dpoae group delays versus electrophysiological measures of cochlear delay in normal human ears group delays of 2 f1 f2 distortion product otoacoustic emissions dpoaes were determined using both f1 and f2 sweep paradigms in 24 normal hearing subjects these dpoae group delays were studied in comparison with cochlear delays estimated from derived band viiith nerve compound action potentials caps and auditory brainstem responses abrs in the same subjects the center frequencies of the derived bands in the electrophysiological experiment were matched with the f2 frequencies in the dpoae recording to ensure that dpoaes and derived caps and abrs were generated at the same places along the cochlear partition thus allowing for a direct comparison the degree to which dpoae group delays are larger in the f2 than in the f1 sweep paradigm is consistent with a theoretical analysis of the so called wave fixed model both dpoae group delays are highly correlated with cap and abr derived measures of cochlear delay the principal result of this study is that roundtrip dpoae group delay in the f1 sweep

the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

evidence for two discrete sources of 2f1 f2 distortion product otoacoustic emission in rabbit i differential dependence on stimulus parameters the results of studies of the physiological vulnerability of distortion product otoacoustic emissions dpoaes suggest that the dpoae at 2f1 f2 in vertebrate ears is generated by more than one source the principal aims of the present study were to provide independent evidence for the existence of more than one dpoae source and to determine the contributions of each to the ear canal 2f1 f2 signal to accomplish these aims specific stimulus parameters were separately and systematically varied to provide detailed parametric information regarding 2f1 f2 dpoae amplitude and phase in normal ears of awake rabbits the findings indicate that two discrete sources demonstrating differential dependence on stimulus parameters dominate the generation of the 2f1 f2 dpoae one source of distortion is dominant above 60 70 db spl at moderate primary frequency separations and at all stimulus levels when the primary tones are closely spaced the other source is dominant below 60 70 db spl at moderate primary frequency

some examples of kinetic schemes whose diffusion limit is il in s exponential fitting this paper is concerned with diffusive approximations of some numerical schemes for several linear or weakly nonlinear kinetic models which are motivated by wide range applications including radiative transfer or neutron transport run and tumble models of chemotaxis dynamics and vlasov fokker planck plasma modeling the well balanced method applied to such kinetic equations leads to time marching schemes involving a scattering s matrix itself derived from a normal modes decomposition of the stationary solution one common feature these models share is the type of diffusive approximation their macroscopic densities solve drift diffusion systems for which a distinguished numerical scheme is il in scharfetter gummel s exponential fitting discretization we prove that these well balanced schemes relax within a parabolic rescaling towards such type of discretization by means of an appropriate decomposition of the s matrix hence are asymptotic preserving

mean exit times for particles driven by weakly colored noise consider a particle whose velocity is an ornstein uhlenbeck process with correlation time varepsilon 2 frac dx dt frac sigma z varepsilon qquad frac dz dt frac z varepsilon 2 frac sqrt 2 xi t varepsilon where xi t is gaussian white noise this represents brownian motion with memory i e a non markovian brownian motion singular perturbation techniques reduce the mean exit time problem to a boundary layer problem which turns out to be the half range expansion problem for the fokker planck operator this is solved via complex variable theory it is found that the spatial density has a milne extrapolation length varepsilon sigma zeta tfrac 1 2 varepsilon sigma 1 46035 cdots where zeta is the riemann zeta function it is also found that the average time at which x t first escapes an interval a 0 b ven that it starts at x 0 0 and z 0 z 0 is e t text ex frac 1 2 sigma 2 left a varepsilo

measuring distortion product otoacoustic emissions using continuously sweeping primaries distortion product otoacoustic emission dpoae level from normal hearing individuals can vary by as much as 30db with small frequency changes a phenomenon known as dpoae fine structure this fine structure is hypothesized to stem from the interaction of components from two different regions of the cochlea the nonlinear generator region and the reflection component from the dp region an efficient procedure to separate these two components would improve the clinical and research utility of dpoae by permitting separate evaluation of different cochlea regions in this paper two procedures for evaluating dpoae fine structure are compared dpoae generated by fixed frequency primaries versus continuously sweeping primaries the sweep dpoae data are analyzed with a least squares fit filter sweep rates of greater than 8s per octave permit rapid evaluation of the cochlear fine structure a higher sweep rate of 2s per octave provided dpoae without fine structure under these conditions the longer latency reflection component falls outside the range of the filter consequently dpoae obtained with sweeping tones can be used either to get more rapid estimates of dpoae fine structure or to obtain estimates of dpoae from the generator region uncontaminated by energy from the reflection region

comparing two proposed measures of cochlear mechanical filter bandwidth based on stimulus frequency otoacoustic emissions it has been hypothesized that the sharpness of the cochlear mechanical filter is related to two measures based on stimulus frequency otoacoustic emissions sfoaes the first is the group delay of the sfoae the second is the bandwidth of the sfoae two tone suppression isoinput tuning characteristic a corollary of this is that natural variability in cochlear mechanical bandwidth within a population would lead to a positive correlation between these two sfoae based measures of tuning within that population to test this prediction sfoae group delay and sfoae two tone suppression isoinput tuning characteristics were measured in a sample of 16 audiometrically normal subjects contrary to the prediction no statistically significant correlation was found between the two bandwidth measures cochlear model simulations were used to aid the interpretation of this result these suggested that a positive correlation between the two measures is expected but that it may well be too weak to detect with the given sample size due to the influence on the sfoae measures of random inhomogeneities in basilar membrane impedance

on a backward forward parabolic equation and its regularization abstract the steady state diffusion of heat in a fluid which flows rapidly but not unidirectionally in a semi infinite channel leads to a singular perturbation of a backwards forwards heat equation with neumann conditions on the channel walls the temperature is prescribed on the whole channel entrance for the perturbed problems but only at the points where the fluid flow is inward for the limiting problem conditions are obtained for uniqueness and the additional arbitrary constants needed to obtain a well posed problem when uniqueness does not hold are characterized conditions for the convergence of the solution of the perturbed problem to that of the limiting problem are also found

algorithms for hyperbolic quadratic eigenvalue problems we consider the quadratic eigenvalue problem or the qep 2 a b c x 0 where a b and c are hermitian with a positive definite the qep is called hyperbolic if x bx 2 4 x ax x cx for all nonzero x c r we show that a relatively efficient test for hyperbolicity can be obtained by computing the eigenvalues of the qep a hyperbolic qep is overdamped if b is positive definite and c is positive semidefinite we show that a hyperbolic qep whose eigenvalues are necessarily real is overdamped if and only if its largest eigenvalue is nonpositive for overdamped qeps we show that all eigenpairs can be found efficiently by finding two solutions of the corresponding quadratic matrix equation using a method based on cyclic reduction we also present a new measure for the degree of hyperbolicity of a hyperbolic qep

a cochlear frequency position function for several species 29 years later accurate cochlear frequency position functions based on physiological data would facilitate the interpretation of physiological and psychoacoustic data within and across species such functions might aid in developing cochlear models and cochlear coordinates could provide potentially useful spectral transforms of speech and other acoustic signals in 1961 an almost exponential function was developed greenwood 1961b 1974 by integrating an exponential function fitted to a subset of frequency resolution integration estimates critical bandwidths the resulting frequency position function was found to fit cochlear observations on human cadaver ears quite well and with changes of constants those on elephant cow guinea pig rat mouse and chicken bekesy 1960 as well as in vivo behavioral anatomical data on cats schucknecht 1953 since 1961 new mechanical and other physiological data have appeared on the human cat guinea pig chinchilla monkey and gerbil it is shown here that the newer extended data on human cadaver ears and from living animal preparations are quite well fit by the same basic function the function essentially requires only empirical adjustment of a single parameter to set an upper frequency limit while a slope parameter can be left constant if cochlear partition length is normalized to 1 or scaled if distance is specified in physical units constancy of slope and form in dead and living ears and across species increases the probability that the function fitting human cadaver data may apply as well to the living human ear this prospect increases the function s value in plotting auditory data and in modeling concerned with speech and other bioacoustic signals since it fits the available physiological data well and consequently if those data are correct remains independent of and an appropriate means to examine psychoacoustic data and assumptions

boundary and initial boundary value problems for separable backward forward parabolic problems a backward forward parabolic equation is considered in a strip which is infinite in the timelike direction with boundary conditions on the sides of the strip the unique bounded solution of the problem is given explicitly by separation of variables in addition a similar problem in a semi infinite strip is treated with initial data at the end of the strip it is shown that the solution can be represented arbitrarily closely in the maximum norm by a sum of functions obtain by separation of variables

influence of inlet and bulk noise on rayleigh benard convection with lateral flow spatiotemporal properties of convective fluctuations and of their correlations are investigated theoretically in the vicinity of the threshold for onset of convection in the presence of a lateral through flow using the full linearized equations of fluctuating hydrodynamics the effect of external forcing by inlet boundary conditions on the downstream evolution of convective fields is separated from the effect of internal bulk thermal forcing with the use of spatial laplace transformations they show how the spatial variation of fluctuations and of their correlations are governed by the six spatial characteristic exponents of the field equations

asymptotic analysis of a backward forward parabolic problem for data handling systems we analyze a pde that is backward parabolic in a part of its domain and parabolic in the remainder such problems arise in many areas such as stochastic fluid models we consider a particular problem that arose as a limiting case of a data handling system with many sources for this model some exact results are available in the literature we obtain asymptotic expansions from these exact solutions by the saddle point method

heavy traffic analysis of a data handling system with many sources a model is considered in which a buffer receives messages from n independent and identical information sources that asynchronously alternate between exponentially distributed periods in the on and off states while on a source transmits at unit rate the buffer depletes through an output channel with a given maximum transmission rate c n this model is useful for a data handling switch in a computer network anick mitra and sondhi bell system tech j 61 1982 pp 1871 1894 have derived an explicit expression for the equilibrium probability g x that the buffer content exceeds x which is convenient for numerical calculations for moderate values of n in this paper the heavy traffic case in which n is large and the system is close to instability is investigated important scalings are introduced and a two term asymptotic approximation to g x is derived with the help of function theoretic techniques numerical comparisons are given that show the quality of the approximation

an accelerated cyclic reduction based solvent method for solving quadratic eigenvalue problem of gyroscopic systems abstract the quadratic eigenvalue problem qep 2 m g k x 0 with m t m being positive definite k t k being negative definite and g t g is associated with gyroscopic systems in guo 2004 a cyclic reduction based solvent crs method was proposed to compute all eigenvalues of the above mentioned qep firstly the problem is converted to find a suitable solvent of the quadratic matrix equation qme m x 2 g x k 0 then using a cayley transformation and a proper substitution the qme is transformed into the nonlinear matrix equation nme z a t z 1 a q with a m k g and q 2 m k the problem finally can be solved by applying the cr method to obtain the maximal symmetric positive definite solution of the nme as long as the qep has no eigenvalues on the imaginary axis or for some cases where the qep has eigenvalues on the imaginary axis however when all eigenvalues of the qep are far away from or near the origin the cayley transformation seems not to be the best one and the convergence rate of the crs method proposed in guo 2004 might be further improved in this paper inspired by using a doubling algorithm to solve the qme we use a mobius transformation instead of the cayley transformation to present an accelerated crs acrs method for solving the qep of gyroscopic systems in addition we discuss the selection strategies of optimal parameter for the acrs method numerical results demonstrate the efficiency of our method

an iterative method for updating gyroscopic systems based on measured modal data abstract an efficient iterative method for updating the mass gyroscopic and stiffness matrices simultaneously using a few of complex measured modal data is developed by using the proposed iterative method the unique symmetric solution can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrices numerical results show that the presented method can be used to update finite element models to get better agreement between analytical and experimental modal parameters

indefinite sturm liouville problems and half range completeness where the function h changes sign on i such problems occur in certain physical models particularly in transport theory and statistical physics see 2 9 11 131 and references therein as for the standard eigenvalue problem it is true under quite general conditions and not difficult to prove that there is a set of eigenfunctions un which is complete in an appropriate hilbert space of functions this is known as full range completeness for the physical problems the question of interest is generally that of half range completeness to formulate this we set

efficient computation of the extreme solutions of x a x 1 a q and x a x 1 a q we propose a new quadratically convergent algorithm having a low computational cost per step and good numerical stability properties which allows the simultaneous approximation of the extreme solutions of the matrix equations x a x 1 a q and x a x 1 a q the algorithm is based on the cyclic reduction method

on the frequency dependence of the otoacoustic emission latency in hypoacoustic and normal ears experimental measurements of the otoacoustic emission oae latency of adult subjects have been obtained as a function of frequency by means of wavelet time frequency analysis based on the iterative application of filter banks the results are in agreement with previous oae latency measurements by tognola et al hear res 106 112 122 1997 as regards both the latency values and the frequency dependence and seem to be incompatible with the steep 1 f law that is predicted by scale invariant full cochlear models the latency frequency relationship has been best fitted to a linear function of the cochlear physical distance using the greenwood map and to an exponential function of the cochlear distance for comparison with derived band abr latency measurements two sets of ears 94 audiometrically normal and 42 impaired with high frequency f 3 khz hearing loss have been separately analyzed significantly larger average latencies were found in the impaired ears in the mid frequency range theoreti

time frequency analysis of linear and nonlinear otoacoustic emissions and removal of a short latency stimulus artifact click evoked otoacoustic emissions ceoaes are commonly recorded as average responses to a repetitive click stimulus if the click train has constant polarity a linear average results if it contains a sequence of clicks of differing polarity and amplitude a nonlinear average can be calculated the purpose of this study was to record both protocols from the same set of ears and characterize the differences between them the major features of ceoaes were similar under both protocols with the exception of a region spanning 0 5 ms in time and 0 2 2 khz in frequency it was assumed that the signal derived from the linear protocol was contaminated by stimulus artifact and so a simple procedure was used involving high pass filtering and time windowing to remove components of this artifact this procedure preserved the short latency high frequency responses it also produced a marked similarity in the time frequency plots of recordings made under the two protocols this result means it is possible to take advantage of the better signal to noise ratio of the linear data compared to its nonlinear counterpart additionally it was shown that ceoaes recorded under the linear protocol appear to be less dependent on the presence of spontaneous otoacoustic emissions soaes

a galerkin method for the forward backward heat equation in this paper a new variational method is proposed for the numeri cal approximation of the solution of the forward backward heat equation the approach consists of first reducing the second order problem to an equivalent first order system and then using a finite element procedure with continuous elements in both space and time for the numerical approximation under suit able regularity assumptions error estimates and the results of some numerical experiments are presented

ray solution of a singularly perturbed elliptic pde with applications to communications networks we analyze a second order linear elliptic pde with mixed boundary conditions this problem arose as a limiting case of a markov modulated queueing model for data handling switches in communications networks we use singular perturbation methods to analyze the problem in particular we use the ray method to solve the pde in the limit where convection dominates diffusion we show that there are both interior and boundary caustics as well as a cusp point where two caustics meet an internal layer boundary layers and a corner layer our analysis leads to approximate formulas for the queue length or buffer content distribution at the switch

heavy traffic analysis of a markov modulated queue with finite capacity and general service times we consider a set of n independent sources each of which alternates between on and off states when a source is on it generates a poisson arrival stream to a finite capacity queue with a general server we derive the balance equations satisfied by the joint steady state distribution of the queue length and the number of on sources then we analyze the problem in the heavy traffic limit where n rightarrow infty and the average arrival rate is nearly equal to the mean service rate the capacity is scaled to be o sqrt n the first two terms in the asymptotic series are characterized as solutions to elliptic partial differential equations pdes with appropriate boundary conditions we then develop numerical and asymptotic methods for solving these pdes the analysis makes use of singular perturbation techniques and special functions

half range solutions of indefinite sturm liouville problems abstract for diffusion equations of indefinite sturm liouville type we develop two equivalent methods of constructing explicit representations for the solutions the first method is based on an eigenfunction expansion whereas the second uses a wiener hopf type integral equation and factorization some illustrative examples are worked out

computations with infinite toeplitz matrices and polynomials we relate polynomial computations with operations involving infinite band toeplitz matrices and show applications to the numerical solution of markov chains of nonlinear matrix equations to spectral factorizations and to the solution of finite toeplitz systems in particular two matrix versions of graeffe s iteration are introduced and their convergence properties are analyzed correlations between graeffe s iteration for matrix polynomials and cyclic reduction for block toeplitz matrices are pointed out the paper contains a systematic treatment of known topics and presentation of new results improvements and extensions

probability representations of a class of two way diffusions there has been little progress in the analysis of two way diffusion in the last few decades due to the difficulties brought by the interface section similar to a free boundary condition in this paper however the equivalent probability model is considered and the interface section is precisely described by an integral equation the solution of two way diffusion is then expressed in an integral form with the integrand being the solution of a classical first passage time model and the solution of a one dimensional integral equation which is relatively easier to solve the exact expression of the two way diffusion enables us to find the explicit solution of the model with infinite horizontal boundaries and without drifting

a numerical method for quadratic eigenvalue problems of gyroscopic systems abstract we consider the quadratic eigenvalues problem qep of gyroscopic systems 2 m g k x 0 where m m g g and k k r n n with m being positive definite guo numerical solution of a quadratic eigenvalue problem linear algebra and its applications 385 2004 391 406 showed that all eigenvalues of the qep can be found by solving the maximal solution of a nonlinear matrix equation z a z 1 a q with quadratic convergence when the qep has no eigenvalues on the imaginary axis the convergence becomes linear or more slower guo 2004 when the qep allows purely imaginary eigenvalues having even partial multiplicities in this paper we consider the general case when the qep has eigenvalues on the imaginary axis we propose an eigenvalue shifting technique to transform the original gyroscopic system to a new gyroscopic system which shifts purely imaginary eigenvalues to eigenvalues with nonzero real parts while keeps other eigenpairs unchanged this transformation ensures that the new method for computing the maximal solution of the nonlinear matrix equation converges quadratically numerical examples illustrate the efficiency of our method

the kinetic boundary layer for the klein kramers equation a new numerical approach we explore a numerical technique for determining the structure of the kinetic boundary layer of the klein kramers equation for noninteracting brownian particles in a fluid near a wall that absorbs the brownian particles the equation is of interest in the theory of diffusion controlled reactions and of the coagulation of colloidal suspensions by numerical simulation of the langevin equation equivalent to the klein kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities the data can be used to construct the solutions of the standard problems at an absorbing wall the milne and the albedo problem we confirm and extend earlier results by burschka and titulaer obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion we briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here

half range completeness for the fokker planck equation half range completeness theorems are proved for eigenfunctions associated to the one dimensional fokker planck equation in a semi infinite medium existence and uniqueness results for perfectly absorbing partially absorbing and purely specularly reflecting boundary conditions are deduced for the stationary and time dependent problems similar results are obtained for a slab geometry

locus of generation for the 2 f1 f2 vs 2 f2 f1 distortion product otoacoustic emissions in normal hearing humans revealed by suppression tuning onset latencies and amplitude correlations the present study used distortion product otoacoustic emission dpoae suppression tuning curves stcs dpoae onset latencies ols and dpoae amplitude correlations to investigate the locus of generation of the 2 f1 f2 dpoae versus the 2 f2 f1 dpoae in humans the results of the tuning study revealed that for the 2 f1 f2 dpoae the tips of the stcs tuned consistently below the geometric mean gm frequency of the primary tones in contrast for the 2 f2 f1 dpoae stcs tuned above the gm of the primaries with 50 of the tip frequencies at or above the 2 f2 f1 frequency place when the average ratio of the 2 f2 f1 to the 2 f1 f2 tip frequencies was computed a factor of 1 44 provided an estimate of the frequency shift needed to align the two dpoae generation sites other results showed that ols for the 2 f2 f1 dpoae were uniformly shorter than those for the 2 f1 f2 with differences at the low frequencies amounting to as much as 6 7 ms further for both dpoaes curves describing latency decreases as

the similarity problem for indefinite sturm liouville operators and the help inequality abstract we study two problems the first one is the similarity problem for the indefinite sturm liouville operator a sgn x d w d x d r d x acting in l w 2 b b it is assumed that w r l loc 1 b b are even and positive a e on b b the second object is the so called help inequality 0 b 1 r f d x 2 k 2 0 b f 2 w d x 0 b 1 w 1 r f 2 w d x where the coefficients w r l loc 1 0 b are positive a e on 0 b both problems are well understood when the corresponding sturm liouville differential expression is regular the main objective of the present paper is to give criteria for both the validity of the help inequality and the similarity to a self adjoint operator in the singular case namely we establish new criteria formulated in terms of the behavior of the corresponding weyl titchmarsh m functions at 0 and at as a biproduct of this result we show that both problems are closely connected namely the operator a is similar to a self adjoint one precisely if the help inequality with w r and r w is valid next we characterize the behavior of m functions in terms of coefficients and then these results enable us to reformulate the obtained criteria in terms of coefficients finally we apply these results for the study of the two way diffusion equation also known as the time independent fokker planck equation

distortion product otoacoustic emission generation mechanisms and their dependence on stimulus level and primary frequency ratio in this study a systematic analysis of the dependence on stimulus level and primary frequency ratio r of the different components of human distortion product otoacoustic emissions has been performed to check the validity of theoretical models of their generation as regards the localization of the sources and the relative weight of distortion and reflection generation mechanisms 2f1 f2 and 2f2 f1 distortion product otoacoustic emissions of 12 normal hearing ears from six human subjects have been measured at four different levels in the range 35 65 db sound pressure level at eight different ratios in the range 1 1 1 45 time frequency filtering was used to separate distortion and reflection components numerical simulations have also been performed using an active nonlinear cochlear model both in the experiment and in the simulations the behavior of the 2f1 f2 distortion and reflection components was in agreement with previous measurements and with the predictions of the two source model the 2f2 f1 response showed a rotating phase component only whose behavior was in general agreement with that predicted for a component generated and reflected within a region basal to the characteristic place of frequency 2f2 f1 although alternative interpretations which are also discussed cannot be ruled out

detecting a definite hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem and associated nearness problems an important class of generalized eigenvalue problems ax lambdabx is those in which a and b are hermitian and some real linear combination of them is definite for the quadratic eigenvalue problem qep lambda 2 a lambdab c x 0 with hermitian a b and c and positive definite a particular interest focuses on problems in which x bx 2 4 x ax x cx is one signed for all non zero x for the positive sign these problems are called hyperbolic and for the negative sign elliptic the important class of overdamped problems arising in mechanics is a sub class of the hyperbolic problems for each of these classes of generalized and quadratic eigenvalue problems we show how to check that a putative member has the required properties and we derive the distance to the nearest problem outside the class for definite pairs a b the distance is the crawford number and we derive bisection and level set algorithms both for testing its positivity and for computing it testing hyperbolicity of a qep is shown to reduce to testing a related pair for definiteness the distance to the nearest non hyperbolic or non elliptic n x n qep is shown to be the solution of a global minimization problem with n 1 dearees of freedom numerical results are given to illustrate the theory and algorithms c 2002 published by elsevier science inc

a note on the fixed point iteration for the matrix equations x a x 1a i the fixed point iteration is a simple method for finding the maximal hermitian positive definite solutions of the matrix equations x a x 1 a i the plus minus equations the convergence of this method may be very slow if the initial matrix is not chosen carefully a strategy for choosing better initial matrices has been recently proposed by ivanov hasanov and uhlig they proved that this strategy can improve the convergence in general and observed from numerical experiments that dramatic improvement happens for the plus equation with some matrices a it turns out that the matrices a are normal for those examples in this note we prove a result that explains the dramatic improvement in convergence for normal and thus nearly normal matrices for the plus equation a similar result is also proved for the minus equation ams classification 15a24 65f30 65h10

finding the impedance of the organ of corti measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities v x f vu vu x f vu x f f fc x where the response v is the velocity of the membrane at measurement position x vu is the umbo velocity f is the frequency of the stimulus and fc x is the local characteristic frequency the frequency dependence of the functions x f and x f is determined from the data and x f and ln x f are shown to be analytic functions in the lower half of the complex frequency plane with re x f a monotonically increasing function of f at fixed x the linear limit of basilar membrane motion is characterized by a transfer function t x f v1 1 estimated by extrapolating v x f vu vu to a small membrane velocity v1 t x f and ln t x f are shown to be analytic functions in the lower half of the complex frequency plane the inverse of the amplitude of the transfer function which has both a deep dip at f fc x

the matrix equation x a tx 1 a q and its application in nano research the matrix equation x a tx 1 a q has been studied extensively when a and q are real square matrices and q is symmetric positive definite the equation has positive definite solutions under suitable conditions and in that case the solution of interest is the maximal positive definite solution the same matrix equation plays an important role in green s function calculations in nano research but the matrix q there is usually indefinite so the matrix equation has no positive definite solutions and one is interested in the case where the matrix equation has no positive definite solutions even when q is positive definite the solution of interest in this nano application is a special weakly stabilizing complex symmetric solution in this paper we show how a doubling algorithm can be used to find good approximations to the desired solution efficiently and reliably

abstract kinetic equations relevant to supercritical media abstract the abstract hilbert space equation t x a x x r is studied with a partial range boundary condition q 0 ran q here t is bounded injective and self adjoint a is fredholm and self adjoint with finite dimensional negative part and q is the orthogonal projection onto the maximal t positive t invariant subspace this models half space stationary transport problems in supercritical media a complete existence and uniqueness theory is developed

iterative solution of two matrix equations we study iterative methods for finding the maximal hermitian positive definite solutions of the matrix equations x a x 1 a q and x a x 1 a q where q is hermitian positive definite general convergence results are given for the basic fixed point iteration for both equations newton s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation numerical results are reported to illustrate the convergence behaviour of various algorithms

full and partial range eigenfunction expansions for sturm liouville problems with indefinite weights this article is concerned with eigenvalue problems of the form au tu in a hilbert space h where ais a selfadjoint positive operator generated by a second order sturm liouville differential expression and t a selfadjoint indefinite multiplicative operator which is one to one emphasis is on the full range and partial range expansionproperties of the eigenfunctions

wavelet and matching pursuit estimates of the transient evoked otoacoustic emission latency different time frequency techniques may be used to investigate the relation between latency and frequency of transient evoked otoacoustic emissions in this work the optimization of these techniques and the interpretation of the experimental result are discussed time frequency analysis of click evoked otoacoustic emissions of 42 normal hearing young subjects has been performed using both wavelet and matching pursuit algorithms wavelet techniques are very effective to provide fast and reliable evaluation of the average latency of large samples of subjects a major advantage of the matching pursuit technique as observed by jedrzejczak et al j acoust soc am 115 2148 2158 2004 is to provide detailed information about the time evolution of the response of single ears at selected frequencies a hybrid matching pursuit algorithm that includes fourier spectral information was developed capable of speeding up computation times and of identifying spurious atoms whose latency frequency relation i

numerical solution of a quadratic eigenvalue problem we consider the quadratic eigenvalue problem qep 2 m g k x 0 where m m t is positive denite k k t is negative denite and g g t the eigenvalues of the qep occur in quadruplets or in real or purely imaginary pairs we show that all eigenvalues of the qep can be found eciently and with the correct symmetry by nding a proper solvent x of the matrix equation mx 2 gx k 0 as long as the qep has no eigenvalues on the imaginary axis this solvent approach works well also for some cases where the qep has eigenvalues on the imaginary axis ams classication 15a18 15a24 65f30

the direct updating of damping and gyroscopic matrices in this paper we develop an efficient numerical method for the finite element model updating of damped gyroscopic systems this model updating of damped gyroscopic systems is proposed to incorporate the measured modal data into the finite element model to produce an adjusted finite element model on the damping and gyroscopic matrices that closely match the experimental modal data

half range analysis of a counter current separator abstract chemical separations are usually accomplished in counter current reactors because in these reactors the chemical equilibrium continually shifts toward increasing the purity of the product stream as it flows through the reactor however as a result of the counter current design these devices are often governed by forward backward two way diffusion equations in this article we analyze the mathematical model of a single interface counter current separator introduced by fitt ockendon and shillor for relatively long reactors for such reactors the mathematical model which is a forward backward diffusion system can be solved by eigenfunction expansions we construct these expansions using complex variable methods developed for kinetic theory from this analysis we obtain explicit formulas for the power of the reactor both in terms of the average purity of the output stream and in terms of the equivalent number of theoretical plates

double evoked otoacoustic emissions i measurement theory and nonlinear coherence an evoked otoacoustic emission oae measurement technique is proposed to better control for probe distortion each double evoking 2e stimulus sequence includes three equal duration subsequences defined as follows s1 t is a single chirp or click s2 t es1 t is a copy of s1 with relative amplitude e and delay and s12 t s1 t s2 t is the superposition of the first two stimuli the pressure response to each subsequence is p1 p2 and p12 respectively the double chirp evoked distortion product 2chdp and double click evoked otoacoustic emission 2ceoae are defined by pd p12 p1 p2 the 2chdp response may be time compressed to analyze as an equivalent 2ceoae response the 2e response family provides a complementary representation between dp measurements and double click evoked oae measurements a technique based on nonlinear coherence quantifies random noise in terms of a nonlinear signal to noise ratio

positive solutions to x a bx 1 b abstract we study the positive semidefinite solutions to the matrix equation x a bx 1 b under the assumption that a 0 we show that a positive solution exists if and only if a certain block tridiagonal operator is positive in which case the solution is given by the shorted operator or generalized schur complement of that operator

partial range completeness and existence of solutions to two way diffusion equations separating variables to solve a two way diffusion equation leads to a nonstandard eigenvalue problem in one variable it is shown that the eigenfunctions having negative eigenvalues are complete on the part of the domain where initial conditions are imposed while those with positive eigenvalues are complete where final conditions are imposed the corresponding exponentially growing and exponentially decaying solutions may be used to expand arbitrary solutions on semi infinite intervals in the time variable a natural iterative procedure for obtaining solutions on finite intervals is shown to converge in some cases a linearly growing solution must also be taken into account

necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation x a x 1a q abstract we consider the problem of when the matrix equation x a x 1 a q has a positive definite solution here q is positive definite we study both the real and the complex case this equation plays a crucial role in solving a special case of the discrete time riccati equation we present both necessary and sufficient conditions for its solvability this result is obtained by using an analytic factorization approach moreover we present algebraic recursive algorithms to compute the largest and smallest the solution of the equation respectively finally we discuss the number of solutions

perturbation analysis of the maximal solution of the matrix equation x a x 1a p consider the nonlinear matrix equation x a x 1 a p where a p are n x n complex matrices with p hermitian positive definite and a denotes the conjugate transpose of a matrix a in this pape

on the matrix equation x atx 1a i simple necessary and sufficient conditions for the matrix equation x atx 1a i to have a positive definite solution are given these conditions are used to explain some properties of the equation and to obtain new information finally we prove a conjecture on the extremal solutions

level dependence of the nonlinear distortion component of distortion product otoacoustic emissions in humans distortion product otoacoustic emissions dpoaes emerge when presenting two primary tones with different frequencies f1 and f2 to the cochlea and are commonly used in diagnosis and research to evaluate the functional state of the cochlea optimal primary tone stimulus levels accounting for the different level dependencies of the traveling wave amplitudes of the two primary tones near the f2 tonotopic place on the basilar membrane are often used to maximize dpoae amplitudes however parameters defining the optimal levels can be affected by wave interference between the nonlinear distortion and coherent reflection components of the dpoae here the components were separated in the time domain using a pulsed stimulus paradigm and optimal levels determined based on the amplitude dependence of the nonlinear distortion components on primary tone stimulus levels level parameters yielding maximum dpoae amplitudes were derived for six normal hearing adults and compared to data recorded with continuous two tone stimulation the level parameters resulting from analysis of the nonlinear distortion components show dependence on stimulus frequency and small standard deviations dpoae input output functions derived for optimal levels exhibit larger slopes wider dynamic range and less variability across subjects than those derived for conventional stimulus and analysis conditions potentially increasing their reliability and sensitivity for assessing cochlea function

input output functions of the nonlinear distortion component of distortion product otoacoustic emissions in normal and hearing impaired human ears distortion product otoacoustic emissions dpoaes arise in the cochlea in response to two tones with frequencies f1 and f2 and mainly consist of two components a nonlinear distortion and a coherent reflection component wave interference between these components limits the accuracy of dpoaes when evaluating the function of the cochlea with conventional continuous stimulus tones here dpoae components are separated in the time domain from dpoae signals elicited with short stimulus pulses the extracted nonlinear distortion components are used to derive estimated distortion product thresholds edpts from semi logarithmic input output i o functions for 20 normal hearing and 21 hearing impaired subjects i o functions were measured with frequency specific stimulus levels at eight frequencies f2 1 8 khz f2 f1 1 2 for comparison dpoaes were also elicited with continuous primary tones both acquisition paradigms yielded edpts which significantly correlated with behavioral thresholds p 0 001

characteristics of the 2f1 f2 distortion product otoacoustic emission in a normal hearing population distortion product otoacoustic emission dpoae fine structure and component characteristics are reported between 0 75 and 16 khz in 356 clinically normal hearing human subjects ages 10 to 65 yr stimulus tones at 55 40 65 55 and 75 75 db spl were delivered using custom designed drivers and a calibration method that compensated for the depth of insertion of the otoacoustic emission oae probe in the ear canal dpoae fine structure depth and spacing were found to be consistent with previous reports with depth varying between 3 and 7 db and average spacing ratios f f between 15 and 25 depending on stimulus level and frequency in general fine structure depth increased with increasing frequency likely due to a diminishing difference between dpoae component levels fine structure spacing became wider with increasing age above 8 khz dpoae components were extracted using the inverse fast fourier transform method adhering to a strict signal to noise ratio criterion for clearer interpretation component data from four age groups between 18 and 55 yr old were available for the stimulus levels of 75 75 db spl the age groups could be differentiated with greater than 90 accuracy when using the level of the component presumed to originate from the dpoae characteristic frequency place this accuracy held even for frequencies at and below 4 khz where the age groups exhibited similar average hearing thresholds

moments of click evoked otoacoustic emissions in human ears group delay and spread instantaneous frequency and bandwidth a click evoked otoacoustic emission ceoae has group delay and spread as first and second order temporal moments varying over frequency and instantaneous frequency and bandwidth as first and second order spectral moments varying over time energy smoothed moments were calculated from a ceoae database over 0 5 15 khz bandwidth and 0 25 20 ms duration group delay and instantaneous frequency were calculated without phase unwrapping using a coherence synchrony measure that accurately classified ears with hearing loss ceoae moment measurements were repeatable in individual ears group delays were similar for ceoaes and stimulus frequency oaes group spread is a frequency specific measure of temporal spread in an emission related to spatial spread across tonotopic generation sites along the cochlea in normal ears group delay and spread increased with frequency and decreased with level a direct measure of cochlear tuning above 4 khz was analyzed using instantaneous frequency and bandwidth synchronized spontaneous oaes were present in most ears below 4 khz and confounded interpretation of moments in ears with sensorineural hearing loss group delay and spread varied with audiometric classification and amount of hearing loss group delay differed between older males and females ceoae moments reveal clinically relevant information on cochlear tuning in ears with normal and impaired hearing

otoacoustic emission latency cochlear tuning and hearing functionality in neonates transient evoked otoacoustic emissions of a large population of neonates 466 ears are analyzed with the aim of establishing if a significant latency difference can be observed between pass 333 and fail 133 ears discriminated with a screening protocol based on band and global reproducibility the ears that did not pass the test in at least one frequency band are named fail for simplicity but they should be more appropriately defined as partial pass in a previous study significantly different average latencies had been observed in adult subjects comparing normal hearing and hearing impaired ears j acoust soc am 111 297 308 2002 but no similar study has been conducted on neonates yet an improved wavelet technique was applied to transient evoked otoacoustic emission data to get accurate experimental measurements of the otoacoustic emission latency the results show statistically significant differences between the latency distributions of the pass and fail populations with the fail latencies longer however non gaussianity of the distributions and systematic errors associated with low reproducibility levels suggested using a conservative approach in the data analysis and interpretation new otoacoustic estimates of cochlear tuning in neonates are also provided

time frequency domain filtering of evoked otoacoustic emissions time domain filtering is a standard analysis technique which is used to disentangle the two main vector components of the distortion product otoacoustic emission response exploiting their different phase frequency relation in this study a time frequency filtering technique based on the continuous wavelet transform is proposed to overcome the intrinsic limitations of the time domain filtering technique and to extend it also to the analysis of stimulus frequency and transient evoked otoacoustic emissions the advantages of the proposed technique are first discussed on a theoretical basis then practically demonstrated by applying it to the analysis of synthesized and real otoacoustic data the results show that the time frequency approach can be empirically optimized to get effective separation of the components of the otoacoustic response associated with either different generation mechanisms or different generation places focusing on a single component of the otoacoustic response with a given time frequency signature may also improve significantly the signal to noise ratio because the random noise contribution tends to be uniformly distributed on the time frequency plane

identification of otoacoustic emissions components by means of adaptive approximations clicks and a set of tone bursts covering the same frequency band were applied as a stimuli evoking otoacoustic emissions oae recorded otoacoustic emissions were decomposed into the basic waveforms by means of high resolution adaptive time frequency approximation method based on the matching pursuit algorithm the method allows for description of the signal components in terms of frequencies time occurrences time spans and energy the analysis of oae s energy density distributions in time frequency space revealed that click responses can be considered as linear superpositions of responses to tone bursts the frequency latency relationship was studied and compared with earlier works the method made possible the exhaustive description of the resonant modes specific for given subject ear they were characterized not only by the close frequencies appearing for different tones but they usually had similar latencies and time spans short time and long time resonant modes were identified the second ones