improved frequency domain elastic wave modeling using weighted averaging difference operators we develop a new finite difference scheme that reduces the number of grid points per wavelength required in frequency domain elastic modeling our approach computes weighted averages of the spatial second order derivative and the mass acceleration terms using a 25 point computational stencil by determining the weighting coefficients to minimize numerical dispersion and numerical anisotropy we reduce the number of grid points to 3 3 per shear wavelength with a resulting error in velocities smaller than 1 our choice of grid points reduces the computer memory needed to store the complex impedance matrix to 4 of that for a conventional second order scheme and to 54 of that for a combined second order scheme the 25 point weighted averaging scheme of this paper makes it possible to accurately simulate realistic models numerical examples show that this technique can achieve the same accurate solutions with fewer grid points than those from previous frequency domain second order schemes our technique can be extended directly to 3 d elastic modeling the computational efficiency will be even greater than that realized for 2 d models

a comparison of the dispersion relations for anisotropic elastodynamic finite difference grids several staggered grid schemes have been suggested for performing finite difference calculations for the elastic wave equations in this paper the dispersion relationships and related computational requirements for the lebedev and rotated staggered grids for anisotropic elastic finite difference calculations in smooth models are analyzed and compared these grids are related to a popular staggered grid for the isotropic problem the virieux grid the lebedev grid decomposes into virieux grids two in two dimensions and four in three dimensions which decouple in isotropic media therefore the lebedev scheme will have twice or four times the computational requirements memory and cpu as the virieux grid but can be used with general anisotropy in two dimensions the rotated staggered grid is exactly equivalent to the lebedev grid but in three dimensions it is fundamentally different the numerical dispersion in finite difference grids depends on the direction of propagation and the grid type and parameters a joint numerical dispersion relation for the two grids types in the isotropic case is derived in order to compare the computational requirements for the two grid types the dispersion averaged over propagation direction and medium velocity are calculated setting the parameters so the average dispersion is equal for the two grids the computational requirements of the two grid types are compared in three dimensions the rotated staggered grid requires at least 20 more memory for the field data and at least twice as many number of floating point operations and memory accesses so the lebedev grid is more efficient and is to be preferred

hybrid modeling of elastic wave propagation in two dimensional laterally inhomogeneous media we have constructed a hybrid scheme for elastic wave propagation in two dimensional laterally inhomogeneous media the algorithm is based on a combination of finite difference techniques and the boundary integral equation method it involves a dedicated application of each of the two methods to specific domains of the model structure finite difference techniques are applied to calculate a set of boundary values wave field and stress field in the vicinity of the heterogeneous domain the continuation of the near field response is then calculated by means of the boundary integral equation method in a numerical example the hybrid method has been applied to calculate a plane wave response for an elastic lens embedded in a homogeneous environment the example shows that the hybrid scheme enables more efficient modeling with the same accuracy than with pure finite difference calculations

numerical study of the interface errors of finite difference simulations of seismic waves numerical simulations of wave propagation produce different errors and the most well known is numerical dispersion which is only valid for homogeneous media however there is a lack of error studies for heterogeneous media or even for the canonical case of media that have two constant velocity layers the error associated with media that have two layers is called an interface error and it typically converges to zero with a lower order of convergence compared to the theoretical convergence rate of the finite difference schemes fds for homogeneous media we evaluated a detailed numerical study of the interface error for three staggered grid fds that are commonly used in the simulation of seismic wave propagation we determined that a standard staggered grid scheme ssgs also known as the virieux scheme a rotated staggered grid scheme rsgs and a lebedev scheme ls preserve the second order of convergence at horizontal vertical solid solid interfaces when the medium parameters have been properly modified such as by harmonic averaging of finely layered media for the stiffness tensor and arithmetic mean for the density however for a fluid solid interface aligned with the grid line a second order convergence can only be achieved by an ssgs in addition the presence of a fluid solid interface reduces the order of convergence for the ls and the rsgs to a first order of convergence the presence of inclined interfaces makes high order second and more convergence impossible

construction and analysis of fourth order finite difference schemes for the acoustic wave equation in nonhomogeneous media in this article we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients these schemes are fourth order accurate in space and time in the case of smooth media and are designed to remain stable and optimal for reflection transmission phenomena in the case of discontinuous coefficients together with a detailed mathematical study various numerical results are presented

asymmetric temporal envelope encoding implications for within and across ear envelope comparison separating sound sources in acoustic environments relies on making ongoing highly accurate spectro temporal comparisons however listeners with hearing impairment may have varying quality of temporal encoding within or across ears which may limit the listeners ability to make spectro temporal comparisons between places of stimulation in this study in normal hearing listeners depth of amplitude modulation am for sinusoidally amplitude modulated sam tones was manipulated in an effort to reduce the coding of periodicity in the auditory nerve the ability to judge differences in am rates was studied for stimuli presented to different cochlear places of stimulation within or across ears it was hypothesized that if temporal encoding was poorer for one tone in a pair then sensitivity to differences in am rate of the pair would decrease results indicated that when the depth of am was reduced from 50 to 20 for one sam tone in a pair sensitivity to differences in am rate decreased sensitivity was greatest for am rates near 90 hz and depended upon the places of stimulation being compared these results suggest that degraded temporal representations in the auditory nerve for one place of stimulation could lead to deficits comparing that temporal information with other places of stimulation separating sound sources in acoustic environments relies on making ongoing highly accurate spectro temporal comparisons however listeners with hearing impairment may have varying quality of temporal encoding within or across ears which may limit the listeners ability to make spectro temporal comparisons between places of stimulation in this study in normal hearing listeners depth of amplitude modulation am for sinusoidally amplitude modulated sam tones was manipulated in an effort to reduce the coding of periodicity in the auditory nerve the ability to judge differences in am rates was studied for stimuli presented to different cochlear places of stimulation within or across ears it was hypothesized that if temporal encoding was poorer for one tone in a pair then sensitivity to differences in am rate of the pair would decrease results indicated that when the depth of am was reduced from 50 to 20 for one sam tone in a pair sensitivity to differences in am rate decreased sensitivity was

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

discontinuous galerkin finite element method for the wave equation the symmetric interior penalty discontinuous galerkin finite element method is presented for the numerical discretization of the second order wave equation the resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal hence the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit time stepping scheme optimal a priori error bounds are derived in the energy norm and the l 2 norm for the semidiscrete formulation in particular the error in the energy norm is shown to converge with the optimal order cal o h min s ell with respect to the mesh size h the polynomial degree ell and the regularity exponent s of the continuous solution under additional regularity assumptions the l 2 error is shown to converge with the optimal order cal o h min s ell numerical results confirm the expected convergence rates and illustrate the versatility of the method

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

seismic modeling with radial basis function generated finite differences abstractseismic exploration is the primary tool for finding and mapping out hydrocarbon deposits we have considered the 2d forward modeling problem the subsurface structures were assumed to be known and the task was to simulate elastic wave propagation throughout the medium many traditional approaches to solving this problem account for material interfaces by allowing model parameter values such as wave speed and density to vary either sharply or smoothly between adjacent data points although simple to implement these strategies typically produce solutions that feature a suboptimal first order convergence to the true solution spatial discretization based on radial basis function generated finite differences rbf fds has previously been shown to offer high accuracy and algebraic simplicity when using scattered layouts of computational nodes we have now developed this method further to provide third order accuracy not only throughout smooth regions but also for wave reflections and transmission

a new family of fourth order locally one dimensional schemes for the 3d elastic wave equation abstract in this paper we present a new family of locally one dimensional lod schemes with fourth order accuracy both in space and time for the three dimensional 3d elastic wave equation it is an extension of our previous lod work on the 3d acoustic wave equation the method is based on the new family of 3d acoustic lod schemes with a source term the constructed scheme is four layer in time and three layer in space it only involves a three point stencil in each spatial direction to achieve fourth order accuracy in each time level only a tridiagonal system is required to solve the stability condition is given and it has more relax restriction for the time step than the classical staggered grid schemes numerical computations are completed and show the performance of the new method

elastic wave propagation in heterogeneous anisotropic media using the lumped finite element method a numerical technique for wave propagation simulation in 2 d heterogeneous anisotropic structures is presented the scheme is flexible in incorporating arbitrary surface topography inner openings liquid solid boundaries and irregular interfaces and it naturally satisfies the free surface conditions of complex geometrical boundaries the algorithm based on a discretization mesh of triangles and quadrilaterals solves the problem using integral equilibrium around each node instead of satisfying elastodynamic differential equations at each node as in the finite difference method this study is an extension of previous work for the elastic isotropic case besides accounting for anisotropy a simplified quadrilateral grid cell with low computational cost is introduced the transversely isotropic medium with a symmetry axis on the horizontal or vertical plane as typically caused by a system of parallel cracks or fine layers is discussed in detail a 2 d algorithm is presented that can handle the situatio

sh wave propagation in heterogeneous media velocity stress finite difference method a new finite difference fd method is presented for modeling sh wave propagation in a generally heterogeneous medium this method uses both velocity and stress in a discrete grid density and shear modulus are similarly discretized avoiding any spatial smoothing therefore boundaries will be correctly modeled under an implicit formulation standard problems quarter plane propagation sedimentary basin propagation are studied to compare this method with other methods finally a more complex example a salt dome inside a two layered medium shows the effect of lateral propagation on seismograms recorded at the surface a corner wave always in phase with the incident wave and a head wave will appear which will pose severe problems of interpretation with the usual vertical migration methods

the role of envelope statistics in detecting changes in interaural correlation the role of envelope statistics in binaural masking level differences bmlds and correlation change detection was investigated in normal hearing listeners thresholds and just noticeable differences jnds were measured for different bandwidths and center frequencies 500 2000 4000 and 8000 hz using gaussian noises gns and low fluctuation noises lfns at a 500 hz center frequency gn noso thresholds were higher than nos thresholds were lower than and correlation change detection jnds were the same as lfn thresholds and jnds at higher center frequencies gn nos thresholds were the same or higher than lfn thresholds and gn correlation change detection jnds were much smaller than lfn jnds using a pulsed sine vocoder a second experiment was performed to investigate if binaural adaptation might contribute to the difference in gn and lfn detection there was no effect of pulse rate thus providing no clear evidence that binaural adaptation plays a role in these tasks both a cross correlation model and a model that utilized the fluctuations in the interaural differences could explain a majority of the variance in the lfn correlation change jnds

algebras associated to elliptic curves this paper completes the classification of artin schelter regular algebras of global dimension three for algebras generated by elements of degree one this has been achieved by artin schelter tate and van den bergh we are therefore concerned with algebras which are not generated in degree one we show that there exist some exceptional algebras each of which has geometric data consisting of an elliptic curve together with an automorphism just as in the case where the algebras are assumed to be generated in degree one in particular we study the elliptic algebras a a and a a where a p2 which were first defined in an earlier paper we omit a set s p2 consisting of 11 specified points where the algebras a a become too degenerate to be regular theorem let a represent a a or a a where a p2 s then a is an artin schelter regular algebra of global dimension three moreover a is a noetherian domain with the same hilbert series as the appropriately graded commutative polynomial ring in three variables this combined with our earlier results completes the classification

reflectionless truncation of target area for axially symmetric anisotropic elasticity this paper presents an approach to numerical simulation of seismic wave propagation in anisotropic elastic media in cylindrical coordinates by means of conservative finite difference scheme on staggered grids an original low cost domain distension based on optimal grids is proposed to restrict computational domain

local time space mesh refinement for simulation of elastic wave propagation in multi scale media this paper presents an original approach to local time space grid refinement for the numerical simulation of wave propagation in models with localized clusters of micro heterogeneities the main features of the algorithm are the application of temporal and spatial refinement on two different surfaces the use of the embedded stencil technique for the refinement of grid step with respect to time the use of the fast fourier transform fft based interpolation to couple variables for spatial mesh refinement the latter makes it possible to perform filtration of high spatial frequencies which provides stability in the proposed finite difference schemes in the present work the technique is implemented for the finite difference simulation of seismic wave propagation and the interaction of such waves with fluid filled fractures and cavities of carbonate reservoirs however this approach is easy to adapt and or combine with other numerical techniques such as finite elements discontinuous galerkin method or finite volumes used for approximation of various types of linear and nonlinear hyperbolic equations

an evaluation of models for diotic and dichotic detection in reproducible noises several psychophysical models for masked detection were evaluated using reproducible noises the data were hit and false alarm rates from three psychophysical studies of detection of 500 hz tones in reproducible noise under diotic n0s0 and dichotic n0s conditions with four stimulus bandwidths 50 100 115 and 2900 hz diotic data were best predicted by an energy based multiple detector model that linearly combined stimulus energies at the outputs of several critical band filters the tone plus noise trials in the dichotic data were best predicted by models that linearly combined either the average values or the standard deviations of interaural time and level differences however these models offered no predictions for noise alone responses the decision variables of more complicated temporal models including the models of dau et al 1996a j acoust soc am 99 3615 3622 and breebaart et al 2001a j acoust soc am 110 1074 1088 were weakly correlated with subjects responses comparisons of the dependencies of each model on envelope and fine structure cues to those in the data suggested that dependence upon both envelope and fine structure as well as an interaction between them is required to predict the detection results

the influence of different segments of the ongoing envelope on sensitivity to interaural time delays the auditory system is sensitive to interaural timing disparities in the fine structure and the envelope of sounds each contributing important cues for lateralization in this study psychophysical measurements were conducted with customized envelope waveforms in order to investigate the isolated effect of different segments of a periodic ongoing envelope on lateralization one envelope cycle was composed of the four segments attack flank hold duration decay flank and pause duration which were independently varied to customize the envelope waveform the envelope waveforms were applied to a 4 khz sinusoidal carrier and just noticeable envelope interaural time differences were measured in six normal hearing subjects the results indicate that attack durations and pause durations prior to the attack are the most important stimulus characteristics for processing envelope timing disparities the results were compared to predictions of three binaural lateralization models based on the normalized cross correlation coefficient two of the models included an additional stage to mimic neural adaptation prior to binaural interaction involving either a single short time constant 5 ms or a combination of five time constants up to 500 ms it was shown that the model with the single short time constant accounted best for the data

interaural correlation sensitivity sensitivity to differences in interaural correlation was measured for 1 3 erb wide bands of noise using a 2ifc task at six frequencies 250 500 750 1000 1250 and 1500 hz the sensitivity index d was measured for discriminations between a number of fixed pairs of correlation values cumulative d functions were derived for each frequency and condition the d for discriminating any two values of correlation may be recovered from the cumulative d function by the difference between cumulative d s for these values two conditions were employed the noisebands were either presented in isolation narrow band condition or in the context of broad contiguous flanking bands of correlated noise fringed condition the cumulative d functions showed greater sensitivity to differences in correlation close to 1 than close to 0 at low frequencies but this difference was less pronounced in the fringed condition also a more linear relationship was observed when cumulative d was plotted as a function of the equivalent signal to noise ratio snr in db for each correlation value rather than directly against correlation the equivalent snr was the snr at which the interaural correlation in an nos stimulus would equal the interaural correlation of the noise used in the experiment the maximum cumulative d declined above 750 hz this decline was steeper for the fringed than for the narrow band condition for the narrow band condition the total cumulative d was variable across listeners all cumulative d functions were closely fitted using a simple two parameter function the complete data sets averaged across listeners from the fringed and narrow band conditions were fitted using functions to describe the changes in these parameters over frequency in order to produce an interpolated family of curves that describe sensitivity at frequencies between those tested these curves predict the spectra recovered by the binaural system when complex sounds such as speech are masked by noise

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

automorphisms and ideals of the weyl algebra let a 1 be the first weyl algebra and let g be its automorphism group we study the natural action of g on the space of isomorphism classes of right ideals of a 1 equivalently of finitely generated rank 1 torsion free right a 1 modules we show that this space breaks up into a countable number of orbits each of which is a finite dimensional algebraic variety our results are strikingly similar to those for the commutative algebra of polynomials in two variables however we do not know of any general principle that would allow us to predict this in advance as a key step in the proof we obtain a new description of the bispectral involution of w1 we also make some comments on the group g from the viewpoint of shafarevich s theory of infinite dimensional algebraic groups

ideals of cubic algebras and an invariant ring of the weyl algebra hasselt univ dept wni b 3590 diepenbeek belgium univ antwerp dept wiskunde informat b 2020 antwerp belgium de naeghel k hasselt univ dept wni agoralaan gebouw d b 3590 diepenbeek belgium koendenaeghel hotmail com nicolas marconnet ua ac be

fourth order finite difference p sv seismograms i describe the properties of a fourth order accurate space second order accurate time two dimensional p sk finite difference scheme based on the madariagavirieux staggered grid formulation the numerical scheme is developed from the first order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses the madariaga virieux staggered grid scheme has the desirable quality that it can correctly model any variation in material properties including both large and small poisson s ratio materials with minimal numerical dispersion and numerical anisotropy dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints wavelength the scheme can be used to accurately simulate wave propagation in mixed acoustic elastic media making it ideal for modeling marine problems explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free surface or within a layer and to satisfy free surface boundary conditions benchmark comparisons of finite difference and analytical solutions to lamb s problem are almost identical as are comparisons of finite difference and reflectivity solutions for elastic elastic and acoustic elastic layered models

modeling elastic fields across irregular boundaries geologists often see the earth as homogeneous blocks separated by smoothly curving boundaries in contrast computer modeling algorithms based on finite difference schemes require elastic constants to be specified on the vertices of a regular rectangular grid how can we convert a continuous geological model into a form suitable for a finite difference grid one common way is to lay the finite difference grid down on the continuous geological model and use whatever elastic constants happen to lie beneath each of the grid points

seismic modeling with radial basis function generated finite differences rbf fd a simplified treatment of interfaces abstract in a previous study of seismic modeling with radial basis function generated finite differences rbf fd we outlined a numerical method for solving 2 d wave equations in domains with material interfaces between different regions the method was applicable on a mesh free set of data nodes it included all information about interfaces within the weights of the stencils allowing the use of traditional time integrators and was shown to solve problems of the 2 d elastic wave equation to 3rd order accuracy in the present paper we discuss a refinement of that method that makes it simpler to implement it can also improve accuracy for the case of smoothly variable model parameter values near interfaces we give several test cases that demonstrate the method solving 2 d elastic wave equation problems to 4th order accuracy even in the presence of smoothly curved interfaces with jump discontinuities in the model parameters

on the internal interfaces in finite difference schemes abstractimplementing sharp internal interfaces in finite difference schemes with high spatial accuracy is challenging the propagation of fields in a locally homogeneous part of a model can be performed with spectral accuracy the implementations of interfaces are generally considered accurate to at best second order this situation can be improved by a proper band limitation of the simulation grid interfaces can be located anywhere on the grid however the fine detail information regarding the interface location must be imprinted correctly in the coarse simulation grid this can be done by starting out with a representation of a sharp material jump in the wavenumber domain and limiting the highest wavenumber to the maximum wavenumber allowed for the simulation grid the resulting wavenumber representation is then transformed to the space domain an alternative procedure is to create a fine grid model that is low pass filtered to remove wavenumbers above the maximum wavenumber allowed for the coarse s

two dimensional nonlinear inversion of seismic waveforms numerical results the nonlinear problem of inversion of seismic waveforms can be set up using least squares methods the inverse problem is then reduced to the problem of minimizing a lp nonquadratic function in a space of many 104to106 variables using gradient methods leads to iterative algorithms each iteration implying a forward propagation generated by the actual sources a backward propagation generated by the data residuals acting as if they were sources and a correlation at each point of the space of the two fields thus obtained which gives the updated model the quality of the results of any inverse method depends heavily on the realism of the forward modeling finite difference schemes are a good choice relative to realism because although they are time consuming they give excellent results numerical tests performed with multioffset synthetic data from a two dimensional model prove the feasibility of the approach if only surface recorded reflections are used the high spatial frequency content of the

an efficient finite difference scheme for electromagnetic logging in 3d anisotropic inhomogeneous media we consider a problem of computing the electromagnetic field in 3d anisotropic media for electromagnetic logging the proposed finite difference scheme for maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis coercivity i e the complete discrete analogy of all continuous equations in every grid cell even for nondiagonal conductivity tensors a special conductivity averaging that does not require the grid to be small compared to layering or fractures and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity all of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3d geometries without sacrificing accuracy

time compact high order difference methods for wave propagation we construct one step explicit difference methods for solution of wave propagation problems with fourth order accuracy in both space and time by using a principle that can be generalized to arbitrary order we use the first order system form and a staggered grid the fourth order accuracy in time is obtained by transferring time derivatives in the truncation error to space derivatives discontinuous coefficients corresponding to interfaces between different materials are considered as a special case of variable coefficients and the method is applied across the discontinuities the accuracy is much improved compared to second order methods even for this type of problem a certain norm is shown to be conserved ensuring good accuracy even for long time integration

a calculus for finely layered anisotropic media matrix algebra and group theory combine to offer a formalism for the simple calculation of the elastic anisotropic homogeneous medium which is equivalent in the long wavelength limit to a heterogeneous distribution of fine layers each layer itself an elastic anisotropic medium the properties of each anisotropic constituent in a set of fine layers map to an element of a commutative group a reverse mapping returns the material properties of the constituent adding group elements gives the group element for the homogeneous medium equivalent to a heterogeneous set of layers addition of an inverse element that is subtraction provides the means to remove a set of layers from an anisotropic medium then if the remaining layer is a stable anisotropic medium a valid decomposition of the original medium into anisotropic constituents is obtained within the group structure eight subgroups corresponding to eight types of elastic symmetry systems may be identified immediately yielding the symmetry of the e

ideal classes of three dimensional artin schelter regular algebras abstract we determine the possible hilbert functions of graded rank one torsion free modules over three dimensional artin schelter regular algebras it turns out that as in the commutative case they are related to castelnuovo functions from this we obtain an intrinsic proof that the space of torsion free rank one modules on a non commutative p 2 is connected a different proof of this fact based on deformation theoretic methods and the known commutative case has recently been given by nevins and stafford sklyanin algebras and hilbert schemes of points math ag 0310045 for the weyl algebra it was proved by wilson invent math 133 1 1998 1 41

interaural fluctuations and the detection of interaural incoherence iv the effect of compression on stimulus statistics the purpose of this experiment was to determine whether the normalized interaural cross correlation cc model or a model based on interaural phase and level differences can better describe incoherence detection data the ability to detect interaural incoherence in three sets of reproducible dichotic noises was tested in six listeners the first set contained noises with a constrained value of the cc and the cc including signal compression the second set contained noises with a constrained value of the cc including signal compression the third set contained noises with constrained values in the fluctuations in the interaural differences modeling showed that neither the cc model nor the model using the interaural differences could account for the data in any set examination of the statistical properties of the stimuli showed that including compression before the calculation of the interaural cc causes a substantial correlation of this metric to the fluctuations in the interaural phase difference this finding implies that it may be more difficult to discriminate between the common types of binaural models than previously thought

discrimination of interaural differences of level as a function of frequency discrimination of interaural differences of level idls was measured for pure tones as a function of frequency and as a function of the interaural difference of phase or level of a standard varying the interaural difference of the standard was assumed to change the lateral position of its intracranial image threshold idls were approximately constant over a frequency range from 200 5000 hz except in a region near 1000 hz where they were slightly elevated thresholds increased as the value of the standard interaural differences of phase or level increased implying that interaural resolution declines as the lateral image moves away from midline the results are generally consistent with the predictions of current models of lateralization but additions to these models are required in order for them to account for the slight frequency dependence of threshold idls

interaural fluctuations and the detection of interaural incoherence iii narrowband experiments and binaural models in the first two articles of this series reproducible noises with a fixed value of interaural coherence 0 992 were used to study the human ability to detect interaural incoherence it was found that incoherence detection is strongly correlated with fluctuations in interaural differences especially for narrow noise bandwidths but it remained unclear what function of the fluctuations best agrees with detection data in the present article ten different binaural models were tested against detection data for 14 and 108 hz bandwidths these models included different types of binaural processing independent interaural phase difference interaural level difference lateral position and short term cross correlation several preprocessing transformations of the interaural differences were incorporated compression of binaural cues temporal averaging and envelope weighting for the 14 hz bandwidth data the most successful model postulated that incoherence is detected via fluctuations of interaural phase and interaural level processed by independent centers that model correlated with detectability at r 0 87 that model proved to be more successful than short term cross correlation models incorporating standard physiologically based model features r 0 78 for the 108 hz bandwidth data detection performance varied much less among different waveforms and the data were less able to distinguish between models

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

sensitivity to interaural envelope correlation changes in bilateral cochlear implant users provision of bilateral cochlear implants cis to people who are deaf is partially justified by improved abilities to understand speech in noise when comparing bilateral vs unilateral listening conditions however bilateral ci listeners generally show only monaural head shadow with little improvement in speech understanding due to binaural unmasking sensitivity to change in interaural envelope correlation which is related to binaural speech unmasking was investigated bilateral ci users were tested with bilaterally synchronized processors at single pitch matched electrode pairs first binaural masking level differences bmlds were measured using 1000 pulse per second pps carriers yielding bmlds of 11 1 6 5 and 8 5 4 2 db for 10 and 50 hz bandwidth masking noises respectively second envelope correlation change just noticeable differences jnds were measured stimuli presented at 1000 pps yielded lower jnds than those presented at 100 pps furthermore perfectly correlated reference stimuli produced lower jnds than uncorrelated references and uncorrelated references generally produced immeasurable jnds about 25 of jnds measured in the ci listeners were in the range of jnds observed in normal hearing listeners presented ci simulations in conclusion ci listeners can perceive changes in interaural envelope correlation but the poor performance may be a major limiting factor in binaural unmasking tested to date in realistic listening environments

time compact difference methods for wave propagation in discontinuous media in b gustafsson and e mossberg siam j sci comput 26 2004 pp 259 271 a fourth order one step method was constructed for the solution of wave propagation problems the method is based on the first order system form of the pde and uses a staggered grid both in space and time the method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity in this paper we will analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior furthermore we shall present more detailed numerical experiments which confirm the theoretical results

interaural envelope correlation change discrimination in bilateral cochlear implantees effects of mismatch centering and onset of deafness bilateral cochlear implant ci listeners can perform binaural tasks but they are typically worse than normal hearing nh listeners to understand why this difference occurs and the mechanisms involved in processing dynamic binaural differences interaural envelope correlation change discrimination sensitivity was measured in real and simulated ci users in experiment 1 11 ci eight late deafened three early deafened and eight nh listeners were tested in an envelope correlation change discrimination task just noticeable differences jnds were best for a matched place of stimulation and increased for an increasing mismatch in experiment 2 attempts at intracranially centering stimuli did not produce lower jnds in experiment 3 the percentage of correct identifications of antiphasic carrier pulse trains modulated by correlated envelopes was measured as a function of mismatch and pulse rate sensitivity decreased for increasing mismatch and increasing pulse rate the experiments led to two conclusions first envelope correlation change discrimination necessitates place of stimulation matched inputs however it is unclear if previous experience with acoustic hearing is necessary for envelope correlation change discrimination second nh listeners presented with ci simulations demonstrated better performance than real ci listeners if the simulations are realistic representations of electrical stimuli real ci listeners appear to have difficulty processing interaural information in modulated signals

ideal classes of three dimensional sklyanin algebras abstract in this paper we classify graded reflexive ideals up to isomorphism and shift in certain three dimensional artin schelter regular algebras this classification is similar to the classification of right ideals in the first weyl algebra a problem that was completely settled recently the situation we consider is substantially more complicated however