isomorphisms of algebras associated with directed graphs given countable directed graphs g and g we show that the associated tensor algebras open image in new window g and open image in new window g are isomorphic as banach algebras if and only if the graphs g are g are isomorphic for tensor algebras associated with graphs having no sinks or no sources the graph forms an invariant for algebraic isomorphisms we also show that given countable directed graphs g g the free semigroupoid algebras open image in new window and open image in new window are isomorphic as dual algebras if and only if the graphs g are g are isomorphic in particular spatially isomorphic free semigroupoid algebras are unitarily isomorphic for free semigroupoid algebras associated with locally finite directed graphs with no sinks the graph forms an invariant for algebraic isomorphisms as well

semi crossed products of c algebras abstract given a c algebra u and endomorphim there is an associated nonselfadjoint operator algebra z x u called the semi crossed product of u with if is an automorphim z x u can be identified with a subalgebra of the c crossed product z x u if u is commutative and is an automorphim satisfying certain conditions z x u is an operator algebra of the type studied by arveson and josephson suppose s is a locally compact hausdorff space s s is a continuous and proper map and is the endomorphim of u c0 s given by necessary and sufficient conditions on the map are given to insure that the semi crossed product z x c0 s is i semiprime ii semisimple ii strongly semisimple

superconformally covariant operators and super w algebras superdifferential operators of order 2n 1 which are covariant with respect to superconformal changes of coordinates on a compact super riemann surface are studied herein it is shown that all such operators arise from super mobius covariant ones a canonical matrix representation is presented and applications to classical super w algebras are discussed

ideals in some continuous nonselfadjoint crossed product algebras abstract let y t be a locally compact dynamical system where the t denotes a continuous one parameter semigroup of maps on y when each t is a homeomorphism a nonselfadjoint crossed product algebra is defined as the subalgebra of the c crossed product c 0 y r supported on t 0 when each t is only continuous the crossed product c 0 y r can still be defined the ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete free action on a smaller space x a generalization of effros hahn is given whereby one may find a meet irreducible ideal over any arc closure in y the meet irreducible ideals form a topological space in the hull kernel topology and there is a one to one correspondence between closed sets in this space and closed ideals in the algebra a subset of this space is homeomorphic to the space of finite arcs in the subarc topology the irrational flow algebra is considered as a special case

abelian mathrm c ast subalgebras of mathrm c ast algebras of real rank zero and inductive limit mathrm c ast algebras

operator algebras and the conjugacy of transformations abstract a family of algebras is associated with each continuous map on a compact hausdorff space these algebras are called conjugacy algebras it is shown that two continuous maps are conjugate if and only if some conjugacy algebra of one is isomorphic to some conjugacy for the other numerous examples of conjugacy algebras are provided

cartan subalgebras in c algebras existence and uniqueness we initiate the study of cartan subalgebras in c algebras with a particular focus on existence and uniqueness questions for homogeneous c algebras these questions can be analyzed systematically using the theory of fiber bundles for group c algebras while we are able to find cartan subalgebras in c algebras of many connected lie groups there are classes of discrete groups for instance non abelian free groups whose reduced group c algebras do not have any cartan subalgebras moreover we show that uniqueness of cartan subalgebras usually fails for classifiable c algebras however distinguished cartan subalgebras exist in some cases for instance in nuclear uniform roe algebras

string geometry and the noncommutative torus we construct a new gauge theory on a pair of d dimensional noncommutative tori the latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra and the noncommutative torus we show that the tachyon algebra of is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus we construct the corresponding real spectral triples and determine their morita equivalence classes using string duality arguments these constructions yield simple proofs of the o d d morita equivalences between d dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory we classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group we compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality symmetric the duality invariant gauge theory is manifestly covariant but contains highly non local interactions we show that it also admits a new sort of particle antiparticle duality which enables the construction of instanton field configurations in any dimension the duality non symmetric on shell projection of the field theory is shown to coincide with the standard non abelian yang mills gauge theory minimally coupled to massive dirac fermion fields

semicrossed products of operator algebras and their c envelopes abstract let a be a unital operator algebra and let be an automorphism of a that extends to a automorphism of its c envelope c env a we introduce the isometric semicrossed product a is z and we show that c env a is z c env a z in contrast the c envelope of the familiar contractive semicrossed product a z may not equal c env a z our main tool for calculating c envelopes for semicrossed products is a new concept the relative semicrossed product of an operator algebra by an endomorphism as an application of our theory we show that if t x is the tensor algebra of a c correspondence x a and is a extendible automorphism of t x that fixes the diagonal elementwise then the contractive semicrossed product satisfies c env t x z o x z where o x denotes the cuntz pimsner algebra of x a this extends the main result of davidson and katsoulis 2010 6

coifman wavelets in 3 d scattering from very rough random surfaces the coifman wavelets are employed to perform galerkin s procedure in the method of moments mom the coiflets are continuous smooth overlapping yet orthogonal which permit significant reduction of the sampling rate and dramatic compression of the matrix size with respect to the pulse based mom in addition the wavelet based impedance matrix is sparse more importantly the vanishing moments of the coiflets of order l 4 provide us with high precision o h sup 5 one point quadrature which knocks down the computational effort in filling the matrix entries from o n sup 2 to o n our approach is different from the conventional wavelet technique which employs wavelets to sparsify an existing impedance matrix under similarity transformation with computational cost in o n sup 2 excellent agreement between this coifman wavelet method and the previous publications is observed

nest representations and dynamical systems abstract a nest representation is a generalized irreducible representation of a banach algebra on hubert space for a free discrete dynamical system every ideal in the semicrossed product algebra is equal to an intersection of kernels of nest representations a proper subset of all such kernels is a topological space homeomorphic to the space of all discrete finite arcs in the dynamical system with the subarc topology for certain continuous dynamical systems the corresponding set of kernels is isomorphic to the topological space of continuous finite arcs a banach algebra isomorphism of semicrossed products implies orbit order conjugacy of the underlying dynamical systems nest algebras and a non free action are also considered

quantum heisenberg manifolds as twisted groupoid c algebras abstract the quantum heisenberg manifolds are noncommutative manifolds constructed by m rieffel as strict deformation quantizations of heisenberg manifolds and have been studied by various authors rieffel constructed the quantum heisenberg manifolds as the generalized fixed point algebras of certain crossed product c algebras and they also can be realized as crossed products of c t 2 by hilbert c bimodules in the sense of abadie et al in this paper we describe how the quantum heisenberg manifolds can also be realized as twisted groupoid c algebras in the final section for a transformation groupoid x z with x compact and e p x a locally trivial principal g bundle where g is a compact abelian group we form a groupoid that is a locally trivial principal g bundle over x z which reduces to the twist groupoid of the second author when g t

projections over quantum homogeneous odd dimensional spheres abstract we give a complete classification of isomorphism classes of finitely generated projective modules or equivalently unitary equivalence classes of projections over the c algebra c s q 2 n 1 of the quantum homogeneous sphere s q 2 n 1 then we explicitly identify as concrete elementary projections the quantum line bundles l k over the quantum complex projective space c p q n associated with the quantum hopf principal u 1 bundle s q 2 n 1 c p q n

n 2 supercovariant operators and krichever novikov algebra the n 2 superdiffeomorphism anomaly is defined on the compact n 2 super riemann surfaces by the inclusion of n 2 superprojective connection the n 2 supercovariant operators which are superconformally covariant are constructed and the relations with the n 2 super poisson operators and the krichever novikov algebra are given

classification of crossed product algebras associated with characters on free groups we study the classification problem of crossed product c algebras of the form cr g x z where g is a discrete group x is a one dimensional character of g and a x is the unique automorphism of cr g such that if u is the left regular representation of g then ax ug x g ug g e g when g fn the free group on n generators we have a complete classification of these crossed products up to isomorphism which generalizes the classification of irrational and rational rotation c algebras we show that these crossed products are determined by two k theoretic invariants that these two invariants correspond to two orbit invariants of the characters under the natural aut fn action and that these two orbit invariants completely classify the characters up to automorphisms of fn the classification of crossed products follows from these results we also consider the same problem for g some other groups

smooth local cosine based galerkin method for scattering problems the smooth local trigonometric slt functions are employed as the basis and testing functions in the galerkin based method of moments mom and sparse impedance matrices are obtained the basic idea of slt is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved moreover by choosing the correct trigonometric basis rapid convergence in the case of smooth functions is ensured the slt system is particularly suitable to handle electrically large scatterers where the integral kernel behaves in a highly oscillatory manner numerical examples demonstrate the scattering of electromagnetic waves from two dimensional objects with smooth contours as well as with sharp edges a comparison of the new approach versus the traditional mom and wavelet methods is provided

some point derivations for semicrossed products abstract we consider point derivations of semicrossed product algebras in particular we focus on point derivations into the upper triangular n n matrices and show that such point derivations are inner finally we consider point derivations corresponding to periodic points where the range is a standard semicrossed product considered in previous work on point derivations for graph algebras again we conclude that all such point derivations are inner

k theoretic invariants for c algebras associated to transformations and induced flows abstract we discuss a technique of studying the k theory of a unital c algebra associated to a homomorphism on a compact metric space y z by examining the non unital c algebra associated to the induced topological flow ind z r y r the thom isomorphism of connes and the schwartzman asymptotic cycle are used to calculate the range of the trace corresponding to an invariant measure on the k0 group of c x r for a continuous flow on a compact metric space x r under certain conditions projections in c x r with trace r corresponding to cross sections to the flow can be constructed for every positive real number r in this range again by combining techniques of connes and schwartzman applications to the calculation of the tracial range of k0 c x r are discussed in particular this invariant is calculated for minimal affine actions of z on n tori which have quasi discrete spectrum and for minimal actions of z on compact abelian groups with topologically discrete spectrum in both cases this tracial invariant is shown to be the preimage of the eigenvalues for y z under the natural projection o r r z s1

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

classification of c algebras generated by representations of the unitriangular group ut 4 z abstract it was recently shown that each c algebra generated by a faithful irreducible representation of a finitely generated torsion free nilpotent group is classified by its ordered k theory for the three step nilpotent group u t 4 z we calculate the ordered k theory of each c algebra generated by a faithful irreducible representation of u t 4 z and see that they are all simple a t algebras we also point out that there are many simple non a t algebras generated by irreducible representations of nilpotent groups

semicrossed products generated by two commuting automorphisms abstract in this paper we study the semicrossed product of a finite dimensional c algebra for two types of z 2 actions and identify them with matrix algebras of analytic functions in two variables we look at the connections with semicrossed by z actions

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

2 0 super beltrami parametrization and superconformal structures the superconformal structure of the 2 0 supergeometry of two dimensional superspace is characterized by the beltrami differentials the superdiffeomorphism transformations of the beltrami variables are given and the superfields with arbitrary conformal weights are studied

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

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

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

algebraic isomorphisms of limit algebras we prove that algebraic isomorphisms between limit algebras are automatically continuous and consider the consequences of this result in particular we give partial solutions to a conjecture and an open problem by power as a further consequence we describe epimorphisms between various classes of limit algebras in this paper we study automatic continuity for limit algebras automatic continuity involves algebraic conditions on a linear operator from one banach algebra into another that guarantee the norm continuity of the operator this is a generalization via the open mapping theorem of the uniqueness of norms problem recall that a banach algebra a is said to have a unique banach algebra topology if any two complete algebra norms on a are equivalent so that the norm topology determined by a banach algebra is unique uniqueness of norms automatic continuity and related questions have played an important and long standing role in the theory of banach algebras 6 29 28 10 11 2 limit algebras whose theory has grown rapidly in recent years are the nonselfadjoint analogues of uhf and af c algebras we first prove that algebraic isomorphisms between limit algebras are automatically continuous theorem 1 4 this proof uses the ideal theory of limit algebras as well as key results from the theory of automatic continuity for banach algebras combining this with 23 theorem 8 3 verifies power s conjecture that the c envelope of a limit algebra is an invariant for purely algebraic isomorphisms for limits of finite dimensional nest algebras and in particular for all triangular limit algebras corollary 1 6 in 5 the first two authors studied triangular limit algebras in terms of their lattices of ideals by combining automatic continuity with this work we show that within the class of algebras generated by their order preserving normalizers see below for definitions algebraically isomorphic algebras are isometrically isomorphic theorem 2 5 this shows that the spectrum or fundamental relation 20 a topological binary relation which provides coordinates for limit algebras and is a useful tool in classifications is a complete algebraic isomorphism invariant for this class corollary 2 6 in recent work the second two authors studied primitivity for limit algebras 9 showing that a variety of limit algebras are primitive these results together with automatic continuity give descriptions of epimorphisms between various classes of limit algebras namely lexicographic algebras theorem 3 2 and z analytic algebras theorem 3 3 received by the editors april 6 1998 and in revised form october 7 1999 2000 mathematics subject classification primary 47d25 46k50 46h40 research partially supported by an nsf grant 2000 american mathematical society

toeplitz algebras and rotational automorphisms associated to polydiscs introduction given a bounded symmetric domain d in cm with d being normalized to be circular and to contain the origin upmeier 22 showed that there is a natural way to associate a c algebra to it this c algebra called the toeplitz c algebra of d and denoted 35 is a solvable c algebra with a composition series jk o k n l of length n where n is the rank of the symmetric domain 22 theorem 3 12 we observe that there is a natural group action on 3 by the compact group g of all biholomorphic automorphisms of d which lie in the connected component of the identity and which fix the origin proposition 1 1 every element 0 in g preserves the solvable series jk o k n l of 3 d we thereby obtain a composition series jk x0 z for the crossed product c algebra 3 xo z in this paper we show by introducing the notion of stratification of composition series see section 2 that the series jk x0 z is exactly the maximal radical series of 3 x0 z section 3 and thus obtain an isomorphism invariant for the latter c algebra when is the polydisc d we determine the k theory of the series jk xo z and their subquotients section 4 techniques from k theory using strong morita equivalence yield a complete classification of the c algebras 3 xo z where d is the n dimensional polydisc up to isomorphism for all 0 in g tn

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

cut down method in the inductive limit decomposition of non commutative tori iii a complete answer in 3 dimension we use the cut down method and a multi dimensional continued fraction approximation to prove that any simple 3 torus is an inductive limit of direct sums of four circle algebras consequently simple 3 tori are classified by the orderedk0 group with distinguished order unit

operator algebras of monomial ideals in noncommuting variables abstract we study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables through the apparatus of subproduct systems and c correspondences we provide a full comparison amongst the related operator algebras for our analysis we isolate a partially defined dynamical system to which we refer as the quantised dynamics of the monomial ideal in addition we revisit several previously considered constructions these include matsumoto s subshift c algebras as well as the tensor and the pimsner algebras associated with dynamical systems or graphs we sort out the various relations by giving concrete conditions and counterexamples that orientate the operator algebras of our context it appears that the boundary c algebras do not arise as the quotient with the compact operators unconditionally we establish a dichotomy to this effect by examining the resulting tensor algebras we identify their boundary representations we analyse their c envelopes and we give criteria for hyperrigidity moreover we completely classify them in terms of the data provided by the monomial ideals for tensor algebras of c correspondences and bounded isomorphisms this is achieved up to the level of local conjugacy in the sense of davidson and roydor for the quantised dynamics for tensor algebras of subproduct systems and algebraic isomorphisms this is achieved up to the level of equality of monomial ideals modulo permutations of the variables in the process we accomplish more in different directions most notably we show that tensor algebras form a complete invariant for isomorphic resp similar subproduct systems of homogeneous ideals up to isometric resp bounded isomorphisms the results on local conjugacy are obtained via an alternative proof of the breakthrough result of davidson and katsoulis on piecewise conjugate systems for our purposes we use appropriate compressions of the fock representation we then apply this alternative proof locally for the partially defined quantised dynamics in this way we avoid the topological graphs machinery and pave the way for further applications these include operator algebras of dynamical systems over commuting contractions or over row commuting contractions

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

crossed products of operator algebras applications of takai duality abstract let g be a partially ordered abelian group with haar measure let a g be a dynamical system and let a be the associated semicrossed product using takai duality we establish a stable isomorphism a s a k g ad g where k g denotes the compact operators in the csl algebra alg l g and denotes the right regular representation of g we also show that there exists a complete lattice isomorphism between the invariant ideals of a and the ad invariant ideals of a k g using takai duality we also continue our study of the radical for the crossed product of an operator algebra and we solve open problems stemming from the earlier work of the authors among others we show that the crossed product of a radical operator algebra by a compact abelian group is a radical operator algebra we also show that the permanence of semisimplicity fails for crossed products by r a final section of the paper is devoted to the study of radically tight dynamical systems i e dynamical systems a g for which the identity rad a g rad a g persists a broad class of such dynamical systems is identified

algebraically irreducible representations and structure space of the banach algebra associated with a topological dynamical system abstract if x is a compact hausdorff space and is a homeomorphism of x then a banach algebra l 1 of crossed product type is naturally associated with this topological dynamical system x if x consists of one point then l 1 is the group algebra of the integers we study the algebraically irreducible representations of l 1 on complex vector spaces its primitive ideals and its structure space the finite dimensional algebraically irreducible representations are determined up to algebraic equivalence and a sufficiently rich family of infinite dimensional algebraically irreducible representations is constructed to be able to conclude that l 1 is semisimple all primitive ideals of l 1 are selfadjoint and l 1 is hermitian if there are only periodic points in x if x is metrizable or all points are periodic then all primitive ideals arise as in our construction a part of the structure space of l 1 is conditionally shown to be homeomorphic to the product of a space of finite orbits and t if x is a finite set then the structure space is the topological disjoint union of a number of tori one for each orbit in x if all points of x have the same finite period then it is the product of the orbit space x z and t for rational rotations of t this implies that the structure space is homeomorphic to t 2

numerical simulation of scattering from rough surfaces a wavelet based approach in this paper a preliminary study is carried out to demonstrate the application of wavelets for improving the computation time and reducing computational memory required for evaluating the statistics of the scattered field from rough surfaces using the method of moments mom in conjunction with a monte carlo simulation in specific haar and the first order b spline wavelet basis functions are applied to the mom formulation of one dimensional rough surfaces in order to compare the computation time and sparsity for wavelets in the same family but of higher order since the scattering coefficient the second moment of the backscatter field per unit area is a gentle function of the surface parameters and the radar attributes it is demonstrated that a relatively high thresholding level can be applied to the impedance matrix which leads to a sparser impedance matrix and faster computation time it is also shown that applying a high threshold level the coefficients of the high order wavelets would increase out of proportion however the effect of these current components averages out when computing the scattering coefficients the resulting sparse impedance matrices are solved efficiently using fast search routines such as the conjugate gradient method a systematic study is carried out to investigate the effect of different threshold levels on the accuracy versus computing speed criterion the computed scattering coefficients are compared to previous results computed using a conventional pulse basis function as well as the existing theoretical solutions for rough surfaces it is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time

on the stable rank of simple c algebras in 16 m a rieffel introduced the notion of stable rank for c algebras for a a unital c algebra the stable rank denoted by sr a is the least integer n such that the set of n tuples over a which generate a as a left ideal is dense in an if no such n exists we set sr a oo for unital c algebras the stable rank was shown to coincide with the bass stable rank which is defined for rings see 12 the stable rank can also be defined for nonunital c algebras but we shall only consider the unital case stable rank is related to nonstable k theory in 16 theorem 10 12 and 3 corollary 7 14 it was shown that if a is a simple unital c algebra of stable rank one then the natural map u a u a o 4 ki a is an isomorphism see also 17 2 and 18 it is a natural question which values occur as the stable rank of simple c algebras suppose that a is simple and infinite then by 7 proposition 1 5 a contains two isometries with orthogonal ranges and so by 16 proposition 6 5 sr a oo in the case of finite simple c algebras the following is known whenever a is simple and stably finite and b is a uhf algebra the tensor product a0 b has stable rank one see 19 this is also the case for every simple approximately homogeneous ah algebra with slow dimension growth see 4 and 8 so in short sr oo for every infinite simple c algebra and sr 1 for various classes of finite simple c algebras in this paper we answer the question above by showing that every n c n u oo is the stable rank of some simple finite c algebra more precisely it is shown that for every n 2 3 4 oo there exists a simple separable and unital ah algebra a of stable rank n in particular the group of invertible elements in a is not dense and like the examples in 20 a does not have slow dimension growth and is not approximately divisible see 5 i thank marius dadarlat for suggesting that i study ah algebras with connecting homomorphisms as described in the following section and juliana erlijman for drawing my attention to some of the powerful tools of differential topology and i thank george elliott for my stay at the fields institute where this paper was written

isomorphisms between topological conjugacy algebras a family of algebras which we call topological conjugacy algebras is associated with each proper continuous map on a locally compact hausdorff space assume that i xi xi is a continuous proper map on a locally compact hausdorff space xi for i 1 2 we show that the dynamical systems x1 1 and x2 2 are conjugate if and only if some topological conjugacy algebra of x1 1 is isomorphic as an algebra to some topological conjugacy algebra of x2 2 this implies as a corollary the complete classification of the semicrossed products c0 x z which was previously considered by arveson and josephson 3 peters 19 hadwin and hoover 8 and power 21 we also obtain a complete classification of all semicrossed products of the form a d z where a d denotes the disc algebra and d d a continuous map which is analytic on the interior in this case a surprising dichotomy appears in the classification scheme which depends on the fixed point set of we also classify more general semicrossed products of uniform algebras

the ideal structure of certain nonselfadjoint operator algebras soit x un systeme dynamique localement compact et z x co x la sous algebre close en norme du produit croise zx co x engendre par les puissances non negatives de dans le cas homeomorphisme on determine la structure ideale de ces algebres dans le cas ou agit librement

a short survey of noncommutative geometry we give a survey of selected topics in noncommutative geometry with some emphasis on those directly related to physics including our recent work with dirk kreimer on renormalization and the riemann hilbert problem we discuss at length two issues the first is the relevance of the paradigm of geometric space based on spectral considerations which is central in the theory as a simple illustration of the spectral formulation of geometry in the ordinary commutative case we give a polynomial equation for geometries on the four sphere with fixed volume the equation involves an idempotent e playing the role of the instanton and the dirac operator d it is of the form e 12 d e 4 5 and determines both the sphere and all its metrics with fixed volume form the expectation x is the projection on the commutant of the algebra of 4 by 4 matrices we also show using the noncommutative analog of the polyakov action how to obtain the noncommutative metric in spectral form on the noncommutative tori fr

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

mutual embeddability equivalence relation for rotation algebras abstract mutual embeddability is an equivalence relation in c algebras in this paper we characterize the classification of rotation algebras in the sense of mutual embeddability

the automorphism group of a simple tracially ai algebra the structure of the automorphism group of a simple tai algebra is studied in particular we show that frac overline rm inn a overline rm inn 0 a is isomorphic as a topological group to an inverse limit of discrete abelian groups for a unital simple ah algebra with bounded dimension growth consequently frac overline rm inn a overline rm inn 0 a is totally disconnected

the jacobson radical for analytic crossed products we characterise the jacobson radical of an analytic crossed product c0 x z answering a question first raised by arveson and josephson in 1969 in fact we characterise the jacobson radical of analytic crossed products c0 x zd this consists of all elements whose fourier coefficients vanish on the recurrent points of the dynamical system and the first one is zero the multidimensional version requires a variation of the notion of recurrence taking into account the various degrees of freedom

principal non commutative torus bundles in this paper we study continuous bundles of c algebras which are non commutative analogues of principal torus bundles we show that all such bundles although in general being very far away from being locally trivial bundles are at least locally rkk trivial using earlier results of echterhoff and williams we shall give a complete classification of principal non commutative torus bundles up to t n equivariant morita equivalence we then study these bundles as topological fibrations forgetting the group action and give necessary and sufficient conditions for any non commutative principal torus bundle being rkk equivalent to a commutative one as an application of our methods we shall also give a k theoretic characterization of those principal t n bundles with h flux as studied by mathai and rosenberg which possess classical t duals

isomorphism and morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of sl2 z abstract let be irrational numbers and a b be matrices in s l 2 z of infinite order we compute the k theory of the crossed product a a z and show that a a z and a b z are isomorphic if and only if mod z and i a 1 is matrix equivalent to i b 1 combining this result and an explicit construction of equivariant bimodules we show that a a z and a b z are morita equivalent if and only if and are in the same g l 2 z orbit and i a 1 is matrix equivalent to i b 1 finally we determine the morita equivalence class of a f for any finite subgroup f of s l 2 z

metric completions of ordered groups and k0 of exchange rings we give a description of the closure of the natural affine continuous function representation of k0 r for any exchange ring r this goal is achieved by extending the results of goodearl and handelman about metric completions of dimension groups to a more general class of pre ordered groups which includes k0 of exchange rings as a consequence the results about k 0 of regular rings which the author gave in an earlier paper can be extended to a wider class of rings which includes c algebras of real rank zero among others also the framework of pre ordered groups developed here allows other potential applications

on the structure of twisted group c algebras we first give general structural results for the twisted group algebras c g of a locally compact group g with large abelian subgroups in particular we use a theorem of williams to realise c g as the sections of a c bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras next we use a device of rosenberg to show that when is a discrete subgroup of a solvable lie group g the k groups k c are isomorphic to certain twisted k groups k g of the homogeneous space g and we discuss how the twisting class h 3 g z depends on the cocycle

a new n 2 supersymmetric korteweg de vries equation there are two known integrable n 2 space supersymmetric extensions of the kdv equation both can be written as hamiltonian systems with a common poisson structure which corresponds to the n 2 supersymmetric form of the second kdv structure by analyzing the conservation laws of the one parameter family of equations that share this hamiltonian structure one finds that a third system is singled out by the existence of nontrivial conservation laws it is conjectured to be integrable

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 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

semicrossed products of simple c algebras let mathcal a alpha and mathcal b beta be c dynamical systems and assume that mathcal a is a separable simple c algebra and that and are automorphisms then the semicrossed products mathcal a times alpha mathbb z and mathcal b times beta mathbb z are isometrically isomorphic if and only if the dynamical systems mathcal a alpha and mathcal b beta are outer conjugate

on inductive limits of matrix algebras over the two torus it will be shown in this paper that certain real rank zero c algebras which are inductive limits of c algebras of the form i m k i c inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i can be expressed as inductive limits of c algebras of the form i m k i c s 1 in particular if both a and b are of real rank zero and are inductive limits of c algebras of the form i m k i c s 1 then also a b is an inductive limit of c algebras of the form i m k i c s 1 hence a b can be classified by its k theory this is a key step in the general classification theory of inductive limit c algebras

scattering from multilayer rough surfaces based on the extended boundary condition method and truncated singular value decomposition electromagnetic scattering from rough surfaces has been investigated extensively for the past decades there exist analytical solutions to rough surface scattering such as small perturbation method spm or kirchhoff approximation ka these solutions however are limited to either small or large roughness regimes recent efforts have been put forth to study electromagnetic scattering of multilayer rough surface in the application of deep soil moisture and ice property estimation in this paper multilayer rough surface scattering is analyzed based on the extended boundary condition method ebcm and truncated singular value decomposition the method of extended boundary condition can accurately handle scattering from a slightly rough surface for mild and large roughness regime ill conditioned matrices can arise from ebcm in this paper we present a regularization scheme to mitigate this ill conditioning effect via truncated singular value decomposition tsvd the truncation parameters are set to enforce power conservation relations across all rough interfaces bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting floquet modes in the scattering directions therefore the electromagnetic wave interactions in multilayer rough surfaces are analyzed in a systematic way finally the results are validated against the analytical spm solution to two rough interface rough surface scattering in addition the formulation is extended to solve scattering from three rough interface rough surfaces several results are reported

instanton expansion of noncommutative gauge theory in two dimensions we show that noncommutative gauge theory in two dimensions is an exactly solvable model a cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a sum over contributions from classical solutions we derive an explicit formula for the partition function of yang mills theory defined on a projective module for an arbitrary noncommutativity parameter which is manifestly invariant under gauge morita equivalence the energy observables are shown to be smooth functions of the construction of noncommutative instanton contributions to the path integral is described in some detail in general there are infinitely many gauge inequivalent contributions of fixed topological charge along with a finite number of quantum fluctuations about each instanton the associated moduli spaces are combinations of symmetric products of an ordinary two torus whose orbifold singularities are not resolved by noncommutativity in particular the weak coupling limit of the gauge theory is independent of and computes the symplectic volume of the moduli space of constant curvature connections on the noncommutative torus

2 0 superconformal anomaly the 2 0 supersymmetric wess zumino polyakov action is constructed and the 2 0 superconformal anomaly is given the anomalous ward identity in the right sector is derived and the known operator product expansion of the n 2 superstress energy tensor is recovered