kcm km n 2 l nef and big for the ample line bundle l 7r lc

lifting kk elements asymptotic unitary equivalence and classification of simple c algebras let a and c be two unital simple c algebras with tracial rank zero suppose that c is amenable and satisfies the universal coefficient theorem denote by kke c a the set of those in kk c a for which k0 c 0 k0 a 0 and 1c 1a suppose that kke c a we show that there is a unital monomorphism c a such that suppose that c is a unital ah algebra and is a continuous affine map for which t p t p for all projections p in all matrix algebras of c and any tt a where t a is the simplex of tracial states of a and is the convex set of faithful tracial states of c we prove that there is a unital monomorphism c a such that induces both and suppose that h c a is a unital monomorphism and hom k1 c aff a we show that there exists a unital monomorphism c a such that h in kk c a t t h for all tracial states t and the associated rotation map can be given by denote by kkt c a the set of compatible pairs where kle c a and is a continuous affine map from t a to together with a result on asymptotic unitary equivalence in h lin asymptotic unitary equivalence and asymptotically inner automorphisms arxiv math 0703610 2007 this provides a bijection from the asymptotic unitary equivalence classes of unital monomorphisms from c to a to where is a subgroup related to vanishing rotation maps as an application combining these results with a result of w winter w winter localizing the elliott conjecture at strongly self absorbing c algebras arxiv 0708 0283v3 2007 we show that two unital amenable simple stable c algebras are isomorphic if they have the same elliott invariant and the tensor products of these c algebras with any uhf algebra have tracial rank zero in particular if a and b are two unital separable simple stable c algebras with unique tracial states which are inductive limits of c algebras of type i then they are isomorphic if and only if they have isomorphic elliott invariants

a universal multicoefficient theorem for the kasparov groups that holds in the same generality as the universal coefficient theorem of rosenberg and schochet there are advantages in some circumstances to using hom k a k b in place of kk a b these advantages derive from the fact that k a can be equipped with order and scale structures similar to those on k0 a with this additional structure the module k a becomes a powerful invariant of c algebras we show that it is a complete invariant for the class of real rank zero ad algebras the ad algebras are a certain kind of approximately subhomogeneous c algebras which may have torsion in k1 ell in addition to classifying these algebras we calculate their automorphism groups up to approximately innerautomorphisms

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

actions on uhf algebras of infinite type we prove that all strongly outer z actions on a uhf algebra of infinite type are strongly cocycle conjugate to each other we also prove that all strongly outer asymptotically representable z actions on a unital simple ah algebra with real rank zero slow dimension growth and finitely many extremal tracial states are cocycle conjugate to each other

classification of homomorphisms into simple z stable c algebras abstract we classify unital monomorphisms into certain simple z stable c algebras up to approximate unitary equivalence the domain algebra c is allowed to be any unital separable commutative c algebra or any unital simple separable nuclear z stable c algebra satisfying the uct such that c b is of tracial rank zero for a uhf algebra b the target algebra a is allowed to be any unital simple separable z stable c algebra such that a b has tracial rank zero for a uhf algebra b or any unital simple separable exact z stable c algebra whose projections separate traces and whose extremal traces are finitely many

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

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

classifying smooth lattice polytopes via toric fibrations we show that any smooth q normal lattice polytope p of dimension n and degree d is a strict cayley polytope if n 2d 1 this gives a sharp answer for this class of polytopes to a question raised by v v batyrev and b nill

wavenumber locking and pattern formation in spatially forced systems we study wavenumber locking and pattern formation resulting from weak spatially periodic one dimensional forcing of two dimensional systems we consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes forcing at close to twice the pattern wavenumber selects stabilizes or creates resonant stripes locked at half the forcing wavenumber if the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns when the unforced system supports traveling waves resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve