tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

asymptotically minimum variance second order estimation for noncircular signals with application to doa estimation this paper addresses asymptotically minimum variance amv algorithms within the class of algorithms based on second order statistics for estimating direction of arrival doa parameters of possibly spatially correlated even coherent narrowband noncircular sources impinging on arbitrary array structures to reduce the computational complexity due to the nonlinear minimization required by the matching approach the covariance matching estimation technique comet is included in the algorithm numerical examples illustrate the performance of the amv algorithm

an ambrosetti prodi type result for periodic solutions of the telegraph equation using leray schander degree theory a theorem of upper and lower solutions and a strong maximum principle for the telegraph equation we prove an ambrosetti prodi type result for periodic solutions of the telegraph equation

c algebras generated by stable relations abstract presentations of certain c algebras such as c0 0 1 mn by generators and relations are proven to be stable by the weakest definition of stability a set p1 pn of star polynomials is stable if operators a1 an which almost satisfy these relations meaning pi a1 an can be perturbed within c a1 an to satisfy these relations exactly homotopy and perturbation results for these c algebras are corollaries in particular we prove some new results about the dimension drop c algebras a n c 0 1 m n 0 1 c i we show that an is semiprojective answering a question of effros and kaminker also we show that whenever an b is a homomorphism approximately contained in a sub c algebra b0 b there is a nearby homomorphism of an into b0 this answers a question raised by elliott we prove technical results regarding mn c0 0 1 which should be useful elsewhere first we show this is projective meaning a star homomorphism mn c0 0 1 b j always lifts to a star homomorphism mn c0 0 1 b secondly we show that for a finitely generated m n a m n c 0 0 1 c 0 0 1 a if the amalgamation is done properly

doa estimation of temporally and spatially correlated narrowband noncircular sources in spatially correlated white noise the main contribution of our work consists in developing for the first time a method of estimating the direction of arrival doa parameters assuming noncircular and temporally and spatially correlated signals this new approach based on a significant enhancement of the two sided instrumental variable signal subspace fitting iv ssf method outperforms its classical version in terms of lower bias and error variance moreover it will be shown that our new method is statistically more efficient than the mode method especially in the case of partly and fully coherent signals where only the extended and the classical two sided iv ssf methods are applicable we also derive an explicit expression for the stochastic cramer rao bound crb of the doa estimates from temporally and spatially correlated signals generated from noncircular sources the new crb is compared to those of circular temporally correlated and noncircular independent and identically distributed signals to show that the crb obtained assuming both noncircular sources and temporally correlated signals is lower than the crbs derived considering only one of these two assumptions this illustrates the potential gain that both noncircularity and temporal correlation provide when considered together it will also be proven that the difference between the three crbs increases with the number of snapshots however as the signal to noise ratio snr increases the crbs merge together and decrease linearly moreover at low snr values it will be shown that temporal correlation is more informative about the unknown doa parameters than noncircularity finally the crb derived assuming noncircular and temporally correlated signals depends on the noncircularity rate the circularity phase separation and the doa separation

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

iterative methods for subspace and doa estimation in nonuniform noise usually direction of arrival doa estimators are derived under the assumption of uniform white noise whose covariance matrix is a scaled identity matrix however in practice the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix in this situation the performance of doa estimators may be deteriorated considerably if the noise nonuniformity is ignored to tackle this problem iterative approaches to subspace estimation are developed and the corresponding subspace based doa estimators are addressed in our proposed methods the signal subspace and noise covariance matrix are first determined by maximizing the log likelihood ll function or solving a least squares ls minimization problem both of which are accomplished in an iterative manner then the doas are determined from the subspace estimate and or noise covariance matrix estimate with the help of traditional doa estimators as the signal subspace and noise covariance matrix can be computed in closed form in each iteration the proposals are computationally attractive furthermore the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold enabling us to handle array uncertainties by incorporating conventional subspace based calibration algorithms simulations and experimental results are included to demonstrate the superiority of the proposed approaches

a maximum principle for periodic solutions of the telegraph equation let l s l u be a linear differential operator acting on functions u v a r that are defined on a fixed manifold v these functions will belong to a certain family b f v r and the definition of b may include some boundary conditions or other requirements that must be satisfied by any function u g b it is said that l satisfies the maximum principle if the differential inequality l u g 0 u g b implies u g 0 in v w x the book 18 is devoted to the study of the maximum principle for second w x w x w x w x w x order operators other related results can be found in 17 5 12 8 2 w x 14 in this paper we study the maximum principle for periodic solutions of the telegraph equation the operator is

direction of arrival estimation for temporally correlated narrowband signals signal direction of arrival doa estimation using an array of sensors has been the subject of intensive research and development during the last two decades efforts have been directed to both better solutions for the general data model and to develop more realistic models so far many authors have assumed the data to be independent and identically distributed i i d samples of a multivariate statistical model although this assumption reduces the complexity of the model it may not be true in certain situations where signals show temporal correlation some results are available on the temporally correlated signal model in the literature the temporally correlated stochastic cramer rao bound crb has been calculated and an instrumental variable based method called iv ssf is introduced also it has been shown that temporally correlated crb is lower bounded by the deterministic crb in this paper we show that temporally correlated crb is also upper bounded by the stochastic i i d crb we investigate the effect of temporal correlation of the signals on the best achievable performance we also show that the iv ssf method is not efficient and based on an analysis of the crb propose a variation in the method which boosts its performance simulation results show the improved performance of the proposed method in terms of lower bias and error variance

computationally efficient angle estimation for signals with known waveforms this paper presents a large sample decoupled maximum likelihood deml angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise the deml estimator decouples the multidimensional problem of the exact ml estimator to a set of 1 d problems and hence is computationally efficient we shall derive the asymptotic statistical performance of the deml estimator and compare the performance with its cramer rao bound crb i e the best possible performance for the class of asymptotically unbiased estimators we will show that the deml estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms we will also show that for moderately correlated signals with known waveforms the deml estimator is no longer a large sample maximum likelihood ml estimator but the deml estimator may still be used for angle estimation and the performance degradation relative to the crb is small we shall show that the deml estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix finally several numerical examples showing the performance of the deml estimator are presented in this paper

c algebras and equivalences for c correspondences abstract we study several notions of shift equivalence for c correspondences and the effect that these equivalences have on the corresponding pimsner dilations among others we prove that non degenerate regular full c correspondences which are shift equivalent have strong morita equivalent pimsner dilations we also establish that the converse may not be true these results settle open problems in the literature in the context of c algebras we prove that if two non degenerate regular full c correspondences are shift equivalent then their corresponding cuntz pimsner algebras are strong morita equivalent this generalizes results of cuntz and krieger and muhly tomforde and pask as a consequence if two subshifts of finite type are eventually conjugate then their cuntz krieger algebras are strong morita equivalent our results suggest a natural analogue of the shift equivalence problem in the context of c correspondences even though we do not resolve the general shift equivalence problem we obtain a positive answer for the class of imprimitivity bimodules

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

instrumental variable approach to array processing in spatially correlated noise fields high performance signal parameter estimation from sensor array data is a problem which has received much attention a number of so called eigenvector ev techniques such as music esprit wsf and mode have been proposed in the literature the ev techniques for array processing require knowledge of the spatial noise correlation matrix that constitutes a significant drawback a novel instrumental variable iv approach to the sensor array problem is proposed the iv technique relies on the same basic geometric properties as the ev methods to obtain parameter estimates however by exploiting the temporal correlation of the source signals no knowledge of the spatial noise covariance is required the asymptotic properties of the iv estimator are examined and an optimal iv method is derived computer simulations are presented to study the properties of the iv estimators in samples of practical length the proposed algorithm is also shown to perform better than music on a full scale passive sonar experiment

the yang mills functional and laplace s equation on quantum heisenberg manifolds in this paper we discuss the yang mills functional and a certain family of its critical points on quantum heisenberg manifolds using noncommutative geometrical methods developed by a connes and m rieffel in our main result we construct a certain family of connections on a projective module over a quantum heisenberg manifold that gives rise to critical points of the yang mills functional moreover we show that there is a relationship between this particular family of critical points of the yang mills functional and laplace s equation on multiplication type skew symmetric elements of quantum heisenberg manifolds recall that laplacian is the leading term for the coupled set of equations making up the yang mills equation

existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system abstract in this paper the existence of positive doubly periodic solutions for nonlinear telegraph system is discussed using the method of upper and lower solutions

crossed products by endomorphisms and reduction of relations in relative cuntz pimsner algebras abstract starting from an arbitrary endomorphism of a unital c algebra a we construct a crossed product it is shown that the natural construction depends not only on the c dynamical system a but also on the choice of an ideal j orthogonal to ker the article gives an explicit description of the internal structure of this crossed product and in particular discusses the interrelation between relative cuntz pimsner algebras and partial isometric crossed products we present a canonical procedure that reduces any given c correspondence to the smallest c correspondence yielding the same relative cuntz pimsner algebra as the initial one in the context of crossed products this reduction procedure corresponds to the reduction of c dynamical systems and allows us to establish a coincidence between relative cuntz pimsner algebras and crossed products introduced

maximum likelihood array processing in spatially correlated noise fields using parameterized signals this paper deals with the problem of estimating signal parameters using an array of sensors this problem is of interest in a variety of applications such as radar and sonar source localization a vast number of estimation techniques have been proposed in the literature during the past two decades most of these can deliver consistent estimates only if the covariance matrix of the background noise is known in many applications the aforementioned assumption is unrealistic recently a number of contributions have addressed the problem of signal parameter estimation in unknown noise environments based on various assumptions on the noise herein a different approach is taken we assume instead that the signals are partially known the received signals are modeled as linear combinations of certain known basis functions the exact maximum likelihood ml estimator for the problem at hand is derived as well as computationally more attractive approximation the cramer rao lower bound crb on the estimation error variance is also derived and found to coincide with the crb assuming an arbitrary deterministic model and known noise covariance

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

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

music like estimation of direction of arrival for noncircular sources this paper examines the asymptotic performance of music like algorithms for estimating directions of arrival doa of narrowband complex noncircular sources using closed form expressions of the covariance of the asymptotic distribution of different projection matrices it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace based algorithms valid for gaussian or non gaussian and complex circular or noncircular sources we also derive different robustness properties from the asymptotic covariance of the estimated doa given by such algorithms these results are successively applied to four algorithms to two attractive music like algorithms previously introduced in the literature to an extension of these algorithms and to an optimally weighted music algorithm proposed in this paper numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance amv algorithms introduced as benchmarks

stochastic crame spl acute r rao bound for noncircular signals with application to doa estimation after providing an extension of the slepian bangs formula for general noncircular complex gaussian distributions this paper focuses on the stochastic crame spl acute r rao bound crb on direction of arrival doa estimation accuracy for noncircular sources we derive an explicit expression of the crb for doa parameters alone in the case of noncircular complex gaussian sources by two different methods one of them consists of computing the asymptotic covariance matrix of the maximum likelihood ml estimator and the other is obtained directly from our extended slepian bangs formula some properties of this crb are proved and finally it is numerically compared with the crbs under circular complex gaussian and complex discrete distributions of sources

maximum likelihood direction of arrival estimation in the presence of unknown nonuniform noise we consider the problem of estimating directions of arrival doas of multiple sources observed on the background of nonuniform white noise with an arbitrary diagonal covariance matrix a new deterministic maximum likelihood ml doa estimator is derived its implementation is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function with respect to the signal and noise nuisance parameters and requires only a few iterations to converge new closed form expressions for the deterministic and stochastic direction estimation cramer rao bounds crbs are derived for the considered nonuniform model our expressions can be viewed as an extension of the well known results by stoica and nehorai 1989 1990 and weiss and friedlander 1993 to a more general noise model than the commonly used uniform one in addition these expressions extend the results obtained by matveyev et al see circuits syst signal process vol 18 p 479 87 1999 to the multiple source case comparisons with the above mentioned earlier results help to discover several interesting properties of doa estimation in the nonuniform noise case to compare the estimation performance of the proposed ml technique with the results of our crb analysis and with the performance of conventional uniform ml simulation results are presented additionally we test our technique using experimental seismic array data our simulations and experimental results both validate essential performance improvements achieved by means of the approach proposed

crossed products by hilbert pro c bimodules versus tensor products abstract we show that if x a and y b are two isomorphic hilbert pro c bimodules then the crossed product a x z of a by x and the crossed product b y z of b by y are isomorphic as pro c algebras we also prove a property of associativity between min and x as well as max and x

array processing in correlated noise fields based on instrumental variables and subspace fitting accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade a number of parametric estimation techniques have been proposed in the literature in general these methods require knowledge of the sensor to sensor correlation of the noise which constitutes a significant drawback this difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise in some applications the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise an instrumental variable iv approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise a computationally simple iv approach has recently been proposed by the authors herein a refined technique that can give significantly better performance is derived a statistical analysis of the parameter estimates is performed enabling optimal selection of certain user specified quantities a lower bound on the attainable error variance is also presented the proposed optimal iv method is shown to attain the bound if the signals have a quasideterministic character

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

a modified likelihood function approach to doa estimation in the presence of unknown spatially correlated gaussian noise using a uniform linear array the problem of modified ml estimation of doas of multiple source signals incident on a uniform linear array ula in the presence of unknown spatially correlated gaussian noise is addressed here unlike previous work the proposed method does not impose any structural constraints or parameterization of the signal and noise covariances it is shown that the characterization suggested here provides a very convenient framework for obtaining an intuitively appealing estimate of the unknown noise covariance matrix via a suitable projection of the observed covariance matrix onto a subspace that is orthogonal complement of the so called signal subspace this leads to a formulation of an expression for a so called modified likelihood function which can be maximized to obtain the unknown doas for the case of an arbitrary array geometry this function has explicit dependence on the unknown noise covariance matrix this explicit dependence can be avoided for the special case of a uniform linear array by using a simple polynomial characterization of the latter a simple approximate version of this function is then developed that can be maximized via the well known iqml algorithm or its variants an exact estimate based on the maximization of the modified likelihood function is obtained by using nonlinear optimization techniques where the approximate estimates are used for initialization the proposed estimator is shown to outperform the map estimator of reilly et al 1992 extensive simulations have been carried out to show the validity of the proposed algorithm and to compare it with some previous solutions

circle actions on c algebras partial automorphisms and a generalized pimsner voiculescu exact sequence abstract we introduce a method to study c algebras possessing an action of the circle group from the point of view of their internal structure and their k theory under relatively mild conditions our structure theorem shows that any c algebra where an action of the circle is given arises as the result of a construction that generalizes crossed products by the group of integers such a generalized crossed product construction is carried out for any partial automorphism of a c algebra where by a partial automorphism we mean an isomorphism between two ideals of the given algebra our second main result is an extension to crossed products by partial automorphisms of the celebrated pimsner voiculescu exact sequence for k groups the representation theory of the algebra arising from our construction is shown to parallel the representation theory for c dynamical systems in particular we generalize several of the main results relating to regular and covariant representations of crossed products

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

an ambrosetti prodi type result for doubly periodic solutions of the telegraph system abstract this article deals with an ambrosetti prodi type result for doubly periodic solutions of the telegraph system by using leray schauder degree theory the method of upper and lower solutions

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

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

continuous fields of c algebras arising from extensions of tensor c categories abstract the notion of extension of a given c category c by a c algebra a is introduced in the commutative case a c the objects of the extension category are interpreted as fiber bundles over of objects belonging to the initial category it is shown that the doplicher roberts algebra dr algebra in the following associated to an object in the extension of a strict tensor c category is a continuous field of dr algebras coming from the initial one in the case of the category of the hermitian vector bundles over the general result implies that the dr algebra of a vector bundle is a continuous field of cuntz algebras some applications to pimsner c algebras are given

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

positive doubly periodic solutions of nonlinear telegraph equations abstract this paper deals with the existence of nontrivial doubly periodic solutions for the nonlinear telegraph equation u tt u xx cu t a t x u b t x f t x u t x r 2 where c 0 is a constant a b c r 2 r f c r 2 r r and a b f are 2 periodic in t and x we show the existence of positive doubly periodic weak solutions when 0 a t x c2 4 and f is either superlinear or sublinear on u by using the krasnoselskii s fixed point theorem in cones