topologies on measured groupoids abstract if an analytic borel group g has a quasiinvariant measure it is known that g is actually a locally compact group with the original borel structure being generated by the topology and the original measure being equivalent to haar measure in this paper a variation is given on the known proof which then extends to show that an analytic measured groupoid has a compact and also a locally compact inessential reduction which is a topological groupoid in the compact case it is proved that every almost homomorphism agrees a e with a strict homomorphism also the topology is used to show that every measured groupoid has a complete countable section 7 and that every locally compact equivalence relation has a complete transversal 3 these are further used to show that some results of feldman et al 7 apply in general and that a locally compact groupoid with continuous haar system has sufficiently many non singular borel g sets provided that the orbit measures are atom free 23

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

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

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

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

dynamical systems associated to separated graphs graph algebras and paradoxical decompositions abstract we attach to each finite bipartite separated graph e c a partial dynamical system e c f where e c is a zero dimensional metrizable compact space f is a finitely generated free group and is a continuous partial action of f on e c the full crossed product c algebra o e c c e c f is shown to be a canonical quotient of the graph c algebra c e c of the separated graph e c similarly we prove that for any field k the algebraic crossed product l k ab e c c k e c alg f is a canonical quotient of the leavitt path algebra l k e c of e c the monoid v l k ab e c of isomorphism classes of finitely generated projective modules over l k ab e c is explicitly computed in terms of monoids associated to a canonical sequence of separated graphs using this we are able to construct an action of a finitely generated free group f on a zero dimensional metrizable compact space z such that the type semigroup s z f k is not almost unperforated where k denotes the algebra of clopen subsets of z finally we obtain a characterization of the separated graphs e c such that the canonical partial action of f on e c is topologically free

extending representations of banach algebras to their biduals we show that a representation of a banach algebra a on a banach space x can be extended to a canonical representation of a on x if and only if certain orbit maps a rightarrow x are weakly compact when this is the case we show that the essential space of the representation is complemented if a has a bounded left approximate identity this provides a tool to disregard the difference between degenerate and nondegenerate representations our results have interesting consequences both in c algebras and in abstract harmonic analysis for example a c algebra a has an isometric representation on an l p space for p in 1 infty setminus 2 if and only if a is commutative moreover the l p operator algebra of a locally compact group is universal with respect to arbitrary representations on l p spaces

equilibrium and ground states from cayley graphs abstract we present a general framework for the study of kms states of generalized gauge actions on the c algebra of a cayley graph which is pointed by considering the neutral element of the group as a distinguished vertex we use this framework to give a concrete description of a particular kind of kms states on the c algebras that we call abelian kms states if the group is nilpotent all kms states are abelian and our analysis gives the full picture in this case we then describe the ground states that are limits of abelian kms states when the temperature goes to zero

graph c algebras with real rank zero given a row finite directed graph e a universal c algebra c e generated by a family of partial isometries and projections subject to the relations determined by e is associated to the graph e the cuntz krieger algebras are those graph c algebras associated to some finite graphs we prove that a graph c algebra c e has real rank zero in the sense that the set of invertible self adjoint elements is dense in the set of all self adjoint elements in c e or in the unitization of c e if c e is nonunital if and only if e satisfies a loop condition k that is analogous to the condition for a finite 0 1 matrix a under which cuntz analyzed the ideal structure of the cuntz krieger algebra oa

purely infinite partial crossed products let a g be a partial dynamical system we show that there is a bijective correspondence between g invariant ideals of a and ideals in the partial crossed product a rg provided the action is exact and residually topologically free assuming in addition a technical condition automatic when a is abelian we show that a rg is purely infinite if and only if the positive nonzero elements in a are properly infinite in a rg as an application we verify pure infiniteness of various partial crossed products including realisations of the cuntz algebras on oa on and oz as partial crossed products

a going down principle for ample groupoids and the baum connes conjecture abstract we study a going down or restriction principle for ample groupoids and its applications the going down principle for locally compact groups was developed by chabert echterhoff and oyono oyono and allows to study certain functors that arise in the context of the topological k theory of a locally compact group in terms of their restrictions to compact subgroups we extend this principle to the class of ample hausdorff groupoids using le gall s groupoid equivariant version of kasparov s bivariant kk theory moreover we provide an application to the baum connes conjecture for ample groupoids which are strongly amenable at infinity this result in turn is then used to relate the baum connes conjecture for an ample groupoid group bundle which is strongly amenable at infinity to the baum connes conjecture for the fibres

the nuclear dimension of graph c algebras abstract consider a graph c algebra c e with a purely infinite ideal i possibly all of c e such that i has only finitely many ideals and c e i is approximately finite dimensional we prove that the nuclear dimension of c e is 1 if i has infinitely many ideals then the nuclear dimension of c e is either 1 or 2

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

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

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

banach algebras generated by an invertible isometry of an l p space abstract we provide a complete description of those banach algebras that are generated by an invertible isometry of an l p space together with its inverse examples include the algebra p f p z of p pseudofunctions on z the commutative c algebra c s 1 and all of its quotients as well as uncountably many exotic banach algebras we associate to each isometry of an l p space a spectral invariant called spectral configuration which contains considerably more information than its spectrum as an operator it is shown that the spectral configuration describes the isometric isomorphism type of the banach algebra that the isometry generates together with its inverse it follows from our analysis that these algebras are semisimple with the exception of p f p z they are all closed under continuous functional calculus and their gelfand transform is an isomorphism as an application of our results we show that banach algebras that act on l 1 spaces are not closed under quotients this answers the case p 1 of a question asked by le merdy 20 years ago

c algebras associated to boolean dynamical systems copyright 2017 elsevier b v or its licensors or contributors this is the authors accepted and refereed manuscript to the article

closed form solutions for analysis of cylindrically conformal microstrip antennas with arbitrary radii an efficient and accurate closed form solution based on the spectral domain method of moments mom is presented to analyze the characteristics of cylindrically conformal microstrip antennas with arbitrary radii first an algorithm that combines the recursive and the uniform asymptotic expansion method in different regions is developed to calculate the spectral domain green s functions for arbitrary dielectric coated cylinders accurately next the integrands of the spectral integrals involved in mom equation are partitioned into two parts i e the fast oscillatory slowly convergent part and the well behaved part consequently all of the integrals in mom analysis can be categorized into two types through the sommerfeld identity and its extension these integrals are cast into closed forms by using the nonlinear approximation method generalized pencil of function method in this method any time consuming numerical integration procedure is eliminated which improves the computational efficiency drastically compared with the results from published references the validity and accuracy of the method are demonstrated

pseudogroups and their etale groupoids abstract a pseudogroup is a complete infinitely distributive inverse monoid such inverse monoids bear the same relationship to classical pseudogroups of transformations as frames do to topological spaces the goal of this paper is to develop the theory of pseudogroups motivated by applications to group theory c algebras and aperiodic tilings our starting point is an adjunction between a category of pseudogroups and a category of etale groupoids from which we are able to set up a duality between spatial pseudogroups and sober etale groupoids as a corollary to this duality we deduce a non commutative version of stone duality involving what we call boolean inverse semigroups and boolean etale groupoids as well as a generalization of this duality to distributive inverse semigroups non commutative stone duality has important applications in the theory of c algebras it is the basis for the construction of cuntz and cuntz krieger algebras and in the case of the cuntz algebras it can also be used to construct the thompson groups we then define coverages on inverse semigroups and the resulting presentations of pseudogroups as applications we show that paterson s universal groupoid is an example of a booleanization and reconcile exel s recent work on the theory of tight maps with the work of the second author

k theorie bivariante pour les algebres de banach et conjecture de baum connes je suis parvenu dans ma these a construire une k theorie bivariante pour les algebres de banach cela m a permis de demontrer la conjecture de baum connes pour les groupes de lie semi simples et les groupes reductifs p adiques ainsi que pour les sous groupes discrets de type fini de sl 3 f avec f une extension finie de q p et pour les sous groupes discrets cocompacts de sp n 1 sl 3 r et sl 3 c j ai aussi demontre une conjecture analogue a la conjecture de baum connes pour les algebres l 1 et plus generalement toutes les bonnes completions des sous groupes fermes des groupes de lie semi simples et des groupes reductifs p adiques

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

poisson boundary of a relativistic diffusion in this article we study the asymptotic behaviour of a random motion in minkowski spacetime representing the random evolution of an object or signal traveling at a speed strictly less than the speed of the light introduced by dudley in his article ark mat 6 241 268 1966 we determine its invariant algebra and give an explicit description of the poisson boundary of its differential generator

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

noncommutative manifolds from graph and k graph c algebras in pren we constructed smooth 1 summable semifinite spectral triples for graph algebras with a faithful trace and in prs we constructed k summable semifinite spectral triples for k graph algebras in this paper we identify classes of graphs and k graphs which satisfy a version of connes conditions for noncommutative manifolds

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

kms weights on groupoid and graph c algebras abstract the paper contains a description of the kms weights for the one parameter action on the reduced c algebra of a second countable locally compact hausdorff etale groupoid arising from a continuous real valued homomorphism satisfying two conditions the result is subsequently applied to identify the kms weights for the gauge action on a simple graph algebra the von neumann algebra generated by the gns representation of an extremal kms weight is a factor and tools are developed to determine its type the paper concludes with three examples to illustrate the results

efficient analysis of printed structures of arbitrary shape on coated cylinders via spatial domain mixed potential green s function we present an approach for the method of moments mom analysis of antennas of arbitrary shape printed on a cylindrical substrate we propose several key components of a code to perform this analysis with the explicit goal of adapting mom codes devised for planar stratified structures for that purpose the background medium green s function is expressed in the mixed potential mp format to allow for efficient numerical integration the spectral dyadic green s function is first recast in the spectral counterpart of the spatial mixed potential form the convergence of the spectral to spatial transform is accelerated by extraction of spectral asymptotic functions and exploitation of the azimuthal periodicity several important issues of implementation numerical stability and accuracy are addressed with a view to incorporate the spatial mp green s function into the mom analysis of printed structures of arbitrary shape using rwg basis functions the numerical results are in good agreement with those obtained by other methods and with measured data

closed form green s function representations in cylindrically stratified media for method of moments applications closed form green s function cfgf representations for cylindrically stratified media which can be used as the kernel of an electric field integral equation are developed the developed cfgf representations can safely be used in a method of moments solution procedure as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder such as the air dielectric and dielectric dielectric interfaces including the axial line rho rho and phi phi which has not been available before in the course of obtaining these expressions the conventional spectral domain green s function representations are rewritten in a different form so that i we can attack the axial line problem and ii the method can handle electrically large cylinders available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently lastly the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method where a modified two level approach is used numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain cfgf representations

quantitative k theory for banach algebras abstract quantitative or controlled k theory for c algebras was used by guoliang yu in his work on the novikov conjecture and later developed more formally by yu together with herve oyono oyono in this paper we extend their work by developing a framework of quantitative k theory for the class of algebras of bounded linear operators on subquotients i e subspaces of quotients of l p spaces we also prove the existence of a controlled mayer vietoris sequence in this framework

semigroupoid c algebras abstract a semigroupoid is a set equipped with a partially defined associative operation given a semigroupoid we construct a c algebra o from it we then present two main examples of semigroupoids namely the markov semigroupoid associated to an infinite 0 1 matrix and the semigroupoid associated to a row finite higher rank graph without sources in both cases the semigroupoid c algebra is shown to be isomorphic to the algebras usually attached to the corresponding combinatorial object namely the cuntz krieger algebras and the higher rank graph c algebras respectively in the case of a higher rank graph d it follows that the dimension function d is superfluous for defining the corresponding c algebra

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

regular representation of groupoid c algebras and applications to inverse semigroups the analogue of the left regular representation of a locally compact groupoid is constructed in the hausdoras well as in the non hausdorcase a necessary and su cient condition for a locally compact groupoid with a cocycle to be morita equi valent to a group action is obtained as an application the c algebras of a class of inverse semigroups is shown to be morita equivalent to crossed products of groups by abelian c

quotients of banach algebras acting on lp spaces we show that the class of banach algebras that can be isometrically represented on an lp space for p 2 is not closed under quotients this answers a question asked by le merdy 20 years ago our methods are heavily reliant on our earlier study of banach algebras generated by invertible isometries of lp spaces

analysis of printed antennas mounted on a coated circular cylinder of arbitrary size an efficient numerical algorithm for the analysis of printed antennas on a dielectric coated circular cylinder is presented the formulation employs the spectral domain approach green s function is evaluated via olver s uniform asymptotic expansions the fourier summation is transformed into integration and the asymptotic part of the integral is evaluated in closed form the whole procedure results in a numerical algorithm that is at least as accurate and efficient as the respective one for the planar structure the present approach can be applied for any source receiver position and any cylinder radius

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

a probabilistic view on singularities the aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity two new and simple singularity theorems whose features are different from the classical singularity theorems are proved using probabilistic methods under some energy conditions and without any causal or initial boundary assumption simple conditions on the energy flow imply probabilistic incompleteness

relativistic diffusions a unifying approach a new wide class of relativistic stochastic processes is introduced all relativistic processes considered so far in the literature are members of this class for each process the stochastic equations of motion are obtained in an arbitrary lorentz frame the associated kolmogorov equation is also derived for the first time in both 3 1 and manifestly covariant forms

two dimensional green s function for scattering and radiation problems in elliptically layered media a recursive solution for the computation of the two dimensional green s function for the multilayer elliptic cylinder is reported it is based on the scattering solution by this canonical scatterer through eigenfunction expansions in terms of mathieu functions the paper reports the mathematical details of the approach as well as several validation tests and comparisons

central limit theorem for a class of relativistic diffusions two similar minkowskian diffusions have been considered on one hand by debbasch and co workers j math phys 40 2891 2001 eur phys j 19 37 2001 23 487 2001 j stat phys 88 945 1997 90 1179 1998 and on the other hand by dunkel and hanggi phys rev e 71 016124 2005 72 036106 2005 we address here two questions asked by debbasch and rivet j stat phys 90 1179 1998 and by dunkel and hanggi phys rev e 71 016124 2005 72 036106 2005 respectively about the asymptotic behavior of such diffusions more generally we establish a central limit theorem for a class of minkowskian diffusions to which the two above ones belong as a consequence we correct a partially wrong guess by dunkel and hanggi phys rev e 71 016124 2005

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

stochastic operators information and entropy for a stochastic operatoru on andl1 space i eu is linear positive and norm preserving on the positive cone ofl1 it is shown thatu decreases relative information between two nonnegativel1 functions furthermore it is shown that the following properties ofu are closely related u is energy decreasing energy preserving u ish decreasing whereh is boltzmann sh functional and the maxwell distributions are fixed points ofu

nest representations of directed graph algebras this paper is a comprehensive study of the nest representations for the free semigroupoid algebra mathfrak l g of a countable directed graph g as well as its norm closed counterpart the tensor algebra mathcal t g we prove that the finite dimensional nest representations separate the points in mathfrak l g and a fortiori in mathcal t g the irreducible finite dimensional representations separate the points in mathfrak l g if and only if g is transitive in components which is equivalent to being semisimple also the upper triangular nest representations separate points if and only if for every vertex x in mathcal t g supporting a cycle x also supports at least one loop edge we also study faithful nest representations we prove that mathfrak l g or mathcal t g admits a faithful irreducible representation if and only if g is strongly transitive as a directed graph more generally we obtain a condition on g which is equivalent to the existence of a faithful nest representation we also give a condition that determines the existence of a faithful nest representation for a maximal type mathbb n nest

an h theorem for the general relativistic ornstein uhlenbeck process we construct conditional entropy four currents for the general relativistic ornstein uhlenbeck process and we prove that the four divergences of these currents are always non negative this h theorem is then discussed in detail in particular the theorem is valid in any lorentzian space time even those presenting well known chronological violations

polish groupoids and functorial complexity we introduce and study the notion of functorial borel complexity for polish groupoids such a notion aims to measure the complexity of classifying the objects of a category in a constructive and functorial way in the particular case of principal groupoids such a notion coincides with the usual borel complexity of equivalence relations our main result is that on one hand for polish groupoids with an essentially treeable orbit equivalence relation functorial borel complexity coincides with the borel complexity of the associated orbit equivalence relation on the other hand for every countable equivalence relation e that is not treeable there are polish groupoids with different functorial borel complexity both having e as orbit equivalence relation in order to obtain such a conclusion we generalize some fundamental results about the descriptive set theory of polish group actions to actions of polish groupoids answering a question of arlan ramsay these include the becker kechris results on polishability of borel g spaces existence of universal borel g spaces and characterization of borel g spaces with borel orbit equivalence relations

column and row operator spaces over qslp spaces and their use in abstract harmonic analysis the notions of column and row operator space were extended by a lambert from hilbert spaces to general banach spaces in this paper we use column and row spaces over quotients of subspaces of general lp spaces to equip several banach algebras occurring naturally in abstract harmonic analysis with canonical yet not obvious operator space structures that turn them into completely bounded banach algebras we use these operator space structures to gain new insights on those algebras

simple labeled graph c algebras are associated to disagreeable labeled spaces abstract by a labeled graph c algebra we mean a c algebra associated to a labeled space e l e consisting of a labeled graph e l and the smallest normal accommodating set e of vertex subsets every graph c algebra c e is a labeled graph c algebra and it is well known that c e is simple if and only if the graph e is cofinal and satisfies condition l bates and pask extend these conditions of graphs e to labeled spaces and show that if a set finite and receiver set finite labeled space e l e is cofinal and disagreeable then its c algebra c e l e is simple in this paper we show that the converse is also true

a class of c algebras generalizing both graph algebras and homeomorphism c algebras i fundamental results we introduce a new class of c algebras which is a generalization of both graph algebras and homeomorphism c algebras this class is very large and also very tractable we prove the so called gauge invariant unique ness theorem and the cuntz krieger uniqueness theorem and compute the k groups of our algebras

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

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

crossed products by minimal homeomorphisms let x be an infinite compact metric space with finite covering dimension and let h x x be a minimal homeomorphism we show that the associated crossed product c algebra a 1 4 c z x h has tracial rank zero whenever the image of k0 a in a t a is dense as a consequence we show that these crossed product c algebras are in fact simple ah algebras with real rank zero when x is connected and h is further assumed to be uniquely ergodic then the above happens if and only if the rotation number associated to h has irrational values by applying the classification result for nuclear simple c algebras with tracial rank zero we show that two such dynamical systems have isomorphic crossed products if and only if they have isomorphic scaled ordered k theory

topological entropy and the af core of a graph c algebra abstract let c e be the c algebra associated with a locally finite directed graph e and a e be the af core of c e for the topological entropy ht e in the sense of brown voiculescu of the canonical completely positive map e on the graph c algebra it is known that if e is finite ht e ht e a e h b e h l e where h b e respectively h l e is the block respectively the loop entropy of e in case e is irreducible and infinite h l e ht e a e h b e t is known recently where e t is the graph e with the edges directed reversely then by monotonicity of entropy h l e ht e is clear in this paper we show that ht e h b e t holds for locally finite infinite graphs e the af core a e is known to be stably isomorphic to the graph c algebra c e c z of certain skew product e c z and we also show that ht e c z ht e a e examples e p p 1 of irreducible graphs with ht e p log p are discussed

a diffusion process in curved space time we construct a curved space time generalization of the special relativistic ornstein uhlenbeck process this is done by deriving a manifestly covariant kolmogorov equation that describes diffusion in curved space times the simple case of diffusion in a spatially flat friedmann robertson walker universe is then considered it is proven that at least in these space times kolmogorov equation admits as possible solution a natural generalization of the flat space time juttner equilibrium solution the first correction to juttner s distribution in a slowly expanding universe is also obtained explicitly

an efficient asymptotic extraction approach for the green s functions of conformal antennas in multilayered cylindrical media asymptotic expressions are derived for the dyadic green s functions of antennas radiating in the presence of a multilayered cylinder where analytic representation of the asymptotic expansion coefficients eliminates the computational cost of numerical evaluation as a result the asymptotic extraction technique has been applied only once for a large summation order in addition the hankel function singularity encountered for source and evaluation points at the same radius has been eliminated using analytical integration

leavitt r algebras over countable graphs embed into l2 r abstract for a commutative ring r with unit we show that the leavitt path algebra l r e of a graph e embeds into l 2 r precisely when e is countable before proving this result we prove a generalised cuntz krieger uniqueness theorem for leavitt path algebras over r

strength of convergence in the orbit space of a groupoid abstract let g be a second countable locally compact hausdorff groupoid with a haar system and let x n be a sequence in the unit space g 0 of g we show that the notions of strength of convergence of x n in the orbit space g 0 g and measure theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid c algebra

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

analysis and measurements of conformal patch array antennas on multilayer circular cylinder in this paper we present a method of moments mom program to analyze different configurations of arrays of cylindrical rectangular patches the patches can be located inside or on the surface of a multilayer circular cylindrical structure and can be arbitrarily rotated the antenna structure is rigorously taken into account by using proper green s functions and the array is analyzed by using an element by element approach the elements of the mom matrix are calculated in the spectral domain and special attention is given to their numerical treatment when analyzing cylindrical antennas with large radii a laboratory model is built to test different configurations of patches and to validate calculated results the agreement between measurements and calculations is very good

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

the suspension of a graph and associated c algebras abstract given a directed graph e we construct for each real number l a quiver whose vertex space is the topological realisation of e and whose edges are directed paths of length l in the vertex space these quivers are not topological graphs in the sense of katsura nor topological quivers in the sense of muhly and tomforde we prove that when l 1 and e is finite the infinite path space of the associated quiver is homeomorphic to the suspension of the one sided shift of e we call this quiver the suspension of e we associate both a toeplitz algebra and a cuntz krieger algebra to each of the quivers we have constructed and show that when l 1 the cuntz krieger algebra admits a natural faithful representation on the l 2 space of the suspension of the one sided shift of e for graphs e in which sufficiently many vertices both emit and receive at least two edges and for rational values of l we show that the toeplitz algebra and the cuntz krieger algebra of the associated quiver are homotopy equivalent to the toeplitz algebra and cuntz krieger algebra respectively of a graph that can be regarded as encoding the lth higher shift associated to the one sided shift space of e

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

hydrodynamic behavior of brownian particles in a position dependent constant force field the diffusion equation in physical space time for a brownian particle driven by an external force field has been derived by smoluchowski in the two particular cases where the external field is uniform or varies linearly with position elastic force in more general cases correction terms must be added to the smoluchowski equation we show here how to use a multi scale chapman enskog expansion to obtain in the hydrodynamic limit the first corrective terms to the smoluchowski equation without any restriction on the friction coefficient and for any sufficiently small position dependent constant force field we also compare our approach with the works of wilemski titulaer and van kampen

af labeled graph c algebras abstract it is known that a graph c algebra c e is approximately finite dimensional af if and only if the graph e has no loops in this paper we consider the question of when a labeled graph c algebra c e l b is af a notion of loop in a labeled space e l b is defined when b is the smallest one among the accommodating sets that are closed under relative complements and it is proved that if a labeled graph c algebra is af the labeled space has no loops a sufficient condition for a labeled space to give rise to an af algebra is also given for graph c algebras c e this sufficient condition is also a necessary one besides we discuss other equivalent conditions for a graph c algebra to be af in the setting of labeled graphs and prove that these conditions are not always equivalent by invoking various examples

a generalized cuntz krieger uniqueness theorem for higher rank graphs we present a uniqueness theorem for k graph c algebras that requires neither an aperiodicity nor a gauge invariance assumption specifically we prove that for the injectivity of a representation of a k graph c algebra it is sufficient that the representation be injective on a distinguished abelian c subalgebra a crucial part of the proof is the application of an abstract uniqueness theorem which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient c algebra each of which is the unique extension of a state on the distinguished abelian c subalgebra

further improvement for fast computation of mixed potential green s functions for cylindrically stratified media a method of fast computation of the mixed potential green s functions mpgfs in spatial domain for cylindrically stratified media has been developed based on the convergence behavior of the mpgfs in spectral domain the discrete complex image method dcim and the extrapolation technique are employed to perform the inverse fourier transform which is different from that of planarly stratified media in order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity the green s functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process for the integral along the deformed sommerfeld integral path with respect to k sub z dcim is used to speed up the computation after the quasistatic components are completely subtracted from the spectral domain green s functions the inverse transform of the remaining parts has an approximated analytical form the proposed method can be used to accurately and efficiently calculate the spatial domain mpgfs which are useful for characterizing conformal patch structures mounted on cylindrically stratified media

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

efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders an efficient and accurate hybrid method based on the combination of the method of moments mom with a special green s function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders the efficiency and accuracy of the method depend strongly on the computation of the green s function which is the kernel of the integral equation that is solved via mom for the unknown equivalent currents representing only the antenna elements three types of space domain green s function representations are used each accurate and computationally efficient in a given region of space consequently a computationally optimized analysis tool for conformal microstrip antennas is obtained input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method

green s functions for probe fed arbitrary shaped cylindrical microstrip antennas the efficiency of a method of moments procedure for microstrip antennas is strongly dependent on the convergence of the inverse fourier transformation ift from the spectral to the spatial domain this is especially true when considering cylindrical microstrip antennas cmas in the cylindrical case the calculation of the two dimensional green s functions stays inherently time consuming in the planar case green s function can be reduced to a one dimensional function the problem however becomes a real bottle neck when probe feeding of a cma is considered as the traditional ift used to calculate the excitation in the spatial domain results in a huge ift time in this paper this problem is explicitly treated the asymptotical behavior of the probe related spectral green s functions gfs is rigorously derived subtracted and the corresponding reaction integrals are inverse fourier transformed without the occurrence of any cylindrical functions this results in a much improved calculation efficiency for this type of feeding evident for both thin and thick substrates numerical results for cmas with complex shaped patches are presented applicable to both smaller and larger bandwidths several structures are fabricated and measurements are in good agreement with simulations