the range of united k theory abstract we prove that the united k theory functor is a surjective functor from the category of real simple separable purely infinite c algebras to the category of countable acyclic crt modules as a consequence we show that every complex kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real c algebra

c algebras of toeplitz type associated with algebraic number fields we associate with the ring r of algebraic integers in a number field a c algebra mathfrak t r it is an extension of the ring c algebra mathfrak a r studied previously by the first named author in collaboration with x li in contrast to mathfrak a r it is functorial under homomorphisms of rings it can also be defined using the left regular representation of the ax b semigroup r rtimes r times on ell 2 r rtimes r times the algebra mathfrak t r carries a natural one parameter automorphism group sigma t t in mathbb r we determine its kms structure the technical difficulties that we encounter are due to the presence of the class group in the case where r is not a principal ideal domain in that case for a fixed large inverse temperature the simplex of kms states splits over the class group the partition functions are partial dedekind zeta functions we prove a result characterizing the asymptotic behavior of quotients of such partial zeta functions which we then use to show uniqueness of the beta kms state for each inverse temperature beta in 1 2

nica toeplitz algebras associated with product systems over right lcm semigroups abstract we prove uniqueness of representations of nica toeplitz algebras associated to product systems of c correspondences over right lcm semigroups by applying our previous abstract uniqueness results developed for c precategories our results provide an interpretation of conditions identified in work of fowler and fowler raeburn and apply also to their crossed product twisted by a product system in the new context of right lcm semigroups as well as to a new doplicher roberts type c algebra associated to the nica toeplitz algebra as a derived construction we develop nica toeplitz crossed products by actions with completely positive maps this provides a unified framework for nica toeplitz semigroup crossed products by endomorphisms and by transfer operators we illustrate these two classes of examples with semigroup c algebras of right and left semidirect products

the c algebra of a vector bundle and fields of cuntz algebras abstract we study the cuntz pimsner algebra associated with the module of continuous sections of a hilbert bundle and prove that it is a continuous bundle of cuntz algebras furthermore we assign to bundles of cuntz algebras carrying a global circle action a class in the representable kk group of the zero grade bundle we explicitly compute such class for the cuntz pimsner algebra of a vector bundle

discrete product systems and twisted crossed products by semigroups a product systemeover a semigrouppis a family of hilbert spaces es s p together with multiplicationses et est we vieweas a unitary valued cocycle onp and consider twisted crossed productsa e pinvolvingeand an action ofpby endomorphisms of ac algebraa whenpis quasi lattice ordered in the sense of nica we isolate a class of covariant representations ofe and consider a twisted crossed productbp e pwhich is universal for covariant representations ofewhenehas finite dimensional fibres and in general is slightly larger in particular whenp nand dim e1 our algebrabn e n is a new infinite analogue of the toeplitz cuntz algebras ton our main theorem is a characterisation of the faithful representations ofbp e p

a k theoretic invariant for dynamical systems soit x t un systeme dynamique de dimension zero on considere le groupe quotient g c x z b x t ou c x z est le groupe des fonctions continues a valeur entiere sur x et b x t est le sous groupe des fonctions de la forme f f on montre que si x t est topologiquement transitif alors il y a un ordre naturel sur g qui fait de g un groupe ordonne

a galerkin formulation of the mib method for three dimensional elliptic interface problems we develop a three dimensional 3d galerkin formulation of the matched interface and boundary mib method for solving elliptic partial differential equations pdes with discontinuous coefficients i e the elliptic interface problem the present approach builds up two sets of elements respectively on two extended subdomains which both include the interface as a result two sets of elements overlap each other near the interface fictitious solutions are defined on the overlapping part of the elements so that the differentiation operations of the original pdes can be discretized as if there was no interface the extra coefficients of polynomial basis functions which furnish the overlapping elements and solve the fictitious solutions are determined by interface jump conditions consequently the interface jump conditions are rigorously enforced on the interface the present method utilizes cartesian meshes to avoid the mesh generation in conventional finite element methods fems we implement the proposed mib galerkin method with three different elements namely rectangular prism element five tetrahedron element and six tetrahedron element which tile the cartesian mesh without introducing any new node the accuracy stability and robustness of the proposed 3d mib galerkin are extensively validated over three types of elliptic interface problems in the first type interfaces are analytically defined by level set functions these interfaces are relatively simple but admit geometric singularities in the second type interfaces are defined by protein surfaces which are truly arbitrarily complex the last type of interfaces originates from multiprotein complexes such as molecular motors near second order accuracy has been confirmed for all of these problems to our knowledge it is the first time for an fem to show a near second order convergence in solving the poisson equation with realistic protein surfaces additionally the present work offers the first known near second order accurate method for c 1 continuous or h 2 continuous solutions associated with a lipschitz continuous interface in a 3d setting

k theory and exact sequences of partial translation algebras abstract in an earlier paper the authors introduced partial translation algebras as a generalisation of group c algebras here we establish an extension of partial translation algebras which may be viewed as an excision theorem in this context we apply this general framework to compute the k theory of partial translation algebras and group c algebras in the context of almost invariant subspaces of discrete groups this generalises the work of cuntz lance pimsner and voiculescu in particular we provide a new perspective on pimsner s calculation of the k theory for a graph product of groups

multilevel image coding with hyperfeatures histograms of local appearance descriptors are a popular representation for visual recognition they are highly discriminant with good resistance to local occlusions and to geometric and photometric variations but they are not able to exploit spatial co occurrence statistics over scales larger than the local input patches we present a multilevel visual representation that remedies this the starting point is the notion that to detect object parts in images in practice it often suffices to detect co occurrences of more local object fragments this can be formalized by coding image patches against a codebook of known fragments or a more general statistical model and locally histogramming the resulting labels to capture their co occurrence statistics local patch descriptors are converted into somewhat less local histograms over label occurrences the histograms are themselves local descriptor vectors so the process can be iterated to code ever larger assemblies of object parts and increasingly abstract or semantic image properties we call these higher level descriptors hyperfeatures we formulate the hyperfeature model and study its performance under several different image coding methods including k means based vector quantization gaussian mixtures and combinations of these with latent dirichlet allocation we find that the resulting high level features provide improved performance in several object image and texture image classification tasks

hecke algebras from groups acting on trees and hnn extensions abstract we study hecke algebras of groups acting on trees with respect to geometrically defined subgroups in particular we consider hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and the stabilizer of an end relative to a vertex stabilizer assuming that the actions are sufficiently transitive we focus on identifying the structure of the resulting hecke algebras give explicit multiplication tables of the canonical generators and determine whether the hecke algebra has a universal c completion the paper unifies algebraic and analytic approaches by focusing on the common geometric thread the results have implications for the general theory of totally disconnected locally compact groups

on c algebras of irreversible algebraic dynamical systems abstract extending the work of cuntz and vershik we develop a general notion of independence for commuting group endomorphisms based on this concept we initiate the study of irreversible algebraic dynamical systems which can be thought of as irreversible analogues of the dynamical systems considered by schmidt to each irreversible algebraic dynamical system we associate a universal c algebra and show that it is a uct kirchberg algebra under natural assumptions moreover we discuss the structure of the core subalgebra which turns out to be closely related to generalized bunce deddens algebras in the sense of orfanos we also construct discrete product systems of hilbert bimodules for irreversible algebraic dynamical systems which allow us to view the associated c algebras as cuntz nica pimsner algebras besides we prove a decomposition theorem for semigroup crossed products of unital c algebras by semidirect products of discrete left cancellative monoids

af embeddings into c algebras of real rank zero abstract it is proved that every separable c algebra of real rank zero contains an af sub c algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two c algebras and such that every projection in a matrix algebra over the large c algebra is equivalent to a projection in a matrix algebra over the af sub c algebra this result is proved at the level of monoids using that the monoid of murray von neumann equivalence classes of projections in a c algebra of real rank zero has the refinement property as an application of our result we show that given a unital c algebra a of real rank zero and a natural number n then there is a unital homomorphism mn1 mnr a for some natural numbers r n1 nr with nj n for all j if and only if a has no representation of dimension less than n

continuous fields of kirchberg c algebras abstract in this paper we study the c algebras associated to continuous fields over locally compact metrizable zero dimensional spaces whose fibers are kirchberg c algebras satisfying the uct we show that these algebras are inductive limits of finite direct sums of kirchberg algebras and they are classified up to isomorphism by topological invariants

phase transition on exel crossed products associated to dilation matrices an integer matrix a md z induces a covering a of td and an endomorphism a f f a of c td for which there is a natural transfer operator l in this paper we compute the kms states on the exel crossed product c td a ln and its toeplitz extension we find that c td a ln has a unique kms state which has inverse temperature log deta its toeplitz extension on the other hand exhibits a phase transition at log deta and for larger the simplex of kms states is isomorphic to the simplex of probability measures on td

semigroups of endomorphisms dirichlet series and phase transitions abstract we study phase transitions of c dynamical systems a in which a is the crossed product of a c algebra by a lattice semigroup of endomorphisms and is a one parameter subgroup of the dual action determined by a real valued scale on the semigroup we show that the kms equilibrium condition is equivalent to a markov type condition on the predual semigroup dynamical system and give criteria for the existence of equilibrium states and of phase transitions in terms of the semigroup action when the semigroup is an integer lattice the partition function of the real scale is a dirichlet series having an euler product expansion on their convergence region there is a phase transition whose geometry is fully determined by the ground states and is independent of the chosen scale generalizing a model recently constructed by bost and connes motivated by earlier work of julia as applications we simplify part of the proof the bost connes theorem on phase transition with spontaneous symmetry breaking and we discuss generalizations to other systems associated to subsets of primes and to number fields of class number 1

c algebras of right lcm monoids and their equilibrium states we study the internal structure of c algebras of right lcm monoids by means of isolating the core semigroup c algebra as the coecient algebra of a fock type module on which the full semigroup c algebra admits a left action if the semigroup has a generalised scale we classify the kms states for the associated time evolution on the semigroup c algebra and provide sucient conditions for uniqueness of the kms state at inverse temperature in a critical interval

nuclearity of semigroup c algebras and the connection to amenability abstract we study c algebras associated with subsemigroups of groups for a large class of such semigroups including positive cones in quasi lattice ordered groups and left ore semigroups we describe the corresponding semigroup c algebras as c algebras of inverse semigroups groupoid c algebras and full corners in associated group crossed products these descriptions allow us to characterize nuclearity of semigroup c algebras in terms of faithfulness of left regular representations and amenability of group actions moreover we also determine when boundary quotients of semigroup c algebras are uct kirchberg algebras this leads to a unified approach to cuntz algebras and ring c algebras

a mortar approach for fluid structure interaction problems immersed strategies for deformable and rigid bodies abstract this paper proposes a new fluid structure interaction immersed computational framework the coupling between an underlying incompressible fluid and an embedded solid is formulated by means of the overlapping domain decomposition method in conjunction with a mortar approach leading to a variationally consistent scheme which is capable of unifying a range of methodologies currently available in the literature this novel framework provides great flexibility and enables the modelling of immersed deformable solids compressible and incompressible as well as rigid bodies through the use of a weak director based formulation a novel null space reduction scheme is employed in order to enhance the conditioning of the resulting system of equations and reduce the computational cost an implicit structure preserving time integration algorithm is used to yield extra stability and robustness and the use of a segmentation technique near the boundary between fluid and solid also leads to enhanced accuracy the methodology is benchmarked against results obtained by using alternative boundary fitted methodologies

on infinite simple c algebras abstract we show that simple c algebras with an infinite element contain nontrivial projections we also prove that various apparently different hypotheses purely infinite on simple c algebras are all equivalent

c envelopes of semicrossed products by lattice ordered abelian semigroups abstract a semicrossed product is a non selfadjoint operator algebra encoding the action of a semigroup on an operator or c algebra we prove that when the positive cone of a discrete lattice ordered abelian group acts on a c algebra the c envelope of the associated semicrossed product is a full corner of a crossed product by the whole group by constructing a c cover that itself is a full corner of a crossed product and computing the shilov ideal we obtain an explicit description of the c envelope this generalizes a result of davidson fuller and kakariadis from z n to the class of all discrete lattice ordered abelian groups

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

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

ring c algebras we associate reduced and full c algebras to arbitrary rings and study the inner structure of these ring c algebras as a result we obtain conditions for them to be purely infinite and simple we also discuss several examples originally our motivation comes from algebraic number theory

fractional skew monoid rings abstract given an action of a monoid t on a ring a by ring endomorphisms and an ore subset s of t a general construction of a fractional skew monoid ring s op a t is given extending the usual constructions of skew group rings and of skew semigroup rings in case s is a subsemigroup of a group g such that g s 1s we obtain a g graded ring s op a s with the property that for each s s the s component contains a left invertible element and the s 1 component contains a right invertible element in the most basic case where g z and s t z the construction is fully determined by a single ring endomorphism of a if is an isomorphism onto a proper corner pap we obtain an analogue of the usual skew laurent polynomial ring denoted by a t t examples of this construction are given and it is proven that several classes of known algebras including the leavitt algebras of type 1 n can be presented in the form a t t finally mild and reasonably natural conditions are obtained under which s op a s is a purely infinite simple ring

equivariant kirchberg phillips type absorption for amenable group actions we show an equivariant kirchberg phillips type absorption theorem for pointwise outer actions of discrete amenable groups on kirchberg algebras with respect to natural model actions on the cuntz algebras mathcal o infty and mathcal o 2 this generalizes results known for finite groups and poly mathbb z groups the model actions are shown to be determined up to strong cocycle conjugacy by natural abstract properties which are verified for some examples of actions arising from tensorial shifts we also show the following homotopy rigidity result which may be understood as a precursor to a general kirchberg phillips type classification theory if two outer actions of an amenable group on a unital kirchberg algebra are equivariantly homotopy equivalent then they are conjugate this marks the first c dynamical classification result up to cocycle conjugacy that is applicable to actions of all amenable groups

classifying c algebras with both finite and infinite subquotients abstract we give a classification result for a certain class of c algebras a over a finite topological space x in which there exists an open set u of x such that u separates the finite and infinite subquotients of a we apply our results to c algebras arising from graphs

amenability of groupoids arising from partial semigroup actions and topological higher rank graphs we consider the amenability of groupoids g equipped with a group valued cocycle c g q with amenable kernel c 1 e we prove a general result which implies in particular that g is amenable whenever q is amenable and if there is countable set d g such that c g u d q for all u g 0 we show that our result is applicable to groupoids arising from partial semigroup actions we explore these actions in detail and show that these groupoids include those arising from directed graphs higher rank graphs and even topological higher rank graphs we believe our methods yield a nice alternative groupoid approach to these important constructions

type iii1 equilibrium states of the toeplitz algebra of the affine semigroup over the natural numbers abstract we complete the analysis of kms states of the toeplitz algebra t n n of the affine semigroup over the natural numbers recently studied by raeburn and the first author by showing that for every inverse temperature in the critical interval 1 2 the unique kms state is of type iii1 we prove this by reducing the type classification from t n n to that of the symmetric part of the bost connes system with a shift in inverse temperature to carry out this reduction we first obtain a parametrization of the nica spectrum of n n in terms of an adelic space combining a characterization of traces on crossed products due to the second author with an analysis of the action of n n on the nica spectrum we can also recover all the kms states of t n n originally computed by raeburn and the first author our computation sheds light on why there is a free transitive circle action on the extremal kms states for 2 that does not ostensibly come from an action of t on the c algebra

tensor algebras of product systems and their c envelopes abstract let g p be an abelian lattice ordered group and let x be a compactly aligned product system over p with coefficients in a we show that the c envelope of the nica tensor algebra n t x coincides with both sehnem s covariance algebra a x p and the co universal c algebra n o x r for injective gauge compatible nica covariant representations of carlsen larsen sims and vittadello we give several applications of this result on both the selfadjoint and non selfadjoint operator algebra theory first we guarantee the existence of n o x r thus settling a problem of carlsen larsen sims and vittadello which was open even for abelian lattice ordered groups as a second application we resolve a problem posed by skalski and zacharias on dilating isometric representations of product systems to unitary representations as a third application we characterize the c envelope of the tensor algebra of a finitely aligned higher rank graph which also holds for topological higher rank graphs as a final application we prove reduced hao ng isomorphisms for generalized gauge actions of discrete groups on c algebras of product systems this generalizes recent results that were obtained by various authors in the case where g p z n

the k theory of toeplitz c algebras of right angled artin groups toeplitz c algebras of right angled artin groups were studied by crisp and laca they are a special case of the toeplitz c algebras t g p associated with quasi lattice ordered groups g p introduced by nica crisp and laca proved that the so called boundary quotients c q of c are simple and purely infinite for a certain class of finite graphs we show that c q can be represented as a full corner of a crossed product of an appropriate c subalgebra of c q built by using c where is a subgraph of with one less vertex by the group z using induction on the number of the vertices of we show that c q are nuclear and moreover belong to the small bootstrap class we also use the pimsner voiculescu exact sequence to find their k theory finally we use the kirchberg phillips classification theorem to show that those c algebras are isomorphic to tensor products of on with 1 n

finite volume formulation of the mib method for elliptic interface problems the matched interface and boundary mib method has a proven ability for delivering the second order accuracy in handling elliptic interface problems with arbitrarily complex interface geometries however its collocation formulation requires relatively high solution regularity finite volume method fvm has its merit in dealing with conservation law problems and its integral formulation works well with relatively low solution regularity we propose an mibfvm to take the advantages of both mib and fvm for solving elliptic interface problems we construct the proposed method on cartesian meshes with vertex centered control volumes a large number of numerical experiments are designed to validate the present method in both two dimensional 2d and three dimensional 3d domains it is found that the proposed mibfvm achieves the second order convergence for elliptic interface problems with complex interface geometries in both l and l2 norms

classification of extensions of classifiable c algebras abstract for a certain class of extensions e 0 b e a 0 of c algebras in which b and a belong to classifiable classes of c algebras we show that the functor which sends e to its associated six term exact sequence in k theory and the positive cones of k 0 b and k 0 a is a classification functor we give two independent applications addressing the classification of a class of c algebras arising from substitutional shift spaces on one hand and of graph algebras on the other the former application leads to the answer of a question of carlsen and the first named author concerning the completeness of stabilized matsumoto algebras as an invariant of flow equivalence the latter leads to the first classification result for nonsimple graph c algebras

mining mid level features for image classification mid level or semi local features learnt using class level information are potentially more distinctive than the traditional low level local features constructed in a purely bottom up fashion at the same time they preserve some of the robustness properties with respect to occlusions and image clutter in this paper we propose a new and effective scheme for extracting mid level features for image classification based on relevant pattern mining in particular we mine relevant patterns of local compositions of densely sampled low level features we refer to the new set of obtained patterns as frequent local histograms or flhs during this process we pay special attention to keeping all the local histogram information and to selecting the most relevant reduced set of flh patterns for classification the careful choice of the visual primitives and an extension to exploit both local and global spatial information allow us to build powerful bag of flh based image representations we show that these bag of flhs are more discriminative than traditional bag of words and yield state of the art results on various image classification benchmarks including pascal voc

the 2 adic ring c algebra of the integers and its representations abstract we study the 2 adic version of the ring c algebra of the integers first we work out the precise relation between the cuntz algebra o 2 and our 2 adic ring c algebra in terms of representations secondly we prove a 2 adic duality theorem identifying the crossed product arising from 2 adic affine transformations on the 2 adic numbers with the analogous crossed product algebra over the real numbers and finally as an outcome of this duality result we construct an explicit imprimitivity bimodule and prove that it transports one canonical representation into the other

a robust approach for object matching and classification using partial dominant orientation descriptor this paper introduces a novel approach to measure the correspondence between objects and exploit it for object and image classification tasks using the proposed partial dominant orientation descriptor pdod in particular the object is represented by a set of stable and informative key locations sampled using difference of gaussian the proposed pdod at each extracted key location takes into account the position and partially computes the dominant orientation of other key locations relative to it thus offering a global distinctive and discriminative characterization this allows us to learn features that are largely invariant to common image transformations including changes in object colors and textures the correspondence in between two objects is performed by finding for each key location in one object the key location in the other object that has the most similar descriptor object classification proceeds by assigning the most relevant category that has maximally similar stored prototype objects to the query object using k nearest neighbors algorithm with adaptive object distance for efficiency we further investigate pdod for image classification by developing powerful image representations based on the popular bag of words model the extensive experiments demonstrate that the proposed approach greatly improves the matching and classification results while achieving the state of the art performances on several challenging benchmark datasets the obtained results suggest also broader applicability to other classification modalities we propose a novel descriptor for complex object matching and classification the proposed descriptor combines both local and global properties of interest points the proposed descriptor is highly distinctive and insensitive to common image transformations adaptive object distance is proposed to measure the similarity between objects we compare our approach with many existing methods and we achieve the state of the art performances on several benchmarks

boundary quotients and ideals of toeplitz c algebras of artin groups abstract we study the quotients of the toeplitz c algebra of a quasi lattice ordered group g p which we view as crossed products by a partial actions of g on closed invariant subsets of a totally disconnected compact hausdorff space the nica spectrum of g p our original motivation and our main examples are drawn from right angled artin groups but many of our results are valid for more general quasi lattice ordered groups we show that the nica spectrum has a unique minimal closed invariant subset which we call the boundary spectrum and we define the boundary quotient to be the crossed product of the corresponding restricted partial action the main technical tools used are the results of exel laca and quigg on simplicity and ideal structure of partial crossed products which depend on amenability and topological freeness of the partial action and its restriction to closed invariant subsets when there exists a generalised length function or controlled map defined on g and taking values in an amenable group we prove that the partial action is amenable on arbitrary closed invariant subsets the topological freeness of the boundary action depends on topological freeness of the restriction to a certain lattice subgroup of g the core of g p which often turns out to be trivial our main results are obtained for right angled artin groups with trivial centre that is those with no cyclic direct factor they include a presentation of the boundary quotient in terms of generators and relations that generalises cuntz s presentation of o n a proof that the boundary quotient is purely infinite and simple and a parametrisation of the ideals of the toeplitz c algebra in terms of subsets of the standard generators of the artin group

erratum to immersed finite element method and its applications to biological systems comput methods appl mech engrg 195 2006 1722 1749

a new proof of kirchberg s 2 stable classification i present a new proof of kirchbergs q2 stable classification theorem two separable nuclear stable unital q2 stable c algebras are isomorphic if and only if their ideal lattices are order isomorphic or equivalently their primitive ideal spaces are homeomorphic many intermediate results do not depend on pure infiniteness of any sort

the tracial rokhlin property for actions of finite groups on c algebras we define tracial analogs of the rokhlin property for actions of finite groups approximate representability of actions of finite abelian groups and approximate innerness we prove the following four analogs of related nontracial results bullet the crossed product of an infinite dimensional simple separable unital c algebra with tracial rank zero by an action of a finite group with the tracial rokhlin property again has tracial rank zero bullet an outer action of a finite abelian group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property if and only if its dual is tracially approximately representable and is tracially approximately representable if and only if its dual has the tracial rokhlin property bullet if a strongly tracially approximately inner action of a finite cyclic group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property then it is tracially approximately representable bullet an automorphism of an infinite dimensional simple separable unital c algebra a with tracial rank zero is tracially approximately inner if and only if it is the identity on k 0 a mod infinitesimals

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

phase transition on the toeplitz algebra of the affine semigroup over the natural numbers abstract we show that the group q q of orientation preserving affine transformations of the rational numbers is quasi lattice ordered by its subsemigroup n n the associated toeplitz c algebra t n n is universal for isometric representations which are covariant in the sense of nica we give a presentation of t n n in terms of generators and relations and use this to show that the c algebra q n recently introduced by cuntz is the boundary quotient of q q n n in the sense of crisp and laca the toeplitz algebra t n n carries a natural dynamics which induces the one considered by cuntz on the quotient q n and our main result is the computation of the kms equilibrium states of the dynamical system t n n r for all values of the inverse temperature for 1 2 there is a unique kms state and the kms 1 state factors through the quotient map onto q n giving the unique kms state discovered by cuntz at 2 there is a phase transition and for 2 the kms states are indexed by probability measures on the circle there is a further phase transition at where the kms states are indexed by the probability measures on the circle but the ground states are indexed by the states on the classical toeplitz algebra t n

noncommutative geometry and motives the thermodynamics of endomotives we combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spectral realization of zeros of l functions the analogue in characteristic zero of the action of the frobenius on l adic cohomology is the action of the scaling group on the cyclic homology of the cokernel in a suitable category of motives of a restriction map of noncommutative spaces the latter is obtained through the thermodynamics of the quantum statistical system associated to an endomotive a noncommutative generalization of artin motives semigroups of endomorphisms of algebraic varieties give rise canonically to such endomotives with an action of the absolute galois group the semigroup of endomorphisms of the multiplicative group yields the bost connes system from which one obtains through the above procedure the desired cohomological interpretation of the zeros of the riemann zeta function in the last section we also give a lefschetz formula for the archimedean local l factors of arithmetic varieties

a variational framework for fluid solid interaction problems based on immersed domains theoretical bases abstract in this work the theoretical bases to handle the fluid solid interaction problem based on the conception of immersed domains are developed starting from a well known governing variational principle from the continuum mechanics the purpose of the present work is twofold firstly a variational principle to model the interaction between a fluid and a thin structure characterized as a shell for which its volume is geometrically neglected is devised by incorporating suitable kinematical assumptions into the original problem this leads to a rather general formulation for the fluid shell interaction problem that embraces methodologies such as the immersed boundary method secondly no longer is the volume of the solid disregarded and the variational principle is manipulated in order to attain a formulation that comprises the problem of an augmented fluid which is extended as a fictitious fluid to the whole domain of analysis interacting with an immersed solid in some parts the formulation resembles the immersed finite element method as well as the recently presented immersed continuous method due to the appearance of a volume force defined over the fictitious fluid domain one of the main differences lies in the fact that in the present approach the volume force is the lagrange multiplier that imposes the continuity of the velocity field along the whole overlapped domain the other noteworthy difference dwells in the handling of the mass conservation for the artificial fluid three aspects of this setting must be pointed out as original contributions of the work i a consistent generalization of the theoretical continuous setting of immersed boundary methods is carried out ii the variational basis for the finite element approximations is clearly posed written and easy to understand and iii when dealing with an immersed solid a more general formulation valid for all classes of combinations fluid solid is developed eliminating the restriction to compressible fluid compressible solid of the immersed continuous method and the incompressible fluid incompressible solid of the immersed finite element method

the graded grothendieck group and the classification of leavitt path algebras this paper is an attempt to show that parallel to elliott s classification of af c algebras by means of k theory the graded k0 group classifies leavitt path algebras completely in this direction we prove this claim at two extremes namely for the class of acyclic graphs graphs with no cycles and multi headed comets or rose graphs graphs in which each head is connected to a cycle or to a collection of loops or a mixture of these graphs i e polycephaly graphs

semigroup c algebras and amenability of semigroups we construct reduced and full semigroup c algebras for left cancellative semigroups our new construction covers particular cases already considered by a nica and also toeplitz algebras attached to rings of integers in number fields due to j cuntz moreover we show how left amenability of semigroups can be expressed in terms of these semigroup c algebras in analogy to the group case