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

finite volume element methods for non definite problems the error estimates for finite volume element method applied to 2 and 3 d non definite problems are derived a simple upwind scheme is proven to be unconditionally stable and first order accurate

on the finite volume element method for general self adjoint elliptic problems the finite volume element method fve is a discretization technique for partial differential equations this paper develops discretization energy error estimates for general self adjoint elliptic boundary value problems with fve based on triangulations on which there exist linear finite element spaces and a very general type of control volumes covolumes the energy error estimates of this paper are also optimal but the restriction conditions for the covolumes given in r e bank and d j rose siam j numer anal 24 1987 pp 777 787 z q cai numer math 58 1991 pp 713 735 are removed the authors finally provide a counterexample to show that an expected l2 error estimate does not exist in the usual sense it is conjectured that the optimal order of u u h 0 omega should be o h for the general case

a node centered finite volume method for a fracture model on triangulations abstract in this paper a node centered finite volume method based on triangulations for a fracture model is presented in which we restrict the pressure to the linear finite element space while the velocity can be approximated by constant vectors element by element the numerical scheme is established just associated with the pressure to avoid the saddle point problem error estimates of o h accuracy for the discrete h1 semi norm and the discrete l2 norm of pressure p and the l2 2 norm of velocity u are developed on general triangulations under an additional assumption about essentially symmetric control volumes the error estimates for the pressure p can be improved to o h3 2 finally numerical experiments are carried out to verify the accuracy and convergence rates for the proposed finite volume scheme

higher order finite volume methods ii inf sup condition and uniform local ellipticity the main purpose of this paper is to study the construction of higher order finite volume methods fvms of triangle meshes we investigate the relationship of the three theoretical notions crucial in the construction of fvms the uniform ellipticity of the family of its discrete bilinear forms its inf sup condition and its uniform local ellipticity both the uniform ellipticity of the family of the discrete bilinear forms and its inf sup condition guarantee the unique solvability of the fvm equations and the optimal error estimate of the approximate solution we characterize the uniform ellipticity in terms of the inf sup condition and a geometric condition on the bijective operator mapping from the trial space onto the test space involved in the construction of fvms we present a geometric interpretation of the inf sup condition moreover since the uniform local ellipticity is a convenient sufficient condition for the uniform ellipticity we further provide sufficient conditions and necessary conditions of the uniform local ellipticity

tilting bundles on toric fano fourfolds this paper constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth 4 dimensional toric fano varieties the tilting bundles lead to a large class of explicit calabi yau 5 algebras obtained as the corresponding rolled up helix algebra a database of the full strong exceptional collections can be found in the package quiverstoricvarieties for the computer algebra system macaulay2

the finite volume element methods for poisson equation based on adini s element in this paper we construct and analyze the finite volume element scheme based on adini s element for poisson equation choosing trial and test spaces as the adini s finite element space and the piecewise linear function space respectively optimal order error estimates in h 1 and l 2 norms are derived in addition the global and locally pointwise superconvergence estimates are also discussed lastly a numerical experiment is carried out which confirms some results of theoretical analysis

a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes abstract we construct a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes where the strict convexity restriction on the meshes is removed the main contributions of this paper include three aspects firstly the classical finite volume element c fve method is extended to severely distorted quadrilateral meshes even with concave cells by virtue of a new overlapping dual partition and a new gradient approximation in fact the choice of this dual partition and gradient approximation is also conducive to the construction of a monotone scheme secondly a new monotonicity correction is suggested based on which we obtain a monotone finite volume element m fve method the resulting m fve method still keeps the local conservation and is easy for implementation finally we analyze theoretically the truncation error and the monotonicity for this scheme besides the existence of a solution to this nonlinear scheme is proved by applying the brouwer s fixed point theorem numerical results demonstrate that the m fve method has the approximate second order accuracy and preserves well the positivity of the solution for both isotropic and anisotropic diffusion problems on severely distorted quadrilateral meshes

superconvergence by l2 projection for a stabilized finite volume method for the stationary navier stokes equations a superconvergence result is established for the stationary navier stokes equations by a stabilized finite volume method and l 2 projection on a coarse mesh like other results in the family of l 2 projection methods the superconvergence presented in this paper is based on some regularity assumption for the navier stokes problem and is applicable to the stabilized finite volume method with quasi uniform partitions

the locally stabilized finite volume method for incompressible flow a locally stabilized finite volume method for the two dimensional incompressible flow governed by stationary stokes and navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem the optimal l 2 error estimate of u h p h determined by stokes equations is also deduced some numerical examples are provided to check the efficiency of this method

enriched multi point flux approximation for general grids it is well known that the two point flux approximation a numerical scheme used in most commercial reservoir simulators has o 1 error when grids are not k orthogonal in the last decade the multi point flux approximations have been developed as a remedy however non physical oscillations can appear when the anisotropy is really strong we found out the oscillations are closely related to the poor approximation of pressure gradient in the flux computation in this paper we propose the control volume enriched multi point flux approximation empfa for general diffusion problems on polygonal and polyhedral meshes non physical oscillations are not observed for realistic and strongly anisotropic heterogeneous material properties described by a full tensor exact linear solutions are recovered for grids with non planar interfaces and a first and second order convergence are achieved for the flux and scalar unknowns respectively

mixed finite element methods on nonmatching multiblock grids we consider mixed finite element methods for second order elliptic equations on nonmatching multiblock grids a mortar finite element space is introduced on the nonmatching interfaces we approximate in this mortar space the trace of the solution and we impose weakly a continuity of flux condition a standard mixed finite element method is used within the blocks optimal order convergence is shown for both the solution and its flux moreover at certain discrete points superconvergence is obtained for the solution and also for the flux in special cases computational results using an efficient parallel domain decomposition algorithm are presented in confirmation of the theory

an integral equation approach to the unsteady convection diffusion equations an integral equation approach is proposed to solve the unsteady convection diffusion equations in this approach the second order adams moulton method is firstly utilized for the time discretization then by using the green s function of the laplace equation in the series form the convection diffusion equation is transformed into an integral equation that is further converted into an algebraic equation system the accuracy convergence and the stability of this integral equation approach are examined by four examples in comparison with the characteristic variational multiscale method and the finite volume element method the integral equation approach shows a higher accuracy compared with the finite volume element method the integral equation approach has a better convergence in solving the convection dominated convection diffusion problems the integral equation approach demonstrates a good stability

on domain decomposition algorithms for covolume methods for elliptic problems in this paper some new two level additive schwarz domain decomposition methods are constructed and used as preconditioners for gmres for the nonsymmetric systems arising from the covolume methods for elliptic problems without any restriction on the coarse mesh size the convergence of the preconditioned gmres is obtained for both circumcentric and barycentric covolume methods with inexact solvers for subproblems the rates of convergence are shown to be independent of the number of subregions and these methods are optimal for generous overlap

the finite volume element method for diffusion equations on general triangulations this paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in mathcal r 2 using a special type of control volume the theory applies to diffusion equations of the form begin gathered nabla a nabla u f quad text in omega hfill u 0 quad text on partial omega hfill end gathered under fairly general conditions the theory establishes o h estimates of the error in a discrete mathcal h 1 seminorm under an additional assumption concerning local uniformity of the triangulation the estimate is improved to o h 2

the finite volume method based on stabilized finite element for the stationary navier stokes problem a finite volume method based on stabilized finite element for the two dimensional stationary navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem we obtain the well posedness of the fvm based on stabilized finite element for the stationary navier stokes equations moreover for quadrilateral and triangular partition the optimal h 1 error estimate of the finite volume solution u h and l 2 error estimate for p h are introduced finally we provide a numerical example to confirm the efficiency of the fvm

the finite volume method and application in combinations abstract in this paper the conventional finite volume method fvm is interpreted as a new kind of galerkin finite element method fem where the same piecewise linear functions are chosen as in both trial and test spaces and some specific integration rules are adopted error analysis is made for the regular delaunay triangulation involving obtuse triangles separated to prove optimal convergence rates of the approximate solutions obtained the new interpretation makes the fvm analysis much easier because we may bypass verification of the nontrivial ladyzhenskaya babuska brezzi lbb condition by the petrov galerkin fem in the existing analysis of fvm more importantly the new interpretation and the simple fvm analysis enable us to construct easily the combinations of fvm with other popular numerical methods such as the finite element method fem the finite difference method fdm the ritz galerkin method rgm etc for solving complicated problems of partial differential equations pde for example for solving singularity problems the combination of rgm fvm is superior to the combination of rgm fdm in flexibility of arbitrary solution domains and also superior to the combination of rgm fem in substantial saving of cpu time since the conservative law of flux may be maintained exactly in the numerical solutions and since obtuse triangles may be included in the delaunay triangulation the fvm and its combinations become very promising for solving elliptic boundary value problems in particular those where singularity solutions exist and those where the obeying of conservative law is crucial the numerical examples of combinations of rgm fvm are given for solving motz s problems to verify the optimal convergence rates the techniques and analysis of fvm and its combinations can be extended to the convection diffusion problems most importantly an important aspect in this paper is the possibility to include obtuse triangles in the error analysis

the method of variably scaled radial kernels for solving two dimensional magnetohydrodynamic mhd equations using two discretizations the crank nicolson scheme and the method of lines mol abstract mhd equations have many applications in physics and engineering the model is coupled equations in velocity and magnetic field and has a parameter namely hartmann the value of hartmann number plays an important role in the equations when this parameter increases using different meshless methods makes the oscillations in velocity near the boundary layers in the region of the problem in the present paper a numerical meshless method based on radial basis functions rbfs is provided to solve mhd equations for approximating the spatial variable a new approach which is introduced by bozzini et al 2015 is applied the method will be used here is based on the interpolation with variably scaled kernels the methodology of the new technique is defining the scale function c on the domain r d then the interpolation problem from the data locations x j r d transforms to the new interpolation problem in the data locations x j c x j r d 1 bozzini et al 2015 the radial kernels used in the current work are multiquadrics mq inverse quadric iq and wendland s function of course the latter one is based on compactly supported functions to discretize the time variable two techniques are applied one of them is the crank nicolson scheme and another one is based on mol the numerical simulations have been carried out on the square and elliptical ducts and the obtained numerical results show the ability of the new method for solving this problem also in appendix we provide a computational algorithm for implementing the new technique in matlab software

multigrid for the mortar finite element method a multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed these problems are posed on domains partitioned into subdomains each of which is independently triangulated in a multilevel fashion the multilevel mortar finite element spaces based on such triangulations which need not align across subdomain interfaces are in general not nested suitable grid transfer operators and smoothers are developed which lead to a variable v cycle preconditioner resulting in a uniformly preconditioned algebraic system computational results illustrating the theory are also presented

stability of sheaves of locally closed and exact forms abstract for any smooth projective variety x of dimension n over an algebraically closed field k of characteristic p 0 with x 1 0 if the truncated symmetric powers t l x 1 0 l n p 1 of x 1 are semi stable then the sheaf b x 1 of exact 1 forms is stable when x is a surface with x 1 0 and x 1 is semi stable the sheaf b x 2 of exact 2 forms is also stable moreover under the same condition the sheaf z x 1 of closed 1 forms is stable when p 3 and z x 1 is semi stable when p 3

a symmetric finite volume scheme for selfadjoint elliptic problems based on a linear finite element space a symmetric finite volume scheme for a self adjoint elliptic boundary value problem is proposed error estimates in l2 norm h1 norm and l norm are derived some post processing techniques are also provided

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

a mortar finite volume method for a fractured model in porous media abstract in this paper we consider a mortar finite volume method for a fractured model of flow in porous media in this model the permeability coefficients are variable between the fracture and the surrounding porous media a finite volume method based on raviart thomas elements combined with the mortar technique of domain decomposition is presented in which sub domains are triangulated independently and the meshes do not match at interfaces the great advantage of the method is avoiding solving the saddle point problem since the numerical scheme is just related to the pressure p and the velocity u can be expressed by p we also prove error estimates of order h on the discrete h 1 norm between the exact solution p and the mortar finite volume solution p and the l 2 2 norm between u and u finally numerical experiments have been performed to show the consistency of the convergence rates with the theoretical analysis

the mortar finite volume method with the crouzeix raviart element for elliptic problems abstract we construct and analyse a mortar finite volume method for the discretization for selfadjoint elliptic boundary value problems in r 2 this method is based on the mortar crouzeix raviart non conforming finite element spaces we prove the optimal order h 1 norm and l 2 norm error estimates between the exact solution and the mortar finite volume approximation of the elliptic problems

a low order anisotropic nonconforming characteristic finite element method for a convection dominated transport problem a low order anisotropic nonconforming rectangular finite element method for the convection diffusion problem with a modified characteristic finite element scheme is studied in this paper the o h 2 order error estimate in l 2 norm with respect to the space one order higher than the expanded characteristic mixed finite element scheme with order o h and the same as the conforming case for a modified characteristic finite element scheme under regular meshes is obtained by use of some distinct properties of the interpolation operator and the mean value technique instead of the so called elliptic projection which is an indispensable tool in the convergence analysis of the previous literature lastly some numerical results of the element are provided to verify our theoretical analysis

an optimal weighted upwinding covolume method on non standard grids for convection diffusion problems in 2d in this paper we develop an optimal weighted upwinding covolume method on non standard covolume grids for convection diffusion problems in two dimensions the novel feature of our method is that we construct the non standard covolume grid in which the nodes of covolumes vary in the interior of different volumes of primary grid depending on the local weighted factors and further on the local peclet s numbers a simple method of finding the local optimal weighted factors is also derived from a non linear function of local peclet s numbers the developed method leads to a totally new scheme for convection diffusion problems which overcomes numerical oscillation avoids numerical dispersion and has high order accuracy some theoretical analyses are given and numerical experiments are presented to illustrate the performance of the method copyright 2006 john wiley sons ltd

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

stability conditions on threefolds with nef tangent bundles abstract in this paper we prove the bogomolov gieseker type inequality conjecture for threefolds with nef tangent bundles as a corollary there exist bridgeland stability conditions on these threefolds

a finite volume method based on the crouzeix raviart element for elliptic pde s in two dimensions we introduce and analyse a finite volume method for the discretization of elliptic boundary value problems in mathbb r 2 the method is based on nonuniform triangulations with piecewise linear nonconforming spaces we prove optimal order error estimates in the l 2 norm and a mesh dependent h 1 norm

frobenius morphisms and derived categories on two dimensional toric deligne mumford stacks abstract for a toric deligne mumford dm stack x we can consider a certain generalization of the frobenius endomorphism for such an endomorphism f x x on a 2 dimensional toric dm stack x we show that the push forward f o x of the structure sheaf generates the bounded derived category of coherent sheaves on x we also choose a full strong exceptional collection from the set of direct summands of f o x in several examples of two dimensional toric dm orbifolds x

a finite volume method on general surfaces and its error estimates abstract in this paper we study a finite volume method and its error estimates for the numerical solution of some model second order elliptic partial differential equations defined on a smooth surface the discretization is defined via a surface mesh consisting of piecewise planar triangles and piecewise polygons the optimal error estimates of the approximate solution are proved in both the h 1 and l 2 norms which are of first order and second order respectively under mesh regularity assumptions some numerical tests are also carried out to experimentally verify our theoretical analysis

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

a combined finite volume nonconforming mixed hybrid finite element scheme for degenerate parabolic problems we propose and analyze a numerical scheme for nonlinear degenerate parabolic convection diffusion reaction equations in two or three space dimensions we discretize the diffusion term which generally involves an inhomogeneous and anisotropic diffusion tensor over an unstructured simplicial mesh of the space domain by means of the piecewise linear nonconforming crouzeix raviart finite element method or using the stiffness matrix of the hybridization of the lowest order raviart thomas mixed finite element method the other terms are discretized by means of a cell centered finite volume scheme on a dual mesh where the dual volumes are constructed around the sides of the original mesh checking the local peclet number we set up the exact necessary amount of upstream weighting to avoid spurious oscillations in the convection dominated case this technique also ensures the validity of the discrete maximum principle under some conditions on the mesh and the diffusion tensor we prove the convergence of the scheme only supposing the shape regularity condition for the original mesh we use a priori estimates and the kolmogorov relative compactness theorem for this purpose the proposed scheme is robust only 5 point 7 point in space dimension three locally conservative efficient and stable which is confirmed by numerical experiments

a discontinuous finite volume method for a coupled fracture model abstract in this paper we present a discontinuous finite volume method for a hybrid dimensional coupled fracture model on triangular meshes in matrix and fracture the pressure is approximated by the discontinuous and continuous piecewise linear elements and in order to retain local conservation property the velocity is sought in the discontinuous lowest order raviart thomas element space and piecewise linear element space the proposed numerical scheme is only associated with the pressure so we avoid solving an indefinite saddle point problem in addition the discontinuous method eliminates the continuity of approximate functions across the interelement boundary so it has the advantage of high localizability and easy handling of complicated geometries optimal order error estimates for the pressure and velocity are proved and numerical experiments are carried out to confirm our theoretical analysis

weil restriction and support varieties this paper extends the comparison results for cohomological support varieties for chevalley groups of the form g fp established by j carlson z lin and d nakano to chevalley groups of the form g fpd other topics considered are complexity and non maximal support varieties for modules techniques developed by j pevtsova and the author together with the use of weil restriction functors are employed

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

a finite difference scheme for two dimensional semiconductor device of heat conduction on composite triangular grids abstract the momentary state of a semiconductor device of heat conduction is described by a system of four nonlinear partial differential equations one elliptic equation is for the electrostatic two parabolic equations are for the electron concentration and the hole concentration and one heat exchange equation is for the temperature according to the necessary of practical numerical simulations and based on the balance equation finite difference schemes for two dimensional transient behavior of a semiconductor device of heat conduction on composite triangular grids are constructed studying their stability and convergence properties the error estimate in the energy norm is obtained finally a numerical example is given

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

preconditioning the bidomain model with almost linear complexity the bidomain model is widely used in electro cardiology to simulate spreading of excitation in the myocardium and electrocardiograms it consists of a system of two parabolic reaction diffusion equations coupled with an ode system its discretisation displays an ill conditioned system matrix to be inverted at each time step simulations based on the bidomain model therefore are associated with high computational costs in this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues the torso the preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi definite a block lu decomposition of the system together with a heuristic approximation referred to as the monodomain approximation are the key ingredients for the preconditioning definition numerical results are provided for two test cases a 2d test case on a realistic slice of the thorax based on a segmented heart medical image geometry a 3d test case involving a small cubic slab of tissue with orthotropic anisotropy the analysis of the resulting computational cost both in terms of cpu time and of iteration number shows an almost linear complexity with the problem size i e of type nlog a n for some constant a which is optimal complexity for such problems

convergence of the discontinuous finite volume method for elliptic problems with minimal regularity this paper investigates convergence of the discontinuous finite volume method dfvm under minimal regularity assumptions on solutions of second order elliptic boundary value problems conventional analysis requires the solutions to be in sobolev spaces h 1 s s 12 here we assume the solutions are in h 1 s s 0 and employ the techniques developed in gudi 2010 18 20 to derive error estimates in a mesh dependent energy norm and the l 2 norm for dfvm the theoretical estimates are illustrated by numerical results which include problems with corner singularity and intersecting interfaces

interpretation of distortion product otoacoustic emission measurements i two stimulus tones the interpretation of common but poorly understood observed characteristics of distortion product emissions is assisted by the development of a simple model this model essentially includes only saturation of the cochlear amplifier with emissions arising naturally from the same nonlinear processes which cause the saturation the model provides useful physical explanations of emission behavior particularly considered as a function of the stimulus intensities of the two primaries i e behavior with fixed stimulus frequencies it is assumed that emission generation consists of two main components which are always present in the total emission but which most often have approximately opposite i e canceling phases one component arises in a small region centered about the peak of the emission generation function while the other arises from the region basal to this peak at low stimulus levels with normal cochlear amplifier operation the peak of the emission generation function is sharp so the emission from the peak region dominates the total emission this peak emission has typically been characterized as the active emission at high stimulus levels where saturation is important or at all levels when the gain of the cochlear amplifier is reduced the summed basal component dominates the total emission the characteristics of this basal emission are similar to and continuous with the characteristics of the truly passive emission i e the emission observed when the cochlear amplifier gain is identically zero under circumstances when the emissions from the peak and basal components are approximately equal there is seen a sharp notch characteristic of phase cancellation the simple model produces emission distributions as a function of independent variation of the two stimulus amplitudes which are in good agreement with observation it is shown that the furosemide assay provides a good estimate of cochlear amplifier gain when a correction factor of about 10 db is added however when using two stimulus tones neither absolute emission amplitudes or emission input output functions or the furosemide assay can adequately distinguish between cases of moderate versus poor cochlear amplifier dysfunction when the cochlear amplifier gains are in the range from about half normal to zero

a new class of high order finite volume methods for second order elliptic equations in the numerical simulation of many practical problems in physics and engineering finite volume methods are an important and popular class of discretization methods due to the local conservation and the capability of discretizing domains with complex geometry however they are limited by low order approximation since most existing finite volume methods use piecewise constant or linear function space to approximate the solution in this paper a new class of high order finite volume methods for second order elliptic equations is developed by combining high order finite element methods and linear finite volume methods optimal convergence rate in h 1 norm for our new quadratic finite volume methods over two dimensional triangular or rectangular grids is obtained

penalty combinations of the ritz galerkin and finite difference methods for singularity problems abstract penalty combination of the ritz galerkin and finite difference methods is presented for solving elliptic boundary value problems with singularities the superconvergence rate o h2 of solution derivatives by the combination can be achieved while using quasiuniform rectangular difference grids where h is the maximal mesh length of difference grids used in the finite difference method and 0 is an arbitrarily small number it is due to its simplicity that the penalty combination of the ritz galerkin and finite difference methods is highly recommended for solving the complicated problems with multiple singularities and multiple interfaces

multigrid for the mortar element method for p1 nonconforming element in this paper a multigrid algorithm is presented for the mortar element method for p1 nonconforming element based on the theory developed by bramble pasciak xu in 5 we prove that the w cycle multigrid is optimal i e the convergence rate is independent of the mesh size and mesh level meanwhile a variable v cycle multigrid preconditioner is constructed which results in a preconditioned system with uniformly bounded condition number

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

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

estimating bone conduction transfer functions using otoacoustic emissions a technique for estimating the nonparametric bone conduction transfer function using distortion product otoacoustic emissions dpoaes is presented individual transfer functions were obtained using dpoaes recorded from a single ear of five normal hearing adults repeatability of the technique was investigated by performing measurements on at least three dates functions were reasonably repeatable and were unique to each individual as expected from subjective measurements input force and dpoae measurements were made for each individual and a model of the auditory periphery representative of an average person was employed the technique is objective and requires only passive cooperation but robust dpoaes are needed and the measurement time can be onerous for a wide frequency band or fine frequency resolution with appropriate adjustments to the model of the auditory periphery the method could be applied with animal models

simultaneous latency estimations for distortion product otoacoustic emissions and envelope following responses the purpose of this research was to simultaneously estimate processing delays in the cochlea and brainstem using the same acoustic stimuli apparent latencies were estimated from ear canal measurements of 2f1 f2 distortion product otoacoustic emissions dpoaes and scalp recordings of the f2 f1 envelope following response efr the stimuli were equal level tone pairs 65db spl with the upper tone f2 set at either 900 or 1800hz to fix the initiation site of the dpoae and efr the frequency of f1 was swept continuously between frequency limits chosen to keep the efr response between 150 and 170hz the average dpoae latencies were 9 6 and 6 2ms for f2 900 and 1800hz and the corresponding efr latencies were 12 4 and 8 8ms in a control condition a third suppressor tone was added near the dpoae response frequency to evaluate whether the potential source at fdp was contributing significantly to the measured emission dpoae latency is the sum of both inward and outward cochlear delays the efr apparent la

superconvergence of finite volume methods for the second order elliptic problem abstract this paper derives a superconvergence result for finite volume approximations of the second order elliptic problem by using a l2 projection post processing technique the superconvergence result is applicable to different kind of finite volume methods and to general quasi uniform meshes

on the coupling of finite volume and discontinuous galerkin method for elliptic problems the coupling of cell centered finite volume method with primal discontinuous galerkin method is introduced in this paper for elliptic problems convergence of the method with respect to the mesh size is proved numerical examples confirm the theoretical rates of convergence advantages of the coupled scheme are shown for problems with discontinuous coefficients or anisotropic diffusion matrix

uniform convergence and preconditioning method for mortar mixed element method for nonselfadjoint and indefinite problems abstract in this paper a mortar version of the modified mixed element method is proposed for nonselfadjoint and indefinite second order elliptic problems it is proven that the modified mortar mixed element method is equivalent to a modified mortar nonconforming element method based on this equivalence the existence uniqueness and uniform convergence of the solution for the modified mortar mixed element method are shown under minimal regularity assumption meanwhile an optimal error estimate for the modified mortar mixed element method is obtained under h2 smoothness assumption furthermore an additive schwarz preconditioning method for solving the discrete problem is provided and the nearly optimal convergence rate for the preconditioned gmres method is proven under the minimal regularity assumption

unified analysis of finite volume methods for the stokes equations we establish a general framework for analyzing the class of finite volume methods for the stokes equations under the framework optimal order convergence for velocity and pressure in various sobolev norms are obtained in a natural and systematic way specifically optimal l 2 error estimates for velocity are obtained for the first time for several different finite volume methods

group delays of distortion product otoacoustic emissions relating delays measured with f1 and f2 sweep paradigms a theoretical analysis is presented of group delays of distortion product otoacoustic emissions dpoaes measured with the phase gradient method the aim of the analysis is to clarify the differences in group delays d1 and d2 obtained using the f1 and the f2 sweep paradigms respectively and the dependence of group delays on the order of the dpoae two models are considered the place fixed and the wave fixed models while in the former model the generation place is assumed to be invariant with both f1 and f2 sweeps in the latter model the shift of generation place is fully accounted for by making a simple local approximation of the cochlear scale invariance a mathematical conversion from phase place to phase frequency gradients is incorporated in the wave fixed model under the assumption that the dpoae as recorded at the best f2 f1 ratio is dominated by the contribution from the generation site and not by e g reflection components the analysis leads to simple expressions for the ratio and difference between d1 and d2 validation of the models against experimental data indicates that lower sideband dpoaes 2f1 f2 3f1 2f2 4f1 3f2 are most consistent with the wave fixed model upper sideband components 2f2 f1 in contrast are not properly described by either the place fixed or the wave fixed model independent whether dpoae generation is assumed to originate at the f2 or at the more basally located f dp characteristic place

on the accuracy of the finite volume element method for diffusion equations on composite grids this paper develops the finite volume element fve method which is similar to the so called control volume finite element method but tailored to composite grid applications fve is described for the general two dimensional diffusion equation in divergence form o h 3 2 discretization error estimates are then developed for the case of triangular elements these results are improved to o h 2 using a special modification involving rectilinear elements at the grid interface

block iterative solvers for higher order finite volume methods recently new higher order finite volume methods fvm were introduced in z cai j douglas m park development and analysis of higher order finite volume methods over rectangles for elliptic equations adv comput math 19 2003 3 33 where the linear system derived by the hybridization with lagrange multiplier satisfying the flux consistency condition is reduced to a linear system for a pressure variable by an appropriate quadrature rule we study the convergence of an iterative solver for this linear system the conjugate gradient cg method is a natural choice to solve the system but it seems slow possibly due to the non diagonal dominance of the system in this paper we propose block iterative methods with a reordering scheme to solve the linear system derived by the higher order fvm and prove their convergence with a proper ordering each block subproblem can be solved by fast methods such as the multigrid mg method the numerical experiments show that these block iterative methods are much faster than cg

error estimates in l 2 h 1 and l in covolume methods for elliptic and parabolic p roblems a unified approach in this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane we introduce a general approach for connecting these methods with finite element method analysis this unified approach is used to prove known convergence results in the h 1 l 2 norms and new results in the max norm for the elliptic problems we demonstrate that the error u u h between the exact solution u and the approximate solution u h in the maximum norm is o h 2 ln h in the linear element case furthermore the maximur norm error in the gradient is shown to be of first order similar results hold for the parabolic problems

interrelations among distortion product phase gradient delays their connection to scaling symmetry and its breaking distortion product otoacoustic emission dpoae phase versus frequency functions and corresponding phase gradient delays have received considerable attention because of their potential for providing information about mechanisms of emission generation cochlear wave latencies and characteristics of cochlear tuning the three measurement paradigms in common use fixed f1 fixed f2 and fixed f2 f1 yield significantly different delays suggesting that they depend on qualitatively different aspects of cochlear mechanics in this paper theory and experiment are combined to demonstrate that simple phenomenological arguments which make no detailed mechanistic assumptions concerning the underlying cochlear mechanics predict relationships among the delays that are in good quantitative agreement with experimental data obtained in guinea pigs to understand deviations between the simple theory and experiment a general equation is found that relates the three delays for any deterministic model of dpoae generation both model independent and exact the general relation provides a powerful consistency check on the measurements and a useful tool for organizing and understanding the structure in dpoae phase data e g for interpreting the relative magnitudes and intensity dependencies of the three delays analysis of the general relation demonstrates that the success of the simple phenomenological approach can be understood as a consequence of the mechanisms of emission generation and the approximate local scaling symmetry of cochlear mechanics the general relation is used to quantify deviations from scaling manifest in the measured phase gradient delays the results indicate that deviations from scaling are typically small and that both linear and nonlinear mechanisms contribute significantly to these deviations intensity dependent mechanisms contributing to deviations from scaling include cochlear reflection and wave interference effects associated with the mixing of distortion and reflection source emissions as in dpoae fine structure finally the ratio of the fixed f1 and fixed f2 phase gradient delays is shown to follow from the choice of experimental paradigm and in the scaling limit contains no information about cochlear physiology whatsoever these results cast considerable doubt on the theoretical basis of recent attempts to use relative dpoae phase gradient delays to estimate the bandwidths of peripheral auditory filters

on the heterogeneous multiscale method with various macroscopic solvers abstract the heterogeneous multiscale method hmm is a general method for efficient numerical solution of problems with multiscales it consists of two components an overall macroscopic solver for macrovariables on a macrogrid and an estimation of the missing macroscopic data from the microscopic model in this paper we present a state of the art review of the hmm with various macroscopic solvers including finite differences finite elements discontinuous galerkin mixed finite elements control volume finite elements nonconforming finite elements and mixed covolumes the first four solvers have been studied in the hmm setting the others are not as example the hmm with the nonconforming finite element macroscopic solver for nonlinear and random homogenization problems is also studied here

uniform convergence of finite volume element method with crouzeix raviart element for non self adjoint and indefinite elliptic problems in this paper we consider the finite volume element method based on the crouzeix raviart element and prove the existence uniqueness and uniform convergence of the finite volume element approximations for the non self adjoint and indefinite elliptic problems under minimal elliptic regularity assumption

group delays of distortion product otoacoustic emissions in the guinea pig this paper presents a comprehensive set of experimental data on group delays of distortion product otoacoustic emissions dpoaes in the guinea pig group delays of the dpoaes with frequencies 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 were measured with the phase gradient method both the f1 and the f2 sweep paradigm were used differences between the two sweep paradigms were investigated for the four dpoaes as well as the group delay differences between the dpoaes analysis revealed larger group delays with the f2 sweep paradigm but only for the lower sideband dpoaes with fdp f1 f2 for the lower sideband cubic distortion product 2f1 f2 the f2 sweep delays were a factor of 1 17 1 54 larger than the f1 sweep delays depending on frequency the upper sideband dpoae 2f2 f1 showed no significant difference between f1 and f2 sweep group delays except for the highest and lowest f2 frequencies comparing the group delays of the dpoaes for each sweep paradigm separately equal group delays were found for all four dpoaes measured with the f1 sweep with the f2 sweep paradigm on the other hand the group delays of the three lower sideband dpoaes occurred to be larger than the group delays of the upper sideband dpoae 2f2 f1 a tentative interpretation of the data in the context of proposed explanatory hypotheses on dpoae group delays is given

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

visualization of the onset of distortion product otoacoustic emissions and measurement of their latency this paper describes a method for visualization of the onset of distortion product otoacoustic emission dpoae waveforms in the time domain the dpoae waveforms are obtained using ensemble averaging of samples of microphone output a rectangular sample window is used and the primary tones are turned on within the sample window the phases of the primary tones f1 and f2 are varied systematically between samples in such a way that the primary tones and all dpoaes e g 2f2 f1 3f1 2f2 2f1 except the dpoae of interest e g 2f1 f2 are cancelled in the ensemble average visualization of the dpoae onset allows measurement of the onset latency osl of the dpoae these direct measurements of osl are compared to phase gradient latencies pgls in the same ears determined by measuring the phase change of the dpoae as a function of dpoae frequency the direct measures of osl vary from 10 to 1 ms decrease with increasing frequency and increasing stimulus level and are shorter in rabbits than humans the direct measures of osl are in general quantitatively similar to pgl estimates but there are exceptions visualization of dpoae onset also allows quantification of dpoae rise times and reveals phase and amplitude changes of the dpoae that occur several milliseconds after onset in rabbits and humans it is proposed that the phase and amplitude changes result from vector summation of multiple components of the dpoae signal each with a different latency

a discontinuous finite volume method for the stokes problems we develop a new discontinuous finite volume method for solving the stokes equations on both triangular and rectangular meshes an optimal error estimate for the approximation of velocity is obtained in a mesh dependent norm first order l 2 error estimates are derived for the approximations of both velocity and pressure

on the accuracy of the mortar finite volume element method with lagrange multipliers abstract in this paper the mortar finite volume element mfve method with lagrange multipliers is considered for second order elliptic boundary value problems we prove l 2 error estimates which are affected by regularities in both the exact solution and the source term meanwhile the uniform convergence of the solution is obtained for the mfve method under minimal regularity assumption

a finite volume method for solving navier stokes problems abstract we develop a finite volume method for solving the navier stokes equations on a triangular mesh we prove that the unique solution of the finite volume method converges to the true solution with optimal order for velocity and for pressure in discrete h 1 norm and l 2 norm respectively

two grid finite volume element method for linear and nonlinear elliptic problems two grid finite volume element discretization techniques based on two linear conforming finite element spaces on one coarse and one fine grid are presented for the two dimensional second order non selfadjoint and indefinite linear elliptic problems and the two dimensional second order nonlinear elliptic problems with the proposed techniques solving the non selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non selfadjoint and indefinite elliptic problem on a much smaller space solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space convergence estimates are derived to justify the efficiency of the proposed two grid algorithms a set of numerical examples are presented to confirm the estimates

time domain demonstration of distributed distortion product otoacoustic emission components distortion product otoacoustic emissions dpoaes were measured in rabbits as time waveforms by employing a phase rotation technique to cancel all components in the final average except the 2f1 f2 dpoae subsequent filtering allowed the dpoae waveform to be clearly visualized in the time domain in most conditions f2 was turned off for 6 ms which produced a gap so that the dpoae was no longer generated these procedures allowed the dpoae onset as well as the decay during the gap to be observed in the time domain dpoaes were collected with l1 l2 65 db sound pressure level primary tone levels for f2 f1 ratios from 1 25 to 1 01 in 0 02 steps findings included the appearance of complex onsets and decays for the dpoae time waveforms as the f2 f1 ratio was decreased and the dpoae level was reduced these complexities were unaffected by interference tones its near the dpoae frequency place fdp but could be removed by its presented above f2 which also increased dpoae levels similar outcomes were o

mortar upwind finite volume element method for convection diffusion problems abstract in this paper we consider the mortar upwind finite volume element method with local linear conforming finite element space for the convection diffusion problems and show that the mortar upwind finite volume element approximations derived are convergent with optimal order in the h 1 norm

the characteristic finite volume element method for the nonlinear convection dominated diffusion problem in modern numerical simulation of prospecting and exploiting oil gas resources and environmental science it is important to consider a numerical method for nonlinear convection dominated diffusion problems based on actual conditions such as the three dimensional characteristics of large scale science engineering computation we present a kind of characteristic finite volume element method some techniques such as calculus of variations commutating operators the theory of prior estimates and techniques are adopted suboptimal order error estimate in l 2 norm and optimal order error estimate in h 1 norm are derived to determine the errors for the approximate solution numerical results are presented to verify the performance of the scheme

a characterization of ordinary abelian varieties by the frobenius push forward of the structure sheaf for an ordinary abelian variety x f e mathcal o x is decomposed into line bundles for every positive integer e conversely if a smooth projective variety x satisfies this property and the kodaira dimension of x is non negative then x is an ordinary abelian variety

the upwind finite volume element method based on straight triangular prism partition for nonlinear convection diffusion problem the upwind finite volume element method based on straight triangular prism partition is put forward for the nonlinear convection diffusion problems some techniques such as calculus of variations commutating operator and prior estimates are adopted optimal order error estimate in l 2 is derived to determine the error in approximate solution numerical experiment shows that the method is effective for avoiding numerical diffusion and nonphysical oscillations and reducing work time

on the construction and analysis of high order locally conservative finite volume type methods for one dimensional elliptic problems locally conservative finite volume type methods based on continuous piecewise polynomial functions of degree r ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension the new methods extend and generalize the classical finite volume method based on piecewise linear functions we derive a priori error estimates in the l2 h1 and l infty norm and discuss superconvergence effects for the error and its derivative explicit residual based a posteriori error bounds in the l2 and energy norm are also derived we compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates

distortion product otoacoustic emission test performance when both 2 f1 f2 and 2 f2 f1 are used to predict auditory status the objective of this study was to determine whether distortion product otoacoustic emission dpoae test performance defined as its ability to distinguish normal hearing ears from those with hearing loss can be improved by examining response and noise amplitudes at 2 f1 f2 and 2 f2 f1 simultaneously in addition there was interest in knowing whether measurements at both dps and for several primary frequency pairs can be used in a multivariate analysis to further optimize test performance dpoae and noise amplitudes were measured at 2 f1 f2 and 2 f2 f1 for 12 primary levels l2 from 10 to 65 db spl in 5 db steps and 9 pairs of primary frequencies 0 5 to 8 khz in 1 2 octave steps all data were collected in a sound treated room from 70 subjects with normal hearing and 80 subjects with hearing loss subjects had normal middle ear function at the time of the dpoae test based on standard tympanometric measurements measurement based stopping rules were used such that the test terminated when the noise

mixed covolume methods for quasi linear second order elliptic problems we consider covolume methods for the mixed formulations of quasi linear second order elliptic problems covolume methods for the mixed formulations of linear elliptic problem was first considered by russell rigorous block centered discretizations on irregular grids improved simulation of complex reservoir systems tech report 3 project report reservoir simulation research corporation tulsa ok 1995 and tested extensively in cai et al comput geosci 1 1997 pp 289 315 jones a mixed finite volume element method for accurate computation of fluid velocities in porous media ph d thesis university of colorado denver 1995 the analysis was carried out by chou and kwak siam j numer anal 37 2000 pp 758 771 for linear symmetric problems where they showed optimal error estimates in l2 norm for the pressure and in h div norm for the velocity in this paper we extend their results to quasi linear problems by following milner s argument math comp 44 1985 pp 303 320 through an adaptation of the duality argument of douglas and roberts math comp 44 1985 pp 39 52 for mixed covolume methods