an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

cored hypergraphs power hypergraphs and their laplacian h eigenvalues abstract in this paper we introduce the class of cored hypergraphs and power hypergraphs and investigate the properties of their laplacian h eigenvalues from an ordinary graph one may generate a k uniform hypergraph called the kth power hypergraph of that graph power hypergraphs are cored hypergraphs but not vice versa sunflowers loose paths and loose cycles are power hypergraphs while squids generalized loose s paths and loose s cycles for 2 s k 2 are cored hypergraphs but not power graphs in general we show that the largest laplacian h eigenvalue of an even uniform cored hypergraph is equal to its largest signless laplacian h eigenvalue especially we find out these largest h eigenvalues for even uniform squids moreover we show that the largest laplacian h eigenvalue of an odd uniform squid loose path and loose cycle is equal to the maximum degree i e 2 we also compute the laplacian h spectra of the class of sunflowers when k is odd the laplacian h spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well

a three dimensional boundary element scheme for acoustic radiation in low mach number flows a boundary element scheme is proposed for acoustical radiation in moving flows the scheme relies upon a transformation valid at low mach numbers which permits the case with flow to be restated as an equivalent problem in the absence of flow but with modified boundary conditions this restatement of the original problem is then amenable to boundary integral representation and boundary element solution results obtained by using this approach are presented for the test case of a pulsating or juddering sphere of finite dimensions in a uniform low mach number flow a fully three dimensional boundary element model is used the validity of the results is established by comparison with an analytic perturbation solution where applicable and by comparison with results from an alternative axisymmetric numerical scheme

on tests against one sided hypotheses in some generalized linear models one sided hypotheses arise naturally in many situations when testing against such hypotheses it is desirable to take the available one sided information into account rather than simply applying a two sided test what we expect to gain by applying a one sided test instead of a two sided test is an increase in the power of the test we consider various tests of one sided hypotheses in a class of models that includes generalized linear and cox regression models the tests are likelihood ratio wald score generalized distance and a pearson chi square it is shown that these test statistics are asymptomatically equivalent in terms of local power this is a generalization of the well known corresponding result for two sided alternatives two examples are also discussed they are on 1 testing for interaction in binomial response models and 2 comparison of treatments with ordinal categorical responses

computation of acoustic propagation in two dimensional sheared ducted flows most aeroacoustic noise prediction methods rely on an acoustic analogy featuring a propagation equation associated with source terms these models were mainly applied to computation of acoustic far fields radiated by simple free flows like jets the assumption is made in many formulations that the radiated acoustic field is not perturbed by the shear flow giving rise to the noise sources these acoustic analogies thus do not provide a full description of acoustic flow interactions the lilley equation was introduced to account to a certain extent for mean shear effects on propagation more recently this problem has been treated by making use of the linearized euler equations which are more flexible and more adequate for numerical simulations as several types of modes are supported by the euler equations problems linked to their coupling have to be considered it is then necessary to investigate acoustic field computations in complex flows our aim in the present article is to validate the wave operator associated with linearized euler equations numerical tests deal with propagation in two dimensional sheared ducted flows results are compared with other solutions deduced from analytical developments and direct numerical simulations this study shows that the linearized euler operator may be used to account for mean effects on wave propagation in the presence of sheared ducted flows processes that are specifically considered are 1 convection effects on axial disturbances 2 refraction effects on oblique wave generation and 3 source radiation effects on propagation in sheared flows

on bootstrap inconsistency and bonferroni based size correction for the subset anderson rubin test under conditional homoskedasticity abstract we focus on the linear instrumental variable model with two endogenous regressors under conditional homoskedasticity and study the subset anderson and rubin 1949 ar test when the nuisance structural parameter the unrestricted slope coefficient of endogenous regressor may be weakly identified weak identification leads to nonstandard null limiting distributions and alternative to the usual chi squared critical value is needed we first investigate the bootstrap validity for the subset ar test based on various plug in estimators and show that the bootstrap provides asymptotic refinement when the nuisance structural parameter is strongly identified but is inconsistent when it is weakly identified this is in contrast to the result of bootstrap validity in moreira et al 2009 then we propose a bonferroni based size correction method that yields correct asymptotic size for all the test statistics considered the power performance of size corrected tests can be further improved by applying the mapping between structural and endogenous parameters in the model monte carlo experiments confirm the bootstrap inconsistency and demonstrate that all the subset tests based on our correction technique control the size

a practical two step method for testing moment inequalities this paper considers the problem of testing a finite number of moment inequalities we propose a two step approach in the first step a confidence region for the moments is constructed in the second step this set is used to provide information about which moments are negative a bonferonni type correction is used to account for the fact that with some probability the moments may not lie in the confidence region it is shown that the test controls size uniformly over a large class of distributions for the observed data an important feature of the proposal is that it remains computationally feasible even when the number of moments is large the finite sample properties of the procedure are examined via a simulation study which demonstrates among other things that the proposal remains competitive with existing procedures while being computationally more attractive

asymptotic performance analysis of bayesian target recognition this article investigates the asymptotic performance of bayesian target recognition algorithms using deformable template representations rigid computer aided design cad models represent the underlying targets low dimensional matrix lie groups rotation and translation extend them to particular instances remote sensors observing the targets are modeled as projective transformations converting three dimensional scenes into random images bayesian target recognition corresponds to hypothesis selection in the presence of nuisance parameters its performance is quantified as the bayes error analytical expressions for this error probability in small noise situations are derived yielding asymptotic error rates for exponential error probability decay

design and analysis of group sequential tests based on the type i error spending rate function summary lan demets 1983 devised a method of constructing discrete group sequential boundaries by using the type i error spending rate function it is extended so as to generate asymmetric as well as symmetric two sided boundaries for clinical trials the design aspect of this procedure is explored in terms of the maximum sample size needed to achieve a desired level of power and the expected stopping times under both null and alternative hypotheses finally these properties are employed in search of appropriate type i error spending rate functions for differing situations

the largest laplacian and signless laplacian h eigenvalues of a uniform hypergraph a b s t r a c t in this paper we show that the largest laplacian h eigen value of a k uniform nontrivial hypergraph is strictly larger than the maximum degree when k is even a tight lower bound for this eigenvalue is given for a connected even uniform hypergraph this lower bound is achieved if and only if it is a hyperstar however when k is odd in certain cases the largest laplacian h eigenvalue is equal to the maximum degree which is a tight lower bound on the other hand tight upper and lower bounds for the largest signless laplacian h eigenvalue of a k uniform connected hypergraph are given for connected k uniform hypergraphs of fixed number of vertices respectively fixed maximum degree the upper respectively lower bound of their largest signless laplacian h eigenvalues is achieved exactly for the complete hypergraph respectively the hyperstar the largest laplacian h eigenvalue is always less than or equal to the

finite element method to study harmonic aeroacoustics problems the analysis of aeroacoustics propagation is required to solve many practical problems as an alternative to euler s linearized equations an equation was established by galbrun in 1931 it assumes the flow verifies euler s equations and the perturbation is small and adiabatic it is a linear second order vectorial equation based on the displacement galbrun s equation derives from a lagrangian density and provides conservative expressions of the aeroacoustics intensity and energy density a caa method dealing with the numerical resolution of galbrun s equation using the finite element method fem is presented the exact solution for the propagation of acoustic modes inside an axisymmetric straight lined duct in the presence of a shear flow is known and compared with the fem solution comparisons are found to be in good agreement and validate a first step in the development of a caa method based on the fem and galbrun s equation the fem is then applied to an axisymmetric duct including a varying cross

on sound propagation in a linear shear flow abstract it is shown that the acoustic wave equation in a linear shear flow always has a critical layer where the doppler shifted frequency vanishes since this is the only singularity of the wave equation apart from the point at infinity the power series solution about the critical layer has infinite radius of convergence two linearly independent solutions are even and odd functions of distance from the critical layer their plots show that acoustic oscillations are suppressed near the critical layer a linear combination of these solutions specifies the general acoustic field the constants of integration are determined from boundary conditions of which several examples are given the total acoustic field is illustrated for rigid and impedance wall conditions the cases illustrated include both real and complex wave fields these wave fields are small amplitude perturbations of the acoustic wave equation in a linear shear flow it is shown in the appendix that the perturbations of vorticity and dilatation are coupled and thus combine features of acoustic and hydrodynamic modes

stability and accuracy of finite element methods for flow acoustics i general theory and application to one dimensional propagation the dispersion properties of finite element models for aeroacoustic propagation based on the convected scalar helmholtz equation and on the galbrun equation are examined the current study focusses on the effect of the mean flow on the dispersion and amplitude errors present in the discrete numerical solutions a general two dimensional dispersion analysis is presented for the discrete problem on a regular unbounded mesh and results are presented for the particular case of one dimensional acoustic propagation in which the wave direction is aligned with the mean flow the magnitude and sign of the mean flow is shown to have a significant effect on the accuracy of the numerical schemes quadratic helmholtz elements in particular are shown to be much less effective for downstream as opposed to upstream propagation even when the effect of wave shortening or elongation due to the mean flow is taken into account these trends are also observed in solutions obtained for simple test problems on finite meshes a similar analysis of two dimensional propagation is presented in an accompanying article

sound propagation in an annular duct with mean potential swirling flow the propagation of pressure disturbances is investigated in an annular duct with mean potential axial and swirling flow the swirling mean motion causes refraction of the acoustic waves as they propagate along the duct a normal mode analysis leads to a non linear eigenvalue problem the numerical solutions are validated with an asymptotic analysis in the limit of large radius the results show that while for a uniform flow the evanescent modes propagate at the same speed only upstream for a swirling flow such modes propagate at different speeds both upstream and downstream moreover most non axisymmetric acoustic modes propagate opposite to the mean flow swirl

eigenvectors of laplacian or signless laplacian of hypergraphs associated with zero eigenvalue abstract let g be a connected m uniform hypergraph in this paper we mainly consider the eigenvectors of the laplacian or signless laplacian tensor of g associated with zero eigenvalue called the first laplacian or signless laplacian eigenvectors of g by means of the incidence matrix of g the number of first laplacian or signless laplacian or h eigenvectors can be obtained explicitly by solving the smith normal form of the incidence matrix over z m or z 2 consequently we prove that the number of first laplacian h eigenvectors is equal to the number of first signless laplacian h eigenvectors when zero is an h eigenvalue of the signless laplacian tensor we establish a connection between first laplacian signless laplacian h eigenvectors and the even odd bipartitions of g

a general product of tensors with applications abstract we study a general product of two n dimensional tensors a and b with orders m 2 and k 1 this product satisfies the associative law and is a generalization of the usual matrix product using this product many concepts and known results of tensors can be simply expressed and or proved and a number of applications of it will be given using the associative law of this tensor product and some properties on the resultant of a system of homogeneous equations on n variables we define the similarity and congruence of tensors which are also the generalizations of the corresponding relations for matrices and prove that similar tensors have the same characteristic polynomials thus the same spectra we study two special kinds of similarity permutational similarity and diagonal similarity and their applications in the study of the spectra of hypergraphs and nonnegative irreducible tensors we also define the direct product of tensors in matrix case it is also called the kronecker product and give its applications in the study of the spectra of two kinds of the products of hypergraphs we also give applications of this general product in the study of nonnegative tensors including a characterization of primitive tensors the upper bounds of primitive degrees and the cyclic indices of some nonnegative irreducible tensors

maximum likelihood estimation of intraclass correlation in the analysis of familial data estimating equation approach summary we introduce a generalized model for estimating intraclass correlation in the analysis of familial data this model incorporates the models of donner koval 1980 donner bull 1983 rosner 1984 and miunoz rosner carey 1986 as special cases we then obtain the maximum likelihood estimates of the parameters of the model in particular we obtain a single estimating equation to be solved iteratively for the estimation of the intraclass correlation p and discuss all the special cases asymptotic variance for the estimate of the intraclass correlation is obtained for all the models and some examples are given

approximation formulae for the acoustic radiation impedance of a cylindrical pipe useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid walled cylindrical ducts the expressions guarantee that simple but necessary physical and mathematical principles are met like hermitian symmetry for the reflection coefficient identical behaviour of positive and negative frequencies and causality for the impulse response a non causal but more accurate expression is also proposed that is suitable for frequency domain applications the formulae are obtained by analytical and numerical fitting to reference results from levine and schwinger for the unflanged case and extracted from the radiation impedance matrix given by zorumski for the infinite flanged case

the largest h eigenvalue and spectral radius of laplacian tensor of non odd bipartite generalized power hypergraphs abstract let g be a simple graph or hypergraph and let a g l g q g be the adjacency laplacian and signless laplacian tensors of g respectively the largest h eigenvalues respectively the spectral radii of l g q g are denoted respectively by max l g max q g respectively l g q g it is known that for a connected non bipartite simple graph g max l g l g q g but this does not hold for non odd bipartite hypergraphs we will investigate this problem by considering a class of generalized power hypergraphs g k k 2 which are constructed from simple connected graphs g by blowing up each vertex of g into a k 2 set and preserving the adjacency of vertices suppose that g is non bipartite or equivalently g k k 2 is non odd bipartite we get the following spectral properties 1 l g k k 2 q g k k 2 if and only if k is a multiple of 4 in this case max l g k k 2 l g k k 2 2 if k 2 mod 4 then for sufficiently large k max l g k k 2 l g k k 2 motivated by the study of hypergraphs g k k 2 for a connected non odd bipartite hypergraph g we give a characterization of l g and q g having the same spectra or the spectrum of a g being symmetric with respect to the origin that is l g and q g or a g and a g are similar via a complex necessarily non real diagonal matrix with modular 1 diagonal entries so we give an answer to a question raised by shao et al that is for a non odd bipartite hypergraph g that l g and q g have the same spectra can not imply they have the same h spectra

on the acoustics of an impedance liner with shear and cross flow the acoustic vortical wave equation is derived describing the propagation of sound in i a unidirectional shear flow with a linear velocity profile upon which is superimposed ii a uniform cross flow together with an impedance wall boundary condition representing the effect of a locally reacting acoustic liner in the presence of bias and shear flow this leads to a third order differential equation in the presence of cross flow and in its absence simplifies to the pridmore brown equation second order also the singularity of the pridmore brown equation for zero doppler shifted frequency is removed by the cross flow because the third order wave equation has no singularities except at the sonic condition its general solution is a linear combination of three linearly independent maclaurin series in powers of the distance from the wall the acoustic field in the boundary layer is matched through the pressure and horizontal and vertical velocity components to the acoustic field in a uniform free stream consisting of incident and reflected waves the scattering coefficients are plotted for several values of the five parameters of the problem namely the angle of incidence free stream and cross flow mach numbers specific wall impedance and helmholtz number using the boundary layer thickness

on the spectral radius of a class of non odd bipartite even uniform hypergraphs abstract in order to investigate the non odd bipartiteness of even uniform hypergraphs starting from a simple graph g we construct a generalized power of g denoted by g k s which is obtained from g by blowing up each vertex into a s set and each edge into a k 2 s set where s k 2 when s k 2 g k s is always odd bipartite we show that g k k 2 is non odd bipartite if and only if g is non bipartite and find that g k k 2 has the same adjacency respectively signless laplacian spectral radius as g so the results involving the adjacency or signless laplacian spectral radius of a simple graph g hold for g k k 2 in particular we characterize the unique graph with minimum adjacency or signless laplacian spectral radius among all non odd bipartite hypergraphs g k k 2 of fixed order and prove that 2 5 is the smallest limit point of the non odd bipartite hypergraphs g k k 2 in addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

a note on permutation tests for variance components in multilevel generalized linear mixed models in many applications of generalized linear mixed models to multilevel data it is of interest to test whether a random effects variance component is zero it is well known that the usual asymptotic chi square distribution of the likelihood ratio and score statistics under the null does not necessarily hold in this note we propose a permutation test based on randomly permuting the indices associated with a given level of the model that has the correct type i error rate under the null results from a simulation study suggest that it is more powerful than tests based on mixtures of chi square distributions the proposed test is illustrated using data on the familial aggregation of sleep disturbance

a finite difference frequency domain numerical scheme for the solution of the gust response problem abstract a numerical method is developed for solving subsonic flows with convected three dimensional vortical waves around lifting airfoils the first order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected vorticity the unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the lagrangian coordinates of the mean flow and an irrotational field whose potential satisfies a nonconstant coefficient inhomogeneous convective wave equation using an elliptic coordinate transformation the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the mach number and reduced frequency extensive comparisons are made with known solutions to unsteady vortical flow problems and it is seen that the agreement is in general very good for reduced frequencies ranging from zero to four

on the acoustic modes in a duct containing a parabolic shear flow abstract the exact solution of the acoustic wave equation in an unidirectional shear flow with a parabolic velocity profile is obtained representing sound propagation in a plane parallel walled duct with two boundary layers over rigid or impedance walls it is shown that there are four cases depending on the critical level s where the doppler shifted frequency vanishes i for propagation upstream the critical levels are outside the duct case ii ii for propagation downstream there may be two case iv one case i or no case iii critical level inside the duct the acoustic wave equation is transformed in each of the four cases to particular forms of the extended hypergeometric equation which has power series solutions some involving logarithmic singularities in the cases where critical levels occur at real or imaginary distance matching of two or three pairs of solutions valid over regions each overlapping the next is needed the particular case of the parabolic velocity profile is used to address general properties of sound in unidirectional shear flows for example it is shown that for ducted shear flows there exist a pair of even and odd eigenfunctions in the absence of critical levels it is also proved in more than one instance that there is no single set of eigenvalues and eigenfunctions valid across one or two shear layers this leads to the general conjecture considering the acoustics of shear flows in ducts that critical levels separate regions with distinct sets of eigenvalues and eigenfunctions

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

acoustic transmission in non uniform ducts with mean flow part ii the finite element method this second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non uniform duct carrying a high speed subsonic compressible flow a finite element scheme based on both the galerkin method and the residual least squares method and with eight noded isoparametric elements is described multi modal propagation is investigated by coupling of the solution in the duct non uniform section to modal expansions in uniform sections the accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified galerkin method as introduced in part i of this pair of papers the results of calculations show that modal interactions particularly in transmitted modes become increasingly important with increasing duct flow mach number power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking

compact implicit maccormack type schemes with high accuracy in this work the maccormack methodology is extended to implicit compact differencing schemes a prefactorization method is developed which splits the implicit matrix into two independent upper and lower matrices which are easier to invert using this method a new class of high order accurate compact maccormack type schemes is derived two fourth order schemes are described and results are shown for three linear and nonlinear caa benchmark problems

randomization based inference within principal strata in randomized studies treatment comparisons conditional on intermediate postrandomization outcomes using standard analytic methods do not have a causal interpretation an alternative approach entails treatment comparisons within principal strata defined by the potential outcomes for the intermediate outcome that would be observed under each treatment assignment in this article we develop methods for randomization based inference within principal strata we compare our proposed methods with existing large sample methods as well as traditional intent to treat approaches this research is motivated by hiv prevention studies where few infections are expected and inference is desired within the always infected principal stratum that is all individuals who would become infected regardless of randomization assignment

comparison of a finite element model with a multiple scales solution for sound propagation in varying ducts with swirling flows a multiple scales ms solution is proposed to study sound propagation in slowly varying ducts with mean swirling flows instead of the standard linearized euler equations the ms method is applied to the so called galbrun s equation this equation is based on an eulerian lagrangian description and corresponds to a wave equation written only in terms of the lagrangian perturbation of the displacement this yields simpler differential equations to solve for the ms model as well as simpler boundary conditions in this paper galbrun s equation is also solved by a mixed pressure displacement finite element method fem the proposed fem model has already been tested in authors previous papers this model is quite general and is extended here to arbitrary mean flows including compressibility and swirling flow effects some ms and fem solutions are then compared in order to validate both models

displacement pressure based mixed finite element formulations for acoustic fluid structure interaction problems summary we present reliable finite element discretizations based on displacement pressure interpolations for the analysis of acoustic fluid structure interaction problems the finite element interpolations are selected using the inf sup condition and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation we show that with our analysis procedure no spurious non zero frequencies are encountered as heretofore calculated with other displacement based discretizations 1997 by john wiley sons ltd

uniform asymptotic approximations for duct acoustic modes in a thin boundary layer flow analytical approximations for the acoustic modes in a duct carrying a uniform core flow with a thin shear layer at the walls are developed using the method of matched asymptotic expansions both two dimensional and cylindrical duct propagation are considered numerical results for eigenvalues calculated using the theory are presented for the two dimensional problem and compared with results from earlier analyses it is found that the new approximations yield a significant increase in accuracy he problem of sound transmission through a duct carrying a uniform core flow with a thin boundary layer at the walls has been of interest for some time such a flow has practical applications in modeling a fully developed real flow profile perhaps the strongest motivation for studying the problem however is the possibility of obtaining analytical results using asymptotic analyses which can yield physical understanding of shear flow propagation phenomena in more realistic flows which must be treated numerically analytical studies based on the assumption of small boundary layer thickness have been carried out by several researchers during the past decade eversman and beckemeyer1 developed an inner expansion for acoustic pressure in the layer from which they were able to derive an approximate equivalent boundary condition applicable at the outer edge of the layer using this condition they showed that the formulation of the shear layer problem reduces to that of the associated uniform flow problem with the well known particle displacement continuity boundary condition as the layer thickness vanishes in a later paper eversman2 employed the equivalent boundary condition to formulate the eigenvalue problem for acoustic modes in an annular duct flow using the known uniform flow solutions in the core flow an approximate eigenvalue equation is developed numerical solution of this single equation yields the acoustic wave numbers and circumvents the task of numerically integrating the differential equation and iterating for the shear flow eigenfunctions the procedure is equally applicable to rectangular duct geometries for which it leads to an eigenvalue equation equivalent to one later derived less formally by tester 3 a slightly different analysis by swinbanks 4 also for rectangular ducts yields similar approximate results other studies less directly related to the present work are discussed in sec iv b ofref 5 the work reported in the present paper arose in the course of some research on shear flow propagation in which it was desirable to obtain analytical representations of the acoustic

a boundary element scheme for evaluation of four pole parameters of ducts and mufflers with low mach number non uniform flow a boundary element scheme is proposed for evaluation of the four pole parameters of ducts and mufflers in the presence of a low mach number non uniform flow a transformation of variable is used such that the governing sound propagation equation reduces to the helmholtz equation in the transformed variable which has a known fundamental solution and is therefore amenable to bem analysis the validity of the results is confirmed by comparison with those of existing one dimensional models of the flow the boundary element scheme has been developed as it enables one to determine effectively the four pole parameters when the flow is non uniform and also high order mode behavior in ducts and mufflers of any given geometry

a mixed finite element method for acoustic wave propagation in moving fluids based on an eulerian lagrangian description a nonstandard wave equation established by galbrun in 1931 is used to study sound propagation in nonuniform flows galbrun s equation describes exactly the same physical phenomenon as the linearized euler s equations lee but is derived from an eulerian lagrangian description and written only in term of the lagrangian perturbation of the displacement this equation has interesting properties and may be a good alternative to the lee only acoustic displacement is involved even in nonhomentropic cases it provides exact expressions of acoustic intensity and energy and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly in this paper galbrun s equation is solved using a finite element method in the axisymmetric case with standard finite elements the direct displacement based variational formulation gives some corrupted results instead a mixed finite element satisfying the inf sup condition is proposed to avoid this problem a first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow obtained from pridmore brown s equation a second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple scale method which is an adaptation for the incompressible case of rienstra s recent work

finite element computation of three dimensional elastoacoustic vibrations abstract in this paper the interior elastoacoustic problem in a 3d domain is solved displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation a non standard discretization is used consisting of classical linear tetrahedral finite element for the solid and raviart thomas elements of lowest order for the fluid a new unknown is introduced on the interface between solid and fluid to impose the transmission conditions

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

numerical study of acoustic modes in ducted shear flow the propagation of small amplitude modes in an inviscid but sheared mean flow inside a duct is studied numerically for isentropic flow in a circula r duct with zero swirl and constant mean flow density the pressure modes are described in te rms of the eigenvalue problem for the pridmore brownequation since for sufficiently high helmholtz and wavenum bers which are of great interest for the applications the fi eld equation is inherently stiff special care is taken to insure the stability of the numerica l algorithm designed to tackle this problem the accuracy of the method is checked against the well known analytical solution for the uniform flow the numerical method is shown t o be consistent with the analytical predictions at least for the helmholtz numbers up to 100 and the circumferential wavenumber as large as 50 typical mach numbers being up to 0 65 in order to gain further insight into the possible structure of the modal solutions and to get an independent verification of the robustness of the nu merical scheme comparison to the asymptotic solution of the problem based on the wkb method is performed the asymptotic solution is also used as a benchmark for computations with high helmholtz numbers where numerical solutions of other authors are not available the bulk of the analysis concentrates on the influence of the w all lining the proposed numerical procedure is adapted in order to include ingard myers boundary conditions in parallel with this the wkb solution is used to check the numerical predictions of the typical behaviour of the axial wavenumber in the complex plane when the wall impedance varies in the complex plane numerical analysis of the problem with zero mean flow at the wa ll and acoustic lining shows that the use of ingard myers condition in combination with an appropriate slipstream approximation instead of the actual no slip mean flow profile gives valid results in the limit of vanishing boundary layer thickness although the boundary layer must be very thin in some cases

a low mach number model for time harmonic acoustics in arbitrary flows this paper concerns the finite element simulation of the diffraction of a time harmonic acoustic wave in the presence of an arbitrary mean flow considering the equation for the perturbation of displacement due to galbrun we derive a low mach number formulation of the problem which is proved to be of fredholm type and is therefore well suited for discretization by classical lagrange finite elements numerical experiments are done in the case of a potential flow for which an exact approach is available and a good agreement is observed

on sound propagation in a nozzle with non uniform swirl abstract the propagation of sound is considered in an axisymmetric mean flow with uniform axial velocity and non uniform swirl with angular velocity proportional to the radius two simplifications are made i that the maximum tangential velocity of the mean flow is small compared to the sound speed ii that the doppler shift due to rotation is much smaller than the wave frequency including doppler shift by the uniform axial flow divided by the maximum angular velocity of swirl it is shown that these conditions are not too restrictive for practical swirling flows in exhaust nozzles and that they allow the solution of the wave equation in terms of confluent hypergeometric functions instead of bessel functions in the case of rigid body rotation this type of radial dependence allows for propagating waves with decaying amplitude in the case of slow swirl and for evanescent and unstable modes in the case of fast swirl the borderline between slow and fast swirl is given by a rotation parameter related to the second approximation ii above and defined as the ratio of the doppler shift due to rotation to the product of the frequency by the radial compactness

a test in the presence of nuisance parameters abstract we are interested in testing 0 against an alternative in the presence of some nuisance parameter the usual procedure for such problems is to use a test statistic that is a function of the data only let q denote the p value at a given value if q does not depend on then in principle we can apply this procedure however a major difficulty that arises in many situations is that q depends on and therefore cannot be used as a p value in such cases the usual approach is to define the p value as the supremum of q over the nuisance parameter space because this approach ignores sample information about it may be unnecessarily conservative this is a serious problem in order restricted inference to overcome this i propose the following obtain say a 99 confidence region for under the null hypothesis now for a given let t be a test statistic and r be the p value the test procedure is to reject the null hypothesis if 0 01 supremum of r over the 99 c

aerodynamics and interaction noise of streamlined bodies in nonuniform flows abstract the unsteady aerodynamics and interaction noise of streamlined bodies are modeled in terms of the euler equations linearized about a nonuniform flow the validity of the inviscid approach is supported by recent les simulations of an airfoil in a gust indicating that for not too small impinging excitations the interaction process is dominated by inertia forces results in the present paper are focused on the aerodynamics and interaction noise of a turbofan modeled as an annular cascade the model accounts for the inflow fan duct coupling and the high frequency of the interaction process two high order numerical algorithms are developed with body fitted coordinate system one algorithm uses a primitive variable formulation the other uses an efficient velocity splitting algorithm and is suitable for broadband computations analytical and numerical analysis of disturbances in rotational flows is developed and exact inflow outflow boundary conditions are derived yielding directly the radiated acoustics the upstream disturbances evolve in rotational flows and as a result the aerodynamic aeroacoustic response of the annular cascade depends on the initial conditions location computational results show that the three dimensional geometry of the annular cascade the mean flow swirl and the blade geometry have strong influence on the blade sectional lift and the radiated sound these results also show the inadequacy of using the popular linear cascade model particularly for realistic fan geometry and inflow conditions

a reverse flow theorem and acoustic reciprocity in compressible potential flows in ducts a reverse flow theorem for acoustic propagation in compressible potential flow has been obtained directly from the field equations without recourse to energy conservation arguments a reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with either acoustically rigid walls or acoustically absorbing walls follows it is found that for a source at a specific end of the duct suitably scaled reflection matrices in direct and reverse flow have a reciprocal relationship scaled transmission matrices obtained for direct flow and reversed flow with simultaneous switching of source location from one end to the other also have a reciprocal relationship a related reverse flow theorem specialized to one dimensional acoustic propagation has also been obtained reciprocity relationships for the scattering coefficients for propagation are derived and are found to be similar though much simpler than in the case of multi mode propagation in one dimensional flow reciprocal relations and power conservation arguments are used to show that scaled power reflection and transmission coefficients are invariant to flow reversal and switching of source location from one end of the duct to the other numerical verification of the reciprocal relationships is given in a companion paper

acoustic vorticity waves in swirling flows the propagation of small disturbances in an annular duct with a mean vortical swirling flow is studied the disturbance velocity is split into a nearly convected part and a nearly sonic part obeying weakly coupled equations a normal mode analysis shows that the eigenvalues are segregated into a finite number of propagating pressure dominated nearly sonic waves and a cluster of infinite number of vorticity dominated nearly convected modes a generalized gust can then be identified with the vorticity dominated nearly convected eigensolutions the nearly convected eigenvalues form two branches on either side of a critical layer which corresponds to purely convected modes an asymptotic analysis is used to investigate the stability of the nearly convected eigensolutions in the vicinity of the critical layer