uniform decay for the unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping in this article we study the existence of solutions and the uniform decay rate of the energy for nonlinear unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping to obtain the existence of solutions we make use of faedo galerkin s approximation and also to show the uniform stabilization we use the perturbed energy method

abstract volterra integrodifferential equations with applications to parabolic models with memory in this paper we are concerned with local existence regularity and continuous dependence upon the initial data of epsilon regular mild solutions for the abstract integrodifferential equation 1 2 we also present a result on unique continuation and a blow up alternative for an epsilon regular mild solution of 1 2 finally we apply our results to three interesting models navier stokes equations with memory diffusion equations with memory and a strongly damped plate equation with memory

an order 16 integer cosine transform it is shown that it is possible to replace the real numbered elements of a discrete cosine transform dct matrix with integers and still maintain the structure i e relative magnitudes and orthogonality among the matrix elements the result is an integer cosine transform ict thirteen icts have been found and some of them have performance comparable to the dct the main advantage of the ict lies in having only integer values which in two cases can be represented perfectly by 6 bit numbers thus providing a potential reduction in the computational complexity

temporal integration and multiple looks revisited weights as a function of time this study tests the hypothesis that temporal integration for detection of tone bursts with various durations can be explained by optimally combining multiple looks of brief signal segments whose contribution to detection increases over time detectability was measured for signals consisting of six consecutive 25 ms 1 khz tone pulses presented in a 50 hz wide masker or in maskers consisting of seven 50 hz wide noises one critical band apart with either coherent or incoherent envelopes the level of each signal pulse varied randomly around masked threshold according to a gaussian distribution the slopes of conditional psychometric functions plotted in terms of d 2 as a function of the squared signal pulse intensity for pulses in a particular temporal position yielded estimates of the contribution to detection provided by each pulse results for three normal listeners showed a small but significant effect of the temporal location of the pulse multiple looks predictions of temporal integration functio

the fine structure of the recovering auditory detection threshold detection thresholds were gathered for a 2 khz gaussian shaped probe standard deviation 0 5 ms centered at intervals of as little as half a millisecond over 0 30 ms following a 200 ms 97 db spl 2 khz tone surprisingly there were small sudden rises and falls superimposed on each subject s generally smooth recovery even more obvious were nonmonotonicities in the standard deviation of the cumulative normal fitted to each threshold s psychometric function

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

energy decay for a damped nonlinear coupled system this paper proves the well posedness and uniform stabilization of a nonlinear coupled system we estimate the energy decay rate by using the multiplier method

on uniform decay of the solution for a damped nonlinear coupled system of wave equations with nonlinear boundary damping and memory term in this paper we are concerned with the existence and energy decay of the solution to the initial boundary value problem for the nonlinear coupled wave equations with nonlinear boundary damping and memory term

global solutions for a nonlinear wave equation abstract in this work the existence of a global solution for the mixed problem associated to the nonlinear equation u m a 1 2 u 2 au n a u 2 a u f is proved in a hilbert space framework by using galerkin method

perceptual weights in auditory level discrimination perceptual weights in level discrimination also called intensity discrimination were determined for 3 7 15 and 24 component tone complexes with flat spectral envelopes using a correlational paradigm each frequency component was randomly and independently perturbed in level on each presentation for the target interval frequency component levels were additionally increased by the level increment to be detected l 20 log10 p p p where p is pressure weights were calculated from the across trial correlation between the level perturbations for each frequency component and the interval chosen by the listener two conditions were investigated 1 l was equal across frequency components and 2 l increased progressively across frequency components for both conditions data for four listeners usually showed the greatest weight for the highest frequency component the two to four highest frequency components generally were most important for level discrimination the effect of increasing l

c matrix transform an approximation to the discrete cosine transform dct called the c matrix transform cmt has been developed by jones et al 3 for n 8 this is extended to n 16 and 32 and its performance is compared with the dct based on some standard criteria cmt is computationally simpler as it involves only integer arithmetic it has potential in signal processing applications because of its closeness to the dct

dependence of post masking on masker duration and its relation to temporal effects in loudness temporal masking of tones by noise was investigated using a post forward masking paradigm the masker level and duration were varied for every masker level employed the rate of decay of masking was found to depend on the duration of the masker specific loudness values were computed from the forward masking functions and an electronic device which simulates these loudness functions is presented in the simulation a series of integrators or a single integration with one long time constant was utilized the effect of the proposed integrators on loudness meters is discussed

on solutions for a hyperbolic system with differential inclusion and memory source term on the boundary in this paper we investigate the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi valued term and a nonlinear memory source term on the boundary

remark on the decay for damped string and beam equations where a is an operator in a hilbert space h m is a real function our results improve those obtained by de brito in a recent paper l we briefly recall the notation and the assumptions in l referring to this paper for other information on physical meaning existence and regularity theory applications and bibliography let a be a self adjoint positive operator in a real hilbert space h with dense domain v we assume that 5 0 is the least eigenvalue of a so a u au u 3 51 1 for u e v let m e cl be a real nondecreasing function such that m s 2 p ks k z 0 p real we have with the notation

spectral weights for overall level discrimination in listeners with sensorineural hearing loss a conditional on a single stimulus coss analysis procedure b g berg j acoust soc am 86 1743 1746 1989 was used to measure the weight or relative reliance that normal hearing and hearing impaired listeners give to different frequencies in the discrimination of the overall level of a multitone complex on each trial two multitone tone complexes comprised of six octave frequencies from 250 to 8000 hz were presented to subjects the levels of the frequencies for each complex were randomly varied the listeners task was to identify the complex with the higher overall intensity level normal hearing listeners used a variety of listening strategies to perform the task showing no general preference to weight one component over another hearing impaired listeners however showed a general tendency to give greatest weight to the spectral information in the region of their hearing loss thirteen of the 14 hearing impaired listeners all of whom had a high frequency sensorineural hearing loss weighted one or more of the high frequency components in the complex the greatest

a dirac field interacting with point nuclear dynamics the system describing a single dirac electron field coupled with classically moving point nuclei is presented and studied the model is a semi relativistic extension of corresponding time dependent one body hartree fock equation coupled with classical nuclear dynamics already known and studied both in quantum chemistry and in rigorous mathematical literature we prove local existence of solutions for data in h sigma with sigma in 1 frac 3 2 in the course of the analysis a second new result of independent interest is discussed and proved namely the construction of the propagator for the dirac operator with several moving coulomb singularities

informational processing of complex sound ii cross dimensional analysis a series of experiments investigated listeners ability simultaneously to process information across different acoustic dimensions on each trial the listener heard a pair of brief n tone sequences n 1 to 12 the frequency intensity and duration of each tone in the sequence varied randomly from trial to trial on average the values of these three parameters were greater for one sequence the target than the other the nontarget the listener s task was to identify the target on each trial for an ideal observer in this task d performance grows as the square root n obtained d grew at a rate slightly less than the square root of n close to cube root of n growth was observed when the average difference occurred in only one of the three tone parameter values within a block of trials although performance fell short of ideal optimum weights were consistently given to each tone and each parameter the results are consistent with a model in which performance depends predominantly on the information content of the sounds regardless of how the information is packaged in the stimulus transmitted information is estimated to be 0 9 2 0 bits within a single acoustic dimension 2 1 3 0 bits when distributed across dimensions

on a certain inequality arising in the theory of differential equations abstract in the present paper we establish some new inequalities related to a certain integral inequality arising in the theory of differential equations the inequalities that we propose here can be used as handy tools in the theory of certain new classes of differential and integral equations

on some new inequalities related to certain inequalities in the theory of differential equations in the present paper we establish some new integral inequalities related to a certain inequality arising in the theory of differential equations the discrete analogues of the main results are also given the analysis used in the proofs is elementary and the results established here provide new estimates for these types of inequalities

exponential decay of solutions of damped nonlinear hyperbolic equations on considere le comportement asymptotique des solutions de certaines equations hyperboliques non lineaires a amortissement lineaire

on the global solvability of kirchhoff equation for non analytic initial data abstract we give sufficient conditions for the global solvability of kirchhoff equation in terms of the spectral resolutions of the initial data u 0 x u t 0 x we assume no smallness conditions and only sobolev type regularity

on coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term in this paper we prove the existence of the solution to the mixed problem for coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of the solution

hyperbolic parabolic singular perturbation for mildly degenerate kirchhoff equations time decay estimates we consider degenerate kirchhoff equations with a small parameter e in front of the second order time derivative it is well known that these equations admit global solutions when e is small enough and that these solutions decay as t with the same rate of solutions of the limit problem of parabolic type in this paper we prove decay error estimates for the difference between a solution of the hyperbolic problem and the solution of the corresponding parabolic problem these estimates show in the same time that the difference tends to zero both as e 0 and as t concerning the decay rates it turns out that the difference decays faster than the two terms separately as t proofs involve a nonlinear step where we separate fourier components with respect to the lowest frequency followed by a linear step where we exploit weighted versions of classical energies

some new finite difference inequalities abstract in this paper we establish some new finite difference inequalities related to a certain integral inequality arising in the theory of differential equations the inequalities obtained here can be used as handy tools in the theory of some new classes of finite difference and sum difference equations

comparing linear regression models applied to psychophysical data relative weights for a profile analysis task were obtained using four regression classification models correlation coefficients linear regression logistic regression and probit regression the aim of the study was to examine the impact of the choice of model on the accuracy and the efficiency with which the relative weights were determined a yes no task was used with observers indicating whether or not there was an increment in level to the central component of an 11 component standard on each presentation the amplitudes of the individual components of the complex were randomly perturbed using draws from a normal distribution when a large number of trials 1250 were used to estimate the relative weights the four methods generated nearly identical weight estimates when smaller numbers of trials were used 112 the different methods generated patterns of relative weights that were largely similar and the patterns deviated only modestly from the large number solution in terms of efficiency the error boundaries of the different methods were nearly indistinguishable all in all the number of trials needed to obtain statistically significant weights is sufficiently large that there is no apparent advantage of using one method over the others work supported by nih nidcd

temporal weights in the level discrimination of time varying sounds to determine how listeners weight different portions of the signal when integrating level information they were presented with 1 s noise samples the levels of which randomly changed every 100 ms by repeatedly and independently drawing from a normal distribution a given stimulus could be derived from one of two such distributions a decibel apart and listeners had to classify each sound as belonging to the soft or loud group subsequently logistic regression analyses were used to determine to what extent each of the ten temporal segments contributed to the overall judgment in experiment 1 a nonoptimal weighting strategy was found that emphasized the beginning and to a lesser extent the ending of the sounds when listeners received trial by trial feedback however they approached equal weighting of all stimulus components in experiment 2 a spectral change was introduced in the middle of the stimulus sequence changing from low pass to high pass noise and vice versa the temporal location of the stimulus change was strongly weighted much as a new onset these findings are not accounted for by current models of loudness or intensity discrimination but are consistent with the idea that temporal weighting in loudness judgments is driven by salient events

construction of group transforms subject to several performance criteria a transform l is defined in this paper and studied subject to the two opposing performance criteria computational effectiveness and accuracy of approximation of a given unitary transform measured in distance related to the hilbert sehmidt norm the matrices which represent the l transform constitute a special class of group matrices which were introduced by frobenius in 1895 these n n matrices depend upon certain free parameters whose choice determines their behavior with respect to the two criteria hence part of these parameters can be chosen to affect the computational performance of l whereas the other part is used to minimize its distance from a given unitary transform the computational complexity of l is eased by making l sparse rather than a product of sparse matrices as in the fft algorithm it is shown that if only one of these two criteria is used then either all the parameters can be used to reduce the computational complexity of l to that of the fast haar transform in nontrivial cases or else all of these parameters can be used to achieve asymptotically distance zero from a given unitary transform if both criteria are used then the more parameters that are used for one of them the less parameters we have to deal with for the other one and vice versa an inverse proportional dependence various examples are given

a quasilinear hyperbolic integrodifferential equation related to a nonlinear string we discuss global existence boundedness and regularity of solu tions to the integrodifferential equation h t x u t x 0 mo 0 for all a 0

on uniform decay of solutions for wave equation of kirchhoff type with nonlinear boundary damping and memory source term in this paper we prove the existence of solution to the mixed problem for wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of solution

novel reversible integer fourier transform with control bits this paper presents a novel concept of the reversible integer discrete fourier transform ridft of order 2r r 2 when the transform is split by the paired representation into a minimum set of short transforms i e transforms of orders 2k k r by means of the paired transform the signal is represented as a set of short signals which carry the spectral information of the signal at specific and disjoint sets of frequencies the paired transform based fast fourier transform fft involves a few operations of multiplication that can be approximated by integer transforms examples of 1 point transforms with one control bit are described control bits allow us to invert such approximations two control bits are required to perform the 8 point ridft and 12 or even 8 bits for the 16 point ridft of real inputs the proposed forward and inverse ridfts are fast and the computational complexity of these transforms is comparative with the complexity of the fft the 8 point direct and inverse ridfts are described in detail

effect of temporal position proportional variance and proportional duration on decision weights in temporal pattern discrimination two experiments investigated how listeners allocate their attention to different segments of a temporal pattern the experiments allowed a direct test of the predictions of the proportion of total duration ptd rule and the component relative entropy core model listeners had to decide whether two sequences of nine tones had the same or different temporal patterns tone duration 25 ms tone frequency 1000 hz a sequence s temporal pattern was determined by the time intervals between each tone s offset and the next tone s onset on same trials the time intervals at corresponding temporal positions in the two sequences were identical on different trials the corresponding time intervals were randomly varied listener attention to different temporal positions within a sequence was assessed by calculating the decision weights at each position the results supported the core model and were inconsistent with the ptd rule manipulating the mean of the time intervals within the sequence had no consistent ef

examining the use of a time varying loudness algorithm for quantifying characteristics of nonlinearly propagated noise l a previous letter by gee et al j acoust soc am 121 el1 el7 2007 revealed likely shortcomings in using common stationary long term spectrum based measures to quantify the perception of nonlinearly propagated noise here the glasberg and moore j audio eng soc 50 331 342 2002 algorithm for time varying loudness is investigated their short term loudness when applied to a shock containing broadband signal and a phase randomized signal with equivalent long term spectrum does not show a significant difference in loudness between the signals further analysis and discussion focus on the possible utility of the instantaneous loudness and the need for additional investigation in this area

yosida approximation and nonlinear hyperbolic equation we are concerned with the initial value problem for nonlinear evolution equations of the form u t m a 1 2 u t 2 au t u t f t on 0 u 0 u o u o u 1 here a is a nonnegative selfadjoint operator in a real hilbert space h 0 is a constant and m is a c 1 class function satisfying m r m o 0 for r 0 with m o constant the equation has its motivation in the mathematical description of small amplitude vibrations of an elastic string

discrete nonlinear integral inequalities in two variables and their applications in this paper some discrete integral inequalities in two variables with more than one nonlinear term are established our results are also applied to show the boundedness of certain boundary value problem for difference equations

smoothing effect and propagations of singularities for viscoelastic plates abstract we study dissipative models for plates and we show that the solutions have a smoothing effect on the initial data for viscous plates while for materials with memory the solution propagates singularities that is the solution of the plate equation of memory type is as regular as the initial data moreover we show that when both dissipations are present the memory type prevails in the sense that the solution propagates singularities finally we prove the existence of global solutions for non linear dissipative equations with small data which decay exponentially as time goes to infinity

regularity for a schrodinger equation with singular potentials and application to bilinear optimal control abstract we study the schrodinger equation i t u u v 0 u v 1 u 0 on r 3 0 t where v 0 x t x a t 1 with a w 2 1 0 t r 3 is a coulombian potential singular at finite distance and v 1 is an electric potential possibly unbounded the initial condition u 0 h 2 r 3 is such that r 3 1 x 2 2 u 0 x 2 dx the potential v 1 is also real valued and may depend on space and time variables we prove that if v 1 is regular enough and at most quadratic at infinity this problem is well posed and the regularity of the initial data is conserved for the solution we also give an application to the bilinear optimal control of the solution through the electric potential

on some finite difference inequalities in two independent variables in this article we establish some new finite difference inequalities in two independent variables which can be used as tools in the study of certain classes of finite difference and sum difference equations

level discrimination of single tones in a multitone complex by normal hearing and hearing impaired listeners a conditional on a single stimulus coss analysis procedure j acoust soc am 86 1743 1746 1989 was used to estimate how well normal hearing and hearing impaired listeners selectively attend to individual spectral components of a broadband signal in a level discrimination task on each trial two multitone complexes consisting of six octave frequencies from 250 to 8000 hz were presented to listeners the levels of the individual tones were chosen independently and at random on each presentation the target tone was selected within a block of trials as the 250 1000 or 4000 hz component on each trial listeners were asked to indicate which of the two complex sounds contained the higher level target as a group normal hearing listeners exhibited greater selectivity than hearing impaired listeners to the 250 hz target while hearing impaired listeners showed greater selectivity than normal hearing listeners to the 4000 hz target which is in the region of their hearing loss both groups of listeners displayed large variability in their ability to selectively weight the 1000 hz target trial by trial analysis showed a decrease in weighting efficiency with increasing frequency for normal hearing listeners but a relatively constant weighting efficiency across frequency for hearing impaired listeners interestingly hearing impaired listeners selectively weighted the 4000 hz target which was in the region of their hearing loss more efficiently than did the normal hearing listeners

a note on a trivial assumption on kernel and model abstract the goal of this note is to point out that the assumption on kernel g t is trivial in j j bae on uniform decay of the solution for a damped nonlinear coupled system of wave equations with nonlinear boundary damping and memory term appl math comput 148 2004 207 223 j j bae on uniform decay of solutions for wave equation of kirchhoff type with nonlinear boundary damping and memory source term 138 2003 463 478 which lead the trivial model also or the process of proof will be false

general decay rate estimates for viscoelastic dissipative systems abstract the linear viscoelastic equation is considered we prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity the proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates

global existence and stability for wave equation of kirchhoff type with memory condition at the boundary abstract we consider a nonlinear wave equation of kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions we proved that the energy decay with the same rate of decay of the relaxation function that is the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially

blow up of solutions for some non linear wave equations of kirchhoff type with some dissipation abstract the initial boundary value problem for non linear wave equations of kirchhoff type with dissipation in a bounded domain is considered we prove the blow up of solutions for the strong dissipative term u t and the linear dissipative term u t by the energy method and give some estimates for the life span of solutions we also show the nonexistence of global solutions with positive initial energy for non linear dissipative term by vitillaro s argument

perceived tonal continuity through two noise bursts separated by silence three experiments measured the perceived continuity of two pure tones flankers through a masker containing a silence experiment 1 used a 2i 2afc procedure one interval contained two noise bursts separated by a silent gap and the other contained two noise bursts separated by a tone of the same duration as the silence discrimination between masker conditions was very accurate when the flankers were absent but was impaired substantially when the flankers were present this was taken as evidence that illusory flanker continuity during the silent gap was heard as similar to the physical presence of a tone in the gap in experiment 2 performance remained poor when the flankers were frequency glides aligned along a common trajectory performance improved significantly when the flankers were misaligned in trajectory in experiment 3 listeners rated directly perceived flanker continuity strong continuity was reported in the silent gap conditions for which poor performance had been observed in experiments

forward masking adaptation or integration the aim of this study was to attempt to distinguish between neural adaptation and persistence or temporal integration as possible explanations of forward masking thresholds were measured for a sinusoidal signal as a function of signal duration for conditions where the delay between the masker offset and the signal offset the offset offset interval was fixed the masker was a 200 ms broadband noise presented at a spectrum level of 40 db re 20 pa and the signal was a 4 khz sinusoid gated with 2 ms ramps the offset offset interval was fixed at various durations between 4 and 102 ms and signal thresholds were measured for a range of signal durations at each interval a substantial decrease in thresholds was observed with increasing duration for signal durations up to about 20 ms at short offset offset intervals the amount of temporal integration exceeded that normally found in quiet the results were simulated using models of temporal integration the temporal window model and adaptation for both models the inclusion of a peripheral nonlinearity similar to that observed physiologically in studies of the basilar membrane was essential in producing a good fit to the data both models were about equally successful in accounting for the present data however the temporal window model provided a somewhat better account of similar data from a simultaneous masking experiment using the same parameters this suggests that the linear time invariant properties of the temporal window approach are appropriate for modeling forward masking overall the results confirm that forward masking can be described in terms of peripheral nonlinearity followed by linear temporal integration at higher levels in the auditory system however the difference in predictions between the adaptation and integration models is relatively small meaning that influence of adaptation cannot be ruled out

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

nonlinear parabolic equations with nonlinear functionals abstract in this paper we study a class of nonlinear parabolic equations in which certain functionals of the solution are involved a priori estimates for the solutions are derived by the use of integral estimates and the existence and uniqueness of the solutions are demonstrated via a retarding argument

existence of global smooth solutions to the initial boundary value problem for the quasi linear wave equation with a degenerate dissipative term let c be a bounded domain with smooth boundary dq in the n dimen sional euclidean space rn and let us consider the initial boundary value problem for the classical quasi linear wave equation with a dissipation u v a lvul vu u x u o in qx o ce 4x 0 uo

cuing effects for informational masking the detection of a tone added to a random frequency multitone masker can be very poor even when the maskers have little energy in the frequency region of the signal this paper examines the effects of adding a pretrial cue to reduce uncertainty for the masker or the signal the first two experiments examined the effect of cuing a fixed frequency signal as the number of masker components and presentation methods were manipulated cue effectiveness varied across observers but could reduce thresholds by as much as 20 db procedural comparisons indicated observers benefited more from having two masker samples to compare with or without a signal cue than having a single interval with one masker sample and a signal cue the third experiment used random frequency signals and compared no cue signal cue and masker cue conditions and also systematically varied the time interval between cue offset and trial onset thresholds with a cued random frequency signal remained higher than for a cued fixed frequency signal for time intervals between the cue and trial of 50 ms or longer thresholds were approximately the same with a signal or a masker cue and lower than when there was no cue without a cue or with a masker cue analyses of possible decision strategies suggested observers attended to the potential signal frequencies particularly the highest signal frequency with a signal cue observers appeared to attend to the frequency of the subsequent signal

inequalities applicable in the theory of finite difference equations in the present paper we establish some new nonlinear finite difference inequalities applicable in the theory of certain classes of finite difference equations in various different situations we also present applications of some of the inequalities to show their importance to the literature

on some new nonlinear discrete inequalities and their applications in this paper some new discrete inequalities in two independent variables which provide explicit bounds on unknown functions are established the inequalities given here can be used as handy tools in the qualitative theory of certain finite difference equations

statistical and computational performance of a class of generalized wiener filters corresp a class of suboptimal wiener filters is considered and their computational and statistical performances and the trade off between the two are studied and compared with those for known classes of suboptimal wiener filters a general model of a suboptimal wiener filter over a group is defined which includes as special cases the known filters based on the discrete fourier transform dft in the case of a cyclic group and the walsh hadamard transform wht in the case of a dyadic group statistical and computational performances of various group filters are investigated the cyclic and the dyadic group filters are known to be computationally the best ones among all the group filters however they are not always the best ones statistically and other not necessarily abelian group filters are studied results are compared with those for the cyclic group filters dft and the general problem of selecting the best group filter is posed that problem is solved numerically for small size signals leq 64 for the first order markov process and random sine wave corrupted by white noise for the first order markov process with the covariance matrix b s l rho s l as rho increases the use of various non abelian groups results in improved statistical performance of the filter as compared to the dft similarly for the random sine wave with covariance matrix b s l cos lambda s l as lambda decreases non abelian groups result in a better statistical performance of the filter than the dft does however that is compensated for by the increased number of computations to perform the filtering

some new nonlinear difference inequalities and their applications in this paper we establish some new nonlinear difference inequalities in two independent variables which can be used as handy tools in the study of qualitative properties of solutions of certain classes of difference equations

linear schrodinger evolution equations with moving coulomb singularities abstract the cauchy problem for schrodinger evolution equations with a finite number of moving coulomb singularities is investigated the case of a single singularity has been studied by several authors see e g baudouin et al 2005 1 and okazawa et al 2010 19 however it seems to be no previous work on plural singularities we shall show that the problem has a unique classical solution by using a time dependent linear transformation of the unknown function which locally freezes the motion of the whole singularities under the simplest collisionless condition in fact a new existence and uniqueness theorem is available for the transformed problem such an abstract framework is established from the viewpoint of linear evolution equations of hyperbolic type in a hilbert space as an innovative modification of those in okazawa 1998 17 and okazawa and yoshii 2011 20

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

the integer transforms analogous to discrete trigonometric transforms the integer transform such as the walsh transform is the discrete transform that all the entries of the transform matrix are integer it is much easier to implement because the real number multiplication operations can be avoided but the performance is usually worse on the other hand the noninteger transform such as the dft and dct has a good performance but real number multiplication is required w derive the integer transforms analogous to some popular noninteger transforms these integer transforms retain most of the performance quality of the original transform but the implementation is much simpler especially for the two dimensional 2 d block transform in image video the saving can be huge using integer operations in 1989 cham had derived the integer cosine transform here we will derive the integer sine hartley and fourier transforms we also introduce the general method to derive the integer transform from some noninteger transform besides the integer transform derived by cham still requires real number multiplication for the inverse transform we modify the integer transform introduced by cham and introduce the complete integer transform it requires no real number multiplication operation no matter what the forward or inverse transform the integer transform we derive would be more efficient than the original transform for example for the 8 point dft and idft there are in total four real numbers and eight fixed point multiplication operations required but for the forward and inverse 8 point complete integer fourier transforms there are totally 20 fixed point multiplication operations required however for the integer transform the implementation is simpler and many of the properties of the original transform are kept

on a quasilinear wave equation with memory equation 1 l with a 0 and n 1 has its roots in a model for the small amplitude vibrations of a string in which the dependence of the tension on the deformation cannot be ignored see for example bernstein 2 carrier 3 41 dickey s and nishida 13 when a 0 1 1 may be used to describe the dynamics of an extensible string with fading memory this equation states that the dynamic equilibrium of a body depends not only on the present state of deformation but also on the previous history of the deformation gradient since the publication of the aforementioned papers equation 1 1 with a 0 has been the subject of intense scrutiny see for example arosio and spagnolo 11 lions 9 medeiros lo menzala ll nishihara 14 151 pohoiaev 16 and yamada 17 181 to name but a few among the facts thus far proved pohoiaev s results and their extension to the degenerate case of arosio and spagnolo are of particular significance they show that if the data satisfy an analytic type condition then solutions are global in time in spite of the abundant literature on the memoryless form of equation l l to our best knowledge equation 1 1 with a f 0 appears to be untouched our main results theorem 5 1 theorem 5 2 and theorem 5 4 will show that under appropriate assumptions on the kernel

approximation of abstract cauchy problems for dissipative operators with respect to metric like functionals abstract this paper discusses approximation of semigroups of locally lipschitz operators by discrete semigroups of local quasi contractions with respect to metric like functionals the main approximation result not only extends a product formula for contractive semigroups generated by maximal dissipative operators in real hilbert spaces but also gives an algorithm for solving a mixed problem for the kirchhoff equation to which the contractive semigroup theory or kato s quasilinear theory cannot directly apply

a rational spectral collocation method for third order singularly perturbed problems a new numerical method is developed for solving a class of third order singularly perturbed boundary value problems first of all the given problem is transformed into a system of two ordinary differential equations odes subject to suitable initial and boundary conditions then the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of odes according to the asymptotic analysis the location and width of boundary layer of the given problem which are chosen as parameters in the sinh transformation can be determined ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method

overall judgment of loudness of time varying sounds listeners can judge the overall loudness of time varying sounds quite easily i e assign a single value that represents the loudness of the entire sound this holds even if the duration is long and the judgment includes memory effects different metrics for calculating overall loudness have been developed they agree that overall loudness is higher than the mean of loudness over time percentiles like the n5 the loudness being exceeded 5 of the time are adopted by iso 532 1 in the present study the concept of an energy mean known from level measurements iso 1996 1 was applied to the loudness domain this equivalent continuous loudness level llp was compared to the n5 using a set of real world sounds that was orthogonal between the two metrics over a wide dynamic range of 30 phon cross modality matching with line length was used in three experiments with a focus on either the overall judgment of loudness continuous judgment while a sound was played or both the llp showed considerably higher correlations with overall judgments than n5 comparing continuous instantaneous judgment with calculated instantaneous loudness suggests that the participants might have focused on the sounds prominent portions

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