masking of speech by amplitude modulated noise the masking of speech by amplitude modulated and unmodulated speech spectrum noise has been evaluated by the measurement of monaural speech recognition in such noise on young and elderly subjects with normal hearing and elderly hearing impaired subjects with and without a hearing aid sinusoidal modulation with frequencies covering the range 2 100 hz as well as an irregular modulation generated by the sum of four sinusoids in random phase relation was used modulation degrees were 100 6 db and 12 db root mean square sound pressure level was equal for modulated and unmodulated maskers for the normal hearing subjects essentially all types of modulated noise provided some release of speech masking as compared to unmodulated noise sinusoidal modulation provided more release of masking than the irregular modulation the release of masking increased with modulation depth it is proposed that the number and duration of low level intervals are essential factors for the degree of masking the release of masking was found to reach a maximum at a modulation frequency between 10 and 20 hz for sinusoidal modulation for elderly hearing impaired subjects the release of masking obtained from amplitude modulation was consistently smaller than in the normal hearing groups presumably related to changes in auditory temporal resolution caused by the hearing loss the average speech to noise ratio required for 30 correct speech recognition varied greatly between the groups for young normal hearing subjects it was 15 db for elderly normal hearing it was 9 db for elderly hearing impaired subjects in the unaided listening condition it was 2 db and in the aided condition it was 3 db the results support the conclusion that within the methodological context of the study age as well as sensorineural hearing loss as such influence speech recognition in noise more than what can be explained by the loss of audibility according to the audiogram and the masking noise spectrum

speech perception in gated noise the effects of temporal resolution previous investigations have suggested that hearing impaired hi listeners have reduced masking release mr compared to normal hearing listeners nh when they listen in modulated noise the current study examined the following questions that have not been clearly answered first when hi listeners are amplified so that their performance is equal to that of nh listeners in quiet and in steady noise do hi listeners still show reduced mr with modulated noise when compared to nh listeners second is the masking release the same for sentences and cv syllables third does forward masking significantly contribute to the variability in performance among hi listeners to compensate for reduced hearing sensitivity for hi listeners the spectrum levels of both speech and noise were adjusted based on the individual hearing loss there was no significant difference between the performance of nh listeners and that of hi listeners in steady noise and in quiet however the amount of mr for sentences and for cv syllables was significantly reduced for hi listeners for sentence recognition the amount of mr seemed to be more related to hearing sensitivity for low to mid frequencies than to forward masking in contrast forward masking thresholds appear to be a major contributor to the amount of mr for syllable recognition

the effects of hearing loss on the contribution of high and low frequency speech information to speech understanding ii sloping hearing loss the speech understanding of persons with sloping high frequency hf hearing impairment hi was compared to normal hearing nh controls and previous research on persons with flat losses hornsby and ricketts 2003 j acoust soc am 113 1706 1717 to examine how hearing loss configuration affects the contribution of speech information in various frequency regions speech understanding was assessed at multiple low and high pass filter cutoff frequencies crossover frequencies defined as the cutoff frequencies at which low and high pass filtering yielded equivalent performance were significantly lower for the sloping hi compared to nh group suggesting that hf hi limits the utility of hf speech information speech intelligibility index calculations suggest this limited utility was not due simply to reduced audibility but also to the negative effects of high presentation levels and a poorer than normal use of speech information in the frequency region with the greatest hearing loss the hf regio

simulation of the effects of loudness recruitment and threshold elevation on the intelligibility of speech in quiet and in a background of speech these experiments simulated the threshold elevation and loudness recruitment associated with three different types of cochlear hearing loss moderate flat condition r2 severe flat condition r3 and moderate to severe sloping condition rx this was done to allow an examination of the effects of these factors on the intelligibility of speech in isolation from other factors that are normally associated with cochlear hearing loss such as reduced frequency selectivity the simulation was performed by splitting the input signal into 13 frequency bands and processing the envelope in each band so as to create loudness sensations in a normal ear that would resemble those produced in an impaired ear with recruitment the bands were then recombined all tests were performed using subjects with normal hearing for speech in quiet simulation of hearing loss produced a reduction in the ability to understand low level speech however speech at sufficiently high levels was highly intelligible in all conditions linear amplification according to the national acoustic laboratory nal prescription gave high intelligibility for speech at normal conversational levels for speech presented at a fixed input level of 65 db spl against a background of a single competing talker simulation of hearing loss produced substantial decrements in performance the speech to background ratios in conditions r2 and rx had to be 11 13 db higher than in the control condition unprocessed stimuli to achieve similar levels of performance linear amplification according to the nal prescription improved performance markedly for the conditions simulating flat losses but was less effective for the condition simulating a sloping loss this indicates that threshold elevation combined with recruitment produces a loss of intelligibility for speech in the presence of a single competing talker that is only partly compensated by linear amplification of the type typically used in hearing aids

complete blow up after tmax for the solution of a semilinear heat equation soit un sous ensemble ouvert borne de r n a frontiere lisse on considere le probleme u t u f u dans o t u 0 sur o t u x o u 0 x x ou f r r est localement de lipschitz non decroissante et f o 0

a numerical method for finding positive solution of diffusive logistic equation abstract using a numerical methods based on sub super solution we will find positive solution for the diffusive logistic equation u au bu 2 0 for x with dirichlet boundary condition

semi implicit integration factor methods on sparse grids for high dimensional systems numerical methods for partial differential equations in high dimensional spaces are often limited by the curse of dimensionality though the sparse grid technique based on a one dimensional hierarchical basis through tensor products is popular for handling challenges such as those associated with spatial discretization the stability conditions on time step size due to temporal discretization such as those associated with high order derivatives in space and stiff reactions remain here we incorporate the sparse grids with the implicit integration factor method iif that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions we combine iif in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly with various sparse grid techniques based on the finite element and finite difference methods and a multi level combination approach the overall method is found to be efficient in terms of both storage and computational time for solving a wide range of pdes in high dimensions in particular the iif with the sparse grid combination technique is flexible and effective in solving systems that may include cross derivatives and non constant diffusion coefficients extensive numerical simulations in both linear and nonlinear systems in high dimensions along with applications of diffusive logistic equations and fokker planck equations demonstrate the accuracy efficiency and robustness of the new methods indicating potential broad applications of the sparse grid based integration factor method

a new family of 5 5 cc 4oc schemes applicable for unsteady navier stokes equations in this paper a new family of implicit compact finite difference schemes for computation of unsteady convection diffusion equation with variable convection coefficient is proposed the schemes which are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter are then applied to unsteady navier stokes system the proposed schemes where transport variable and its first derivatives are carried as the unknowns combine virtues of compact discretization and pade scheme for spatial derivative these schemes which are based on a five point stencil with constant coefficients named as 5 5 constant coefficient 4th order compact 5 5 cc 4oc give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods these schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable they efficiently capture both transient and steady solutions of linear and nonlinear convection diffusion equations with dirichlet as well as neumann boundary conditions subsequently the proposed schemes are applied to problems governed by the incompressible navier stokes equations the results obtained are in excellent agreement with analytical and available numerical results in all cases establishing efficiency and accuracy of the proposed schemes

nonlocal reactive transport with physical and chemical heterogeneity localization errors the origin of nonlocality in macroscale models for subsurface chemical transport is illustrated it is argued that media that are either nonperiodic e g media with evolving heterogeneity or periodic viewed on a scale wherein a unit cell is discernible must display some nonlocality in the mean a metaphysical argument suggests that owing to the scarcity of information on natural scales of heterogeneity and on scales of observation associated with an instrument window constitutive theories for the mean concentration should at the outset of any modeling effort always be considered nonlocal the intuitive appeal to nonlocality is reinforced with an analytical derivation of the constitutive theory for a conservative tracer without appeal to any mathematical approximations deng et al 1993 present a first order nonlocal eulerian theory for transport of a conservative solute in an infinite nondeforming domain under steady flow conditions hu et al this issue extended these results to account for nonequilibrium linear sorption with random partition coefficient kd but deterministic constant reaction rate kr these theories are localized herein and comparisons are made between the fully nonlocal fnl nonlocal in time nlt and fully localized fl theories for conservative transport there is little difference between the first order fl and fnl models for spatial moments up to and including the third however for conservative transport the first order nlt model differs significantly from the fnl model in the third spatial moments for reactive transport all spatial moments differ between the fnl and fl models the second transverse horizontal and third longitudinal horizontal moments for the nlt model differ from the fnl model these results suggest that localized first order transport models for conservative tracers are reasonable if only lower order moments are desired however when the chemical reacts with its environment the localization approximation can lead to significant error in all moments and a fnl model will in general be required for accurate simulation

implementation of a variable stepsize variable formula method in the time integration part of a code for treatment of long range transport of air pollutants abstract a mathematical model consisting of two partial differential equations is used to study the long range transport of sulphur di oxide and sulphate over europe the discretization of the first order space derivatives the advection terms is carried out by a pseudospectral fourier algorithm a special technique is applied in the discretization of the second order space derivatives the diffusion terms two large systems of ordinary differential equations are solved at each time step it is shown that these systems can efficiently be treated by a variable stepsize variable formula method vsvfm based on the use of predictor corrector schemes the stepsize selection strategy and the formula selection strategy are discussed in detail an attempt to carry out both an accuracy control and a stability control is made at each time step the great efficiency of the vsvfm implemented in our software as well as the reliability of the results are illustrated by numerical experiments in which real meteorological data for 1979 at the grid points of a space domain covering the whole of europe were used the main ideas implemented in the time integration part might be applied in many other situations where the systems of ordinary differential equations arising after the space discretization are only moderately stiff so that the stability requirements are dominant over the accuracy requirements on a large part of the time interval but the use of implicit time integration algorithms that require solving systems of algebraic equations at each time step is not justified as an illustration only it should be mentioned that such an application has been carried out in connection with models describing long range transport of nitrogen pollutants over europe

fourth order time stepping for stiff pdes a modification of the exponential time differencing fourth order runge kutta method for solving stiff nonlinear pdes is presented that solves the problem of numerical instability in the scheme as proposed by cox and matthews and generalizes the method to nondiagonal operators a comparison is made of the performance of this modified exponential time differencing etd scheme against the competing methods of implicit explicit differencing integrating factors time splitting and fornberg and driscoll s sliders for the kdv kuramoto sivashinsky burgers and allen cahn equations in one space dimension implementation of the method is illustrated by short matlab programs for two of the equations it is found that for these applications with fixed time steps the modified etd scheme is the best

the blow up rate of solutions of semilinear heat equations on caracterise le comportement asymptotique de la solution de l equation de la chaleur semilineaire u t u exp u dans o t u k sur o t u x 0 x k pour xe k 0 dans un voisinage d un point d explosion quand t approche du temps d explosion fini t

a new augmented singular transform and its partial newton correction method for finding more solutions to nonvariational quasilinear elliptic pdes abstract in this paper in order to find more solutions to a nonvariational quasilinear pde a new augmented singular transform ast is developed to form a barrier surrounding previously found solutions so that an algorithm search from outside cannot pass the barrier and penetrate into the inside to reach a previously found solution thus a solution found by the algorithm must be new mathematical justifications of ast formulation are established a partial newton correction method is designed accordingly to solve the augmented problem and to satisfy a constraint in ast the new method is applied to numerically investigate bifurcation symmetry breaking phenomena to a non variational quasilinear elliptic equation through finding multiple solutions such phenomena are numerically captured and visualized for the first time and still open for theoretical verification since the formulation is general and simple it opens a door to solve other multiple solution problems

relations between frequency selectivity temporal fine structure processing and speech reception in impaired hearing frequency selectivity temporal fine structure tfs processing and speech reception were assessed for six normal hearing nh listeners ten sensorineurally hearing impaired hi listeners with similar high frequency losses and two listeners with an obscure dysfunction od tfs processing was investigated at low frequencies in regions of normal hearing through measurements of binaural masked detection tone lateralization and monaural frequency modulation fm detection lateralization and fm detection thresholds were measured in quiet and in background noise speech reception thresholds were obtained for full spectrum and lowpass filtered sentences with different interferers both the hi listeners and the od listeners showed poorer performance than the nh listeners in terms of frequency selectivity tfs processing and speech reception while a correlation was observed between the monaural and binaural tfs processing deficits in the hi listeners no relation was found between tfs processing and frequency selectivity the effect of noise on tfs processing was not larger for the hi listeners than for the nh listeners finally tfs processing performance was correlated with speech reception in a two talker background and lateralized noise but not in amplitude modulated noise the results provide constraints for future models of impaired auditory signal processing

masking of speech by amplitude modulated noise abstract the degree of masking of human speech by environmental noise may be influenced by amplitude variations in the noise the listener s condition with respect to age and auditory function may affect his sensitivity to such noise also fatigue effects are possible after prolonged exposure to masking noise these aspects have been tested in the present study the results show that in general amplitude modulation of a masking noise reduces its speech masking effect as compared to unmodulated noise of the same r m s sound level and spectrum age did not affect the release of masking found in am noise however hearing impaired listeners obtained much less release of speech masking than those with normal hearing small but statistically significant fatigue effects were found after up to 60 min exposure to noise at 60 db spl the speech to noise ratio needed for 30 correct speech recognition was significantly affected by both age and hearing loss

a detailed numerical treatment of the boundary conditions imposed by the skull on a diffusion reaction model of glioma tumor growth clinical validation aspects abstract the study of the diffusive behavior of glioma tumor growth is an active field of biomedical research with considerable therapeutic implications an important aspect of the corresponding computational problem is the mathematical handling of boundary conditions this paper aims at providing an explicit and thorough numerical formulation of the adiabatic neumann boundary conditions imposed by the skull on the diffusive growth of gliomas and in particular on glioblastoma multiforme gbm additionally a detailed exposition of the numerical solution process for a homogeneous approximation of glioma invasion using the crank nicolson technique in conjunction with the conjugate gradient system solver is provided the entire mathematical and numerical treatment is also in principle applicable to mathematically similar physical chemical and biological phenomena a comparison of the numerical solution for the special case of pure diffusion in the absence of boundary conditions or equivalently in the presence of adiabatic boundaries placed in infinity with its analytical counterpart is presented numerical simulations for various adiabatic boundary geometries and non zero net tumor growth rate support the validity of the corresponding mathematical treatment through numerical experimentation on a set of real brain imaging data a simulated tumor has shown to satisfy the expected macroscopic behavior of glioblastoma multiforme including the adiabatic behavior of the skull the paper concludes with a number of remarks pertaining to both the biological problem addressed and the more generic diffusion reaction context

a numerical investigation of sign changing solutions to superlinear elliptic equations on symmetric domains in this paper we investigate numerically sign changing solutions of superlinear elliptic equations on symmetric domains based upon the symmetric criticality principle of palais the existence of sign changing solutions which re2ect the symmetry

non symmetric low index solutions for a symmetric boundary value problem abstract we consider the equation u w u 3 on a square domain in r 2 with dirichlet boundary conditions where w is a given positive function that is invariant under all euclidean symmetries of the square this equation is shown to have a solution u with morse index 2 that is neither symmetric nor antisymmetric with respect to any nontrivial symmetry of the square part of our proof is computer assisted an analogous result is proved for index 1

effects of spectral smearing and temporal fine structure distortion on the fluctuating masker benefit for speech at a fixed signal to noise ratio normal hearing listeners receive less benefit from momentary dips in the level of a fluctuating masker for speech processed to degrade spectral detail or temporal fine structure tfs than for unprocessed speech this has been interpreted as evidence that the magnitude of the fluctuating masker benefit fmb reflects the ability to resolve spectral detail and tfs however the fmb for degraded speech is typically measured at a higher signal to noise ratio snr to yield performance similar to normal speech for the baseline stationary noise condition because the fmb decreases with increasing snr this snr difference might account for the reduction in fmb for degraded speech in this study the fmb for unprocessed and processed tfs removed or spectrally smeared speech was measured in a paradigm that adjusts word set size rather than snr to equate stationary noise performance across processing conditions compared at the same snr and percent correct level but with different set sizes processed and unprocessed stimuli yielded a similar fmb for four different fluctuating maskers speech modulated noise one opposite gender interfering talker two same gender interfering talkers and 16 hz interrupted noise these results suggest that for these maskers spectral or tfs distortions do not directly impair the ability to benefit from momentary dips in masker level

multiple critical points of invariant functionals and applications abstract this paper deals with some multiplicity results of periodic orbits of hamiltonian systems and for solution of a non linear dirichlet problem these results follow from an abstract theorem of lusternik schnirelman type as applied to an invariant equation of the form lu delta f u 0 in a hilbert space x l sub 2 omega r sub n where l is an unbounded self adjoint operator and f is a c sub 1 strictly convex function author

factors affecting masking release for speech in modulated noise for normal hearing and hearing impaired listeners the speech reception threshold for sentences in stationary noise and in several amplitude modulated noises was measured for 8 normal hearing listeners 29 sensorineural hearing impaired listeners and 16 normal hearing listeners with simulated hearing loss this approach makes it possible to determine whether the reduced benefit from masker modulations as often observed for hearing impaired listeners is due to a loss of signal audibility or due to suprathreshold deficits such as reduced spectral and temporal resolution which were measured in four separate psychophysical tasks results show that the reduced masking release can only partly be accounted for by reduced audibility and that when considering suprathreshold deficits the normal effects associated with a raised presentation level should be taken into account in this perspective reduced spectral resolution does not appear to qualify as an actual suprathreshold deficit while reduced temporal resolution does temporal resolution and age are shown to be the main factors governing masking release for speech in modulated noise accounting for more than half of the intersubject variance their influence appears to be related to the processing of mainly the higher stimulus frequencies results based on calculations of the speech intelligibility index in modulated noise confirm these conclusions

fully implicit finite differences methods for two dimensional diffusion with a non local boundary condition three new fully implicit methods which are based on the 5 5 crank nicolson method the 5 5 n h noye hayman implicit method and the 9 9 n h implicit method are developed for solving the heat equation in two dimensional space with non local boundary conditions the latter is fourth order while the others are second order while the implicit methods developed here like the scheme based on the standard implicit backward time centered space btcs method use a large amount of central processor cpu time the high accuracy of the new fourth order fully implicit scheme is significant like the btcs method the new methods are also unconditionally stable

finite difference approximations for a class of nonlocal parabolic boundary value problems abstract we consider finite difference approximations for a class of nonlocal parabolic boundary value problems which arise in thermoelasticity and poroelasticity approximations for both fixed and natural boundary conditions are considered together with an analysis of their stability an example arising in testing poroelastic annular cylindrical samples is considered under various boundary conditions and for realistic values of the physical parameters

mathematical treatment of context effects in phoneme and word recognition percent recognition of phonemes and whole syllables measured in both consonant vowel consonant cvc words and cvc nonsense syllables is reported for normal young adults listening at four signal to noise s n ratios similar data are reported for the recognition of words and whole sentences in three types of sentence high predictability hp sentences with both semantic and syntactic constraints low predictability lp sentences with primarily syntactic constraints and zero predictability zp sentences with neither semantic nor syntactic constraints the probability of recognition of speech units in context pc is shown to be related to the probability of recognition without context pi by the equation pc 1 1 pi k where k is a constant the factor k is interpreted as the amount by which the channels of statistically independent information are effectively multiplied when contextual constraints are added empirical values of k are approximately 1 3 and 2 7 for word and sentence context respe

temporal masking functions for listeners with real and simulated hearing loss a functional simulation of hearing loss was evaluated in its ability to reproduce the temporal masking functions for eight listeners with mild to severe sensorineural hearing loss each audiometric loss was simulated in a group of age matched normal hearing listeners through a combination of spectrally shaped masking noise and multi band expansion temporal masking functions were obtained in both groups of listeners using a forward masking paradigm in which the level of a 110 ms masker required to just mask a 10 ms fixed level probe 5 10 db sl was measured as a function of the time delay between the masker offset and probe onset at each of four probe frequencies 500 1000 2000 and 4000 hz temporal masking functions were obtained using maskers that were 0 55 1 0 and 1 15 times the probe frequency the slopes and y intercepts of the masking functions were not significantly different for listeners with real and simulated hearing loss the y intercepts were positively correlated with level of hearing loss while the slopes were negatively correlated the ratio of the slopes obtained with the low frequency maskers relative to the on frequency maskers was similar for both groups of listeners and indicated a smaller compressive effect than that observed in normal hearing listeners

consonant identification in noise using hilbert transform temporal fine structure speech and recovered envelope speech for listeners with normal and impaired hearing consonant identification ability was examined in normal hearing nh and hearing impaired hi listeners in the presence of steady state and 10 hz square wave interrupted speech shaped noise the hilbert transform was used to process speech stimuli 16 consonants in a c a syllables to present envelope cues temporal fine structure tfs cues or envelope cues recovered from tfs speech the performance of the hi listeners was inferior to that of the nh listeners both in terms of lower levels of performance in the baseline condition and in the need for higher signal to noise ratio to yield a given level of performance for nh listeners scores were higher in interrupted noise than in steady state noise for all speech types indicating substantial masking release for hi listeners masking release was typically observed for tfs and recovered envelope speech but not for unprocessed and envelope speech for both groups of listeners tfs and recovered envelope speech yielded similar levels of performance and consonant confusion patterns the masking release observed for tfs and recovered envelope speech may be related to level effects associated with the manner in which the tfs processing interacts with the interrupted noise signal rather than to the contributions of tfs cues per se

generalized integrating factor methods for stiff pdes the integrating factor if method for numerical integration of stiff nonlinear pdes has the disadvantage of producing large error coefficients when the linear term has large norm we propose a generalization of the if method and in particular construct multistep type methods with several orders of magnitude improved accuracy we also consider exponential time differencing etd methods and point out connections with a particular application of the commutator free lie group methods we present a new fourth order etdrk method with improved accuracy the methods considered are compared in several numerical examples

on optimal scaling algorithm for finding positive solution of elliptic equation abstract using a numerical method we will show the existence of positive solution for the elliptic equation u x f x u x with dirichlet boundary condition for varying

quasi implicit and two level explicit finite difference procedures for solving the one dimensional advection equation a variety of explicit and implicit algorithms has been studied dealing with the solution of the one dimensional advection equation these schemes are based on the weighted finite difference approximations this solution approach proves to be very effective this procedure is carried out in many disciplines including hydrology oceanography and meteorology the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach it is worth noting that from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain weights thus leading to more accurate techniques quasi implicit and two level explicit finite difference techniques are considered in this article to approximately solve the one dimensional advection problem stability of the techniques are investigated using the von neumann stability analysis the results of a numerical experiment are presented and the accuracy and central processor unit cpu time needed are discussed and compared numerical tests show that the new third order or fourth order methods are more accurate than either of the second order techniques

a rescaling algorithm for the numerical calculation of blowing up solutions on presente un algorithme a invariance d echelle pour le calcul numerique des solutions a singularites explosives des equations d evolution non lineaires

a finite element approach for finding positive solutions of a logistic equation with a sign changing weight function in this article we describe the mathematical modeling and use finite element approximation to study the existence and multiplicity of numerical positive solutions of well known generalized logistic equation with sign changing weight function we investigate the range of the real parameter involved in this problem to achieve the numerical solutions and discuss the behavior of the branch of the solutions using matlab 7 0

l 0 stable splitting methods for the simple heat equation in two space dimensions with homogeneous boundary conditions l 0 stable splitting methods which are third and fourth order accurate in time are developed for the numerical solution of the simple diffusion equation in two space dimensions the methods are seen to evolve from first and second order pade approximants to the exponential function the local truncation errors of the methods are compared and the costs of implementing the algorithms are estimated by arithmetic operations counts the methods are tested on a constant coefficients problem for which there is a discontintlty between initial conditions and boundary conditions

the effects of hearing loss on the contribution of high and low frequency speech information to speech understanding the speech understanding of persons with flat hearing loss hi was compared to a normal hearing nh control group to examine how hearing loss affects the contribution of speech information in various frequency regions speech understanding in noise was assessed at multiple low and high pass filter cutoff frequencies noise levels were chosen to ensure that the noise rather than quiet thresholds determined audibility the performance of hi subjects was compared to a nh group listening at the same signal to noise ratio and a comparable presentation level although absolute speech scores for the hi group were reduced performance improvements as the speech and noise bandwidth increased were comparable between groups these data suggest that the presence of hearing loss results in a uniform rather than frequency specific deficit in the contribution of speech information measures of auditory thresholds in noise and speech intelligibility index sii calculations were also performed these data suggest that differences in performance between the hi and nh groups are due primarily to audibility differences between groups measures of auditory thresholds in noise showed the effective masking spectrum of the noise was greater for the hi than the nh subjects

integral equation formulation of an unsteady diffusionconvection equation with variable coefficient and velocity in this paper we present an integral equation formulation for the time dependent diffusionconvection equation with variable coefficient and velocity with sources the formulation is based on usage of the steady fundamental solution of the convectiondiffusion equation for a known velocity and coefficient fields which may change with location and time the formulation avoids the usage of the gradient of the unknown field function and thus avoids making the problem nonlinear two discretization approaches are proposed and compared a standard single domain boundarydomain element technique and a domain decomposition approach the validity of the formulation and comparison of discretization approaches is preformed on several challenging test cases mesh convergence is reported and the advantages and disadvantages of both approaches are examined

a high order scheme for unsteady heat conduction equations abstract in this work a high order scheme is proposed for solving the heat conduction problems in this scheme the governing equation of heat conduction is firstly written into a system of first order partial differential equations which are integrated over the control volumes around each node point and a finite time step the resulting time integrals are approximated by numerical quadrature with an undetermined weighting parameter the error analysis allows us to determine the parameter and the ratio of the time step to the square of grid spacing by making the error of the scheme as small as possible both theoretical and numerical results show that the proposed high order scheme can achieve at least sixth order accuracy at the expense of the same computing cost as the traditional finite volume method and the high order scheme demonstrates a better performance than the high order compact finite difference method and the runge kutta discontinuous galerkin method

a numerical method for finding positive solution of logistic equation abstract using a numerical methods based on sub super solution we will show the existence of positive solution for the well known logistic equation u g x u x u x 2 for x with dirichlet boundary condition

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

a second order accurate finite difference scheme for a class of nonlocal parabolic equations with natural boundary conditions abstract a difference scheme is derived for a class of nonlocal parabolic equations with natural boundary conditions by the method of reduction of order it is shown that the scheme is uniquely solvable and unconditionally convergent with the convergence rate of order o h 2 2 a numerical example with some comparisons is presented

speech reception by listeners with real and simulated hearing impairment effects of continuous and interrupted noise the effects of audibility and age on masking for sentences in continuous and interrupted noise were examined in listeners with real and simulated hearing loss the absolute thresholds of each of ten listeners with sensorineural hearing loss were simulated in normal hearing listeners through a combination of spectrally shaped threshold noise and multi band expansion for octave bands with center frequencies from 0 25 8 khz each individual hearing loss was simulated in two groups of three normal hearing listeners an age matched and a non age matched group the speech to noise ratio s n for 50 correct identification of hearing in noise test hint sentences was measured in backgrounds of continuous and temporally modulated 10 hz square wave noise at two overall levels for unprocessed speech and for speech that was amplified with the nal rp prescription the s n in both continuous and interrupted noise of the hearing impaired listeners was relatively well simulated in both groups of normal hearing listeners thus release from masking the difference in s n obtained in continuous versus interrupted noise appears to be determined primarily by audibility minimal age effects were observed in this small sample observed values of masking release were compared to predictions derived from intelligibility curves generated using the extended speech intelligibility index esii rhebergen et al 2006 j acoust soc am 120 3988 3997

on coordinate transformation and grid stretching for sparse grid pricing of basket options we evaluate two coordinate transformation techniques in combination with grid stretching for pricing basket options in a sparse grid setting the sparse grid technique is a basic technique for solving a high dimensional partial differential equation by creating a small hypercube sub grid in the composite sparse grid we can also determine hedge parameters accurately we evaluate these techniques for multi asset examples with up to five underlying assets in the basket

solving parabolic integro differential equations by an explicit integration method vasudeva murthy a s and j g verwer solving parabolic integro differential equations by an explicit integration method journal of computational and applied mathematics 39 1992 121 132 the subject of this note is the numerical integration in time of nonclassical parabolic initial boundary value problems which involve nonlocal integral terms over the spatial domain the integral terms may appear in the boundary conditions and or in the governing partial differential equation itself these terms generally complicate the application of standard methods our purpose here is to draw attention to an explicit method the runge kutta chebyshev method whose application remains straightforward in many cases of practical interest we discuss two numerical examples to illustrate this a comparison is made respectively with the implicit bdf code dassl and with the keller box scheme

a robust numerical method for the r13 equations of rarefied gas dynamics application to lid driven cavity in this work we present a finite difference scheme to compute steady state solutions of the regularized 13 moment r13 equations of rarefied gas dynamics the scheme allows fast solutions for 2d and 3d boundary value problems bvps with velocity slip and temperature jump boundary conditions the scheme is applied to the lid driven cavity problem for knudsen numbers up to 0 7 the results compare well with those obtained from more costly solvers for rarefied gas dynamics such as the integro moment method imm and the direct simulation monte carlo dsmc method the r13 equations yield better results than the classical navier stokes fourier equations for this boundary value problem since they give an approximate description of knudsen boundary layers at moderate knudsen numbers the r13 based numerical solutions are computationally economical and may be considered as a reliable alternative mathematical model for complex industrial problems at moderate knudsen numbers

a local minimax newton method for finding multiple saddle points with symmetries in this paper a local minimax newton method is developed to solve for multiple saddle points the local minimax method siam j sci comput 23 2001 pp 840 865 is used to locate an initial guess and a version of the generalized newton method is used to speed up convergence when a problem possesses a symmetry the local minimax method is invariant to the symmetry thus the symmetry can be used to greatly enhance the efficiency and stability of the local minimax method but such an invariance is sensitive to numerical error and the haar projection has been used to enforce the symmetry siam j numer anal submitted in this paper we prove that the newton method is invariant to symmetries and that such an invariance is insensitive to numerical error when a symmetric degeneracy takes place it is proved that the newton direction can be easily solved in an invariant subspace thus the newton method can be used not only to speed up convergence but also to avoid using the haar projection if the symmetric degeneracy is removable by a discretization finally numerical examples are presented to illustrate the theory

efficient spectral sparse grid methods and applications to high dimensional elliptic problems we develop in this paper some efficient algorithms which are essential to implementations of spectral methods on the sparse grid by smolyak s construction based on a nested quadrature more precisely we develop a fast algorithm for the discrete transform between the values at the sparse grid and the coefficients of expansion in a hierarchical basis and by using the aforementioned fast transform we construct two very efficient sparse spectral galerkin methods for a model elliptic equation in particular the chebyshev legendre galerkin method leads to a sparse matrix with a much lower number of nonzero elements than that of low order sparse grid methods based on finite elements or wavelets and can be efficiently solved by a suitable sparse solver ample numerical results are presented to demonstrate the efficiency and accuracy of our algorithms

constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems a new numerical algorithm for solving semilinear elliptic problems is presented a variational formulation is used and critical points of a c1 functional subject to a constraint given by a level set of another c1 functional or an intersection of such level sets of finitely many functionals are sought first constrained local minima are looked for then constrained mountain pass points the approach is based on the deformation lemma and the mountain pass theorem in a constrained setting several examples are given showing new numerical solutions in various applications

a crank nicolson adi galerkin legendre spectral method for the two dimensional riesz space distributed order advection diffusion equation abstract in the paper a crank nicolson alternating direction implicit adi galerkin legendre spectral scheme is presented for the two dimensional riesz space distributed order advection diffusion equation the gauss quadrature has a higher computational accuracy than the mid point quadrature rule which is proposed to approximate the distributed order riesz space derivative so that the considered equation is transformed into a multi term fractional equation moreover the transformed equation is solved by discretizing in space by the adi galerkin legendre spectral scheme and in time using the crank nicolson difference method stability and convergence analysis are verified for the numerical approximation a lot of numerical results are demonstrated to justify the theoretical analysis

a mountain pass method for the numerical solution of semilinear wave equations it is well known that periodic solutions of semilinear wave equations can be obtained as critical points of related functionals in the situation that we studied there is usually an obvious solution obtained as a solution of linear problem we formulate a dual variational problem in such a way that the obvious solution is a local minimum we then find additional non obvious solutions via a numerical mountain pass algorithm based on the theorems of ambrosetti rabinowitz and ekeland numerical results are presented

multi element probabilistic collocation method in high dimensions we combine multi element polynomial chaos with analysis of variance anova functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity specifically we employ the multi element probabilistic collocation method mepcm 1 and so we refer to the new method as mepcm a we investigate the dependence of the convergence of mepcm a on two decomposition parameters the polynomial order m and the effective dimension n with n n and n the nominal dimension numerical tests for multi dimensional integration and for stochastic elliptic problems suggest that n m for monotonic convergence of the method we also employ mepcm a to obtain error bars for the piezometric head at the hanford nuclear waste site under stochastic hydraulic conductivity conditions finally we compare the cost of mepcm a against monte carlo in several hundred dimensions and we find mepcm a to be more efficient for up to 600 dimensions for a specific multi dimensional integration problem involving a discontinuous function

the effects of age and cochlear hearing loss on temporal fine structure sensitivity frequency selectivity and speech reception in noise temporal fine structure tfs sensitivity frequency selectivity and speech reception in noise were measured for young normal hearing nhy old normal hearing nho and hearing impaired hi subjects two measures of tfs sensitivity were used the tfs lf test interaural phase difference discrimination and the tfs2 test discrimination of harmonic and frequency shifted tones these measures were not significantly correlated with frequency selectivity after partialing out the effect of audiometric threshold suggesting that insensitivity to tfs cannot be wholly explained by a broadening of auditory filters the results of the two tests of tfs sensitivity were significantly but modestly correlated suggesting that performance of the tests may be partly influenced by different factors the nho group performed significantly more poorly than the nhy group for both measures of tfs sensitivity but not frequency selectivity suggesting that tfs sensitivity declines with age in the absence of elevated audiometric thresholds or broadened auditory filters when the effect of mean audiometric threshold was partialed out speech reception thresholds in modulated noise were correlated with tfs2 scores but not measures of frequency selectivity or tfs lf test scores suggesting that a reduction in sensitivity to tfs can partly account for the speech perception difficulties experienced by hearing impaired subjects

efficient semi implicit schemes for stiff systems when explicit time discretization schemes are applied to stiff reaction diffusion equations the stability constraint on the time step depends on two terms the diffusion and the reaction the part of the stability constraint due to diffusion can be totally removed if the linear diffusions are treated exactly using integration factor if or exponential time differencing etd methods for systems with severely stiff reactions those methods are not efficient because the reaction terms in if or etd are still approximated with explicit schemes in this paper we introduce a new class of semi implicit schemes which treats the linear diffusions exactly and explicitly and the nonlinear reactions implicitly a distinctive feature of the scheme is the decoupling between the exact evaluation of the diffusion terms and implicit treatment of the nonlinear reaction terms as a result the size of the nonlinear system arising from the implicit treatment of the reactions is independent of the number of spatial grid points it only depends on the number of original equations unlike the case in which standard implicit temporal schemes are directly applied to the reaction diffusion system the stability region for this class of methods is much larger than existing methods using an explicit treatment of reaction terms in particular the one with second order accuracy is unconditionally linearly stable with respect to both diffusion and reaction direct numerical simulations on test equations as well as morphogen systems from developmental biology show the new semi implicit schemes are efficient robust and accurate

phoneme recognition in vocoded maskers by normal hearing and aided hearing impaired listeners this study compared modulation benefit for phoneme recognition obtained by normal hearing nh and aided hearing impaired hi listeners consonant and vowel recognition scores were measured using nonsense syllables in the presence of a steady state noise and four vocoded speech maskers vocoded maskers were generated by modulating the steady state noise in either one or six frequency channels with the speech envelope extracted from the speech of either a single talker or a four talker babble aided hi listeners obtained lower consonant recognition scores than nh listeners in all masker conditions vowel recognition scores for aided hi listeners were comparable to nh scores except in the six channel vocoded masker conditions where they were relatively lower analysis using the extended speech intelligibility index developed by rhebergen versfeld and dreschler 2006 j acoust soc am 120 6 3988 3997 suggested that the signal to noise ratio deficit observed in aided hi listeners was largely due to uncompensated audibility loss there was no significant difference between modulation masking release obtained by nh and aided hi listeners for both consonant and vowel recognition

numerical solution of the three dimensional advection diffusion equation the study of advection diffusion equation continues to be an active field of research the subject has important applications to fluid dynamics as well as many other branches of science and engineering in this paper several different numerical techniques will be developed and compared for solving the three dimensional advection diffusion equation with constant coefficient these techniques are based on the two level fully explicit and fully implicit finite difference approximations the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes another nice feature of the modified equivalent partial differential equation approach is that a high order of accuracy can be combined with excellent stability properties the new second order accurate methods are free of numerical diffusion the results of a numerical experiment are presented and the accuracy and central processor cpu time needed are discussed and compared

temporal modulation transfer functions for listeners with real and simulated hearing loss a functional simulation of hearing loss was evaluated in its ability to reproduce the temporal modulation transfer functions tmtfs for nine listeners with mild to profound sensorineural hearing loss each hearing loss was simulated in a group of three age matched normal hearing listeners through spectrally shaped masking noise or a combination of masking noise and multiband expansion tmtfs were measured for both groups of listeners using a broadband noise carrier as a function of modulation rate in the range 2 to 1024 hz the tmtfs were fit with a lowpass filter function that provided estimates of overall modulation depth sensitivity and modulation cutoff frequency although the simulations were capable of accurately reproducing the threshold elevations of the hearing impaired listeners they were not successful in reproducing the tmtfs on average the simulations resulted in lower sensitivity and higher cutoff frequency than were observed in the tmtfs of the hearing impaired listeners discrepancies in performance between listeners with real and simulated hearing loss are possibly related to inaccuracies in the simulation of recruitment

a numerical method for finding positive solution of diffusive logistic equation with constant yield harvesting abstract we consider a reaction diffusion equation u x au x bu x 2 ch x 0 with dirichlet boundary condition by using a numerical method based on sub super solution we will show the existence of positive solution

a mountain pass algorithm with projector in this paper we present an enhanced version of the minimax algorithm of chen ni and zhou that offers the additional guarantee that the solution found is a fix point of a projector on a cone positivity negativity and monotonicity can be expressed in this way the convergence of the algorithm is proved by means of a computational deformation lemma instead of the usual deformation lemma used in the calculus of variations

numerical procedures for a boundary value problem with a non linear boundary condition numerical techniques based on finite difference schemes leading to parallel algorithms have been developed for obtaining approximate solutions to an initial boundary value problem for the two dimensional parabolic partial differential equation pde with a non linear boundary condition this class of parabolic pdes plays a very important role in many branches of science and engineering the non linear condition is in the form of a double integral giving the specification of mass in the solution domain not only the problem has both neumann and dirichlet boundary conditions but the dirichlet boundary condition is in a non standard form while sharing some common features with the one dimensional models the solution of two dimensional equations are substantially more difficult thus some considerations are taken to be able to extend some ideas of one dimensional case due to the structure of the boundary conditions a reduced one dimensional parabolic equation for the new unknown v y t email protected 1 0u x y t dx can be formulated the resulting problem has a non local boundary condition the new two dimensional parabolic pde with neumann s boundary conditions will be solved numerically by using the method of lines semi discretization approach the space derivatives in the pde are approximated by finite difference replacements the solution of the resulting system of first order linear ordinary differential equations satisfies a recurrence relation which involves a matrix exponential function the accuracy in time is controlled by choosing several subdiagonal pade approximants to replace this matrix exponential term numerical techniques are developed to compute the required solution using a splitting method leading to algorithms for sequential and parallel implementation the algorithms are tested on a model problem from the literature the article concludes with the results of some numerical experiments

comparison of frequency selectivity and consonant recognition among hearing impaired and masked normal hearing listeners frequency selectivity and consonant recognition were determined for normal hearing and hearing impaired listeners using techniques that facilitate comparisons of performance among listeners whose absolute thresholds vary in magnitude and configuration first for each of six subjects with cochlear hearing loss masked thresholds in notched noise and narrow band noise maskers were obtained and compared to results for three normal hearing listeners whose thresholds were precisely matched to the impaired listeners by masking with spectrally shaped broadband noise second for hearing impaired listeners and their masked normal hearing controls measurements of consonant recognition were obtained at several speech presentation levels selected on the basis of articulation index predictions to assure equal speech spectrum audibility across listeners the results suggest that frequency selectivity is poorer for hearing impaired listeners than for masked normal hearing listeners even when thresholds among subjects are equated but the deviation from normal frequency selectivity is smaller than estimated from comparisons with normal hearing listeners in quiet critical ratios for hearing impaired listeners are equivalent to normal although frequency selectivity is reduced there is no consistent difference in consonant recognition between hearing impaired subjects and masked normal hearing subjects when performance is assessed under conditions that assure equal speech spectrum audibility across subjects

numerical investigation of the parabolic mixed derivative diffusion equation via alternating direction implicit methods the two dimensional analogue of a two parameter mixed derivative equation is considered via two numerical methods the adi and compact adi method these methods are compared and the influence of the kinematic viscosity and viscoelasticity is discussed in relation to the solutions obtained the two schemes are proven to be conditionally stable and the methods compared via an error analysis

an efficient and stable method for computing multiple saddle points with symmetries in this paper an efficient and stable numerical algorithm for computing multiple saddle points with symmetries is developed by modifying the local minimax method established in y li and j zhou siam j sci comput 23 2001 pp 840 865 y li and j zhou siam j sci comput 24 2002 pp 840 865 first an invariant space is defined in a more general sense and a principle of invariant criticality is proved for the generalization then the orthogonal projection to the invariant space is used to preserve the invariance and to reduce computational error across iterations simple averaging formulas are used for the orthogonal projections numerical computations of examples with various symmetries of which some can and others cannot be characterized by a compact group of linear isomorphisms are carried out to confirm the theory and to illustrate applications the mathematical features of various problems demonstrated in these examples fall into two categories nodal solutions of saddle point type with large morse indices and nonradial positive solutions via symmetry breaking in radially symmetric elliptic problems the new numerical algorithm generates these rather unstable solutions in an efficient and stable way the existence of many unstable solutions and their behavior found in this paper remain to be investigated

behavioral measures of cochlear compression and temporal resolution as predictors of speech masking release in hearing impaired listeners hearing impaired hi listeners often show less masking release mr than normal hearing listeners when temporal fluctuations are imposed on a steady state masker even when accounting for overall audibility differences this difference may be related to a loss of cochlear compression in hi listeners behavioral estimates of compression using temporal masking curves tmcs were compared with mr for band limited 500 4000 hz speech and pure tones in hi listeners and age matched noise masked normal hearing nmnh listeners compression and pure tone mr estimates were made at 500 1500 and 4000 hz the amount of mr was defined as the difference in performance between steady state and 10 hz square wave gated speech shaped noise in addition temporal resolution was estimated from the slope of the off frequency tmc no significant relationship was found between estimated cochlear compression and mr for either speech or pure tones nmnh listeners had significantly steeper off frequency temporal masking recovery slopes than did hi listeners and a small but significant correlation was observed between poorer temporal resolution and reduced mr for speech the results suggest either that the effects of hearing impairment on mr are not determined primarily by changes in peripheral compression or that the tmc does not provide a sufficiently reliable measure of cochlear compression

the significance of heterogeneity of evolving scales to transport in porous formations flow takes place in a heterogeneous formation of spatially variable conductivity which is modeled as a stationary space random function to model the variability at the regional scale the formation is viewed as one of a two dimensional horizontal structure a constant head gradient is applied on the formation boundary such that the flow is uniform in the mean a plume of inert solute is injected at t 0 in a volume v0 under ergodic conditions the plume centroid moves with the constant mean flow velocity u and a longitudinal macrodispersion coefficient dl may be defined as half of the time rate of change of the plume second spatial moment with respect to the centroid for a log conductivity covariance cy of finite integral scale i at first order in the variance y2 and for a travel distance l ut i dl y2ui and transport is coined as fickian ergodicity of the moments is ensured if l i where l is the initial plume scale some field observations have suggested that heterogeneity may be of evolving scales and that the macrodispersion coefficient may grow with l without reaching a constant limit anomalous diffusion to model such a behavior previous studies have assumed that cy is stationary but of unbounded integral scale with cy ar 1 0 for large lag r under ergodic conditions it was found that asymptotically dl aul1 i e non fickian behavior and anomalous dispersion the present study claims that an ergodic behavior is not possible for a given finite plume of initial size l since the basic requirement that l i cannot be satisfied for cy of unbounded scale for instance the centroid does not move any more with u but is random figure 1 owing to the large scale heterogeneity in such a situation the actual effective dispersion coefficient dl is defined as half the rate of change of the mean second spatial moment with respect to the plume centroid in each realization this is the accessible entity in a given experiment we show that in contrast with dl the behavior of dl is controlled by l and it has the fickian limit dl aul1 figure 3 we also discuss the case in which y is of stationary increments and is characterized by its variogram y then u and dl can be defined only if y is truncated equivalently an infrared cutoff is carried out in the spectrum of y however for a bounded u it is shown that dl depends only on y furthermore for y ar dl aul2l 1 i e dispersion is fickian for 0 1 whereas for 1 2 transport is non fickian since 2 dl cannot grow faster than l ut this is in contrast with a recently proposed model neuman 1990 in which the dispersion coefficient is independent of the plume size and it grows approximately like l1 5

diffusion subject to the specification of mass abstract existence uniqueness and continuous dependence upon the data are demonstrated for the solution u u x t of the diffusion equation ut uxx s x t 0 u x 0 x 0 ux 1 t g t 0 0 b 0 x dx m 0 a numerical procedure is discussed and results of numerical experiments are presented

an efficient time splitting compact finite difference method for gross pitaevskii equation abstract we propose an efficient time splitting compact finite difference method for gross pitaevskii equation gpe in our method we solve the gpe in time with time splitting technique and in space by the compact finite difference method to find the numerical solution of the resulting discretized system in one dimension 1d two dimensions 2d and three dimensions 3d we apply the fast discrete sine transform in 1d 2d and 3d respectively and get an efficient solver for the discretized system in 1d 2d and 3d respectively our numerical algorithm at every time step does not need linear algebraic equations solver whose computation cost will be much higher when the spatial dimension increases the method also has the merit that it is unconditionally stable and conservative moreover the method can achieve spectral like accuracy in space when high order compact finite difference method is applied extensive numerical tests for the gpe in 1d 2d and 3d are presented to demonstrate the power and accuracy of the proposed numerical method

masking release for hearing impaired listeners the effect of increased audibility through reduction of amplitude variability the masking release i e better speech recognition in fluctuating compared to continuous noise backgrounds observed for normal hearing nh listeners is generally reduced or absent in hearing impaired hi listeners one explanation for this lies in the effects of reduced audibility elevated thresholds may prevent hi listeners from taking advantage of signals available to nh listeners during the dips of temporally fluctuating noise where the interference is relatively weak this hypothesis was addressed through the development of a signal processing technique designed to increase the audibility of speech during dips in interrupted noise this technique acts to i compare short term and long term estimates of energy ii increase the level of short term segments whose energy is below the average energy and iii normalize the overall energy of the processed signal to be equivalent to that of the original long term estimate evaluations of this energy equalizing eeq technique included consonant identification and sentence reception in backgrounds of continuous and regularly interrupted noise for hi listeners performance was generally similar for processed and unprocessed signals in continuous noise however superior performance for eeq processing was observed in certain regularly interrupted noise backgrounds

galerkin method with trigonometric basis on stable numerical differentiation abstract this paper considers the p p 1 2 3 order numerical differentiation on function y in 0 2 they are transformed into corresponding fredholm integral equation of the first kind computational schemes with analytic solution formulas are designed using galerkin method on trigonometric basis convergence and divergence are all analysed in corollaries 5 1 5 2 and a priori error estimate is uniformly obtained in theorem 6 1 7 1 7 2 therefore the algorithm achieves the optimal convergence rate o 2 2 1 1 2 or 1 with periodic sobolev source condition of order 2 p besides we indicate a noise independent a priori parameter choice when the function y possesses the form of k 0 p 1 a k t k k 1 n 1 b k cos k t k 1 n 2 c k sin k t b n 1 c n 2 0 in particular in numerical differentiations for functions above good filtering effect error approaches 0 is displayed with corresponding parameter choice in addition several numerical examples are given to show that even derivatives with discontinuity can be recovered well

unconditional stability of alternating difference schemes with intrinsic parallelism for the fourth order parabolic equation in this paper the difference method with intrinsic parallelism for the fourth order parabolic equation is studied the general alternating difference schemes are constructed and proved to be unconditionally stable the alternating group explicit scheme alternating segment explicit implicit scheme and alternating segment crank nicolson scheme are the special cases of the general schemes constructed here numerical results are presented to examine the convergence stability and accuracy of the general schemes

a high linking algorithm for sign changing solutions of semilinear elliptic equations where n is a bounded domain with regular boundary the operator can be replaced by a more general second order uniformly elliptical operator in divergence form the solutions we are interested in nding are of minimax type and sign changing nonlinear elliptic equations of type 1 1 arise naturally in physics engineering and mathematical biology it is known that many such equations have multiple solutions their study has attracted the attention of many pure and applied mathematicians during the past two decades let us assume that f satis es the following regularity and growth conditions a1 f x t is locally lipschitz continuous in