on decomposition numbers of the cyclotomic q schur algebras abstract let s be the cyclotomic q schur algebra associated to the ariki koike algebra h we construct a certain subalgebra s 0 of s and show that it is a standardly based algebra in the sense of du and rui s 0 has a natural quotient s 0 which turns out to be a cellular algebra in the case where the modified ariki koike algebra h is defined s 0 coincides with the cyclotomic q schur algebra associated to h in this paper we discuss a relationship among the decomposition numbers of s s 0 and s 0 in particular we show that some important part of the decomposition matrix of s coincides with a part of the decomposition matrix of s 0

a covariance approximation method for near field direction finding using a uniform linear array most narrowband high resolution bearing estimation algorithms were proposed based on the assumption of a far field source environment when this assumption is violated i e some sources are in the near field these algorithms generally provide unsatisfactory performances a new algorithm is proposed to handle this near field problem using a uniform linear array the received signal covariance matrix for near field sources is viewed as a corrupted measurement of the ideal signal covariance matrix for far field sources located at the same bearings taking this viewpoint the authors reconstruct a far field approximation ffa covariance matrix from the received covariance matrix to reduce the corruptions therefore existing high resolution bearing estimation techniques can be directly applied to estimate the bearings of the near field sources the properties of the proposed approach are investigated in detail simulation results demonstrating the effectiveness of this approach are included

performance analysis of higher order esprit for localization of near field sources most existing array processing techniques for estimating the directions of arrival doas or signal copy rely heavily on the plane wave assumption of far field sources when the sources are located relatively close to the array these techniques may no longer perform satisfactorily in this paper we present an asymptotic performance analysis of an esprit like method for passive localization of nearfield sources the algorithm which is based on fourth order cumulants is formulated for observations collected from a single uniformly spaced linear array we examine the least squares version of the algorithm and derive the expressions for the asymptotic variance of the estimated doas relative to a reference sensor and estimated ranges of the sources we also derive an algorithm independent bound on the asymptotic variance of the estimated parameters this bound can be used as a measure against the theoretically predicted algorithmic performance some insight into the achievable performance of this algorithm is obtained by numerical evaluation of the bound for several test cases of interest and the results are compared with those obtained by numerical evaluation of the theoretically predicted performance monte carlo simulations are used to verify the theoretical analysis

efficient application of music algorithm under the coexistence of far field and near field sources this correspondence is concerned with source localization and classification for scenarios where both the far field and near field narrowband sources may coexist we propose an efficient music based solution that requires neither a multidimensional search nor high order statistics hos we also derive the stochastic cramer rao bound crb for the problem under consideration the performance of the proposed method is compared with an existing method and with the crb

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

passive localization of near field sources by path following a new algorithm for passively estimating the ranges and bearings of multiple narrow band sources using a uniform linear sensor array is presented the algorithm is computationally efficient and converges globally it minimizes the music cost function subject to geometrical constraints imposed by the curvature of the received wavefronts the estimation problem is reduced to one of solving a set of two coupled 2d polynomial equations the proposed algorithm solves this nonlinear problem using a modification of the path following or homotopy method for an array having m sensors the algorithm reduces the global 2d search over range and bearing to 2 m spl minus 1 independent 1d searches this imparts a high degree of parallelism that can be exploited to obtain source location estimates very efficiently

on rotational invariance of lattice boltzmann schemes we propose the derivation of acoustic type isotropic partial differential equations that are equivalent to linear lattice boltzmann schemes with a density scalar field and a momentum vector field as conserved moments the corresponding linear equivalent partial differential equations are generated with a new berliner version of the taylor expansion method the details of the implementation are presented these ideas are applied for the d2q9 d2q13 d3q19 and d3q27 lattice boltzmann schemes some limitations associated with necessary stability conditions are also presented

the schur algebra we study a class of endomomorphism algebras of certain q permutation modules over the hecke algebra of type b whose summands involve both parabolic and quasi parabolic subgroups and prove that these algebras are integrally free and quasi hereditary and are stable under base change some consequences for decomposition numbers are discussed the notion of a q schur algebra was introduced by dipper and james dj2 who used these algebras to parametrize the irreducible representations of the finite general linear groups in non describing characteristics with hindsight these algebras had already appeared earlier in an entirely different quantum group context ji inspired by physics in ji jimbo considered the endomorphism algebras of tensor spaces as hecke algebra modules in his context a q schur algebra can be viewed as a quotient of the quantized enveloping algebra associated to gln in pw these algebras were shown to be quasi hereditary the quasi heredity property is an embodiment in classical algebra of the geometric derived category stratification exhibited by perverse sheaves ps it means more applications can be deduced from a ring theoretic point of view see e g dps3 and the possibility is raised of even deeper results in the future as suggested by cps2 certainly these algebras play a central role in the representation theories of the finite and quantum general linear groups naturally one asks are there such algebras for types other than a our paper ds showed that there were similar quasi hereditary quotients of quantized enveloping algebras for all types of root systems however no connection with hecke algebras and finite groups of lie type was found there this paper aims at the same question and constructs possible algebras directly from hecke algebras hence from finite groups of lie type we restrict attention to the type b case imitating the definition of a q schur algebra we introduce the notion of a q schur algebra these algebras are the endomorphism algebras of certain modules over the hecke algebra of type b called tensor spaces whose summands involve not only parabolic subgroups but also quasi parabolic subgroups of the weyl group of type b a main result of our paper shows that qschur algebras are quasi hereditary we speculate that similar constructions exist for other classical types only type d remains actually since type c is equivalent received by the editors march 3 1997 and in revised form october 28 1998 2000 mathematics subject classification primary 20c08 20g05 20c33 the authors would like to thank arc for support under the large grant a69530243 as well as nsf and the universities of virginia and new south wales for their cooperation the first author also thanks the newton institute at cambridge for its hospitality c 2000 american mathematical society

multiple target tracking using maximum likelihood principle proposes a method tracking algorithm tal based on the maximum likelihood ml principle for multiple target tracking in near field using outputs from a large uniform linear array of passive sensors the targets are assumed to be narrowband signals and modeled as sample functions of a gaussian stochastic process the phase delays of these signals are expressed as functions of both range and bearing angle track parameters of respective targets a new simplified likelihood function for ml estimation of these parameters is derived from a second order approximation on the inverse of the data covariance matrix maximization of this likelihood function does not involve inversion of the m spl times m data covariance matrix where m denotes number of sensors in the array instead inversion of only a d spl times d matrix is required where d denotes number of targets in practice d spl lt m and hence tal is computationally efficient tracking is achieved by estimating track parameters at regular time intervals wherein targets move to new positions in the neighborhood of their previous positions tal preserves ordering of track parameter estimates of the d targets over different time intervals performance results of tal are presented and it is also compared with methods by sword and by swindlehurst and kailath 1988 almost exact asymptotic expressions for the cramer rao bound crb on the variance of angle and range estimates are derived and their utility is discussed

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

passive localization of near field sources with a polarization sensitive array the least squares virtual esprit algorithm ls vespa is extended to jointly estimate the direction of arrival doa and ranges of multiple near field sources impinging on an array of crossed dipoles the algorithm utilizes fourth order cumulants for direct estimation of the arrival angle and range parameters via the eigenvalues of certain constructed matrices compared with several existing algorithms the loss of array aperture is effectively avoided as a result the proposed method can estimate doas and ranges of n 1 polarized near field sources using n dual polarization sensors simulation results show that the proposed method outperforms a fourth order statistics based esprit like method

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

some results on energy conserving lattice boltzmann models we consider the problem of energy conserving lattice boltzmann models a major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers we propose a theoretical framework based on the knowledge of the partial equivalent equations of the lattice boltzmann scheme at several orders of precision with the help of linearized models inviscid and dissipative advective acoustics and classical acoustics we suggest natural sets of relations for the parameters of lattice boltzmann schemes the application is proposed for three two dimensional schemes numerical test cases for simple linear and nonlinear waves establish that the main difficulty in the previous contributions can now be overcome

maximum likelihood source localization and unknown sensor location estimation for wideband signals in the near field in this paper we derive the maximum likelihood ml location estimator for wideband sources in the near field of the sensor array the ml estimator is optimized in a single step as opposed to other estimators that are optimized separately in relative time delay and source location estimations for the multisource case we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single source parameters the proposed algorithm is shown to yield superior performance over other suboptimal techniques including the wideband music and the two step least squares methods and is efficient with respect to the derived cramer rao bound crb from the crb analysis we find that better source location estimates can be obtained for high frequency signals than low frequency signals in addition large range estimation error results when the source signal is unknown but such unknown parameter does not have much impact on angle estimation in some applications the locations of some sensors may be unknown and must be estimated the proposed method is extended to estimate the range from a source to an unknown sensor location after a number of source location frames the location of the uncalibrated sensor can be determined based on a least squares unknown sensor location estimator

enhanced puma for direction of arrival estimation and its performance analysis direction of arrival doa estimation is a problem of significance in many applications in practice due to the occurrence of coherent signals and or when the number of available snapshots is small it is a challenge to find doas accurately this problem is revisited here through a new enhanced principal singular vector utilization for modal analysis epuma doa estimation approach which improves the threshold performance by first generating p k doa candidates for k sources where p geq k and then judiciously selecting k of them the asymptotic variance of epuma is theoretically derived and numerical results are provided to validate the asymptotic analysis and illustrate the practical merits of epuma

estimating the bearings of near field cyclostationary signals by exploiting favorable characteristics of a uniform linear array ula the far field approximation ffa method reduces the deterioration of most high resolution bearing estimation techniques due to the invalidity of the planar wavefront assumption when near field sources exist we first present a new technique that provides better performance than existing bearing estimation techniques for cyclostationary signals then the proposed technique incorporating with the ffa method is proposed to estimate signal bearings in the presence of near field sources without revising the planar wavefront assumption several simulation examples confirm the theoretical work and show the effectiveness of the proposed technique

linear lattice boltzmann schemes for acoustic parameter choices and isotropy properties in this paper we investigate the numerous possible parameter choices for linear lattice boltzmann schemes according to the definition of the order of isotropy given in augier et al in press 4 this property written in a general framework that includes all of the d dq q schemes can be understood through a group operation the resulting relationships between the parameters of the scheme defining the equilibrium states and relaxation times yield a rigorous methodology that should be followed if one is to ensure isotropy at a given order for acoustic applications in two spacial dimensions namely d 2q 9 and d 2q 1 3 schemes this methodology is used to propose a full description of the sets of parameters that are isotropic at order m email protected 1 2 3 4 5 for d 2q 9 and email protected 1 2 for d 2q 1 3 we include numerical illustrations for the d 2q 9 scheme obtained with the code lbmpy developed in the laboratory of mathematics of the university paris sud

asymptotic performance analysis of direction finding algorithms based on fourth order cumulants in the narrow band array processing context the use of higher order statistics has been often advocated because consistent and asymptotically unbiased parameter estimates can be obtained without it being necessary to know to model or to estimate the spatial covariance of the noise as long as it is normally distributed however experimentation shows that this noise insensitivity is traded for increased variability of the parameter estimates the main purpose of this contribution is to derive and work out closed form expressions of the asymptotic covariance of music like direction of arrival estimates based on two fourth order cumulant matrices the diagonal slice and the contracted quadricovariance this is compared with the standard covariance based music estimate establishing on a rational basis the domain of applicability of higher order statistics for doa estimation in particular the actual impact of the noise variance and of the dynamic range of the sources is investigated this asymptotic performance analysis is achieved within a general framework which we believe to be of general interest

the cumulant lattice boltzmann equation in three dimensions theory and validation we propose analyze and validate a lattice boltzmann model with a cumulant collision operator the new model is analytically and numerically shown to poses smaller errors than a moment based multiple relaxation time lattice boltzmann model we demonstrate the usability of the cumulant lattice boltzmann model by simulations of flow around a sphere for reynolds numbers from 200 to 105

a weighted linear prediction method for near field source localization this paper proposes a low computational cost method for the near field narrowband source localization problem which does not require multidimensional search or high order statistics the proposed method is based on the second order statistics sos of the outputs of a uniform linear array ula more precisely the range and angle parameters are estimated through a weighted linear prediction lp algorithm applied to a properly chosen array output correlation sequence detailed performance analysis and derivation of the optimal weightings are provided simulation results are finally presented to validate the theoretical analysis results and to assess the performance of the proposed method

mismatch of near field bearing range spatial geometry in source localization by a uniform linear array many near field source localization algorithms intentionally simplifies the exact spatial geometry among the emitter and the sensors in order to speed up the signal processing involved for example the fresnel approximation is a second order taylor series approximation such intentional approximation introduces a systemic error in the algorithm s modeling of the actual objective reality from which the measured data arise a mismatch thus exists between the algorithm s presumptions versus the data it processes this modeling mismatch will introduce a systematic bias in the bearing range estimates of the near field source localization algorithm this bias is non random and adds towards the random estimation errors due to the additive and or multiplicative noises the open literature currently offers no rigorous mathematical analysis on this issue this proposed project aims to fill this literature gap by deriving explicit formulas of the degrading effects in three dimensional source localization due to approximating the source sensor geometry by any order of the taylor s series expansion

near field multiple source localization by passive sensor array the localization of multiple near field sources in a spatially white gaussian noise environment is studied a modified two dimensional 2 d version of the multiple signal classification music algorithm is used to localize the signal sources range and bearing a global optimum maximum likelihood searching approach to localize these sources is discussed it is shown that in the single source situation the covariances of both the 2 d music estimator and the maximum likelihood estimator mle approach the cramer rao lower bound as the number of snapshots increases to infinity in the multiple source situation it is observed that for a high signal to noise ratio snr and a large number of snapshots the root mean square errors rmses of both localization techniques are relatively small however for low snr and or small number of snapshots the performance of the mle is much superior that of the modified 2 d music

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

a modified path following algorithm using a known algebraic path a new computationally efficient path following algorithm is presented for source localization that uses a uniform linear sensor array an algebraic relation is demonstrated between the bearing of a source under a plane wave assumption and the actual source bearing and range this relation can be used as a path to follow to the peak of the 2 d music spectrum as a result in the case of an array that has m sensors with n sources this new algorithm can reduce the number of searches to n independent 1 d searches following the known algebraic path

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

crb based design of linear antenna arrays for near field source localization this paper is devoted to the cramer rao bound crb on the angle and range of a narrow band near field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter first we prove that the conditional and unconditional crbs are proportional for an arbitrary parametrization of the steering vector that may include but is not limited to the source doa range or polarization then a taylor expansion of the crb is conducted to obtain accurate nonmatrix closed form expressions of the crb on angle and range in contrast to the existing expressions our expressions are simple interpretable and more general because the sensors are only constrained to be placed along some axis our analysis leads to the characterization and design of a class of centro symmetric linear arrays with improved near field angle and range estimation capabilities

equivalent partial differential equations of a lattice boltzmann scheme we show that when we formulate the lattice boltzmann equation with a small time step dt and an associated space scale dx a taylor expansion joined with the so called equivalent equation methodology leads to establishing macroscopic fluid equations as a formal limit we recover the euler equations of gas dynamics at the first order and the compressible navier stokes equations at the second order

stable lattice boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves we follow the mathematical framework proposed by bouchut 2003 22 and present in this contribution a dual entropy approach for determining equilibrium states of a lattice boltzmann scheme this method is expressed in terms of the dual of the mathematical entropy relative to the underlying conservation law it appears as a good mathematical framework for establishing a h theorem for the system of equations with discrete velocities the dual entropy approach is used with d1q3 lattice boltzmann schemes for the burgers equation it conducts to the explicitation of three different equilibrium distributions of particles and induces naturally a nonlinear stability condition satisfactory numerical results for strong nonlinear shocks and rarefactions are presented we prove also that the dual entropy approach can be applied with a d1q3 lattice boltzmann scheme for systems of linear and nonlinear acoustics and we present a numerical result with strong nonlinear waves for nonlinear acoustics we establish also a negative result with the present framework the dual entropy approach cannot be used for the shallow water equations

quartic parameters for acoustic applications of lattice boltzmann scheme using the taylor expansion method we show that it is possible to improve the lattice boltzmann method for acoustic applications we derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the scheme to enforce fourth order accuracy the corresponding discrete equations are solved with the help of symbolic manipulation the solutions are obtained in the case of d3q27 lattice boltzmann scheme various numerical tests support the coherence of this approach

implementation of the compact interpolation within the octree based lattice boltzmann solver musubi abstract a sparse octree based parallel implementation of the lattice boltzmann method for non uniform meshes is presented in this paper to couple grids of different resolutions a second order accurate compact interpolation is employed and further extended into three dimensions the compact interpolation requires only four source elements from the adjacent level for both two and three dimensions thus improves the computational efficiency moreover a weight based domain decomposition algorithm and the level wise arrangement of elements is explained in detail the second order convergence for both velocity and strain rate are validated numerically in the taylor green vortex test case additionally the 3d flow around a sphere in the reynolds number range of 100 1000 is investigated good agreement between simulated results and those from literature is observed which provides further evidence for the accuracy of our method

theory of the lattice boltzmann equation symmetry properties of discrete velocity sets the lattice boltzmann equation replaces continuous particle velocity space by a finite set the velocity distribution function then varies over a finite dimensional vector space instead of over an infinite dimensional function space the number of linearly independent moments of the distribution function in a lattice boltzmann model cannot exceed the number of velocities finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory given a finite velocity set it is important to know which moments are free of these dependences elementary group theory is applied to the solution of this problem it is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments the construction of some standard two and three dimensional models is reviewed from this viewpoint and procedures for constructing higher dimensional models are suggested