isophoric arrays massively thinned phased arrays with well controlled sidelobes traditional filled phased arrays have an element placed in every location of a uniform lattice with half wavelength spacing between the lattice points massively thinned arrays have fewer than half the elements of their filled counterparts such drastic thinning is normally accompanied by loss of sidelobe control this paper describes a class of massively thinned linear and planar arrays that show well behaved sidelobes in spite of the thinning the term isophoric is derived from greek roots to denote uniform weight in isophoric arrays element placement based on difference sets forces uniformly weighted spatial coverage this constraint forces the array power pattern to pass through v uniformly spaced equal and constant values that are less than 1 k times the main beam peak where v is the aperture size in half wavelengths and k is the number of elements in the array the net result is reduced peak sidelobes especially when compared to cut and try random placement approaches an isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that k is approximately the square root of v where more than one beam must be generated at a time isophoric array designs may be used to advantage even within a traditional filled array by interweaving two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time two independent antenna power patterns can be generated each with a sidelobe region that is approximately a constant value of 1 2k relative to the main beam where k is the number of elements in the subarray

particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

calculation of brs cohomology with spectral sequences a method for finding the general form of the brs cohomology spaceh for the various gauge and supersymmetry theories is presented the method is adapted for use in the space of integrated local polynomials of the gauge fields and ghosts with arbitrary numbers of fields and dervivatives the technique uses the hodge decomposition in a fock space with a euclidean inner product and combines this with spectral sequences to generate simple and soluble equations whose solutions span a simple spacee isomorphic to the complicated spaceh the technique is illustrated for pedagogic purposes by the detailed calculation of the ghost charge zero and one sectors ofh for yang mills theory with gauge groupso 32 in ten dimensions the method is appropriate for supersymmetric theories gravity supergravity and superstrings where higher order terms with many derivatives occur naturally in the effective action

algebraic characterization of the wess zumino consistency conditions in gauge theories a new way of solving the descent equations corresponding to the wess zumino consistency conditions is presented the method relies on the introduction of an operator which allows to decompose the exterior space time derivatived as a brs commutator the case of the yang mills theories is treated in detail

a hybrid approach based on pso and hadamard difference sets for the synthesis of square thinned arrays a hybrid approach for the synthesis of planar thinned antenna arrays is presented the proposed solution exploits and combines the most attractive features of a particle swarm algorithm and those of a combinatorial method based on the noncyclic difference sets of hadamard type numerical experiments validate the proposed solution showing improvements with respect to previous results

the seiberg witten map for the 4d noncommutative bf theory we describe the seiberg witten map taking the 4d noncommutative bf theory ncbf into its pure commutative version the existence of this map is in agreement with the hypothesis that such maps are available for any noncommutative theory with schwarz type topological sectors and represents a strong indication for the renormalizability of these theories in general

a novel principle for optimization of the instantaneous fourier plane coverage of correction arrays a novel principle for the design of correlation arrays is introduced based upon the maximization of the distance between samples simulated annealing is applied to the problem of finding solutions for moderate numbers of elements up to 12 the resulting arrays have symmetric crystalline structures

results on the wess zumino consistency condition for arbitrary lie algebras the so called covariant poincare lemma on the induced cohomology of the space time exterior derivative in the cohomology of the gauge part of the brst differential is extended to cover the case of arbitrary nonreductive lie algebras as a consequence the general solution of the wess zumino consistency condition with a nontrivial descent can for arbitrary super lie algebras be computed in the small algebra of the one form potentials the ghosts and their exterior derivatives for particular lie algebras that are the semidirect sum of a semisimple lie subalgebra with an ideal a theorem by hochschild and serre is used to characterize more precisely the cohomology of the gauge part of the brst differential in the small algebra in the case of an abelian ideal this leads to a complete solution of the wess zumino consistency condition in this space as an application the consistent deformations of 2 1 dimensional chern simons theory based on iso 2 1 are rediscussed

w gauge structures and their anomalies an algebraic approach starting from flat two dimensional gauge potentials we propose the notion of w gauge structure in terms of a nilpotent becchi rouet stora brs differential algebra the decomposition of the underlying lie algebra with respect to an sl 2 subalgebra is crucial for the discussion of conformal covariance in particular the appearance of a projective connection different sl 2 embeddings lead to different w gauge structures we present a general soldering procedure which allows one to express zero curvature conditions for the w currents in terms of conformally covariant differential operators acting on the w gauge fields and to obtain at the same time the complete nilpotent brs differential algebra generated by w currents gauge fields and the ghost fields corresponding to w diffeomorphisms as illustrations we treat the cases of sl 2 itself and the two different sl 2 embeddings in sl 3 viz the w 1 3 and w 2 3 gauge structures in some detail in these cases we determine algebraically w anomalie

sparse 2 d array placement for arbitrary pattern mask and with excitation constraints a simple deterministic approach we present a novel algorithm for the synthesis of planar 2 d arrays subject to arbitrary pattern masks and excitation constraints e g dynamic range the algorithm is simple and deterministic and considers the radiating element pattern the procedure starts with a conventional constrained fixed grid synthesis on a regular lattice yielding a goal radiated field next element locations are selected sequentially by maximizing projection on field difference to goal while excitation amplitudes are computed using fixed grid constrained synthesis for irregular lattices the final result is the sparse layout and constrained excitation coefficients the proposed method is validated against literature results application examples are given for circular flat top isoflux and triangular flat top shaped beam patterns with constraints on excitation coefficients dynamic range both for isotropic and patch type element patterns

hybrid ads based techniques for radio astronomy array design a set of techniques are presented that are based on the exploitation of low correlation sequences called almost difference sets adss to design correlator arrays for radio astronomy applications three approaches are discussed with different objectives and performances ads based analytical designs ga optimized arrangements and pso optimized arrays are presented and applied to the synthesis of open ended y and cross array configurations to maximize the u v coverage or to minimize the peak sidelobe level psl representative numerical results are illustrated to point out the features and performances of the proposed approaches and to assess their effectiveness in comparison with state of the art design methodologies as well the presented analysis indicates that the proposed approaches overcome existing pso based correlator arrays in terms of psl control e g 1 0 db reduction and tracking u v coverage e g up to 2 enhancement also improving the speed of convergence of the synthesis process

rectangular thinned arrays based on mcfarland difference sets a new class of analytical rectangular thinned arrays with low peak sidelobe level psl is introduced the proposed synthesis technique exploits binary sequences derived from mcfarland difference sets to design thinned layouts on a lattice of p p p 2 positions for any prime p the pattern features of the arising massively thinned arrangements characterized by only p p 1 active elements are discussed and the results of an extensive numerical analysis are presented to assess advantages and limitations of the mcfarland based arrays

sparse array beampattern synthesis via alternating direction method of multipliers in this paper we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers admm unlike the usual weighted l 1 norm we utilize the l p norm of the array weight vector where 0 as the objective function to enhance its sparsity for arbitrary array configurations to solve the resultant nonconvex and nonlinear optimization problem we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes and then the array weight vector and auxiliary variables are updated alternately via admm to determine the array weight vector with the l p norm we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives on the other hand we divide the objective function of auxiliary variables into multiple nonlinear subfunctions each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two sided constraints furthermore we extend our methodology to the symmetric excitation case with symmetric array configurations numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations

becchi rouet stora cohomology of zero curvature systems ii the noncomplete ladder case the yang mills type theories and their brs cohomologies are analyzed within the zero curvature formalism

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

aperiodic array layout optimization by the constraint relaxation approach an optimization procedure for the layout assessment of electrically large but finite planar arrays is presented the synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints moreover the size of the radiators is taken into account which results in a hard nonoverlapping between the elements constraint the latter should not be violated if we want the attained solution not only to obey the far field mask but also to be physically realizable as stated the optimization problem is twofold an antenna design is associated with a packing problem in order to take the constraints on the layout into account and solve the whole problem we propose the constraint relaxation approach which is equipped with a packing algorithm our study is applied to various initial geometries and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented which show the applicability and merit of the method

algebraic characterization of vector supersymmetry in topological field theories a cohomological characterization of a class of linearly broken ward identities is provided the examples of the topological vector supersymmetry and of the landau ghost equation are discussed the existence of these linearly broken ward identities lies in the brst exactness of suitable antifield dependent cocycles with negative ghost number this algebraic set up turns out to be related to the cohomological reformulation of the noether theorem given by g barnich f brandt and m henneaux commun math phys 174 57 93 1995 m henneaux j pure appl algebra 100 3 1995

sparse array design for azimuthal direction of arrival estimation we propose a novel approach to the design of array geometries for azimuthal direction of arrival doa estimation the proposed array design is related to that of minimum redundancy arrays but the array sensors are not required to lie on a uniform grid based on the proposed array geometry design we develop a subspace based doa estimation technique which allows to estimate the doas of more sources than sensors using only second order statistics of the received data this doa estimation technique is related to the covariance augmentation technique but in contrast to the latter technique it provides nonambiguous doa estimates for the full 360 azimuth field of view

b r s algebras analysis of the consistency equations in gauge theory we compute all possible anomalous terms in quantum gauge theory in the natural class of polynomials of differential forms by using the appropriate cohomological and algebraic methods we do it for all dimensions of spacetime and all structure groups with reductive lie algebras

algebraic fiber bundles abstracr when x is a finite simplicial complex and g is any of a certain class of groups a classification of g principal bundles over x in terms of projective modules over a ring r g x is given this generalizes swan s classification of vector bundles and uses the results of mulvey often r can be taken to be noetherian in this case spec r is usually reducible with cohomologically trivial irreducible components information is derived concerning the nature of projective modules over such rings and some results are obtained indicating how such information reflects information about x

a new realization for the d 2 topological algebra we derive topological algebras for two dimensional models admitting a d b decomposition with b the brst operator in general the topological algebra we obtain is not derived from the twisting of an n 2 supersymmetry algebra we show for the particular case of an abelian model described by a ladder of matter how to derive n 2 supersymmetry generators from the odd generators of the topological algebra

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

synthesis of unequally spaced antenna arrays by using differential evolution synthesis of unequally spaced linear antenna arrays is considered in this paper a recently developed new differential evolution algorithm is applied to solve the problem both position only and position phase synthesis have been studied effect of angle resolution has also been investigated synthesis results show that our algorithm is able to obtain better synthesis result reliably and efficiently

synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations an iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented the algorithm consists in solving a sequence of weighted l1 convex optimization problems the method can thus be readily implemented and efficiently solved in the optimization procedure the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements the method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach whose computation time is several orders of magnitude below those of so called global optimization algorithms

ads based guidelines for thinned planar arrays we propose an analytical technique based on almost difference sets adss for thinning planar arrays with well controlled sidelobes the method allows one to synthesize bidimensional arrangements with peak sidelobe levels psls predictable and deducible from the knowledge of the array aperture the filling factor and the autocorrelation function of the ads at hand the numerical validation concerned with both small and very large apertures points out that the expected psl values are significantly below those of random arrays and comparable with those from different sets dss although obtainable in a wider range of configurations

square array antennas based on hadamard difference sets a regular method for synthesizing a planar aperiodic thinned array antenna aa with a low peak sidelobe level is suggested it is based on using specific combinatorial constructions noncyclic difference sets dss the method uses the fact that when the elements of an equiamplitude aa are arranged according to a ds law its power pattern takes constant value in the net of uniformly located space points in the sidelobe region and this value is less than where is the element number in distinction to the method using cyclic dss see leeper 1999 which enables one to build planar aas only on rectangular grids with co prime sidelengths the represented method omits such a constraint the most important class of the noncyclic 2 d dss is represented by the sets of hadamard type sets based on such sets rectangular and square aperiodic roughly half filled aas can be built here the numerical results obtained for the square aas with the element number in the array up to 300 are presented

synthesis of sparse planar arrays using modified real genetic algorithm in array design the positions of sparse array elements is an important concern for optimal performance in terms of its ability to achieve minimum peak sidelobe level sll this paper proposes a modified real genetic algorithm mga based on resetting of chromosome for the element position optimization of sparse planar arrays with rectangular boundary and here the multiple optimization constraints include the number of elements the aperture and the minimum element spacing by simplifying the space between the elements from the actual distance to chebychev distance the mga searches a smaller solution space by means of indirect description of individual and it can avoid infeasible solution during the optimization process by two novel genetic operators finally the simulation results confirming the great efficiency and the robustness of the proposed method are shown in this paper

zero curvature conditions and conformal covariance two dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated the analysis is based on the kostant decomposition of simple lie algebras in terms of representations with respect to their principal sl 2 subalgebra

linear array thinning using iterative fft techniques a new approach for the synthesis of thinned uniformly spaced linear arrays featuring a minimum sidelobe level is presented the method is based on the iterative fourier technique to derive element excitations from the prescribed array factor using successive forward and backward fourier transforms array thinning is accomplished by setting the amplitudes of the largest element excitations to unity and the others to zero during each iteration cycle the number of turned on elements depends on the array filling factor and the total count of element positions the effectiveness of the new method will be demonstrated for various 200 element linear arrays and compared with published results

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

a new family of almost difference sets and some necessary conditions almost difference sets have important applications in cryptography and coding theory in this paper new families of almost difference sets are constructed some necessary conditions for the existence of v k spl lambda t almost difference sets in z sub v are derived

yang mills cohomology in four dimensions the local polynomial cohomology space of the yang mills brs operator in four dimensions is computed in order to simplify the analysis without omitting the physically interesting cases the investigation is limited to polynomials whose fadeev popov charge and uv naive dimensions have upper bounds furthermore the results are used to compute a la stora the local functional yang mills anomalies from which the uniqueness of the adler bardeen jackiw anomaly follows

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

peak sidelobe level reduction with a hybrid approach based on gas and difference sets this paper presents an approach for the optimization of the beam pattern produced by massively thinned arrays the method which combines the most attractive features of a genetic algorithm and those of a combinatorial technique namely the difference sets method is aimed at synthesizing massively thinned antenna arrays in order to suitably reduce the peak sidelobe level selected numerical results are presented in order to assess the effectiveness and reliability of the proposed approach

on the robustness to element failures of linear ads thinned arrays the robustness of the analytical thinning based on almost difference sets adss is analyzed when faulty elements are present in linear arrays peak sidelobe level psl statistics of the damaged layouts are numerically inferred from representative simulations dealing with different aperture sizes and element failure rates

local brst cohomology in the antifield formalism i general theorems we establish general theorems on the cohomologyh s d of the brst differential modulo the spacetime exterior derivative acting in the algebra of localp forms depending on the fields and the antifields sources for the brst variations it is shown thath k s d is isomorphic toh k d in negative ghost degree k k 0 where is the koszul tate differential associated with the stationary surface the cohomology grouph1 d in form degreen is proved to be isomorphic to the space of constants of the motion thereby providing a cohomological reformulation of noether s theorem more generally the grouph k d in form degreen is isomorphic to the space ofn k forms that are closed when the equations of motion hold the groupsh k d k 2 are shown to vanish for standard irreducible gauge theories the grouph2 d is then calculated explicitly for electromagnetism yang mills models and einstein gravity the invariance of the groupsh k s d under the introduction of non minimal variables and of auxiliary fields is also demonstrated in a companion paper the general formalism is applied to the calculation ofh k s d in yang mills theory which is carried out in detail for an arbitrary compact gauge group

diffeomorphism cohomology in beltrami parametrization considering local conformal field theories on a riemann surface by coupling conformal matter fields with a complex structure parametrized by a beltrami differential the local diffeomorphism cohomology modulo d of the becchi rouet stora operator is computed directly by means of the spectral sequences method then thanks to both power counting and locality principles of the feynman algorithm the local theory is analyzed on the one hand in the ghost number one sector consistent anomalies turn out to be exactly after elimination of a trace anomaly involving matter fields the well known holomorphically split diffeomorphism anomaly due to the vacuum on the other hand in the ghost number zero sector local observables of the theory namely the vertex operators are generically calculated as well as all possible classical actions for lagrangian conformal models

a quantum field theoretic description of linking numbers and their generalization it is shown that the linking number of two surfaces of dimensionp andn p 1 in ann dimensional manifold has a natural description in terms of the two point funciton of a simple topological field theory the two point function of a more general theory whose partition function yields the ray singer torsion provides a definition for a generalized linking number

a note on local brst cohomology of yang mills type theories with free abelian factors we extend previous work on antifield dependent local becchi rouet stora tyutin brst cohomology for matter coupled gauge theories of yang mills type to the case of gauge groups that involve free abelian factors more precisely we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of lagrangians in general spacetime dimensions we then discuss explicit solutions in the case of specific models our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models as well as for divergences counterterms and for gauge anomalies that may appear during perturbative quantization

the milnor patching property abstract this paper gives a complete answer to the following question if r is a commutative ring in which every height 1 ideal is a local set theoretic complete intersection e g r could be regular and r 1 and r 2 are r algebras which are flat or of finite type when is it the case that projective r modules are precisely those r modules constructed by patching a projective r 1 module to a projective r 2 module over r 1 r r 2 in other words we give a classification theorem for situtations in which the conclusion to the milnor patching theorem holds our answer takes the form of a necessary and sufficient condition whose truth or falsity is very easy to check in most particular situations

lie algebra cohomology and group structure of gauge theories we explicitly construct the adjoint operator of coboundary operator and obtain the hodge decomposition theorem and the poincare duality for the lie algebra cohomology of the infinite dimensional gauge transformation group we show that the adjoint of the coboundary operator can be identified with the brst adjoint generator q for the lie algebra cohomology induced by brst generator q we also point out an interesting duality relation poincare duality with respect to gauge anomalies and wess zumino witten topological terms we consider the consistent embedding of the brst adjoint generator q into the relativistic phase space and identify the noncovariant symmetry recently discovered in qed with the brst adjoint nother charge q

robust beamforming with magnitude response constraints using iterative second order cone programming the problem of robust beamforming for antenna arrays with arbitrary geometry and magnitude response constraints is one of considerable importance due to the presence of the non convex magnitude response constraints conventional convex optimization techniques cannot be applied directly a new approach based on iteratively linearizing the non convex constraints is then proposed to reformulate the non convex problem to a series of convex subproblems each of which can be optimally solved using second order cone programming socp moreover in order to obtain a more robust beamformer against array imperfections the proposed method is further extended by optimizing its worst case performance using again socp different from some conventional methods which are restricted to linear arrays the proposed method is applicable to arbitrary array geometries since the weight vector rather than its autocorrelation sequence is used as the variable simulation results show that the performance of the proposed method is comparable to the optimal solution previously proposed for uniform linear arrays and it also gives satisfactory results under different array specifications and geometries tested

synthesis of linear and planar arrays with minimum element selection a new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed in the method the number of elements in an array is minimized while constraining the amplitude response error in the mainlobe region the attenuation in the sidelobe region and the array dimensions an iterative constrained optimization method is used where the amplituderesponse error is linearly approximated at each iteration while concurrently minimizing a re weighted l1 norm of the array coefficients to ensure robustness of the array we constrain a sensitivity parameter namely the white noise gain to be above a prescribed level furthermore the method also provides the additional flexibility of controlling the array dimensions symmetry properties and element positions of the array two variants have been developed in the first variant both the array coefficients and the positions of the elements are optimized in the second variant only the array coefficients are optimized while the elements are fixed at predefined positions experimental comparisons with several state of the art competing methods show that the proposed method provides greater flexibility of controlling the robustness beampattern response error array dimensions and element positions while at the same time the number of elements is less than or equal to that of the competing methods

vector bundles and k theory over topological algebras functional analysis techniques mainly pertaining to the theory of intinitedimensional representations have been recently applied mostly by soviet mathematicians to compute hermitian k groups related to the classification of quadratic forms with coefftcients in group rings see for instance the relevant survey articles by miseenko 59 801 in this concern it has been pointed out that without loss of generality one may profitably consider instead as coefficient ring an abstract c algebra 59 p 931 in a similar framework namely that of vector bundles with coefftcients in c algebras topological invariants of elliptic operators related to the classical atiyah singer formula have also been studied by miieenko in 60 see also 61 i whereas kasparov has given in 42 a similar study by still applying c algebra techniques cf the comments at the end of this paper besides vector bundles over banach algebras and in particular c algebras commutative or not have already been applied by kandelaki 37 381 and independently by fujii 27 one of their main results being a generalization of the serre swan theorem 41 for complex vector bundles cf theorem 4 2 in this paper furthermore connections with the theory of extensions of c algebras 12 bdf theory have also been considered by kandelaki 39 401 on the other hand topological in particular locally m convex algebras necessarily not normed ones have been recently used in connection for instance with applications to relativistic quantum theory 18 191 thus the extension of the preceding considerations to vector bundles with coefftcients in topological algebras more general than normed ones and in particular in locally m convex ones 55 581 is naturally revealed now this task is further feasible as a consequence of the generalization within the topological algebras theory framework of previous relevant work concerning applications of algebraic topology and complex analysis to banach algebras theory 24 53 55 621 452 0022 247x 83 3 00

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

algebraic characterization of gauge anomalies on a nontrivial bundle we discuss the algebraic way of solving the descent equations corresponding to the brst consistency condition for the gauge anomalies and the chern simons terms on a nontrivial bundle the method of decomposing the exterior space time derivative as a brst commutator is extended to the present case

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods