gravity coupled with matter and the foundation of non commutative geometry we first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds its unitary representations correspond to riemannian metrics and spin structure whileds is the dirac propagatords x x d 1 whered is the dirac operator we extend these simple relations to the non commutative case using tomita s involutionj we then write a spectral action the trace of a function of the length element which when applied to the non commutative geometry of the standard model will be shown cc to give the sm lagrangian coupled to gravity the internal fluctuations of the non commutative geometry are trivial in the commutative case but yield the full bosonic sector of sm with all correct quantum numbers in this slightly non commutative case the group of local gauge transformations appears spontaneously as a normal subgroup of the diffeomorphism group

on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

sup t norm and inf residuum are one type of relational product unifying framework and consequences we present a simple framework which enables us to consider the well known sup t norm and inf residuum products of relations as two particular cases of a single more general type of product we present basic properties of the framework and consequences for the theory of fuzzy relations informally the paper implies that in many cases of fuzzy relational modeling such as in solving fuzzy relational equations there is no need to develop the methods for sup t norm and inf residuum products separately because these methods are just two particular instances of a single method

notes on solution sets of inf t fuzzy relational equations on complete brouwerian lattices and fuzzy relational equations on complete brouwerian lattices this paper clarifies several hypotheses and results given in q q xiong and x p wang solution sets of fuzzy relational equations on complete brouwerian lattices information sciences 177 21 47574767 2007 and in q q xiong and x p wang fuzzy relational equations on complete brouwerian lattices information sciences 193 0 141152 2012 which in their current form are confusing and need to be improved

de rham complex for quantized irreducible flag manifolds it is shown that quantized irreducible flag manifolds possess a canonical q analogue of the de rham complex generalizing the well known situation for the standard podle quantum sphere this analogue is obtained as the universal differential calculus of a distinguished first order differential calculus the corresponding differential d can be written as a sum of differentials and the universal differential calculus corresponding to the first order differential calculi d and are given in terms of generators and relations relations to well known quantized exterior algebras are established the dimensions of the homogeneous components are shown to be the same as in the classical case the existence of a volume form is proven

a comparative study of adjoint triples adjoint triples are helpful as basic operators used in several domains for example adjoint triples play an important role in two important frameworks multi adjoint logic programming and multi adjoint concept lattices this paper shows that adjoint triples are an interesting generalization of t norms and their residuated implications since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework furthermore these operators will be related to other important general triples specifically implication triples and the definition of these latter operators will be improved

quantum weighted projective and lens spaces we generalize to quantum weighted projective spaces in any dimension previous results of us on k theory and k homology of quantum projective spaces tout court for a class of such spaces we explicitly construct families of fredholm modules both bounded and unbounded that is spectral triples and prove that they are linearly independent in the k homology of the corresponding c algebra we also show that the quantum weighted projective spaces are base spaces of quantum principal circle bundles whose total spaces are quantum lens spaces we construct finitely generated projective modules associated with the principal bundles and pair them with the fredholm modules thus proving their non triviality

a unified framework and sparse bayesian perspective for direction of arrival estimation in the presence of array imperfections self calibration methods play an important role in reducing the negative effects of array imperfections during direction of arrival doa estimation however the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios such as low signal to noise ratio snr and limited snapshots this paper aims at formulating a unified framework and sparse bayesian perspective for array calibration and doa estimation a comprehensive model of the array output is presented first when a single type of array imperfection is considered with mutual coupling gain phase uncertainty and sensor location error treated as typical examples the spatial sparsity of the incident signals is then exploited and a bayesian method is proposed to realize array calibration and source doa estimation the array perturbation magnitudes are assumed to be small according to most application scenarios and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear cramer rao lower bounds crlbs for the array calibration and doa estimation precisions are also obtained the sparse bayesian method is finally extended to deal with the doa estimation problem when more than one type of array perturbation coexists

minimal solutions of general fuzzy relation equations on linear carriers an algebraic characterization abstract this paper considers a general fuzzy relation equation which has minimal solutions if it is solvable in this case an algebraic characterization is introduced which provides an interesting method to compute minimal solutions in this general setting moreover a comparison with other frameworks is also given

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array in array signal processing high resolution direction of arrival doa estimation algorithms are known to be sensitive to system errors in practice the system should be properly calibrated before doa estimation in this paper a calibration method of gain and phase errors of linear equispaced arrays leas is considered a class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed the statistical performance analyses of the calibration algorithms due to finite data perturbations are presented expressions for average bias abias and square root of average variance srav of the calibration algorithms are derived using first order approximation these statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations the more inferior performance that may be obtained based on this conclusion the simple and optimal gain and phase error calibration algorithms for such model are obtained

formal concept analysis via multi adjoint concept lattices several fuzzifications of formal concept analysis have been proposed to deal with uncertain information in this paper we focus on concept lattices under a multi adjoint paradigm which enriches the language providing greater flexibility to the user in that he she can choose from a number of different connectives multi adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature the main results of the paper being the representation theorem of this paradigm and the embedding of other well known approaches

the locally finite part of the dual coalgebra of quantized irreducible flag manifolds for quantized irreducible flag manifolds the locally finite part of the dual coalgebra is shown to coincide with a natural quotient coalgebra overline u of u q mathfrak g on the way the coradical filtration of overline u is determined a graded version of the duality between overline u and the quantized coordinate ring is established this leads to a natural construction of several examples of quantized vector spaces as an application covariant first order differential calculi on quantized irreducible flag manifolds are classified

bearing estimation without calibration for randomly perturbed arrays the bearing estimation problem of linearly periodic arrays with the presence of sensor position errors is discussed conventional approaches for solving this problem generally consist of two steps calibrating sensor locations and then performing bearing estimation based on the calibrated sensor locations approaches to carrying out bearing estimation based on the toeplitz and eigenstructure reconstruction of the covariance matrix without the need for calibration are proposed the toeplitz approximation method tam and a modification of it mtam are used to reconstruct a matrix with toeplitz structure to further enhance the capabilities of the tam and mtam an iterative algorithm incorporating with the tam itam and the mtam imtam is proposed to iteratively reconstruct both the toeplitz and the desired eigenstructure from the observed covariance matrix computer simulations show that the mtam is more effective than the tam moreover the iterative methods are superior to the noniterative ones at the price of computations

on the solvability of bipolar max product fuzzy relation equations with the product negation abstract this paper studies the solvability of the max product fuzzy relation equations in which a negation operator is considered specifically the residuated negation of the product t norm has been introduced in these equations in order to increase the flexibility of the standard fuzzy relation equations introduced by sanchez in 1976 the solvability and the set of solutions of these bipolar equations have been studied in different scenarios depending on the considered number of variables and equations

using concept lattice theory to obtain the set of solutions of multi adjoint relation equations an important goal in the fuzzy relation equations framework is to obtain the whole set of solutions this paper introduces algebraic properties in the multi adjoint concept lattice setting moreover using the relationship between these concept lattices and multi adjoint relation equations the complete set of solutions of these general equations is characterized and computed avoiding the necessity of considering minimal solutions

sparse power angle spectrum estimation a novel method for estimating the power angle spectrum pas is presented that decomposes the true pas into a small set of basis functions the basis coefficients for this sparse representation are found by enforcing equality to the covariance or bartlett pas subject to a minimum lscr1 norm constraint the method referred to as sparse pas estimation spase can be implemented conveniently using existing linear programming lp solvers further because only a few clusters are required in the representation the method enables reduced complexity stochastic models for the channel and possibly allows reduced overhead in channel feedback schemes application of the method to simulated channels and multiple input multiple output mimo propagation data demonstrates the utility of the method

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

multi adjoint relation equations definition properties and solutions using concept lattices this paper generalizes fuzzy relation equations following the multi adjoint philosophy moreover the solutions of these general fuzzy relation equations and the concepts of a multi adjoint property oriented concept lattice are related and several results are obtained from the theory of concept lattices as a consequence of this relevant relation more properties about these general equations can be proven from the theory of concept lattices and the algorithms developed to compute concept lattices can be used to obtain solutions furthermore an interesting application to fuzzy logic programming has been introduced in which an important problem in this topic has been interpreted in terms of solving a multi adjoint relation equation

a novel online mutual coupling compensation algorithm for uniform and linear arrays in this paper a novel online mutual coupling compensation algorithm especially tailored to uniform and linear arrays is presented it is conceived to simultaneously compensate for mutual coupling and estimate the direction of arrivals doas of signals impinging on the array since the estimated calibration matrix can be embedded within any classical super resolution direction finding method an alternating minimization procedure based on closed form solutions is performed to estimate the mutual coupling matrix in the field of complex symmetric toeplitz matrices unlike many existing array calibration methods it requires neither the presence of calibration sources nor previous calibration information as initialization computer simulations show the effectiveness of the proposed technique and prove that the nice statistical properties of classical super resolution doa estimation algorithms can be restored despite the presence of mutual coupling

spectral triples on the jiang su algebra we construct spectral triples on a class of particular inductive limits of matrix valued function algebras in the special case of the jiang su algebra we employ a particular af embedding

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

hopf von neumann algebra bicrossproducts kac algebra bicrossproducts and the classical yang baxter equations two groups g1 g2 are said to be a matched pair if each acts on the space of the other and these actions say obey a certain compatibility condition for every matched pair of locally compact groups g1 g2 we construct an associated coinvolutive hopf von neumann algebra m g1 l g2 by simultaneous cross product and cross coproduct for non trivial these bicrossproduct hopf von neumann algebras are non commutative and non cocommutative if the modules for the actions are also matched then these bicrossproducts are kac algebras in this case we show that the dual kac algebra is of the same form with the roles of g1 g2 and of interchanged examples exist with g1 a simply connected lie group and choices of g2 determined by suitable solutions of the classical yang baxter equations on the complexification of the lie algebra of g1

dirac operators on quantum projective spaces we construct a family of self adjoint operators d n n is an element of z which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space cpql for any l 2 and 0 q 1 they provide 0 dimensional equivariant even spectral triples if l is odd and n 1 2 l 1 the spectral triple is real with ko dimension 2l mod 8

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

quantum bundle description of quantum projective spaces we realise heckenberger and kolb s canonical calculus on quantum projective n 1 space c q c p n 1 as the restriction of a distinguished quotient of the standard bicovariant calculus for the quantum special unitary group c q su n we introduce a calculus on the quantum sphere c q s 2n 1 in the same way with respect to these choices of calculi we present c q c p n 1 as the base space of two different quantum principal bundles one with total space c q su n and the other with total space c q s 2n 1 we go on to give c q c p n 1 the structure of a quantum framed manifold more specifically we describe the module of one forms of heckenberger and kolb s calculus as an associated vector bundle to the principal bundle with total space c q su n finally we construct strong connections for both bundles

strong connections on quantum principal bundles a gauge invariant notion of a strong connection is presented and characterized it is then used to justify the way in which a global curvature form is defined strong connections are interpreted as those that are induced from the base space of a quantum bundle examples of both strong and non strong connections are provided in particular such connections are constructed on a quantum deformation of the two sphere fibrations2 rp2 a certain class of stronguq 2 connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq dependent hermitian metric a particular form of the yang mills action on a trivialuq 2 bundle is investigated it is proved to coincide with the yang mills action constructed by a connes and m rieffel furthermore it is shown that the moduli space of critical points of this action functional is independent ofq

an eigenstructure method for estimating doa and sensor gain phase errors in this paper we consider the problem of direction of arrival doa estimation in the presence of sensor gain phase errors under some mild assumptions we propose a new doa estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate by combining the new doa estimation with the conventional gain phase error estimation a method is proposed to simultaneously estimate the doa and gain phase errors without joint iteration theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors however the resolution capability of the proposed method is lower than that of the method in a j weiss and b friedlander eigenstructure methods for direction finding with sensor gain and phase uncertainties circuits systems signal process vol 9 no 3 pp 271 300 1990 named as the wf method in order to improve the resolution capability and maintain phase error independence a combined strategy is developed using the proposed and wf methods the advantage of the proposed methods is that they are independent of phase errors leading to the cancellation of phase error calibration during the operation life of an array moreover the proposed methods avoid the problem of suboptimal convergence which occurs in the wf method the drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other and they are not applicable to a linear array simulation results verify the effectiveness of the proposed methods

do we need minimal solutions of fuzzy relational equations in advance minimal solutions play a crucial role in description of all solutions to a fuzzy relational equation the reason is that all solutions form a convex set with respect to fuzzy set inclusion therefore having all extremal solutions we can represent the entire solution set as a union of intervals bounded from above by the greatest solution and from below by the minimal solutions however when computing the intervals we obtain many duplicate solutions the obvious question is as follows is there another way of representing the solution set for instance without the need of having all the minimal solutions in advance we provide the positive answer to this question

sensor array calibration using a maximum likelihood approach high resolution array processing algorithms for source localization are known to be sensitive to errors in the model for the sensor array spatial response in particular unknown gain phase and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array processing algorithms this paper describes a calibration algorithm that estimates the calibration matrix consisting of the unknown gain phase and mutual coupling coefficients as well as the sensor positions using a set of calibration sources in known locations the estimation of the various parameters is based on a maximum likelihood approach cramer rao lower bound crb expressions for the sensor positions and the calibration matrix parameters are also derived numerical results are shown to illustrate the potential usefulness of the proposed calibration algorithm toward better accuracy and resolution in parametric array processing algorithms

conditions under which the solution sets of fuzzy relational equations over complete brouwerian lattices form lattices it is well known that the solution set of a fuzzy relational equation with sup inf composition is a join semilattice in general not a meet semilattice this paper investigates the conditions under which the solution sets of fuzzy relational equations with sup inf composition over complete brouwerian lattices form lattices we first give some properties of the decompositions of elements in complete lattices then present a necessary and sufficient condition that the meet of a solution with any other solution is again a solution finally we show some necessary and sufficient conditions that the solution sets are lattices

direction of arrival estimation using a sparse representation of array covariance vectors a new direction of arrival doa estimation method is proposed based on a novel data model using the concept of a sparse representation of array covariance vectors sracv in which doa estimation is achieved by jointly finding the sparsest coefficients of the array covariance vectors in an overcomplete basis the proposed method not only has high resolution and the capability of estimating coherent signals based on an arbitrary array but also gives an explicit error suppression criterion that makes it statistically robust even in low signal to noise ratio snr cases simulation experiments are conducted to validate the effectiveness of the proposed method the performance is compared with several existing doa estimation methods and the cramer rao lower bound crlb

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

on fuzzy relational equations and the covering problem previous studies have shown that fuzzy relational equations fres based on either the max continuous archimedean t norm or the max arithmetic mean composition can be transformed into the covering problem which is an np hard problem exploiting the properties common to the continuous archimedean t norm and the arithmetic mean this study proposes a generalization of them as the u norm enabling fres that are based on the max continuous u norm composition also to be transformed into the covering problem this study also proposes a procedure for transforming the covering problem into max product fres consequently max continuous u norm fres can be solved by extending any procedure for solving either the covering problem or max product fres

quantized algebras of functions on homogeneous spaces with poisson stabilizers let g be a simply connected semisimple compact lie group with standard poisson structure k a closed poisson lie subgroup 0 q 1 we study a quantization c gq kq of the algebra of continuous functions on g k using results of soibelman and dijkhuizen stokman we classify the irreducible representations of c gq kq and obtain a composition series for c gq kq we describe closures of the symplectic leaves of g k refining the well known description in the case of flag manifolds in terms of the bruhat order we then show that the same rules describe the topology on the spectrum of c gq kq next we show that the family of c algebras c gq kq 0 q 1 has a canonical structure of a continuous field of c algebras and provides a strict deformation quantization of the poisson algebra mathbb c g k finally extending a result of nagy we show that c gq kq is canonically kk equivalent to c g k

asymptotically optimal blind calibration of uniform linear sensor arrays for narrowband gaussian signals an asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband gaussian signals is proposed rather than taking the direct maximum likelihood ml approach for joint estimation of all the unknown model parameters which leads to a multi dimensional optimization problem with no closed form solution we revisit paulraj and kailath s p k s classical approach in exploiting the special toeplitz structure of the observations covariance however we offer a substantial improvement over p k s ordinary least squares ls estimates by using asymptotic approximations in order to obtain simple non iterative quasi linear optimally weighted ls owls estimates of the sensors gains and phases offsets with asymptotically optimal weighting based only on the empirical covariance matrix of the measurements moreover we prove that our resulting estimates are also asymptotically optimal w r t the raw data and can therefore be deemed equivalent to the ml estimates mle which are otherwise obtained by joint ml estimation of all the unknown model parameters after deriving computationally convenient expressions of the respective cramer rao lower bounds we also show that our estimates offer improved performance when applied to non gaussian signals and or noise as quasi mle in a similar setting the optimal performance of our estimates is demonstrated in simulation experiments with a considerable improvement reaching an order of magnitude and more in the resulting mean squared errors w r t p k s ordinary ls estimates we also demonstrate the improved accuracy in a multiple sources directions of arrivals estimation task

solving systems of fuzzy relation equations by fuzzy property oriented concepts this paper relates systems of fuzzy relation equations with the theory of fuzzy property oriented concept lattices consequently the results obtained from this theory of concept lattices can be transformed in order to obtain properties about the former moreover the algorithms developed to obtain concept lattices can be applied to obtain solutions for systems of fuzzy relation equations

minimum mean square distance estimation of a subspace we consider the problem of subspace estimation in a bayesian setting since we are operating in the grassmann manifold the usual approach which consists of minimizing the mean square error mse between the true subspace u and its estimate u may not be adequate as the mse is not the natural metric in the grassmann manifold gn p i e the set of p dimensional subspaces in rn as an alternative we propose to carry out subspace estimation by minimizing the mean square distance between u and its estimate where the considered distance is a natural metric in the grassmann manifold viz the distance between the projection matrices we show that the resulting estimator is no longer the posterior mean of u but entails computing the principal eigenvectors of the posterior mean of uut derivation of the minimum mean square distance mmsd estimator is carried out in a few illustrative examples including a linear gaussian model for the data and bingham or von mises fisher prior distributions for u in all scenarios posterior distributions are derived and the mmsd estimator is obtained either analytically or implemented via a markov chain monte carlo simulation method the method is shown to provide accurate estimates even when the number of samples is lower than the dimension of u an application to hyperspectral imagery is anally investigated

multi adjoint property oriented and object oriented concept lattices this paper presents a generalisation of the classical property and object oriented concept lattices to a fuzzy environment based on the philosophy of the multi adjoint paradigm these concept lattices are generalisations of rough set theory used to consider two different sets the set of objects and the set of attributes to apply the corresponding modal operators as in formal concept analysis first of all the paper presents several specific properties of adjoint triples in which the duals of several supports are considered these properties are then used to introduce the multi adjoint property and object oriented concept lattices in which different adjoint triples can be used in non linear sets as well as the corresponding representation fundamental theorems moreover these lattices are related to the multi adjoint concept lattice in which negation operators are not needed as a result this relation allows the properties to be translated from one to another

the use of two relations in l fuzzy contexts in the analysis of relations among the elements of two sets it is usual to obtain different values depending on the point of view from which these relations are measured the main goal of the paper is the modelization of these situations by means of a generalization of the l fuzzy concept analysis called l fuzzy bicontext we study the l fuzzy concepts of these l fuzzy bicontexts obtaining some interesting results specifically we will be able to classify the biconcepts of the l fuzzy bicontext finally a practical case is developed using this new tool

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

computing the lattice of all fixpoints of a fuzzy closure operator we present a fast bottom up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees along with the partial order on the set of all fixpoints fuzzy closure operators appear in several areas of fuzzy logic and its applications including formal concept analysis fca that we use as a reference area of application in this paper several problems in fca such as computing all formal concepts from data with graded attributes or computing non redundant bases of all attribute dependencies can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data the development of a general algorithm that is applicable in particular to these problems is the ultimate purpose of this paper we present the algorithm its theoretical foundations and experimental evaluation

conditions for the existence of the least solution and minimal solutions to fuzzy relation equations over complete brouwerian lattices this paper discusses properties and existence conditions of minimal solutions to sup inf fuzzy relation equations over complete brouwerian lattices the relationship between minimal solutions to a system of fuzzy relation equations and minimal solutions to a fuzzy relation equation in the system is illustrated by two examples necessary and sufficient conditions for the existence of the least solution and minimal solutions to a system of fuzzy relation equations are given

cs decomposition based bayesian subspace estimation in numerous applications it is required to estimate the principal subspace of the data possibly from a very limited number of samples additionally it often occurs that some rough knowledge about this subspace is available and could be used to improve subspace estimation accuracy in this case this is the problem we address herein and in order to solve it a bayesian approach is proposed the main idea consists of using the cs decomposition of the semi orthogonal matrix whose columns span the subspace of interest this parametrization is intuitively appealing and allows for non informative prior distributions of the matrices involved in the cs decomposition and very mild assumptions about the angles between the actual subspace and the prior subspace the posterior distributions are derived and a gibbs sampling scheme is presented to obtain the minimum mean square distance estimator of the subspace of interest numerical simulations and an application to real hyperspectral data assess the validity and the performances of the estimator

casimir operators for suq n explicit simple expressions are given for casimir operators of q deformed suq n these expressions are similar to the corresponding casimir operators of non deformed su n the proof of invariance is based on direct applications of the commutation relations that define suq n written in a convenient basis

q analogs of iu n and u n 1 the starting point is the nonsemisimple inhomogeneous lie algebra un i2n denoted also as iu n where i2n represents an abelian subalgebra in semidirect product with the homogeneous part u n this is realized by explicitly giving the matrix elements of the generators on a modified gelfand zetlin basis that allows representations of infinite dimensions the enveloping algebra is q lifted by introducing q brackets in the matrix elements giving uq iu n the deformation of the abelian structure of i2n is studied for q 1 some implications are pointed out the important invariants are constructed for arbitrary n the results are compared to the corresponding ones for jimbo s construction of uq u n 1 on a gelfeld zetlin basis finally the related construction of uq u n 1 is presented and discussed here uq su 1 1 the q analog of relativistic motion in a plane is analyzed in the context of this formalism

noncommutative kahler structures on quantum homogeneous spaces abstract building on the theory of noncommutative complex structures the notion of a noncommutative kahler structure is introduced in the quantum homogeneous space case many of the fundamental results of classical kahler geometry are shown to follow from the existence of such a structure allowing for the definition of noncommutative lefschetz hodge kahler dirac and laplace operators quantum projective space endowed with its heckenberger kolb calculus is taken as the motivating example the general theory is then used to show that the calculus has cohomology groups of at least classical dimension