high resolution schemes for conservation laws with locally varying time steps we develop upwind methods which use limited high resolution corrections in the spatial discretization and local time stepping for forward euler and second order time discretizations l infty stability is proven for both time stepping schemes for problems in one space dimension these methods are restricted by a local cfl condition rather than the traditional global cfl condition allowing local time refinement to be coupled with local spatial refinement numerical evidence demonstrates the stability and accuracy of the methods for problems in both one and two space dimensions

harmonic wavelet analysis a new harmonic wavelet is suggested unlike wavelets generated by discrete dilation equations whose shape cannot be expressed in functional form harmonic wavelets have the simple structure w x exp i4 pi x exp i2 pi x i2 pi x this function w x is concentrated locally around x 0 and is orthogonal to its own unit translations and octave dilations its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain rather than in the x domain an efficient implementation of a discrete transform using this wavelet is based on the fast fourier transform fft fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the fft the same process works backwards for the inverse transform

representation of lie algebra t3 and 2 variable 2 parameter bessel functions abstract in this paper we deal with the problem of framing 2 variable 2 parameter bessel functions 2v2pbf into the context of the representation q w m 0 of the 3 dimensional lie algebra t 3 further we derive generating relations and identities involving 2v2pbf furthermore we deduce some new and known relations involving various other forms of generalized bessel functions gbf and bessel functions bf as applications of these results

wavelet expansion based stochastic response of chain like mdof structures abstract this paper presents a wavelet expansion based approach for response determination of a chain like multi degree of freedom mdof structure subject to full non stationary stochastic excitations specifically the generalized harmonic wavelet ghw is first utilized as the expansion basis to solve the dynamic equation of structures via the galerkin treatment in this way a linear matrix relationship between the deterministic response and excitation can be derived further considering the ghw based representation of the stochastic processes a time varying power spectrum density psd relationship on a certain wavelet scale or frequency band between the excitation and response is derived finally pertinent numerical simulations including deterministic dynamic analysis and monte carlo simulations of both the response psd and the story drift based reliability are utilized to validate the proposed approach

a multilevel wavelet collocation method for solving partial differential equations in a finite domain abstract a multilevel wavelet collection method for the solution of partial differential equations is developed two different approaches of treating general boundary conditions are suggested both are based on the wavelet interpolation technique developed in the present research the first approach uses wavelets as a basis and results in a differential algebraic system of equations where the algebraic part arises from boundary conditions the second approach utilizes extended wavelets which satisfy boundary conditions exactly this approach results in a system of coupled ordinary differential equations the method is tested on the one dimensional burgers equation with small viscosity the solutions are compared with those resulting from the use of other numerical algorithms the present results indicate that the method is competitive with well established numerical algorithms

effects of spectro temporal modulation changes produced by multi channel compression on intelligibility in a competing speech task these experiments are concerned with the intelligibility of target speech in the presence of a background talker using a noise vocoder stone and moore j acoust soc am 114 1023 1034 2003 showed that single channel fast acting compression degraded intelligibility but slow compression did not stone and moore j acoust soc am 116 2311 2323 2004 showed that intelligibility was lower when fast single channel compression was applied to the target and background after mixing rather than before and suggested that this was partly due to compression after mixing introducing comodulation between the target and background talkers experiment 1 here showed a similar effect for multi channel compression in experiment 2 intelligibility was measured as a function of the speed of multi channel compression applied after mixing for both eight and 12 channel vocoders with one compressor per channel intelligibility decreased as compression speed increased for the eight channel vocoder a compresso

infinite variable bessel functions in two dimensional wannier stark systems we discuss the spectrum and the eigenfunctions of a 2d wannier stark system in both the tight binding and single band approximations we show that the unfamiliar infinite variable bessel functions play a crucial role in these considerations furthermore a closed formula for the eigenfunction for an arbitrary tight binding ansatz in terms of an expansion in wannier states is derived finally we give a closed form solution for the wannier stark states in the scope of the single band approximation

temporal integration of loudness in listeners with hearing losses of primarily cochlear origin to investigate how hearing loss of primarily cochlear origin affects the loudness of brief tones loudness matches between 5 and 200 ms tones were obtained as a function of level for 15 listeners with cochlear impairments and for seven age matched controls three frequencies usually 0 5 1 and 4 khz were tested in each listener using a two interval two alternative forced choice 2i 2afc paradigm with a roving level up down adaptive procedure results for the normal listeners generally were consistent with published data e g j acoust soc am 99 1633 1644 1996 the amount of temporal integration defined as the level difference between equally loud short and long tones varied nonmonotonically with level and was largest at moderate levels no consistent effect of frequency was apparent the impaired listeners varied widely but most showed a clear effect of level on the amount of temporal integration overall their results appear consistent with expectations based on knowledge of the general properties of their loudness growth functions and the equal loudness ratio hypothesis which states that the loudness ratio between equal spl long and brief tones is the same at all spls the impaired listeners amounts of temporal integration at high spls often were larger than normal although it was reduced near threshold when evaluated at equal sls the amount of temporal integration well above threshold usually was in the low end of the normal range two listeners with abrupt high frequency hearing losses slopes 50 db octave showed larger than normal maximal amounts of temporal integration 40 to 50 db this finding is consistent with the shallow loudness functions predicted by our excitation pattern model for impaired listeners in modeling sensorineural hearing loss edited by w jesteadt erlbaum mahwah nj 1997 pp 187 198 loudness functions derived from impaired listeners temporal integration functions indicate that restoration of loudness in listeners with cochlear hearing loss usually will require the same gain whether the sound is short or long

discretization of nonlinear models by sinc collocation interpolation methods abstract this paper deals with the solution of initial boundary value problems for nonlinear evolution equations in one and two space dimensions the solution technique is based on collocation interpolation methods which use sinc functions the paper aims to provide a guideline towards a large number of nonlinear problems of interest in applied sciences

simultaneous space time adaptive wavelet solution of nonlinear parabolic differential equations dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time these methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time the same time step is used for all spatial locations and all scales this approach clearly does not fully exploit space time intermittency we propose an adaptive wavelet collocation method for solving highly intermittent problems e g turbulence on a simultaneous space time computational domain which naturally adapts both the space and time resolution to match the solution besides generating a near optimal grid for the full space time solution this approach also allows the global time integration error to be controlled the efficiency and accuracy of the method is demonstrated by applying it to several highly intermittent 1d t dimensional and 2d t dimensional test problems in particular we found that the space time method uses roughly 18 times fewer space time grid points and is roughly 4 times faster than a dynamically adaptive explicit time marching method while achieving similar global accuracy

generating functions of multivariable generalized bessel functions and jacobi elliptic functions it is pointed out that the jacobi elliptic functions are the natural basis to get generating functions of the multivariable generalized bessel functions analytical and numerical results are given of interest for applications

a conservative space time mesh refinement method for the 1 d wave equation part i construction we propose a new method for space time refinement for the 1 d wave equation this method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme our approach results in a non interpolatory scheme whose stability condition is not affected by the transition between the two grids

harmonic wavelets towards the solution of nonlinear pde in this paper harmonic wavelets which are analytically defined and band limited are studied together with their differentiable properties harmonic wavelets were recently applied to the solution of evolution problems and more generally to describe evolution operators in order to consider the evolution of a solitary profile and to focus on the localization property of wavelets it seems to be more expedient to make use of functions with limited compact support either in space or in frequency the connection coefficients of harmonic wavelets are explicitly computed in the following at any order and characterized by some recursive formulas in particular they are functionally and finitely defined by a simple formula for any order of the basis derivatives

a dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain a dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where sharp transitions occur the scheme handles general boundary conditions the method is applied to the solution of the one dimensional burgers equation with small viscosity a moving shock problem and a nonlinear thermoacoustic wave problem the results indicate that the method is very accurate and efficient

theory of two index bessel functions and applications to physical problems in this article the theory of two index bessel functions is presented their generating function series expansion and integral representations are discussed their usefulness in physical problems is also discussed in the context of analysis of radiation emitted by relativistic electrons in two frequency undulators finally the theoretical analysis proving addition and multiplication theorems for two index bessel functions are completed and their modified forms are introduced

an adaptive multiresolution method on dyadic grids we propose a modified adaptive multiresolution scheme for solving d dimensional hyperbolic conservation laws which is based on cell average discretization in dyadic grids adaptivity is obtained by interrupting the refinement at the locations where appropriate scale wavelet coefficients are sufficiently small one important aspect of such a multiresolution representation is that we can use the same binary tree data structure for domains of any dimension the tree structure allows us to succinctly represent the data and efficiently navigate through it dyadic grids also provide a more gradual refinement as compared with the traditional quad trees 2d or oct trees 3d that are commonly used for multiresolution analysis we show some examples of adaptive binary tree representations with significant savings in data storage when compared to quad tree based schemes as a test problem we also consider this modified adaptive multiresolution method using a dynamic binary tree data structure applied to a transport equation in 2d domain based on a second order finite volume discretization highlights we describe an adaptive multiresolution method for d dimensional pdes the method is based on cell average discretization on a dyadic grid the grid refinement is dynamically adapted to the current solution the same binary tree structure is used for domains of any dimension the method is tested on a transport problem in a two dimensional domain

wavelet solutions for the dirichlet problem a modified classical penalty method for solving a dirichlet boundary value problem is presented this new fictitious domain penalty method eliminates the traditional need of generating a complex computation grid in the case of irregular domains it is based on the fact that one can expand the boundary measure under the chosen basis which leads to a fast approximate calculation of boundary integral the compact support and orthonormality of the basis are essential for representing the boundary measure numerically and therefore for implementing this methodology

fully adaptive multiresolution finite volume schemes for conservation laws the use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by a harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation in this approach the solution is still represented at each time step on the finest grid resulting in an inherent limitation of the potential gain in memory space and computational time the present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes in which the solution is represented and computed in a dynamically evolved adaptive grid a crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages several solutions to this problem are proposed analyzed and compared in terms of accuracy and complexity

the spherical bessel and struve functions and operational methods abstract we review some aspects of the theory of spherical bessel functions and struve functions by means of an operational procedure essentially of umbral nature capable of providing the straightforward evaluation of their definite integrals and of successive derivatives the method we propose allows indeed the formal reduction of these family of functions to elementary ones of gaussian type we study the problem in general terms and present a formalism capable of providing a unifying point of view including anger and weber functions too the link to the multi index bessel functions is also briefly discussed

a unified point of view on the theory of generalized bessel functions abstract bessel functions have been generalized in a number of ways and many of these generalizations have been proved to be important tools in applications in this paper we present a unified treatment thus proving that many of the seemingly different generalizations may be viewed as particular cases of a two variable function of the type introduced by miller during the sixties

multiresolution representation of data a general framework in this paper we present a general framework for a multiresolution representation of data which is obtained by the discretization of mappings this framework which can be viewed as a generalization of the theory of wavelets includes discretization corresponding to unstructured grids in several space dimensions and thus is general enough to enable us to embed most numerical problems in a multiresolution setting furthermore this framework allows for nonlinear data dependent multiresolution representation schemes and thus enables us to design adaptive data compression algorithms in this paper we also study the stability of linear schemes for a multiresolution representation and derive sufficient conditions for existence of a multiresolution basis

multiplication theorems for generalized and double index bessel functions abstract using the generating function method we obtain a multiplication theorem for the two variables one parameter generalized cylinder function j n x y and two multiplication theorems for the double index bessel function j m n x

harmonic wavelet based data filtering for enhanced machine defect identification a filter construction technique is presented for enhanced defect identification in rotary machine systems based on the generalized harmonic wavelet transform a series of sub frequency band wavelet coefficients are constructed by choosing different harmonic wavelet parameter pairs the energy and entropy associated with each sub frequency band are then calculated the filtered signal is obtained by choosing the wavelet coefficients whose corresponding sub frequency band has the maximum energy to entropy ratio experimental studies using rolling bearings that contain different types of structural defects have confirmed that the developed new technique enables high signal to noise ratio for effective machine defect identification

space time adaptive wavelet methods for parabolic evolution problems with respect to space time tensor product wavelet bases parabolic initial boundary value problems are equivalently formulated as bi infinite matrix problems adaptive wavelet methods are shown to yield sequences of approximate solutions which converge at the optimal rate in case the spatial domain is of product type the use of spatial tensor product wavelet bases is proved to overcome the so called curse of dimensionality i e the reduction of the convergence rate with increasing spatial dimension

multiresolution schemes for conservation laws with viscosity this paper presents multiresolution schemes for the efficient numerical solution of one dimensional conservation laws with viscosity the method originally developed by a harten commun pure appl math to appear for hyperbolic conservation laws computes the cell average multiresolution representation of the solution which provides much information about the solution s regularity as a consequence the possibly expensive eno essentially nonoscillatory reconstruction as well as numerous flux computations are performed only near discontinuities and thereby the numerical solution procedure becomes considerably more efficient the multiresolution scheme is also expected to follow possibly unsteady irregularities from one time step to the next when viscosity is added predicting the location of the irregularity becomes a problem of estimating the change in shock thickness to this end we derive shock width estimates for our 1d prototype equations which when combined with the stability restriction of the numerical scheme provide a reliable mechanism for enlarging the original multiresolution stencil the numerical experiments for scalar conservation laws indicate the feasibility of multiresolution schemes for the viscous case as well

additivity of masking in normally hearing and hearing impaired subjects the effects of combining two equally effective maskers were studied in normally hearing and elderly hearing impaired subjects the additivity of nonsimultaneous masking was investigated by measuring thresholds for a brief 4 khz signal in the presence of a broadband noise forward masker a backward masker and a combination of both for the normally hearing subjects combining two equally effective nonsimultaneous maskers resulted in up to a 15 db greater increase in threshold than the 3 db predicted by an energy summation model excess masking however the hearing impaired subjects showed little or no excess masking the difference between the two groups is consistent with a theory linking excess masking to the compressive transfer function measured on the basilar membrane bm in the hearing impaired subjects the transfer function is more linear accounting for the lack of excess masking the additivity of simultaneous masking was investigated by measuring thresholds for a 100 ms 4 khz signal in the presence of either a 400 ms broadband noise masker or a 400 ms sinusoidal masker at the same frequency as the signal and then combining two equally effective maskers a noise and a tone the maximum amount of excess masking 3 to 4 db was similar across the two groups of subjects consistent with an explanation based on the use of different detection cues for the tonal and noise maskers it is argued that while peripheral compression may underlie excess masking for pairs of nonsimultaneous maskers it is unlikely that in simultaneous masking where the maskers are close in frequency to the signal the two maskers are compressed individually before their effects are combined it is further suggested that bm nonlinearity may underlie the effects of the upward spread of masking and the nonlinear growth of forward masking as well as accounting for the additivity of simultaneous masking when the masker frequencies are well below that of the signal

epstein hubbell elliptictype integral and its generalizations abstract a survey of the evaluation series expansions properties and approximation of the epstein hubbell elliptictype integral is considered we review different generalizations of this integral r k k k m s k v etc and examine some of their important properties including asymptotic expansions in the neighborhood of k 2 1 we express j k and its generalizations in terms of hypergeometric series of argument k 4 furthermore we show that a new infinite series of epstein hubbell integral obtained recently by some authors using the residue theory of complex variables can be easily deduced from known transformations it is shown that the elliptictype integrals can be expressed as the differintegral of elementary functions

touchard like polynomials and generalized stirling numbers abstract the theory of touchard polynomials is generalized using a method based on the definition of exponential operators which extend the notion of the shift operator the proposed technique along with the use of the relevant operational formalism allows the straightforward derivation of properties of this family of polynomials and their relationship to different forms of stirling numbers

symbolic methods for the evaluation of sum rules of bessel functions the use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials we rederive in this way known sum rules and addition theorems for bessel functions furthermore we obtain a set of new closed form sum rules involving various special polynomials and bessel functions the examples we consider are relevant for applications ranging from plasma physics to quantum optics

generating relations of tricomi and hermite tricomi functions using lie algebra representation abstract this paper is an attempt to stress the usefulness of the multi variable special functions in this paper we derive generating relations involving multi variable tricomi and hermite tricomi functions by using lie algebraic method further we derive certain new and known generating relations involving other forms of tricomi hermite tricomi and bessel functions as applications

on two dimensional bessel functions the general properties of two dimensional generalized bessel functions are discussed various asymptotic approximations are derived and applied to analyse the basic structure of the two dimensional bessel functions as well as their nodal lines

solution of nonlinear initial boundary value problems by sinc collocation interpolation methods abstract this paper deals with the solution of initial boundary value problems for nonlinear evolution equations in one and two space dimensions the solution technique is based on collocation interpolation methods which use sinc functions the application refers to some direct and inverse type problems

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

wavelet algorithms for numerical resolution of partial differential equations abstract numerical algorithms for the approximation of non linear partial differential equations are presented on one hand they are based on adaptive spaces of the approximation provided by wavelets and on the other hand on efficient approximations of evolution operators on these spaces numerical experiments are described on 1d test problems

definitions of non stationary vibration power for time frequency analysis and computational algorithms based upon harmonic wavelet transform abstract while the vibration power for a set of harmonic force and velocity signals is well defined and known it is not as popular yet for a set of stationary random force and velocity processes although it can be found in some literatures in this paper the definition of the vibration power for a set of non stationary random force and velocity signals will be derived for the purpose of a time frequency analysis based on the definitions of the vibration power for the harmonic and stationary random signals the non stationary vibration power defined as the short time average of the product of the force and velocity over a given frequency range of interest can be calculated by three methods the wigner ville distribution the short time fourier transform and the harmonic wavelet transform the latter method is selected in this paper because band pass filtering can be done without phase distortions and the frequency ranges can be chosen very flexibly for the time frequency analysis three algorithms for the time frequency analysis of the non stationary vibration power using the harmonic wavelet transform are discussed the first is an algorithm for computation according to the full definition while the others are approximate noting that the force and velocity decomposed into frequency ranges of interest by the harmonic wavelet transform are constructed with coefficients and basis functions for the second algorithm it is suggested to prepare a table of time integrals of the product of the basis functions in advance which are independent of the signals under analysis how to prepare and utilize the integral table are presented the third algorithm is based on an evolutionary spectrum applications of the algorithms to the time frequency analysis of the vibration power transmitted from an excitation source to a receiver structure in a simple mechanical system consisting of a cantilever beam and a reaction wheel are presented for illustration

repeated derivatives of composite functions and generalizations of the leibniz rule we use the properties of hermite and kampe de feriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher order polynomial these results are extended to product of functions of the above argument thus giving rise to expressions which can formally be interpreted as generalizations of the familiar leibniz rule finally examples of practical interest are discussed

computational aspects of harmonic wavelet galerkin methods and an application to a precipitation front propagation model this article is dedicated to harmonic wavelet galerkin methods for the solution of partial differential equations several variants of the method are proposed and analyzed using the burgers equation as a test model the computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited the resulting variants of the method have computational complexities ranging from o n 3 to o n n being the space dimension per time step a pseudo spectral wavelet scheme is also described and compared to the methods based on connection coefficients the harmonic wavelet galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts with the front locations being exposed in the sizes of the localized wavelet coefficients

using the refinement equation for evaluating integrals of wavelets the wavelet galerkin method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets this paper studies the problem from the point of view of stationary subdivision schemes one of the main results is to identify these integrals as components of the unique solution of a certain eigenvector moment problem associated with the coefficients of the refinement equation asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach

wavelet galerkin methods for second kind integral equations we use vector valued multiwavelets on compact sets to develop a galerkin method for systems of integral equations of the second kind we propose a compression strategy for the coefficient matrix of the linear system obtained from this method and show that the compressed scheme preserves almost optimal convergence rate of the original scheme and yields a sparse matrix with a bounded condition number

hierarchical dobinski type relations via substitution and the moment problem we consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson a a 1 monomials of the form exp a ra r 1 2 under the composition of their exponential generating functions they turn out to be of sheffer type we demonstrate that two key properties of these sequences remain preserved under substitutional composition a the property of being the solution of the stieltjes moment problem and b the representation of these sequences through infinite series dobinski type relations we present a number of examples of such composition satisfying properties a and b we obtain new dobinski type formulae and solve the associated moment problem for several hierarchically defined combinatorial families of sequences

adaptive harmonic wavelet transform with applications in vibration analysis an adaptive harmonic wavelet transform is developed by taking advantage of the flexibility of the generalized harmonic wavelets it first constructs a partition tree which contains a great number of disjoint partitions of the frequency axis of a signal with each corresponding to an orthogonal harmonic wavelet basis then it searches the tree for the partition to represent the signal most sparsely since the corresponding basis is adapted to the composition of the signal the transform can well reveal its characteristics this is demonstrated with analysis examples of some simulated and vibration signals as well as comparisons with the conventional orthogonal harmonic wavelet transforms and wavelet packet transform

effect of spatial separation extended bandwidth and compression speed on intelligibility in a competing speech task the benefit for speech intelligibility of extending the bandwidth of hearing aids was assessed when the target speech sentences and background two talkers were co located or spatially separated also the relative benefits of slow and fast compression were assessed sixteen hearing impaired hi subjects with mild to moderate high frequency hearing loss and eight normal hearing nh subjects were tested the target and interfering sounds were recorded using a kemar manikin and were located at 60 azimuth either co located or spatially separated simulated binaural hearing aid processing using five channel slow or fast compression was performed offline with gains set individually for each hi subject upper cutoff frequencies were 5 7 5 or 10 khz processed stimuli were presented via headphones for both nh unaided and hi subjects there was no significant effect of cutoff frequency for the co located condition but a small but significant benefit from increasing the cutoff frequency from 5 to 7

wavelet transforms versus fourier transforms this note is a very basic introduction to wavelets it starts with an orthogonal basis of piecewise constant functions constructed by dilation and translation the wavelet transform maps each f x to its coefficients with respect to this basis the mathematics is simple and the transform is fast faster than the fast fourier transform which we briefly explain but approximation by piecewise constants is poor to improve this first wavelet we are led to dilation equations and their unusual solutions higher order wavelets are constructed and it is surprisingly quick to compute with them always indirectly and recursively

a class of high resolution difference schemes for nonlinear hamilton jacobi equations with varying time and space grids based on a simple projection of the solution increments of the underlying partial differential equations pdes at each local time level this paper presents a difference scheme for nonlinear hamilton jacobi h j equations with varying time and space grids the scheme is of good consistency and monotone under a local cfl type condition moreover one may deduce a conservative local time step scheme similar to osher and sanders scheme approximating hyperbolic conservation law cl from our scheme according to the close relation between cls and h j equations second order accurate schemes are constructed by combining the reconstruction technique with a second order accurate runge kutta time discretization scheme or a lax wendroff type method they keep some good properties of the global time step schemes including stability and convergence and can be applied to solve numerically the initial boundary value problems of viscous h j equations they are also suitable to parallel computing numerical errors and the experimental rate of convergence in the lp norm p 1 2 and infty are obtained for several one and two dimensional problems the results show that the present schemes are of higher order accuracy

enabling local time stepping in the parallel implicit solution of reaction diffusion equations via space time finite elements on shallow tree meshes for many applications local time stepping offers an interesting and worthwhile alternative to the by now well established global time step control in fact local time stepping can allow for a highly detailed resolution of localized features of the solution with strongly reduced computational cost when compared to global time step control however local time stepping is not applicable in a straight forward manner in the context of fully implicit time discretizations here we present a method for the efficient parallel adaptive solution of non linear partial differential equations in particular reaction diffusion equations using spatially adapted time step sizes in the context of a fully implicit solution strategy our proposed method uses a discontinuous galerkin method in time approach within a full space time approach moreover it is designed from scratch for efficient parallel computation we employ shallow tree based mesh data structures in order to ensure a low memory footprint of the adaptive meshes by solving the time dependent partial differential equation on a d 1 dimensional non conforming mesh space time adaptivity is naturally achieved in combination with a discontinuous galerkin method in time the size of the arising systems can be precisely controlled we additionally introduce and discuss a stabilization scheme for space time mortar element methods that also has a highly positive impact on the efficiency of preconditioning techniques for the arising systems of equations we present results from extensive numerical experiments that address the question of convergence and efficiency linear and non linear solver performance parallel scalability up to 2048 cores as well as accuracy for the linear heat equation and a real world non linear reaction diffusion equation from the field of computational electrocardiology

the natural integral equations of plane elasticity problem and its wavelet methods in this paper we apply interpolatory hermite type trigonometric wavelet to investigate the numerical solution of the natural boundary integral equation of plane elasticity problem by galerkin method in our fast algorithm the computational formulae of entries of the stiffness matrix yield simple close form and for one 2 j 3x2 j 3 stiffness matrix we only need to compute 2 2 j 2 2 j 1 entries the error estimates of the approximate solution are given and the test examples are presented in the end

the ramanujan master theorem and its implications for special functions abstract we study a number of possible extensions of the ramanujan master theorem which is formulated here by using methods of umbral nature we discuss the implications of the procedure for the theory of special functions like the derivation of formulae concerning the integrals of products of families of bessel functions and the successive derivatives of bessel type functions we stress also that the procedure we propose allows a unified treatment of many problems appearing in applications which can formally be reduced to the evaluation of exponential or gaussian like integrals

coherent vortex simulation of weakly compressible turbulent mixing layers using adaptive multiresolution methods an adaptive mulitresolution method based on a second order finite volume discretization is presented for solving the three dimensional compressible navier stokes equations in cartesian geometry the explicit time discretization is of second order and for flux evaluation a 2 4 mac cormack scheme is used coherent vortex simulations cvs are performed by decomposing the flow variables into coherent and incoherent contributions the coherent part is computed deterministically on a locally refined grid using the adaptive multiresolution method while the influence of the incoherent part is neglected to model turbulent dissipation the computational efficiency of this approach in terms of memory and cpu time compression is illustrated for turbulent mixing layers in the weakly compressible regime and for reynolds numbers based on the mixing layer thickness between 50 and 200 comparisons with direct numerical simulations allow to assess the precision and efficiency of cvs

phase shifting for nonseparable 2 d haar wavelets in this paper we present a novel and efficient solution to phase shifting 2 d nonseparable haar wavelet coefficients while other methods either modify existing wavelets or introduce new ones to handle the lack of shift invariance we derive the explicit relationships between the coefficients of the shifted signal and those of the unshifted one we then establish their computational complexity and compare and demonstrate the superior performance of the proposed approach against classical interpolation tools in terms of accumulation of errors under successive shifting

effects of low pass filtering on the intelligibility of speech in noise for people with and without dead regions at high frequencies people with high frequency sensorineural hearing loss differ in the benefit they gain from amplification of high frequencies when listening to speech using vowel consonant vowel vcv stimuli in quiet that were amplified and then low pass filtered with various cutoff frequencies vickers et al j acoust soc am 110 1164 1175 2001 found that the benefit from amplification of high frequency components was related to the presence or absence of a cochlear dead region at high frequencies for hearing impaired subjects without dead regions performance improved with increasing cutoff frequency up to 7 5 khz the highest value tested subjects with high frequency dead regions showed no improvement when the cutoff frequency was increased above about 1 7 times the edge frequency of the dead region the present study was similar to that of vickers et al but used vcv stimuli presented in background noise ten subjects with high frequency hearing loss including eight from the study of vickers et al were tested five had dead regions starting below 2 khz and five had no dead regions speech stimuli at a nominal level of 65 db were mixed with spectrally matched noise amplified according to the cambridge prescriptive formula for each subject and then low pass filtered the noise level was chosen separately for each subject to give a moderate reduction in intelligibility relative to listening in quiet for subjects without dead regions performance generally improved with increasing cutoff frequency up to 7 5 khz on average more so in noise than in quiet for most subjects with dead regions performance improved with cutoff frequency up to 1 5 2 times the edge frequency of the dead region but hardly changed with further increases calculations of speech audibility using a modified version of the articulation index showed that application of the cambridge formula was at least partially successful in making high frequency components of the speech audible for subjects with dead regions and that such subjects often failed to benefit from increased audibility of the speech at high frequencies

solving pdes with the aid of two dimensional haar wavelets two dimensional haar wavelets are applied for solution of the partial differential equations pdes the proposed method is mathematically simple and fast to demonstrate the efficiency of the method two test problems solution of the diffusion and poisson equations are discussed computer simulation showed that the method guarantees the necessary exactness already for a small number of grid points

new sum rule for products of bessel functions with application to plasma physics in our investigations of the linear theory of the stability of relativistic beam plasma systems immersed in a magnetic field we have been led to consider sum rules for an infinite series of products of bessel functions of the form j n n jj2n n in this work we report on the sum of this series treated as a special case of a more general infinite series we also mention the extension of the results beyond the range of the parameters for which formulae are explicitly given and indicate how intermediate results obtained may be useful in their own right finally an additional application of our result is indicated

products of bessel functions and associated polynomials symbolic methods of umbral nature are exploited to derive series expansion for the products of bessel functions it is shown that the product of two cylindrical bessel functions can be written in terms of jacobi polynomials the procedure is extended to products of an arbitrary number of functions and the link with previous researchers is discussed we show that the technique we propose and the use of the ramanujan master theorem allow the derivation of integrals of practical interest

effects of compression and onset offset asynchronies on the detection of one tone in the presence of another the weaker of two temporally overlapping complex tones can be easier to hear when the tones are asynchronous than when they are synchronous this study explored how the use of fast and slow five channel amplitude compression as might be used in hearing aids affected the ability to use onset and offset asynchronies to detect one signal complex tone when another masking complex tone was presented almost simultaneously a 2 1 compression ratio was used with normal hearing subjects and individual compression ratios and gains recommended by the cam2 hearing aid fitting method were used for hearing impaired subjects when the signal started before the masker there was a benefit of compression for both normal hearing and hearing impaired subjects when the signal finished after the masker there was a benefit of fast compression for the normal hearing subjects but no benefit for most of the hearing impaired subjects except when the offset asynchrony was relatively large 100 ms the benefit of compression probably occurred because the compression improved the effective signal to masker ratio hence reducing backward and forward masking this apparently outweighed potential deleterious effects of distortions in envelope shape and the introduction of partially correlated envelopes of the signal and masker

multiresolution algorithms for the numerical solution of hyperbolic conservation laws given any scheme in conservation form and an appropriate uniform grid for the numerical solution of the initial value problem for one dimensional hyperbolic conservation laws we describe a multiresolution algorithm that approximates this numerical solution to a prescribed tolerance in an efficient manner to do so we consider the grid averages of the numerical solution for a hierarchy of nested diadic grids in which the given grid is the finest and introduce an equivalent multiresolution representation the multiresolution representation of the numerical solution consists of its grid averages for the coarsest grid and the set of errors in predicting the grid averages of each level of resolution in this hierarchy from those of the next coarser one once the numerical solution is resolved to our satisfaction in a certain locality of some grid then the prediction errors there are small for this particular grid and all finer ones this enables us to compress data by setting to zero small components of the representation which fall below a prescribed tolerance therefore instead of computing the time evolution of the numerical solution on the given grid we compute the time evolution of its compressed multiresolution representation algorithmically this amounts to computing the numerical fluxes of the given scheme at the points of the given grid by a hierarchical algorithm which starts with the computation of these numerical fluxes at the points of the coarsest grid and then proceeds through diadic refinements to the given grid at each step of refinement we add the values of the numerical flux at the center of the coarser cells the information in the multiresolution representation of the numerical solution is used to determine whether the solution is locally well resolved when this is the case we replace the costly exact value of the numerical flux with an accurate enough approximate value which is obtained by an inexpensive interpolation from the coarser grid the computational efficiency of this multiresolution algorithm is proportional to the rate of data compression for a prescribed level of tolerance that can be achieved for the numerical solution of the given scheme

an adaptive multiresolution scheme with local time stepping for evolutionary pdes we present a fully adaptive numerical scheme for evolutionary pdes in cartesian geometry based on a second order finite volume discretization a multiresolution strategy allows local grid refinement while controlling the approximation error in space for time discretization we use an explicit runge kutta scheme of second order with a scale dependent time step on the finest scale the size of the time step is imposed by the stability condition of the explicit scheme on larger scales the time step can be increased without violating the stability requirement of the explicit scheme the implementation uses a dynamic tree data structure numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid fully adaptive three dimensional computations for reaction diffusion equations illustrate the additional speed up of the local time stepping for a thermo diffusive flame instability

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

definite integrals and operational methods abstract an operational method already employed to formulate a generalization of the ramanujan master theorem is applied to the evaluation of integrals of various types this technique provides a very flexible and powerful tool yielding new results encompassing different aspects of the special function theory

three dimensional adaptive mesh refinement for hyperbolic conservation laws a local adaptive mesh refinement algorithm for solving hyperbolic systems of conservation laws in three space dimensions is described the method is based on the use of local grid patches superimpo

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

numerical approximations to nonlinear conservation laws with locally varying time and space grids an explicit time differencing technique is introduced to approximate nonlinear conservation laws this differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments previous stability requirements i e the cfl condition placed a global bound on the size of the time increments for scalar monotone approximations in one space dimension using this variable step time differencing convergence to the correct physical solution is proven given only a local cfl condition

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

prediction of absolute thresholds and equal loudness contours using a modified loudness model the loudness model described by moore et al j audio eng soc 45 224 240 1997 forms the basis for a recent ansi standard for the calculation of the loudness of steady sounds however the model does not give accurate predictions of the absolute thresholds published in a recent iso standard here it is described how the assumed middle ear transfer function in the model can be modified to give more accurate absolute threshold predictions the modified model also gives reasonably accurate predictions of the equal loudness contours published in a recent iso standard

galerkin trigonometric wavelet methods for the natural boundary integral equations a simply supported boundary value problem of biharmonic equations in the unit disk is reduced into an equivalent second kind natural boundary integral equation nbie with hypersingular kernel in the sense of hadamard finite part trigonometric hermite interpolatory wavelets introduced by quak math comput 65 1996 683 722 as trial functions are used to its galerkin discretization with 2 j 1 degrees of freedom on the boundary it is proved that the stiffness matrix is a block diagonal matrix and its diagonal elements are some symmetric and block circulant submatrices the simple computational formulae of the entries in stiffness matrix are obtained these show that we only need to compute 2 2 j j 1 elements of a 2 j 2x2 j 2 stiffness matrix the error estimates for the approximation solutions are established finally numerical examples are given

harmonic and musical wavelets the concept of a harmonic wavelet is generalized to describe a family of mixed wavelets with the structure w m n x exp i n 2 x exp i m 2 x i n m 2 x it is shown that this family provides a complete set of orthogonal basis functions for signal analysis by choosing the real numbers m and n not necessarily integers appropriately wavelets whose frequency content ascends according to the musical scale can be generated these musical wavelets provide greater frequency discrimination than is possible with harmonic wavelets whose frequency interval is always an octave an example of the wavelet analysis of music illustrates possible applications

lie theoretic generating relations of hermite 2d polynomials in this paper we derive some generating relations involving hermite 2d polynomials h2dp hm n u x y of two variables with an arbitrary 2d matrix u as parameter using lie theoretic approach certain known or new generating relations for the polynomials related to h2dp are also obtained as special cases

a new class of sum rules for products of bessel functions we derive a new class of sum rules for products of bessel functions of the first kind using standard algebraic manipulations we extend some of the well known properties of jn some physical applications of the results are also discussed a comparison with the newberger b s newberger j math phys 52 1278 1982 sum rules is performed on a typical example

a conservative space time mesh refinement method for the 1 d wave equation part ii analysis we introduced in 2 a new method for space time refinement for the 1 d wave equation this method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme in this second part we analyse the accuracy of this scheme in a detailed way by means of a plane wave analysis and numerical experiments that permit us to point out spurious numerical phenomena and explain how to control them

harmonic wavelet method towards solution of the fredholm type integral equations of the second kind periodic harmonic wavelets phw were applied as basis functions in solution of the fredholm integral equations of the second kind two equations were solved in order to find out advantages and disadvantages of such choice of the basis functions it is proved that phw satisfy the properties of the multiresolution analysis

connection coefficients on an interval and wavelet solutions of burgers equation a definition of connection coefficients is introduced and techniques of computation are presented we use semi implicit time difference scheme to solve burgers equation by applying the evaluations of connection coefficients in calculating the integrals of the variational form comparisons of accuracy and robustness of numerical solutions are mentioned in the examples

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed