cuntz krieger algebras of infinite graphs and matrices we show that the cuntz krieger algebras of infinite graphs and infinite 0 1 matrices can be approximated by those of finite graphs we then use these approximations to deduce the main uniqueness theorems for cuntz krieger algebras and to compute their k theory since the finite approximating graphs have sinks we have to calculate the k theory of cuntz krieger algebras of graphs with sinks and the direct methods we use to do this should be of independent interest

representations of etale groupoids on l p spaces for p 1 we study representations of etale groupoids on l p spaces our main result is a generalization of renault s disintegration theorem for representations of etale groupoids on hilbert spaces we establish a correspondence between l p representations of an etale groupoid g contractive l p representations of c c g and tight regular l p representations of any countable inverse semigroup of open slices of g that is a basis for the topology of g we define analogs f p g and f red p g of the full and reduced groupoid c algebras using representations on l p spaces as a consequence of our main result we deduce that every contractive representation of f p g or f red p g is automatically completely contractive examples of our construction include the following natural families of banach algebras discrete group l p operator algebras the analogs of cuntz algebras on l p spaces and the analogs of af algebras on l p spaces our results yield new information about these objects their matricially normed structure is uniquely determined more generally groupoid l p operator algebras provide analogs of several families of classical c algebras such as cuntz krieger c algebras tiling c algebras and graph c algebras

goodness of fit tests based on rao s divergence under sparseness assumptions in many practical situations the classical fixed cells assumptions to test goodness of fit are inappropriate and we consider an alternative set of assumptions which we call sparseness assumptions it is proved that under general conditions the proposed family of statistics based on rao s divergence is asymptotically normal when the sample size n and the number of cells m n tend to infinity so that n m n n 0 this result is extended to contiguous alternatives and subsequently it is possible to find the asymptotically most efficient member of the family

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

duals of compact lie groups realized in the cuntz algebras and their actions on c algebras abstract as a first step towards a new duality theorem for compact groups we consider a representation category t g of a compact lie group g u d c whose objects are the tensor powers of the defining representation and whose arrows are the intertwiners we associate to t g in a natural way a c algebra og which can be identified with the fixed points of the cuntz algebra od under the natural action of g og carries a canonical endomorphism g and t g can be reconstructed from og g if g su d then og is simple we give conditions for an endomorphism of a unital c algebra a to determine an action of t su d on a such actions correspond to monomorphisms of osu d into a with natural intertwining properties

actions of symbolic dynamical systems on c algebras ii simplicity of c symbolic crossed products and some examples a c symbolic dynamical system mathcal a rho sigma consists of a unital c algebra mathcal a and a finite family rho alpha alpha in sigma of endomorphisms of mathcal a indexed by symbols of satisfying some conditions the endomorphisms rho alpha alpha in sigma yield both a subshift and a c algebra of a hilbert c bimodule the obtained c algebra is regarded as a crossed product of mathcal a by the subshift we will study simplicity condition of these c algebras some examples such as irrational rotation cuntz krieger algebras will be studied

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

extensions of cuntz krieger algebras abstract we show that a c algebra looking like a cuntz krieger algebra is a cuntz krieger algebra this implies that in an appropriate sense the class of cuntz krieger algebras is closed under extensions of real rank zero

multiple equilibria for unlinked and weakly linked cellular structural forms abstract it is demonstrated that a structural form comprising n unlinked or weakly linked separate identical cells can by its nature suffer an explosion of unstable post buckling states associated with an n fold compound critical point examples of rigid link models and atomic matrix cellular models employing a lennard jones potential are included attention is paid to criteria for the appearance of homogeneous localized but distributed and thoroughly localized solutions for the atomic models generalized coordinates that exploit local and global symmetries of unlinked cells are introduced in a block diagonalization context to clarify the bifurcation structure a discretized lagrangian formulation is introduced to untangle the paths for weakly linked cells

poset block equivalence of integral matrices given square matrices b and b with a poset indexed block structure for which an ij block is zero unless i j when are there invertible matrices u and v with this required zero block structure such that ubv b we give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain r as one application when r is a field we classify such matrices up to similarity by matrices respecting the block structure we also give complete invariants for equivalence under the additional requirement that the diagonal blocks of u and v have determinant 1 the invariants involve an associated diagram the k web of r module homomorphisms the study is motivated by applications to symbolic dynamics and c algebras

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

the noncommutative geometry of graph c algebras i the index theorem we investigate conditions on a graph c algebra for the existence of a faithful semifinite trace using such a trace and the natural gauge action of the circle on the graph algebra we construct a smooth 1 summable semi finite spectral triple the local index theorem allows us to compute the pairing with k theory this produces invariants in the k theory of the fixed point algebra and these are invariants for a finer structure than the isomorphism class of c e

endomorphisms of c algebras cross products and duality for compact groups on definit une nouvelle sorte de produit croise d une c algebre par des semigroupes d endomorphismes avec des proprietes reliees a la symetrie de permutation et a l existence de conjugues un groupe compact est alors defini intrinsequement par son action duale sur le produit croise cette construction donne une caracterisation des duaux de groupes compacts abstraits qui est hors d atteinte de la theorie de dualite de taunaka kein et est independante de cette theorie ceci resout le probleme de demontrer l existence d un groupe de jauge global compact en physique des particules etant seulement donnees les observables locales

structural stability of multi folding structures with contact problem this paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability of a folding multi layered truss both analyses are based on bifurcation theory and include geometrical nonlinearity the dynamic analysis includes an allowance for contact between nodes comparisons are made between published experimental folding patterns and the patterns obtained from both numerical methods in which bifurcations are demonstrated as elastic unstable snap through behaviour several folding patterns are identified during the elastic instability where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading the authors suggest that the understanding of the behaviour will be very useful for the development of light weight structures subject to dynamic loading based on the bifurcation static analysis and dynamic analysis using both the displacement control method and the load control method

the brauer group of a locally compact groupoid we define the brauer group br g of a locally compact groupoid g to be the set of morita equivalence classes of pairs a consisting of an elementary c bundle a over g 0 satisfying fell s condition and an action of g on a by isomorphisms when g is the transformation groupoid x h then br g is the equivariant brauer group br h x in addition to proving that br g is a group we prove three isomorphism results first we show that if g and h are equivalent groupoids then br g and br h are isomorphic this generalizes the result that if g and h are groups acting freely and properly on a space x say g on the left and h on the right then br g x h and br h g x are isomorphic secondly we show that the subgroup br0 g of br g consisting of classes a with a having trivial dixmier douady invariant is isomorphic to a quotient e g of the collection tw g of twists over g finally we prove that br g is isomorphic to the inductive limit ext g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of the groups e g x where x varies over all principal g spaces x and g x is the imprimitivity groupoid associated to x

invariance of the cuntz splice we show that the cuntz splice induces stably isomorphic graph c algebras this result is a key step towards the recent complete classification of unital graph c algebras both with respect to k theoretical classification and with respect to geometrical classification in terms of an equivalence relation on the underlying graphs

about distances of discrete distributions satisfying the data processing theorem of information theory the distances of discrete probability distributions are considered necessary and sufficient conditions for validity of the data processing theorem of information theory are established these conditions are applied to the burbea rao 1982 divergences and bregman 1967 distances

an arc length method including line searches and accelerations this paper describes a method for introducing line searches into the arc length solution procedure such line searches may be used at each iteration to calculate an optimum scalar step length which scales the normal iterative vector in practice a loose tolerance is provided so that on many iterations the line searches are avoided however on difficult iterations the line searches are shown to lead to a substantial improvement in the convergence characteristics a simple single parameter acceleration is also developed using line search concepts the new arc length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs significant improvements are demonstrated in relation to the standard arc length method

graph inverse semigroups their characterization and completion abstract graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of c algebras in this paper we characterize such semigroups and show how they may be completed under suitable conditions to form what we call the cuntz krieger semigroup of the graph this semigroup is proved to be the ample semigroup of a topological groupoid associated with the graph and the semigroup analogue of the leavitt path algebra of the graph

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

e theory for c algebras over topological spaces abstract we define e theory for separable c algebras over second countable topological spaces and establish its basic properties this includes an approximation theorem that relates the e theory over a general space to the e theories over finite approximations to this space we obtain effective criteria for determining the invertibility of e theory elements over possibly infinite dimensional spaces furthermore we prove a universal multicoefficient theorem for c algebras over totally disconnected metrisable compact spaces

the k theoretical range of cuntz krieger algebras abstract we augment restorff s classification of purely infinite cuntz krieger algebras by describing the range of his invariant on purely infinite cuntz krieger algebras we also describe its range on purely infinite graph c algebras with finitely many ideals and provide unital range results for purely infinite cuntz krieger algebras and unital purely infinite graph c algebras

congruences on graph inverse semigroups abstract graph inverse semigroups were defined by ash and hall in 1975 they found necessary and sufficient conditions for the semigroups to be congruence free in this paper we give a classification of congruences on a graph inverse semigroup in terms of the underlying graph as a consequence we show that the inverse graph semigroup of a finite graph is congruence noetherian

the structure of gauge invariant ideals of labelled graph c algebras abstract in this paper we consider the gauge invariant ideal structure of a c algebra c e l b associated to a set finite receiver set finite and weakly left resolving labelled space e l b where l is a labelling map assigning an alphabet to each edge of the directed graph e with no sinks it is obtained that if an accommodating set b is closed under relative complements there is a one to one correspondence between the set of all hereditary saturated subsets of b and the gauge invariant ideals of c e l b for this we introduce a quotient labelled space e l b r arising from an equivalence relation r on b and show the existence of the c algebra c e l b r generated by a universal representation of e l b r finally we give necessary and sufficient conditions for simplicity of certain labelled graph c algebras

bifurcation hierarchy of symmetric structures abstract a group theoretic method for the analysis of bifurcation behavior of regular polygonal symmetric structures is described possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups which express the symmetry in particular we offer a complete description of those double bifurcation points which occur due to group symmetry the type the number and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations the existence of a potential function plays a substantial role for the existence of bifurcation paths as a result of these all possible bifurcation process can be known a priori as a natural consequence of bifurcation hierarchy before actual numerical analysis an implementation of this method in numerical analysis shows its validity and usability

the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources abstract we catalogue the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph the primitive ideals in the cuntz krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group the cuntz krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic

finite digraphs and kms states abstract the paper contains a description of the kms states of a generalized gauge action on the c algebra of a finite graph

on the convexity of some divergence measures based on entropy functions three measures of divergence between vectors in a convex set of a n dimensional real vector space are defined in terms of certain types of entropy functions and their convexity property is studied among other results a classification of the entropies of degree alpha is obtained by the convexity of these measures these results have applications in information theory and biological studies

semigroups of non unital endomorphisms of c algebras and compact group duality we show that the fixed point algebra og of the cuntz algebra on n 2 3 under the canonical action of a strongly compact group g of unitaries on the generating hubert space h is simple if the defining representation of g is a direct sum of finite dimensional representations whose determinant takes values in finite subgroups of the circle we use this result to define the doplicher roberts cross product of a unital c algebra a with centre cl by a semigroup of not necessarily unital endomorphisms generated by a countable orthogonal collection p i i n fulfilling natural conditions as an application we give necessary and sufficient conditions in order that a p is isomorphic to o g with the regular representation of a compact and metrizable group g and the set of endomorphisms induced by an irreducible decomposition of

on the classification of nonsimple graph c algebras we prove that a graph c algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six term exact sequence in k theory we prove that a similar classification also holds for a graph c algebra with a largest proper ideal that is an af algebra our results are based on a general method developed by the first named author with restorff and ruiz as a key step in the argument we show how to produce stability for certain full hereditary subalgebras associated to such graph c algebras we further prove that except under trivial circumstances a unique proper nontrivial ideal in a graph c algebra is stable