pullback and pushout constructions in c algebra theory abstract a systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of c algebras particular emphasis is given to the relations with tensor products both with the minimal and the maximal c tensor norm thus it is shown that pullback and pushout diagrams are stable under tensoring with a fixed algebra and stable under crossed products with a fixed group general tensor products between diagrams are also investigated the relations between the theory of extensions and pullback and pushout diagrams are explored in some detail the crowning result is that if three short exact sequences of c algebras are given with appropriate morphisms between the sequences allowing for pullback or pushout constructions at the levels of ideals algebras and quotients then the three new c algebras will again form a short exact sequence under some mild extra conditions as a generalization of a theorem of t a loring it is shown that each morphism between a pair of c algebras combined with its extension to the stabilized algebras gives rise to a pushout diagram this result has applications to corona extendibility and conditional projectivity finally the pullback and pushout constructions are applied to the class of noncommutative cw complexes defined by s eilers t a loring and g k pedersen j reine angew math 1998 499 101 143 to show that this category is stable under tensor products and under restricted direct sums

on tracial approximation let c be a class of unital c algebras the class tac of c algebras which can be tracially approximated in the egorov like sense first considered by lin by the c algebras in c is studied lin considered the case that c consists of finite dimensional c algebras or the tensor products of such with c 0 1 in particular the question is considered whether for any simple separable a tac there is a c algebra b which is a simple inductive limit of certain basic homogeneous c algebras together with c algebras in c such that the elliott invariant of a is isomorphic to the elliott invariant of b an interesting case of this question is answered in the final part of the paper the question is also considered which properties of c algebras are inherited by tracial approximation results of this kind are obtained which are used in the proof of the main theorem of the paper and also in the proof of the classification theorem of the second author given in z niu a classification of tracially approximately splitting tree algebra in preparation and z niu a classification of certain tracially approximately subhomogeneous c algebras phd thesis university of toronto 2005 which also uses the main result of the present paper

the riemann hilbert problem and the generalized neumann kernel on multiply connected regions this paper presents and studies fredholm integral equations associated with the linear riemann hilbert problems on multiply connected regions with smooth boundary curves the kernel of these integral equations is the generalized neumann kernel the approach is similar to that for simply connected regions see r wegmann a h m murid m m s nasser the riemann hilbert problem and the generalized neumann kernel j comput appl math 182 2005 388 415 there are however several characteristic differences which are mainly due to the fact that the complement of a multiply connected region has a quite different topological structure this implies that there is no longer perfect duality between the interior and exterior problems we investigate the existence and uniqueness of solutions of the integral equations in particular we determine the exact number of linearly independent solutions of the integral equations and their adjoints the latter determine the conditions for solvability an analytic example on a circular annulus and several numerically calculated examples illustrate the results

geometric structure of dimension functions of certain continuous fields abstract for a continuous field of c algebras a we give a criterion to ensure that the stable rank of a is one in the particular case of a trivial field this leads to a characterization of stable rank one completing accomplishments by nagisa osaka and phillips further for certain continuous fields of c algebras we study when the cuntz semigroup satisfies the riesz interpolation property and we also analyze the structure of its functionals as an application we obtain a positive answer to a conjecture posed by blackadar and handelman in a variety of situations

recovering the elliott invariant from the cuntz semigroup let a be a simple separable c algebra of stable rank one we prove that the cuntz semigroup of c t a is determined by its murray von neumann semigroup of projections and a certain semigroup of lower semicontinuous functions with values in the cuntz semigroup of a this result has two consequences first specializing to the case that a is simple finite separable and z stable this yields a description of the cuntz semigroup of c t a in terms of the elliott invariant of a second suitably interpreted it shows that the elliott functor and the functor de fined by the cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent

classification of c homomorphisms from c0 0 1 to a c algebra abstract a class of c algebras is described for which the c homomorphisms from c 0 0 1 to the algebra may be classified by means of the cuntz semigroup functor examples are given of algebras simple and non simple for which this classification fails it is shown that a suitable suspension of the cuntz semigroup functor deals successfully with some of these counterexamples

radial and circular slit maps of unbounded multiply connected circle domains infinite product formulae for conformally mapping an unbounded multiply connected circle domain to an unbounded canonical radial or circular slit domain or to domains with both radial and circular

gauss seidel newton armijo approach for minimization problems on the non negative orthant application to spatial price equilibrium problems abstract to deal with the optimization problem min x 0 x we propose a gauss seidel type iterative approach where variables are modified sequentially one at a time gsna algorithm or by blocks bgsna algorithm relying on both the newton approach and an armijo rule an inaccurate line search is performed at each step to determine a step size insuring global convergence both robustness global convergence and efficiency rate of local convergence are analyzed under minimal hypotheses even weaker than those often required to prove the convergence of gauss seidel methods these procedures are applied to spatial price equilibrium problems and the numerical results indicate that they are competitive with minos

a charge simulation method for the numerical conformal mapping of interior exterior and doubly connected domains abstract a simple numerical method is described for computing the following three conformal maps a from a domain interior to a closed jordan curve onto the interior of the unit disk b from a domain exterior to a closed jordan curve onto the exterior of the unit disk and c from a doubly connected domain bounded by two closed jordan curves onto a circular annulus the numerical method is based on the charge simulation method or the method of fundamental solutions applied to the dirichlet problem of laplace s equation in which a pair of conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials without integration typical examples show that numerical results of high accuracy can be obtained by the simple method if the domains have no concave corners

the cuntz semigroup the elliott conjecture and dimension functions on c algebras we prove that the cuntz semigroup is recovered functorially from the elliott invariant for a large class of c algebras in particular our re sults apply to the largest class of simple c algebras for which k theoretic classification can be hoped for this work has three significant consequences first it provides new conceptual insight into elliott s classification program proving that the usual form of the elliott conjecture is equivalent among z stable algebras to a conjecture which is in general substantially weaker and for which there are no known counterexamples second and third it resolves for the class of algebras above two conjectures of blackadar and handelman concerning the basic structure of dimension functions on c algebras we also prove in passing that the cuntz pedersen semigroup is recovered functorially from the elliott invariant for a large class of simple unital c algebras

recursive subhomogeneous algebras we introduce and characterize a particularly tractable class of unital type 1 c algebras with bounded dimension of irreducible representations algebras in this class are called recursive subhomogeneous algebras and they have an inductive description through iterated pullbacks which allows one to carry over from algebras of the form many of the constructions relevant in the study of the stable rank and k theory of simple direct limits of homogeneous c algebras our characterization implies in particular that if is a separable c algebra whose irreducible representations all have dimension at most and if for each the space of dimensional irreducible representations has finite covering dimension then is a recursive subhomogeneous algebra we demonstrate the good properties of this class by proving subprojection and cancellation theorems in it consequences for simple direct limits of recursive subhomogeneous algebras with applications to the transformation group c algebras of minimal homeomorphisms will be given in separate papers

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

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

a variable dimension solution approach for the general spatial price equilibrium problem algorithms are presented that are specifically designed for solving general nonlinear multicommodity spatial price equilibrium problems i e problems with nonlinear transportation cost functions nonlinear supply and demand functions inter commodity congestion effects intercommodity substitution and complementarity effects and interactions among transportation links and among spatially separated markets the algorithms are specializations of an iterative method for solving nonlinear complementarity problems that requires solving a system of nonlinear equations at each iteration the algorithms exploit the network structure of the problems to reduce the size of the system of equations to be solved at each iteration the decision rules for determining which equations are to be included in the system at each iteration are extremely simple and the remainder of the computational work is carried out by the nonlinear equation solver because of this the algorithms are very easy to implement with readily available software in addition since the decision rules only require sign information only the final system needs to be solved with precision

numerical conformal mapping of multiply connected regions onto the fifth category of koebe s canonical slit regions abstract this paper presents a boundary integral method for approximating the conformal mapping from bounded multiply connected regions onto the fifth category of koebe s classical canonical slit regions the method is based on a uniquely solvable boundary integral equation with generalized neumann kernel the results of some test calculations illustrate the performance of the presented method

computing nonlinear network equilibria this paper examines the problem of computing nonlinear network equilibria using a newton iteration by exploiting the network structure we are able to show that the iteration is globally convergent monotonic and locally quadratically convergent using only simple algebraic arguments

a general dynamic spatial price equilibrium model formulation solution and computational results abstract this paper presents a general dynamic finite horizon spatial price equilibrium model inventorying is allowed at both supply and demand markets and backordering is also permitted for as many time periods as dictated by the competitive equilibrium the case of perishable commodities where inventorying may be practicable for only one or several time periods is handled within the model by appropriately defined feasibility conditions alternative variational inequality formulations are given and then exploited akin to the work for static spatial price equilibrium problems to construct gauss seidel schemes computational experience for these schemes and for equilibration methods is given for a number of scenarios

a parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model this paper presents a parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model we first reformulate the model as a linear complementarity problem and then apply the parametric principal pivoting algorithm for its solution this reformulation leads to the study of an arc arc weighted adjacency matrix associated with a simple digraph having weights on the nodes several basic properties of such a matrix are derived using these properties we show how the parametric principal pivoting algorithm can be greatly simplified in this application finally we report some computational experience with the proposed technique for solving some large problems

equation of motion for point vortices in multiply connected circular domains the paper gives the equation of motion for n point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles called the circular domain the velocity field induced by the point vortices is described in terms of the schottky klein prime function associated with the circular domain the explicit representation of the equation enables us not only to solve the euler equations through the point vortex approximation numerically but also to investigate the interactions between localized vortex structures in the circular domain as an application of the equation we consider the motion of two point vortices with unit strength and of opposite signs when the multiply connected domain is symmetric with respect to the real axis the motion of the two point vortices is reduced to that of a single point vortex in a multiply connected semicircle which we investigate in detail

a nystrom method for boundary integral equations in domains with corners we give a convergence and error analysis for a nystrom method on a graded mesh for the numerical solution of boundary integral equations for the harmonic dirichlet problem in plane domains with corners

distance between unitary orbits of normal elements in simple c algebras of real rank zero let x y x y be two normal elements in a unital simple c c algebra a we introduce a function d c x y d c x y and show that in a unital simple af algebra there is a constant 1 c 0 1 c 0 such that c d c x y dist u x u y d c x y c d c x y dist u x u y d c x y where u x u x and u y u y are the closures of the unitary orbits of x and of y respectively we also generalize this to unital simple c c algebras with real rank zero stable rank one and weakly unperforated k 0 k 0 group more complicated estimates are given in the presence of non trivial k 1 k 1 information

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions this paper presents a boundary integral equation method with the adjoint generalized neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions for each canonical region two integral equations are solved before one can approximate the boundary values of the mapping function cauchy s type integrals are used for computing the mapping function and its inverse for interior points this method also works for regions with piecewise smooth boundaries three examples are given to illustrate the effectiveness of the proposed method

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

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

fast conformal mapping of multiply connected regions abstract an iterative method is presented which constructs for an unbounded region g with m holes and sufficiently smooth boundary a circular region h and a conformal mapping from h to g with the usual normalization both h and are uniquely determined by g with a few modifications the method can also be applied to a bounded region g with m holes the canonical region h is then the unit disc with m circular holes the proposed method also determines the centers and radii of the boundary circles of h and requires at each iterative step the solution of a riemann hilbert rh problem which has a unique solution numerically the rh problem can be treated efficiently by the method of successive conjugation using the fast fourier transform fft the iteration for the solution of the rh problem converges linearly the conformal mapping method converges quadratically the results of some test calculations exemplify the performance of the method

dimension and stable rank in the k theory of c algebras in topological k theory which can be viewed as the algebraic side of the theory of vector bundles some of the interesting properties which one investigates are for example the conditions under which bundles must possess trivial direct summands or the extent to which the cancellation property for direct whitney sums of bundles holds such properties turn out to be controlled in part by the dimension of the base space and results describing the nature of this control are among what are frequently called stability results 17 during the past few years there has been a sudden flowering of a theory for c algebras see surveys 35 36 37 since c algebras are profitably thought of as non commutative locally compact spaces with the finitely generated projective modules being the appropriate generalization of vector bundles according to swan s theorem 40 it would be natural to look for stability results for c algebras but until now the theory has been focussed on the c groups of c algebras and there has been little discussion of stability properties presumably in part for lack of an appropriate concept of dimension for c algebras one of the main objectives of this paper is to introduce a concept of dimension for c algebras which directly generalizes the classical concept of dimension for compact spaces 16 20 22 and to develop some techniques for calculating it notably for c algebras which are obtained as crossed product algebras for an action of the group of integers in algebraic k theory which is the generalization of topological c theory to rings a substantial number of stability properties have been discovered 2 39 42 48 within that theory the concept which has played a role most analogous to that of dimension is the bass stable rank but despite its many successes the bass stable rank has often been difficult to calculate even for relatively uncomplicated rings another main objective of the present paper is to make accessible for application to c algebras some of the stability results from algebraic c theory this comes about from the fact that the concept of dimension which we introduce dominates the bass stable rank i was led to seek stability results for c algebras by my desire to determine whether the cancellation property for projective modules holds for the irrational rotation c algebras discussed in 30 which as elliott 11 has suggested can appropriately be called 2 dimensional non commutative tori in more concrete terms the question is whether two projections in such an algebra which have the same trace must be unitarily equivalent the present paper provides the general theory which is needed for the affirmative answer which i obtained in a subsequent paper i will derive the

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

a simplified fornberg like method for the conformal mapping of multiply connected regions comparisons and crowding we present a new fornberg like method for the numerical conformal mapping of multiply connected regions exterior to circles to multiply connected regions exterior to smooth curves the method is based on new symmetric conditions for analytic extension of functions given on circular boundaries we also briefly discuss a similar method due to wegmann and compare some computations with both methods some examples of regions which exhibit crowding of the circles are also presented

the generalized linear complementarity problem revisited given a vertical block matrixa we consider in this paper the generalized linear complementarity problem vlcp q a introduced by cottle and dantzig we formulate this problem as a linear complementarity problem with a square matrixm a formulation which is different from a similar formulation given earlier by lemke our formulation helps in extending many well known results in linear complementarity to the generalized linear complementarity problem we also show that the class of vertical block matrices which cottle and dantzig s algorithm can process is the same as the class of equivalent square matrices which lemke s algorithm can process we also present some degree theoretic results on a vertical block matrix

pullbacks c x algebras and their cuntz semigroup abstract in this paper we analyse the structure of the cuntz semigroup of certain c x algebras for compact spaces of low dimension that have no k 1 obstruction in their fibres in a strong sense the techniques developed yield computations of the cuntz semigroup of some surjective pullbacks of c algebras as a consequence this allows us to give a complete description in terms of semigroup valued lower semicontinuous functions of the cuntz semigroup of c x a where a is a not necessarily simple c algebra of stable rank one and vanishing k 1 for each closed two sided ideal we apply our results to study a variety of examples

equivariant homomorphisms rokhlin constraints and equivariant uhf absorption abstract we classify equivariant homomorphisms between c dynamical systems associated to actions of finite groups with the rokhlin property in addition the given actions are classified an obstruction is obtained for the cuntz semigroup of a c algebra allowing such an action we also obtain an equivariant uhf absorption result

numerical conformal mapping via the bergman kernel using the generalized minimum residual method abstract the bergman kernel function is known to satisfy a certain boundary integral equation of the second kind for boundaries that possess symmetrical qualities the integral equation can be transformed into another integral equation that uses only a small part of the original boundary this paper applies an iterative procedure known as the generalized minimum residual method for the computation of the riemann mapping function via the bergman kernel the complexity of this procedure is o n 2 where n is the number of collocation points on the boundary of the region numerical implementation on some test regions is also presented

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

regularity properties in the classification program for separable amenable c algebras we report on recent progress in the program to classify separable amenable c algebras our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank strict comparison of positive elements and z stability and on the importance of the cuntz semigroup we include a brief history of the program s successes since 1989 a more detailed look at the villadsen type algebras which have so dramatically changed the landscape and a collection of announcements on the structure and properties of the cuntz semigroup

an iterative sor algorithm for multi period spatial equilibria abstract this paper presents an iterative algorithm for the solution of multi period spatial equilibrium problems formulated in a net import format we first present a net import formulation for the problem and then apply the sor based iterative algorithm for its solution we later show that the algorithm can be extended to problems with sparse network and with congestion on the flows finally we report computational experience with the proposed algorithm for the solution of some large problems

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

an algebraic approach to the radius of comparison the radius of comparison is an invariant for unital c algebras which extends the theory of covering dimension to noncommutative spaces we extend its definition to general c algebras and give an algebraic as opposed to functional theoretic reformulation this yields new permanence properties for the radius of comparison which strengthen its analogy with covering dimension for commutative spaces we then give several applications of these results new examples of c algebras with finite radius of comparison are given and the question of when the cuntz classes of finitely generated hilbert modules form a hereditary subset of the cuntz semigroup is addressed most interestingly perhaps we treat the question of when a full hereditary subalgebra b of a stable c algebra a is itself stable giving a characterization in terms of the radius of comparison we also use the radius of comparison to quantify the least n for which a c algebra d without bounded 2 quasitraces or unital quotients has the property that mn d is stable

hilbert c modules over a commutative c algebra this paper studies the problems of embedding and isomorphism for countably generated hilbert c modules over commutative c algebras when the fiber dimensions differ sufficiently relative to the dimension of the spectrum we show that there is an embedding between the modules this result continues to hold over recursive subhomogeneous c algebras for certain modules including all modules over c0 x w hen dimx 3 isomorphism and embedding are determined by the restrictions to the sets where the fiber dimensions are constant these considerations yield results for the cuntz semigroup including a computation of the cuntz semigroup for c0 x w hen dimx 3 in terms of cohomological data about x

boundary integral equations with the generalized neumann kernel for laplace s equation in multiply connected regions this paper presents a new boundary integral method for the solution of laplace s equation on both bounded and unbounded multiply connected regions with either the dirichlet boundary condition or the neumann boundary condition the method is based on two uniquely solvable fredholm integral equations of the second kind with the generalized neumann kernel numerical results are presented to illustrate the efficiency of the proposed method

the equivariant cuntz semigroup we introduce an equivariant version of the cuntz semigroup that takes an action of a compact group into account the equivariant cuntz semigroup is naturally a semimodule over the representation semiring of the given group moreover this semimodule satisfies a number of additional structural properties we show that the equivariant cuntz semigroup as a functor is continuous and stable moreover cocycle conjugate actions have isomorphic associated equivariant cuntz semigroups one of our main results is an analog of julg s theorem the equivariant cuntz semigroup is canonically isomorphic to the cuntz semigroup of the crossed product we compute the induced semimodule structure on the crossed product which in the abelian case is given by the dual action as an application of our results we show that freeness of a compact lie group action on a compact hausdorff space can be characterized in terms of a canonically defined map into the equivariant cuntz semigroup extending results of atiyah and segal for equivariant k theory finally we use the equivariant cuntz semigroup to classify locally representable actions on direct limits of one dimensional nccw complexes generalizing work of handelman and rossmann

numerical conformal mapping via the szego kernel abstract a new method to compute the riemann mapping function is numerically implemented and tested on examples the method expresses the szego kernel as the solution of a second kind integral equation the equation has its origin in an earlier non numerical work of stein and one of the authors 8 the experimental results show the algorithm to be effective and stable

isomorphism of hilbert modules over stably finite c algebras abstract it is shown that if a is a stably finite c algebra and e is a countably generated hilbert a module then e gives rise to a compact element of the cuntz semigroup if and only if e is algebraically finitely generated and projective it follows that if e and f are equivalent in the sense of coward elliott and ivanescu cei and e is algebraically finitely generated and projective then e and f are isomorphic in contrast to this we exhibit two cei equivalent hilbert modules over a stably finite c algebra that are not isomorphic

parallel slits map of bounded multiply connected regions abstract in this paper we present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a parallel slit region the method is based on some uniquely solvable boundary integral equations with adjoint classical adjoint generalized and modified neumann kernels these boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region some numerical examples are presented to illustrate the efficiency of the presented method

numerical conformal mapping of multiply connected regions onto the second third and fourth categories of koebeʼs canonical slit domains abstract this paper presents a boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region g onto the second third and fourth categories of koebe s canonical slit domains the method can be also used for calculating the conformal mappings of simply and doubly connected regions the method is an extension of the author s method for the first category of koebe s canonical slit domains see m m s nasser numerical conformal mapping via a boundary integral equation with the generalized neumann kernel siam j sci comput 31 2009 1695 1715 three numerical examples are presented to illustrate the performance of the proposed method

secondary schottky klein prime functions associated with multiply connected planar domains in recent years a general mathematical framework for solving applied problems in multiply connected domains has been developed based on use of the schottky klein s k prime function of an underlying compact riemann surface known as the schottky double of the domain in this paper we describe additional function theoretic objects that are naturally associated with planar multiply connected domains and which we refer to as secondary s k prime functions the basic idea develops and extends an observation of burnside dating back to 1892 applications of the new functions to represent conformal slit maps of mixed type that have been a topic of recent interest in the literature are given other possible applications are also surveyed

numerical conformal mapping via the bergman kernel a new method to compute the riemann mapping function via the bergman kernel is presented the method expresses the bergman kernel as the solution of a second kind integral equation involving the neumann kernel for symmetric regions the integral equation can be transformed into a new one that uses only a small part of the original boundary numerical implementations on some test regions are also presented

numerical conformal mapping of multiply connected regions by fornberg like methods we develop a new algorithm for computing conformal maps from regions exterior to non overlapping disks to unbounded multiply connected regions exterior to non overlapping smoothly bounded jordan regions the method is an extension of fornberg s original newton like method for mapping of the disk to simply connected regions a fortran program based on the algorithm has been developed and tested for the 2 and 3 disk case numerical examples are reported

continuous fields of c algebras over finite dimensional spaces abstract let x be a finite dimensional compact metrizable space we study a technique which employs semiprojectivity as a tool to produce approximations of c x algebras by c x subalgebras with controlled complexity the following applications are given all unital separable continuous fields of c algebras over x with fibers isomorphic to a fixed cuntz algebra o n n 2 3 are locally trivial they are trivial if n 2 or n for n 3 finite such a field is trivial if and only if n 1 1 a 0 in k 0 a where a is the c algebra of continuous sections of the field we give a complete list of the kirchberg algebras d satisfying the uct and having finitely generated k theory groups for which every unital separable continuous field over x with fibers isomorphic to d is automatically locally trivial or trivial in a more general context we show that a separable unital continuous field over x with fibers isomorphic to a kk semiprojective kirchberg c algebra is trivial if and only if it satisfies a k theoretical fell type condition

every classifiable simple c algebra has a cartan subalgebra we construct cartan subalgebras in all classifiable stably finite c algebras together with known constructions of cartan subalgebras in all uct kirchberg algebras this shows that every classifiable simple c algebra has a cartan subalgebra

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

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

the cancellation theorem for projective modules over irrational rotation c algebras on montre que deux modules projectifs sur a qui sont isomorphes de facon stable sont en fait isomorphes

a class of polynomially solvable linear complementarity problems although the general linear complementarity problem lcp is np complete there are special classes that can be solved in polynomial time one example is the type where the defining matrix is nondegenerate and for which the n step property holds in this paper we consider an extension of the property to the degenerate case by introducing the concept of an extended n step vector and matrix it is shown that the lcp defined by such a matrix is polynomially solvable as well

numerical conformal mapping via a boundary integral equation with the generalized neumann kernel we present a unified boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region g onto the five classical canonical slit domains the method is based on a uniquely solvable boundary integral equation with the generalized neumann kernel using the proposed method the approximate mapping functions onto the five canonical slit domains can be computed in a unified way by solving linear systems with a common coefficient matrix the method can be also used for calculating the conformal mappings of simply and doubly connected regions the performance of the method is illustrated by several examples for regions with smooth boundaries and with piecewise smooth boundaries

linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits abstract in this paper we present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a disk with circular slits the method is based on some uniquely solvable boundary integral equations with classical adjoint and generalized neumann kernels these boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region some numerical examples are presented to illustrate the efficiency of the presented method

the cone of lower semicontinuous traces on a c algebra the cone of lower semicontinuous traces is studied with a view to its use as an invariant its properties include compactness hausdorffness and continuity with respect to inductive limits a suitable notion of dual cone is given the cone of lower semicontinuous 2 quasitraces on a non exact c algebra is considered as well these results are applied to the study of the cuntz semigroup it is shown that if a c algebra absorbs the jiang su algebra then the subsemigroup of its cuntz semigroup consisting of the purely non compact elements is isomorphic to the dual cone of the cone of lower semicontinuous 2 quasitraces this yields a computation of the cuntz semigroup for the following two classes of c algebras c algebras that absorb the jiang su algebra and have no non zero simple subquotients and simple c algebras that absorb the jiang su algebra 1 introduction the most standard invariants in the classification of nu clear c algebras are their k groups and their traces the traces at least for simple c algebras are assumed to be bounded in the unital case and lower semicontinuous and densely finite in the non unital case if one has in mind the classification of non simple c algebras it is clear that these two kinds of traces will not suffice and a broader class should be considered in this paper we study the properties of the cone of all lower semicontinuous traces on a c algebra with the purpose of applying our results to questions in the classification of non simple c algebras one sign that this is natural is that this cone in particular determines the lattice of closed two sided ideals an important invariant in its own right see 3 4 we shall also consider lower semicontinuous 2 quasitraces since these appear naturally as functionals on the cuntz semigroup of the algebra if the