local weyl modules for equivariant map algebras with free abelian group actions suppose a finite group acts on a scheme x and a finite dimensional lie algebra g the associated equivariant map algebra is the lie algebra of equivariant regular maps from x to g examples include generalized current algebras and twisted multiloop algebras local weyl modules play an important role in the theory of finite dimensional represen tations of loop algebras and quantum affine algebras in the current paper we extend the definition of local weyl modules previously defined only for generalized current algebras and twisted loop algebras to the setting of equivariant map algebras where g is semisimple x is affine of finite type and the group is abelian and acts freely on x we do so by defin ing twisting and untwisting functors which are isomorphisms between certain categories of representations of equivariant map algebras and their untwisted analogues we also show that other properties of local weyl modules e g their characterization by homological prop erties and a tensor product property extend to the more general setting considered in the current paper

continuation of acoustic near fields this paper deals with the analytic continuation of a coherent pressure field specified on a finite sheet located close to and conformal to the surface of a vibrator this analytic continuation is an extension or extrapolation of the given measured field into a region outside and tangential to the original finite sheet and is based on the green s function the transfer function relating acoustic quantities on the two conformal surfaces the continuation of the measured pressure field is an inverse problem that requires the use or regularization theory especially when noise is present in the data an iteration algorithm is presented that is successful in continuing the pressure field into the tangential sheet the results are accurate close to the original boundary and taper decay toward zero with distance away from it the algorithm is tested on numerical and experimental data from a point driven rectangular plate results show the successful extrapolation continuation of this data into an area nearly double that of the original pressure field this algorithm is not limited to planar surfaces and can be applied to arbitrarily shaped surfaces

estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

numerical simulation of optimal deconvolution in a shallow water environment a fast technique for deconvolving signals in a dispersive multipath shallow water environment using inverse filters is compared with the more commonly used deconvolution technique of time reversal also known as phase conjugation the objective of such techniques is to improve the accuracy of sound transmission from a source array to some receiving space time reversal provides benefits in this regard but here the additional performance that can be gained from inverse filters is examined several strategies for obtaining a set of inverse filters are discussed each aimed at improving the accuracy of the reconstruction of the desired time signals through inverse techniques it will be shown that an optimal inversion in the sense of achieving a flat system response in the frequency domain does not necessarily achieve a realizable time domain filter a fast field model using oases of the giglio basin shallow water test facility is used as the basis for evaluating the various focusing strategies for single receiver locations it will be seen that inverse filter arrays provide enhanced temporal and spatial focusing when compared to time reversal arrays in addition inverse filtering allows multiple receivers to be used thereby increasing bandwidth or improving redundancy

on the sampling conditions for reconstruction of an acoustic field from a finite sound source a simple and accurate method for the estimation of ultrasonic transducer fields is developed in the method the angular spectrum is employed to evaluate the three dimensional propagation from a measured plane to an arbitrary parallel plane the implementation uses a discrete convolution that is described in detail relative to conventional spatial frequency representations the implementation of the angular spectrum method in this paper has the advantage of being free from artifacts enabling sample spacing to be greater than one half wavelength using memory efficiently and interpolating the measured data the loosened sampling requirement and natural interpolation of the method permit efficient reconstruction of the full three dimensional acoustic field from a coarse sound pressure measurement on single plane

analysis of the numerically implemented angular spectrum approach based on the evaluation of two dimensional acoustic fields part ii characteristics as a function of angular range the numerically implemented angular spectrum approach asa is investigated in terms of the characteristics of the asa as a function of angular range over which the angular spectrally decomposed plane waves are superimposed to construct an acoustic field radiated by a source the investigation is based on the evaluation of the 2 d fields radiated by striplike planar sources and 1 d linear phased arrays with different aperture sizes and on the comparison with those obtained by using the analytical solution derived with the point spread function method the convergence and the spatial aliasing of the asa s results are systematically dealt with a region well converging to the analytical solution as the angular range increases is found to exist before the aliasing comes up analytical formulas to determine the boundaries of this region are given based on the instantaneous frequency concept an analytical expression for optimal selection of the angular range used is derived hence the sampling frequency can be chosen to be optimal and adaptive to the discretization size of the source plane without worrying that the number of the samples for the discretization size should be chosen to be a power of two that the fast fourier transform fft usually needs an excellent agreement of the asa s results with the analytical solution is demonstrated when using the optimal selection of the angular range for the specified parameters the analysis made in this paper can be extended to the case of 3 d fields

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

fractal just infinite nil lie superalgebra of finite width abstract the grigorchuk and gupta sidki groups play fundamental role in modern group theory they are natural examples of self similar finitely generated periodic groups as their natural analogues there are constructions of nil lie p algebras over a field of characteristic 2 40 and arbitrary positive characteristic 52 in characteristic zero similar examples of lie algebras do not exist by a result of martinez and zelmanov 32 the second author constructed analogues of the grigorchuk and gupta sidki groups in the world of lie superalgebras of arbitrary characteristic the virtue of that construction is that the lie superalgebras have clear monomial bases 41 that lie superalgebras have slow polynomial growth and are graded by multidegree in the generators in particular a self similar lie superalgebra q is z 3 graded by multidegree in 3 generators its z 3 components lie inside an elliptic paraboloid in space the components are at most one dimensional thus the z 3 grading of q is fine an analogue of the periodicity is that homogeneous elements of the grading q q 0 q 1 are ad nilpotent in particular q is a nil finely graded lie superalgebra which shows that an extension of the mentioned result of martinez and zelmanov 32 to the lie superalgebras of characteristic zero is not valid but computations with q are rather technical in this paper we construct a similar but simpler and smaller example namely we construct a 2 generated fractal lie superalgebra r over arbitrary field we find a clear monomial basis of r and unlike many examples studied before we find also a clear monomial basis of its associative hull a the latter has a quadratic growth the algebras r and a are z 2 graded by multidegree in the generators positions of their z 2 components are bounded by pairs of logarithmic curves on plane the z 2 components of r are at most one dimensional thus the z 2 grading of r is fine as an analogue of periodicity we establish that homogeneous elements of the grading r r 0 r 1 are ad nilpotent in case of n graded algebras a close analogue to being simple is being just infinite unlike previous examples of lie superalgebras we are able to prove that r is just infinite but not hereditary just infinite our example is close to the smallest possible example because r has a linear growth with a growth function r m 3 m as m moreover r is of finite width 4 char k 2 in case char k 2 we obtain a lie algebra of width 2 that is not thin thus we have got a more handy analogue of the grigorchuk and gupta sidki groups the constructed lie superalgebra r is of linear growth of finite width 4 and just infinite it also shows that an extension of the result of martinez and zelmanov 32 to the lie superalgebras of characteristic zero is not valid

optimal selection of parameters for the angular spectrum approach to numerically evaluate acoustic fields optimal selection of parameters is presented for the angular spectrum approach asa to the numerical calculation of acoustic fields radiated by planar transducers and linear arrays with and without focusing the parameters include spatial sampling interval discretization size of a source plane in which a source is located and the angular range over which the plane waves decomposed from the source using the discrete fourier transform dft are chosen to superimpose and construct the fields the concept of instantaneous frequency is applied to the fourier transformed green s function to determine the angular range of the plane waves used for the construction with minimal spatial aliasing error based on the minimization of spatial frequency and spatial aliasing errors in a constructed field optimal selection of the parameters is worked out the asa with the optimal selection is then applied to computing the fields radiated by planar transducers and linear arrays into water and a layered oil water medi

the virasoro algebra three theroems are proved with suitable hypotheses in each case characterizations are found for the virasoro algebra for some of its representations and for the ramond neveu schwarz superalgebra built around the virasoro algebra

study of acoustic resonance in enclosures using eigenanalysis based on boundary element methods it is well known that from the modal theory of room acoustics resonance will occur if the driving frequency of a sound source located in a room coincides with one of the natural frequencies of the sound field in this study an eigenanalysis technique based on the boundary element method bem is developed for extracting eigenmodes of a sound field in an enclosure a method of singular value search in conjunction with a golden section optimization algorithm is utilized for efficient calculation of eigenmodes in particular modes associated with repeated eigenvalues can be well resolved by the technique developed in this research enclosures of various geometries have been analyzed by using the developed algorithm in a numerical simulation satisfactory agreement has been achieved between the bem results the fem results and the analytical solutions if available

acoustic imaging using under determined inverse approaches frequency limitations and optimal regularization this paper presents an acoustic imaging technique based on an under determined inverse approach the principle is to quantify an elementary source distribution on a source surface from acoustic pressure measurements the acoustic transfer system between elementary sources and microphone positions very under determined is then reduced to a square system using singular value decomposition the high frequency limitation of this method is studied as well as the regularization techniques that have to be used at low frequency a monte carlo simulation is carried out to compare the efficiency of generalized cross validation and l curve validation to choose the tikhonov regularization parameter a combined validation criterion is finally proposed to take advantage of both approaches

iterative regularization method in generalized inverse beamforming abstract beamforming based on microphone array is a method to identify sound sources it can visualize the sound field of the source plane and reveal interesting acoustic information generalized inverse beamforming gib is one important branch of beamforming techniques due to its high identification accuracy and computational efficiency however in real testing situation errors caused by measurement noise and configuration problems may seriously reduce the beamforming accuracy as an inverse problem the stability of gib can be improved with regularization methods we proposed a new iterative regularization method for gib by iteratively redefining the form of regularization matrix and calculating the corresponding solution moreover the new method is applied to functional beamforming and double layer antenna beamforming respectively numerical simulations and experiments are implemented the results show that the proposed regularization method leads to more robust beamforming output and higher accuracy in both the two applications

sound equalization in a large region of a rectangular enclosure l the work presented by santillan j acoust soc am 110 1989 1997 2001 about equalization at low frequencies in rectangular enclosures is extended and topics that remained unaddressed in the original study are treated in this paper a modification is introduced to the original cost function that leads to a least squares problem formulation that demonstrates increased robustness and the multiple error lms least mean square adaptive algorithm is employed to approximate the coefficients of the equalization filters to their optimum values other issues studied in this paper include the dependence of the limits of the zone of equalization on factors such as the damping constant of the modes of the enclosure the number of sources and the driving frequency

comments on analysis of the numerically implemented angular spectrum approach based on the evaluation of two dimensional acoustic fields part i and part ii j acoust soc am 99 1339 1348 1349 1359 1996 the aim of this comment is to show that when the normal velocity of the transducer is no longer constant the algorithm that has been recently proposed by wu et al j acoust soc am 99 1339 1348 for part i and 1349 1359 for part ii 1996 cannot eliminate aliasing nor remove the phase error in the angular spectrum in fact in recent articles wu et al proposed and used a new numerical algorithm for eliminating the aliasing in the spectrum moreover they have shown that the phase error can be easily removed in their investigation they used a planar transducer and linear array to show the effectiveness of their algorithm the normal velocity of the planar transducer or of the elementary transducers in the case of the array has been supposed constant

fractal nil graded lie superalgebras abstract the grigorchuk and gupta sidki groups play fundamental role in modern group theory they are natural examples of self similar finitely generated periodic groups the author constructed their analogue in case of restricted lie algebras of characteristic 2 31 shestakov and zelmanov extended this construction to an arbitrary positive characteristic 41 thus we have examples of self similar finitely generated restricted lie algebras with a nil p mapping in characteristic zero similar examples of lie algebras do not exist by a result of martinez and zelmanov 27 the goal of the present paper is to construct analogues of the grigorchuk and gupta sidki groups in the world of lie superalgebras of an arbitrary characteristic we construct two examples r q of finitely generated self similar lie superalgebras over a field k of an arbitrary characteristic and study their properties and properties of their associative hulls in case char k 2 these examples turn into restricted lie algebras the virtue of the present construction is that the lie superalgebras have clear monomial bases these lie superalgebras have slow polynomial growth and are multigraded by multidegree in the generators the lie superalgebra r is z 2 graded while q has a multidegree z 3 gradation and a z 2 gradation both algebras r and q have similar constructions computations for r are simpler but q enjoys some more specific interesting properties the z 3 components of q lie inside an elliptic paraboloid in space they are at most one dimensional thus the z 3 grading of q is fine in the z 2 gradation of q all components q n m n m z are infinite dimensional except for q 00 0 the z 2 gradation also yields a continuum of different decompositions into a direct sum of two locally nilpotent subalgebras q q q in both examples ad a is nilpotent a being even or odd with respect to the z 2 grading as lie superalgebras this property is an analogue of the periodicity of the grigorchuk and gupta sidki groups in particular q is a nil finely graded lie superalgebra which shows that an extension of a theorem due to martinez and zelmanov 27 for the lie superalgebras of characteristic zero is not valid both lie superalgebras are self similar contain infinitely many copies of themselves let us also call them fractal due to this property

inverse problem with beamforming regularization matrix applied to sound source localization in closed wind tunnel using microphone array abstract microphone arrays have become a standard technique to localize and quantify source in aeroacoustics the simplest approach is the beamforming that provides noise source maps with large main lobe and strong side lobes at low frequency since a decade the focus is set on deconvolution techniques such as damas or clean sc while the source map is clearly improved these methods require a large computation time in this paper we propose a sound source localization technique based on an inverse problem with beamforming regularization matrix called hybrid method with synthetic data we show that the side lobes are removed and the main lobe is narrower moreover if the sound noise source map provided by this method is used as input in the damas process the number of damas iterations is highly reduced the hybrid method is applied to experimental data obtained in a closed wind tunnel in both cases of acoustic or aeroacoustic data the source is correctly detected the proposed hybrid method is found simple to implement and the computation time is low if the number of scan points is reasonable

irreducible finite dimensional representations of equivariant map algebras suppose a finite group acts on a scheme x and a finite dimensional lie algebra g the corresponding equivariant map algebra is the lie algebra m of equivariant regular maps from x to g we classify the irreducible finite dimensional representations of these algebras in particu lar we show that all such representations are tensor products of evaluation representations and one dimensional representations and we establish conditions ensuring that they are all evaluation representations for example this is always the case if m is perfect our results can be applied to multiloop algebras current algebras the onsager algebra and the tetrahedron algebra doing so we easily recover the known classifications of irreducible finite dimensional representations of these algebras moreover we obtain previously unknown classifica tions of irreducible finite dimensional representations of other types of equivariant map algebras such as the generalized onsager algebra

the relationship of singular value decomposition to wave vector filtering in sound radiation problems singular value decomposition svd has recently been suggested as a filtering tool to analyze acoustic radiation the relationship between this filtering technique and the more familiar wave vector filtering is examined for a geometry with a preferred axis the source modes are found to consist approximately of a single wave number and the accompanying radiation modes are thus beams some simple examples are worked out to illustrate the general behavior of the filtering and some of the properties of the beams are given

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

modeling of nonlinear ultrasound propagation in tissue from array transducers a computationally efficient model capable of simulating finite amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described it is based on a second order operator splitting approach tavakkoli et al j acoust soc am 104 2061 2072 1998 with a fractional step marching scheme whereby the effects of diffraction attenuation and nonlinearity can be computed independently over incremental steps this approach is an extension to that of christopher and parker j acoust soc am 90 507 521 90 488 499 1991 wherein linear and nonlinear effects are propagated separately over incremental steps and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources results of the model are compared with published data predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented

a global version of grozman s theorem let x be a manifold the classification of all equivariant bilinear maps between tensor density modules over x has been investigated by grozman funct anal appl 14 2 58 59 1980 who has provided a full classification for those which are differential operators here we investigate the same question without the hypothesis that the maps are differential operators in our paper the geometric context is algebraic geometry and the manifold x is the circle text spec mathbb c z z 1 our main motivation comes from the fact that such a classification is required to complete the proof of the main result of iohara and mathieu proc lond math soc 2012 in press indeed it requires to also include the case of deformations of tensor density modules

a new class of unitary representations for affine lie algebras on considere la construction de representations irreductibles unitarisables pour des algebres de lie affines on construit des representations pour des algebres de lie affines qui sont unitarisables par rapport a une forme venant d une algebre de lie de dimension finie

sound equalization in enclosures using modal reconstruction the equalization of complex sound pressure in an enclosure is investigated in this paper the sound field in the enclosure is modeled with the sum of a series of modes this sound field is controlled by multiple sources distributed in the enclosure so that a certain region in the enclosure has a desired complex sound pressure first the optimum solution which minimizes the average potential energy of the error pressure over the region is derived where the error is defined as the difference between the desired sound pressure and the sound pressure caused by the sources by using the optimum solution the achievable best performance can be known for the given region and the source distribution the optimum solution can also be a useful tool for finding an effective source distribution since the performance of the optimum solution depends only on the source distribution furthermore the eigenvalues of the source coupling matrix which appears in the derivation of the optimum solution indicates the effectiveness of the source distribution the effectiveness of source distribution is discussed with nine examples of source distributions in a two dimensional enclosure the multipoint equalization method to approximate the optimum solution is also discussed for the practical use

finite weight modules over twisted affine lie superalgebras abstract this work provides the first step toward the classification of irreducible finite weight modules over twisted affine lie superalgebras we divide the class of such modules into two subclasses called hybrid and tight we reduce the classification of hybrid irreducible finite weight modules to the classification of cuspidal modules of finite dimensional cuspidal lie superalgebras which is discussed in a work of dimitrov mathieu and penkov

whittaker modules for heisenberg algebras and imaginary whittaker modules for affine lie algebras abstract we classify the irreducible whittaker modules for finite and infinite dimensional heisenberg algebras and for the lie algebra obtained by adjoining a degree derivation to an infinite dimensional heisenberg algebra we use these modules to construct a new class of modules for non twisted affine lie algebras which we call imaginary whittaker modules we show that the imaginary whittaker modules of non zero level are irreducible

integrable representations for toroidal extended affine lie algebras abstract let g be any untwisted affine kac moody algebra any fixed complex number and g the corresponding toroidal extended affine lie algebra of nullity two for any k tuple 1 k of weights of g and k tuple a a 1 a k of distinct non zero complex numbers we construct a class of modules v a for the extended affine lie algebra g we prove that the g module v a is completely reducible we also prove that the g module v a is integrable when all weights i in are dominant thus we obtain a new class of irreducible integrable weight modules for the toroidal extended affine lie algebra g

on the variation and invertibility of room impulse response functions this paper presents results concerning variations in impulse response functions measured in different rooms the variation of these functions for changing source and receiver positions and orientation was examined by assessing the change in energies of the direct and reflected signal components the various source receiver positions and orientation examined during these tests correspond to typical positions occupied by human speakers in rooms it was found that the response functions changed drastically with the variation of these recording parameters the feasibility of inverting deconvolving such functions by using digital signal processing techniques was also examined it was found that when the exact response function was employed then such an operation was feasible leading to enhancement and reduction in the reverberant energy present in signals e g speech recorded under similar conditions however when a response recorded at a different position in the same enclosure was employed then in general the inverse filtering operation increased the distortions present in the signals this indicates that signal dereverberation by impulse response deconvolution has a limited scope in most practical situations

transducer sensitivity compensation using diagonal preconditioning for time reversal and tikhonov inverse filtering in acoustic systems filters are commonly used in sound reproduction and communication systems as a means of compensating for the response of the electro acoustic plant two commonly used filter designs in the field of acoustics are the time reversal filter and the tikhonov inverse filter in this paper the influence of transducer sensitivities on the performance of these filters is examined it is shown that the sensitivity of the transducers can negatively affect the performance of the resulting filter to compensate for the decrease in performance diagonal preconditioning can be implemented in the system it is shown that by using diagonal matrices which minimize the condition number of the system the loss in performance arising from unbalanced sensitivities is minimized this paper proposes an algorithm to find such a set of diagonal matrices and results are presented showing the improvements in performance arising from the modified filter design

inverse filtering of room acoustics a novel method is proposed for realizing exact inverse filtering of acoustic impulse responses in room this method is based on the principle called the multiple input output inverse theorem mint the inverse is constructed from multiple finite impulse response fir filters transversal filters by adding some extra acoustic signal transmission channels produced by multiple loudspeakers or microphones the coefficients of these fir filters can be computed by the well known rules of matrix algebra inverse filtering in a sound field is investigated experimentally it is shown that the proposed method is greatly superior to previous methods that use only one acoustic signal transmission channel the results prove the possibility of sound reproduction and sound reception without any distortion caused by reflected sounds

acoustical inverse problems regularization direct definition of filter factors using signal to noise ratio abstract acoustic imaging aims at localization and characterization of sound sources using microphone arrays in this paper a new regularization method for acoustic imaging by inverse approach is proposed the method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors in place of regularization using classical methods such as truncated singular value decomposition and tikhonov regularization the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation defined from the estimated measurement noise the thresholding operation is achieved using modified filter functions the originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the tikhonov filter this has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems theoretical results show that this method is comparatively more accurate than tikhonov regularization and truncated singular value decomposition

a study of the failure of numerical solutions in boundary element analysis of acoustic radiation problems abstract in the numerical implementation of the boundary element method to exterior acoustic problems the approximating equations give incorrect results for the surface pressure when the frequency is in the neighbourhood of some critical values in previous papers this failure has been attributed to ill conditioning problems which prevail as the singularity is approached but issues such as whether the coefficient matrix will become singular or whether one will obtain good results when the effects of ill conditioning can be annihilated have not been discussed this paper presents a discussion of these questions numerical results for two dimensional sound radiation from a radially vibrating infinite cylinder show that the problem encountered in the vicinity of the critical frequencies is not basically an ill conditioning problem and that the coefficient matrix does not become singular for a finite number of boundary elements

a method for computing acoustic fields based on the principle of wave superposition a method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition the superposition integral which is shown to be equivalent to the helmholtz integral is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator the strengths of the sources that produce this condition can in turn be used to compute the corresponding surface pressures the results of several numerical experiments are presented that demonstrate the simplicity of the method also the advantages that the superposition method has over the more commonly used boundary element methods are discussed these include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary element formulation

on the polynomial representations of current algebras abstract we obtain a sufficient condition for a representation of a lie algebra of the form l g where g is a finite dimensional simple lie algebra over an algebraically closed field f of zero characteristic and is an associative commutative algebra over f to be polynomial as a corollary we classify integrable graded irreducible modules over an extended loop algebra with finite dimensional homogeneous spaces the criteria is applied also to irreducible conformal modules over current algebras

estimation of acoustic source strength by inverse methods part ii experimental investigation of methods for choosing regularization parameters two regularization methods tikhonov regularization and singular value discarding are used to improve the accuracy of reconstruction of acoustic source strength by inverse techniques in this paper some methods are investigated for choosing the tikhonov regularization parameter and the singular values to be discarded of these we concentrate on the use of ordinary cross validation and generalized cross validation these methods can provide an appropriate regularization parameter without prior knowledge of either the acoustic source strength or the contaminating measurement noise some experimental results obtained using a randomly vibrating simply supported plate mounted in a baffle are presented to illustrate the performance of the methods for choosing the regularization parameters

regularization in global sound equalization based on effort variation sound equalization in closed spaces can be significantly improved by generating propagating waves that are naturally associated with the geometry as for example plane waves in rectangular enclosures this paper presents a control approach termed effort variation regularization based on this idea effort variation equalization involves modifying the conventional cost function in sound equalization which is based on minimizing least squares reproduction errors by adding a term that is proportional to the squared deviations between complex source strengths calculated independently for the sources at each of the two walls perpendicular to the direction of propagation simulation results in a two dimensional room of irregular shape and in a rectangular room with sources randomly distributed on two opposite walls demonstrate that the proposed technique leads to smaller global reproduction errors and better equalization performance at listening positions outside of the control region compared to effort regularization and compared to a simple technique that involves driving groups of sources identically

classification of simple lie algebras on a lattice let z for some n 1 the aim of the paper is to classify all simple graded lie algebras l l such that diml 1 for all the classification involves two affine lie algebras namely a 1 1 and a 2 2 and a familly w parametrized by a dense open set of the space of all embeddings c the family wl of generalized witt algebras indexed by all embeddings l c appears as a sub family in general the algebras w are described as lie algebras of symbols of twisted pseudo differential operators

beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array for sound field reproduction using multichannel spatial sound systems such as wave field synthesis and ambisonics sound field extrapolation is a useful tool for the measurement description and characterization of a sound environment to be reproduced in a listening area in this paper the inverse problem theory is adapted to sound field extrapolation around a microphone array for further spatial sound and sound environment reproduction a general review of inverse problem theory and analysis tools is given and used for the comparative evaluation of various microphone array configurations classical direct regularization methods such as truncated singular value decomposition and tikhonov regularization are recalled on the basis of the reviewed background a new regularization method adapted to the problem at hand is introduced this method involves the use of an a priori beamforming measurement to define a data dependent discrete smoothing norm for the regularization of the inverse problem this method which represents the main contribution of this paper shows promising results and opens new research avenues

comparison of methods for parameter selection in tikhonov regularization with application to inverse force determination in performing transfer path analysis of structure borne sound transmission the operational forces at the excitation points and or at the connections within the structure borne paths are required these forces can be obtained by using inverse techniques but the measured data used will contain some unknown errors therefore the reconstructed forces may include large errors due to the inversion of an ill conditioned matrix of these measured data in this study tikhonov regularization is used in order to improve the conditioning of the matrix inversion several methods are available to select the optimal regularization parameter the purpose of this paper is to compare the performance of the ordinary and generalized cross validation methods and the l curve criterion simulations are carried out representing measurements on a rectangular plate for different noise levels in measured data also the robustness of the conclusions is investigated by varying the shape of the plates the force positions and the noise levels included in the measured data the l curve method is found to perform better than ocv or gcv particularly for high noise levels in the operational responses but less well when these noise levels are low it is therefore found to be less susceptible to producing large reconstruction errors but it tends to over regularize the solution in the presence of low noise leading to under estimates of the forces in practice measurements of operational responses may be susceptible to noise contamination which suggests that the l curve method is likely to be the most appropriate method in practical situations nevertheless it is important to obtain good estimates of the likely noise in the signals before determining the most appropriate regularization technique ordinary cross validation method is generally found to have a better performance than generalized cross validation method if the matrix condition numbers are high since the need for regularization is greater with high condition numbers it is consequently found that the ordinary cross validation method gives more reliable results overall than the generalized cross validation method

l1 generalized inverse beam forming algorithm resolving coherent incoherent distributed and multipole sources abstract to resolve coherent incoherent distributed compact and multipole aerodynamic sound sources with phased array pressure data a new source detection algorithm is developed based on l1 generalized inverse techniques to extract each coherent signal a cross spectral matrix is decomposed into eigenmodes subsequently the complex source amplitude distribution that recovers each eigenmode is solved using generalized inverse techniques with reference solutions which include multipoles as well as a monopole namely the source distribution consisting of pre defined source types is solved as an l1 norm problem using iteratively re weighted least squares irls the capabilities of the proposed algorithm are demonstrated using various benchmark problems to compare the results with several existing beam forming algorithms and it is found that distributed sources as well as dipoles with arbitrary orientation can be identified regardless of coherency with another source the resolution is comparable to existing deconvolution techniques such as damas or clean and the computational cost is only several times more than that of damas2 the proposed algorithm is also examined using previous model scale test data taken in an open jet wind tunnel for a study on jet flap interaction and some indication of dipole radiation is discerned near the flap edge

classification of the indecomposable bounded admissible modules over the virasoro lie algebra with weightspaces of dimension not exceeding two in view of 1 2 any bounded admissible modulea over the virasoro lie algebra open image in new window is a finite length extension of irreducible modules with one dimensional weightspaces to each extension of finite lengthn are associatedn 1 invariants a1 1 n we prove that we have i j 0 1 6 n 1b for all i j with 1 i j n in the casen 2 this result allows us to construct all the indecomposable bounded admissible open image in new window modules where the dimensions of the weightspaces are less than or equal to two in particular we obtain all the extensions of two irreducible bounded open image in new window modules