statistical errors in acoustic intensity measurements abstract a bivariate stochastic process is used to evaluate sources of error in acoustic intensity measurements three acoustic intensity estimators are examined for both bias and random errors all three acoustic intensity estimators are shown to be biased by the presence of a second uncorrelated acoustic source it is further shown that the presence of phase errors introduces additional bias which may limit the accuracy at low frequency an expression is derived for the normalized standard error of the acoustic intensity estimates the normalized standard error is a strong function of the coherence function and the phase angle spectrum with maximum error occurring at low frequency and low coherence further interpretation of the normalized standard error is given by using two monopole acoustic sources as components in the bivariate process

parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences we show that a linear partial differential operator with constant coefficients p d is surjective on the space of e valued ultra distributions over an arbitrary convex set if e is a nuclear frechet space with property dn in particular this holds if e is isomorphic to the space of tempered distributions s or to the space of germs of holomorphic functions over a one point set h 0 this result has an interpretation in terms of solving the scalar equation p d u f such that the solution u depends on parameter whenever the right hand side f also depends on the parameter in the same way a suitable analogue for surjective convolution operators over rd is obtained as well to get the above results we develop a splitting theory for short exact sequences of the form 0 x y z 0 where z is a frechet schwartz space and x y are pls spaces like the spaces of distributions or real analytic functions or their subspaces in particular an extension of the dn splitting theorem of vogt and wagner is obtained

convolutions transforms and convex bodies the paper studies convex bodies and star bodies in bbb r n by using radon transforms on grassmann manifolds p cosine transforms on the unit sphere and convolutions on the rotation group of bbb r n it presents dual mixed volume characterizations of i intersection bodies and l p balls which are related to certain volume inequalities for cross sections of convex bodies it considers approximations of special convex bodies by analytic bodies and various finite sums of ellipsoids which preserve special geometric properties convolution techniques are used to derive formulas for mixed volumes mixed surface measures and p cosine transforms they are also used to prove characterizations of geometric functionals such as surface area and dual quermassintegrals

a separable frechet space of almost universal disposition abstract the gurari space is the unique separable banach space g which is of almost universal disposition for finite dimensional banach spaces which means that for every e 0 for all finite dimensional normed spaces e f for every isometric embedding e e g there exists an e isometric embedding f f g such that f e e we show that g n with a special sequence of semi norms is of almost universal disposition for finite dimensional graded frechet spaces the construction relies heavily on the universal operator on the gurari space recently constructed by garbulinska wegrzyn and the third author in addition we consider a non graded sequence of semi norms on g n with which the space g n is of almost universal disposition for finite dimensional frechet spaces with a fixed sequence of semi norms in both cases this yields in particular that g n is universal in the class of all separable frechet spaces

error analysis of two microphone measurements in ducts with flow in an earlier work h boden and m abom j acoust soc am 79 541 549 1986 the influence of errors on two microphone measurements in ducts without flow has been studied the aim of this article is mainly to extend the earlier work to include the effects of mean flow and also of attenuation during the sound propagation first a short review of the various existing two microphone methods is made the errors in the measured input data are then analyzed and special attention is paid to the effects of neglected attenuation nonideal microphones and flow noise the influence of errors on the calculated quantities has been investigated and the conclusions from the earlier work have been extended to the case with flow it is also shown that the neglect of attenuation between the microphones leads to a low frequency limit for the applicability of the two microphone method finally a new technique for measuring the mach number using a two microphone method is suggested

splitting of exact sequences of frechet spaces in the absence of continuous norms abstract in the present paper we study the splitting of a short exact sequence 0 g e s f 0 of nuclear frechet spaces where f need not admit a continuous norm i e e or f may be spaces of continuous functions on an open subset of r n or on a compact c manifold if e is such a space then we give a necessary and sufficient condition for the splitting of the sequence in terms of a condition on s and of linear topological invariants loc and dnloc this is used to give a structure theory of the space s n a space which is isomorphic to many spaces of smooth functions and to study the splitting of differential complexes the paper offers a different approach to problems which have been studied in domanski vogt j funct anal 153 1998 203

the practical assessment of errors in sound intensity measurement abstract many sources of error in two transducer sound intensity measurements have been discussed in the literature many of these errors are difficult to assess in a practical situation but two in particular can be calculated these are the error associated with phase mis match and random error the use of the known phase mis match is discussed as regards its use in evaluating the quality of a particular measurement and the use of coherence is discussed as regards its use in calculating random error

on the statistical distributions of active intensity directions abstract pressure and pressure differences measured using closely spaced microphone pairs enable the calculation of active intensity directions these directions are exploited in various applications such as acoustical analysis and modelling multichannel audio systems source localization and real time blind source separation despite their widespread usage the distribution of the active intensity directions in the presence of interference has not been investigated before except for the diffuse sound field case for which the distribution becomes uniform in this paper the interference problem has been formulated using the pressure and pressure differences algebra of random variables fractional linear transformations and brownian motion have been used for the exposition of the model distributions it is shown that the distribution is wrapped cauchy for a single sound source in the presence of independent interference in an anechoic chamber in a direct plus diffuse sound field the distribution is offset cauchy for a nonstationary target source and von mises for the special case of a stationary target source related to the brownian motion in the presence of multiple independent sound sources the distribution can be modeled as mixtures of circular cauchy distributions and a uniform distribution

random errors in sound power determination based on intensity measurement abstract two measurement procedures are in common use in sound power determination with the intensity technique sampling at discrete points and continuous scanning in both cases the resulting estimates are subject to random errors associated with the finite averaging time a discussion of the random errors of sound power estimates determined with the two procedures is presented and it is shown that the errors and accordingly statistical confidence intervals can be determined while the measurements are being made

expression for the estimation of time averaged acoustic energy density using the two microphone method l acoustic energy density has been shown to exhibit lower spatial variance in reactive sound fields compared to the acoustic potential energy estimate offered by microphones making it a very useful measure of the acoustic energy within an enclosure previously frequency domain time averaged energy density estimates have come about by estimating the pressure average and particle velocity between two closely spaced microphones using either analog or digital electronics a frequency domain expression can be obtained by adding the weighted sum of the auto spectral densities of both the pressure and particle velocity magnitude the purpose of this letter is to derive an expression for the time averaged acoustic energy density in the frequency domain using the auto and cross spectral densities between the two closely spaced microphones the resulting expression is validated numerically

random errors in sound intensity estimation abstract the use of measured coherence functions in predicting the random errors of sound intensity estimates is discussed the existing theory is re examined it is shown that the well known expressions can be misleading and are of little use in some situations an alternative expression for the random errors of frequency band estimates of sound intensity is derived this expression is examined theoretically and experimentally the expression is verified but it turns out that it can be rather time consuming to predict the random error reliably under extreme conditions because of random errors in the predicted error itself

acoustic power measurement for single and annular stream duct nozzle systems utilizing a modal decomposition scheme a refined acoustic impulse technique developed recently at lockheed georgia company 1 2 was used to evaluate the adequacy of single point in duct pressure measurements for determining the acoustic power for incident reflected and transmitted fields for single and annular stream duct nozzle systems at various flow conditions the spatial distributions of incident and reflected pressure fields were measured at several radial and azimuthal locations inside the duct a modal decomposition scheme developed for this purpose was used to derive the acoustic power of each duct mode from the complex pressure measurements the total sums of these individual modal acoustic powers were compared with the area weighted acoustic power distributions that were evaluated from measured pressure data it was found that a single point measurement near the duct wall is adequate for estimating the transmitted power for both single and annular stream duct nozzle systems the in duct incident reflected and transmitted powers computed from the sum of the plane and higher order modes agrees well with corresponding powers derived from the area weighted pressures

a positive answer to the busemann petty problem in three dimensions we prove that in e3 the busemann petty problem concerning cen tral sections of centrally symmetric convex bodies has a positive answer together with other results this settles the problem in each dimension

quasi banach spaces of almost universal disposition we show that for each p 0 1 p 0 1 there exists a separable p banach space gpgp of almost universal disposition that is having the following extension property for each e 0e 0 and each isometric embedding g x yg x y where y is a finite dimensional p banach space and x is a subspace of gpgp there is an e isometry f y gpf y gp such that x f g x x f g x for all x xx x such a space is unique up to isometries does contain an isometric copy of each separable p banach space and has the remarkable property of being locally injective amongst p banach spaces we also present a nonseparable generalization which is of universal disposition for separable spaces and separably injective no separably injective p banach space was previously known for p 1p 1

determination of energy density in ducts by a three microphone phaseless method and estimation of measurement uncertainties a new method to measure the total energy density of waves traveling in opposite directions in ducts is suggested in order to completely eliminate phase errors that lead to bias errors and are difficult to control in industrial tests only the auto power spectral densities are measured by the three microphones the inversion of a linear system based on a propagation model where the two opposite waves are partially coherent makes it possible to obtain the energy density the sensitivity of this method to errors in the speed of sound errors of microphone calibration and errors of microphone positions in the duct is analyzed to complete the study on the robustness of the method an evaluation of the statistical errors is carried out the total uncertainty is used to make recommendations on the choice of the experimental parameters the selection of the frequency limits permits to maintain the measurement uncertainty within a given confidence interval

the lp busemann petty centroid inequality abstract the ratio between the volume of the p centroid body of a convex body k in r n and the volume of k attains its minimum value if and only if k is an origin symmetric ellipsoid this result the lp busemann petty centroid inequality was recently proved by lutwak yang and zhang in this paper we show that all the intrinsic volumes of the p centroid body of k are convex functions of a time like parameter when k is moved by shifting all the chords parallel to a fixed direction the lp busemann petty centroid inequality is a consequence of this general fact

brunn minkowski inequality for mixed intersection bodies abstract dual of the brunn minkowski inequality for mixed projection bodies are established for mixed intersection bodies

regularity of solutions of convolution equations this paper investigates the regularity of solutions of convolution equations in the frame of classes of ultradifferentiable functions and ultradistributions we improve previous work by bonet chou fernandez galbis meise and others

the brunn minkowski inequality in 1978 osserman 124 wrote an extensive survey on the isoperimetric inequality the brunn minkowski inequality can be proved in a page yet quickly yields the classical isoperimetric inequality for important classes of subsets of rn and deserves to be better known this guide explains the relationship between the brunn minkowski inequality and other inequalities in geometry and analysis and some applications

intersection bodies and dual mixed volumes the setting for this article is euclidean n space ky n 2 let x denote the set of convex bodies compact convex subsets with nonempty interiors in r and let x denote the subset of x that contains the centered centrally symmetric with respect to the origin bodies for ue s let e denote the hyperplane through the origin that is orthogonal to u and let ki e denote the image of the orthogonal projection of the body ke x onto e we shall use v to denote i dimensional lebesgue measure for v and v we shall usually write v and u shephard 38 poses the question if k l e xe and

frequency domain expressions for the estimation of time averaged acoustic energy density this paper builds on earlier work by the same authors to derive expressions for the time averaged acoustic energy density in the frequency domain using the auto and cross spectral densities of multiple microphone elements expressions for the most common three dimensional geometric arrangements are derived simplified expressions for use with two channel spectrum analysers are also presented

statistical errors in the estimation of time averaged acoustic energy density using the two microphone method time averaged acoustic energy density can be estimated using the auto and cross spectral densities between two closely spaced microphones in this paper an analysis of the random errors that arise using two microphone measurements is undertaken an expression for the normalized random error of the time averaged acoustic energy density spectral density estimate is derived this expression is verified numerically the lower and upper bounds of the normalized random error are derived it is shown that the normalized random error of the estimate is not a strong function of the sound field properties and is chiefly dependent on the number of records averaged

a splitting theorem for the space of smooth functions we will show using purely linear functional analytic methods that each exact complex0 f c s0 p0 c s1 p1 c s2 p2 wherepiare matrices of convolution operators in particular linear differential operators with constant coefficients splits fromp1on in the category of topological vector spaces moreover we characterize when these complexes split completely the obtained result covers all known particular cases as well as some more general cases independently of the analytic nature ofpi the result is a consequence of studying splitting of short exact sequences0 f jx qg 0 wheref x gare graded frechet spaces i e frechet spaces equipped with fixed reduced spectra representing them andj qare consistent with the graded structures we characterize splitting of in case i forgare spacesc where is an open subset in rn or ii gis the space of all sequences

uncertainty analysis of the two microphone method accurate duct acoustic propagation models are required to characterize and subsequently reduce aircraft engine noise the boundary conditions for these models ultimately rely on accurate measurements of the acoustic impedance for candidate nacelle liners the standard two microphone method is widely used to estimate acoustic impedance but does not provide uncertainty estimates that are essential for data quality assessment and model validation a systematic framework is presented in this paper to propagate the experimental 95 confidence interval uncertainty estimates in the measured quantities to the calculated acoustic impedance data using the two microphone method for small and large input uncertainties one method is an analytical small perturbation technique using multivariate statistics this method provides useful analytical scaling information a second monte carlo method is utilized to validate the analytical multivariate method both methods are applied to the two microphone method for simulated data representative of sound hard and sound soft acoustic materials the results indicate that for realistic experimental parameters the uncertainty in the input measurements results in nonlinear perturbations therefore the small perturbation technique fails and the monte carlo method should be used to obtain uncertainty estimates furthermore the nonlinear perturbations also distort the output statistical distributions of the calculated acoustic impedance and reflection coefficient which results in significant deviation from gaussian behavior the distortion is a function of the acoustic impedance of the specimen itself finally the monte carlo method is applied to experimental data for a ceramic tubular specimen and compared to the multivariate results to demonstrate the implementation and usefulness of the technique

lp affine isoperimetric inequalities the lp analogues of the petty projection inequality and the busemannpetty centroid inequality are established an affine isoperimetric inequality compares two functionals associated with convex or more general bodies where the ratio of the functionals is invariant under non degenerate linear transformations these isoperimetric inequalities are more powerful than their better known euclidean relatives

splitting of closed ideals in algebras of entire functions and the property for a plurisubharmonic weight function p on cn let ap cn denote the dfn algebra of all entire functions on cn which do not grow faster than a power of exp p we prove that the splitting of many finitely generated closed ideals of a certain type in ap cn the splitting of a weighted 0 complex related with p and the linear topological invariant dn of the strong dual of ap cn are equivalent moreover we show that these equivalences can be characterized by convexity properties of p phrased in terms of greatest plurisubharmonic minorants for radial weight functions p this characterization reduces to a covexity property of the inverse of p using these criteria we present a wide range of examples of weights p for which the equivalences stated above hold and also where they fail for p a nonnegative plurisubharmonic psh function on cn let ap cn denote the algebra of all entire functions f such that if z l 0 depending on f algebras of this type arise at various places in complex analysis and functional analysis e g as fourier transforms of certain convolution algebras the structure of their closed ideals has been studied for a long time primarily in the work of schwartz 25 ehrenpreis 9 malgrange 17 and palamodov 23 in connection with the existence and approximation of systems of convolution equations the question whether a certain parameter dependence of the right hand side of such an equation is shared also by its solutions is closely related with the question of the existence of a continuous linear right inverse the existence of such a right inverse is equivalent to the splitting of the closed ideal i associated to the corresponding equation also since the quotient space ap cn i is quite often identified with the space ap v of holomorphic functions on the variety v of i which satisfy the restricted growth conditions the latter question is equivalent to the existence of a linear extension operator from ap v to ap cn answers to these questions for various algebras have been given e g by grothendieck see lveves 28 cohoon 7 djakov and mityagin 8 and vogt 33 the fact that for p z izl8 s 1 all closed ideals in ap c are cornplemented was observed by taylor 27 then meise 19 extended taylor s resultsx using a more functional analytic approach he showed that the structural property dn of the strong dual ap cn b of ap cn implies that all slowly decreasing ideals received by the editors july 29 1986 1980 mathematics subject classification 1985 reon primary 32e25 46e25 secondary 46a12 32al