third order differential equations describing pseudospherical surfaces third order differential equations which describe pseudospherical surfaces are considered the complete classification of a class of such equations is given a linear problem with one or more parameters also known as zero curvature representation for which the equation is the integrability condition is explicitly given the classification provides five large families of differential equations third order nonlinear dispersive wave equations such as the camassa holm equation and degasperis procesi equation are examples contained in the classification many other explicit examples are included

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

generalized multiple riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations in this paper based on symbolic computation and the idea of rational expansion method a generalized multiple riccati equations rational expansion method gmrere is proposed to uniformly construct a series of exact complexiton solutions for nonlinear partial differential equations compared with most existing tanh function methods and rational expansion methods the proposed method not only recovers some known solutions but also finds some new and general complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

fourth order evolution equations which describe pseudospherical surfaces abstract differential equations that describe pseudospherical surfaces are considered these equations are equivalent to the structure equations of a metric with gaussian curvature k 1 they can also be described as the compatibility condition of an associated linear problem also referred to as a zero curvature representation a complete and explicit classification of a class of fourth order evolution equations is given the classification provides four huge classes referred to as types i iv of fourth order evolution equations that describe pseudospherical surfaces together with the associated one or more parameter linear problems the differential equations of each type are determined by choosing certain arbitrary differentiable functions fourth order member of the burgers hierarchy and a modified kuramoto sivashinsky equation are examples of equations described by types i and iv respectively many other explicit examples are presented

hamiltonian structure and integrability of the stationary kuramoto sivashinsky equation in this article the stationary kuramoto sivashinsky ks equation is studied it is shown first that this equation can be transformed into a one dimensional hamiltonian system describing the motion of a particle in a time dependent potential second working with this formalism and coming back then to the initial ks equation a subset of initial conditions is derived for which the corresponding solutions u x will behave like the dominant pole 120 x x0 3 deduced from the painleve analysis and will explode in a finite time finally special attention is given to the well known kuramoto tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain this solution explodes also like 120 x x0 3

conservation laws and calapso guichard deformations of equations describing pseudo spherical surfaces the relation between the chern and tenenblat approach to conservation laws of equations describing pseudo spherical surfaces conservation laws from pseudo spherical structure and the more familiar riccati equation approach conservation laws from associated linear problem is investigated two examples cylindrical korteweg de vries kdv and lund regge equations are presented chern and tenenblat s point of view is then connected with the theory of soliton surfaces a generalization of the original chern tenenblat construction of conservation laws results and a reasonable family of large deformations for scalar equations describing pseudo spherical surfaces the equations describing calapso guichard surfaces can be introduced it is shown that these equations are also the integrability condition of linear problems

cross correlation procedures for measuring noise and distortion in agc hearing aids the magnitude squared coherence function msc has been used to measure noise and distortion in linear and compression hearing aids however the msc will overestimate the distortion in a linear time varying system such as a compression amplifier the reduction in coherence caused by varying the gain in an otherwise linear system can be substantial and can lead to large errors in estimating the distortion present in a compression hearing aid the effects of gain changes in a linear system can be reduced by measuring the normalized system input output cross correlation which emphasizes the variance in the system phase response and deemphasizes the system gain fluctuations estimates of the total noise and distortion produced using the msc phase variance and notched noise measurement techniques are compared for additive noise clipping distortion and compression amplification the msc is found to give the most accurate results for estimating the noise and distortion in a linear time invariant system and the notched noise measurements are the most accurate for a compression system the phase variance is found to give reasonable measurements for a time varying gain as long as the system variations are slow relative to the length of the analysis data segments

fifth order evolution equations describing pseudospherical surfaces we consider differential equations which describe pseudospherical surfaces with associated 1 forms i fi1dx fi2dt 1 i 3 we characterize all such equations of type ut uxxxxx g u ux uxxxx whose associated 1 forms satisfy fp1 pf11 p p p r 2 p 3 in addition to a generic technical assumption we also classify all of these equations which are independent of any of the real parameters p p obtaining as particular cases the fifth order korteweg de vries the sawada kotera and the kaup kupershmidt equations we determine huge classes of equations describing pseudospherical surfaces and their respective linear problems in which particular cases are obtained by merely specifying certain functions which depend on u and its derivatives with respect to x

quality ratings for frequency shaped peak clipped speech peak clipping is a common form of distortion in hearing aids and can reduce the subjective quality of the amplified speech in a typical hearing aid frequency response shaping precedes symmetric peak clipping the effect of peak clipping on speech quality ratings was therefore studied using sentence test materials that were processed using different frequency response contours and then clipped at different clipping thresholds the quality of each processed sentence was rated on a ten point scale by normal hearing subjects the experimental results indicate that the clipping threshold and the interaction of the frequency response shaping with the clipping threshold significantly affect speech quality it is also shown that the distortion effects on speech quality can be modeled by a distortion index computed from the magnitude squared coherence of the speech processing system in response to a shaped noise input signal

correspondence theorems for hierarchies of equations of pseudo spherical type hierarchies of evolution equations of pseudo spherical type are introduced thereby generalizing the notion of a single equation describing pseudo spherical surfaces due to s s chern and k tenenblat and providing a connection between differential geometry and the study of hierarchies of equations which are the integrability condition of sl 2 r valued linear problems as an application it is shown that there exist local correspondences between any two suitably generic solutions of arbitrary hierarchies of equations of pseudo spherical type

on differential equations describing pseudo spherical surfaces abstract we give a complete classification of the evolution equations u t f u u x k u x k which describe pseudo spherical surfaces without any a priori assumptions on the presence of a spectral parameter we also prove a local existence theorem to the effect that given two differential equations describing pseudo spherical surfaces not necessarily evolutionary there exists under a technical assumption a smooth mapping transforming any suitably generic solution of one equation into a solution of the other

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

coherence and the speech intelligibility index the speech intelligibility index sii ansi s3 5 1997 provides a means for estimating speech intelligibility under conditions of additive stationary noise or bandwidth reduction the sii concept for estimating intelligibility is extended in this paper to include broadband peak clipping and center clipping distortion with the coherence between the input and output signals used to estimate the noise and distortion effects the speech intelligibility predictions using the new procedure are compared with intelligibility scores obtained from normal hearing and hearing impaired subjects for conditions of additive noise and peak clipping and center clipping distortion the most effective procedure divides the speech signal into low mid and high level regions computes the coherence sii separately for the signal segments in each region and then estimates intelligibility from a weighted combination of the three coherence sii values

pseudo spherical surfaces and integrability of evolution equations abstract a complete classification of evolution equations u t f x t u u x u x k which describe pseudo spherical surfaces is given thus providing a systematic procedure to determine a one parameter family of linear problems for which the given equation is the integrability condition it is shown that for every second order equation which admits a formal symmetry of infinite rank formal integrability such a family exists kinematic integrability it is also shown that this result cannot be extended as proven to third order formally integrable equations this fact notwithstanding a special case is proven and moreover several equations of interest including the harry dym cylindrical kdv and a family of equations solved by inverse scattering by calogero and degasperis are shown to be kinematically integrable conservation laws of equations describing pseudo spherical surfaces are studied and several examples are given

transformations of solutions for equations and hierarchies of pseudo spherical type it is known that if an equation describes non trivial one parameter families of pseudo spherical surfaces its conservation laws generalized nonlocal symmetries and backlund transformations can be studied by geometrical means 4 10 in this letter it is pointed out that there exist correspondences or generalized backlund transformations between arbitrary solutions satisfying some genericity conditions of any two single equations describing pseudo spherical surfaces then the notion of a hierarchy of equations of pseudo spherical type is introduced and a theorem stating that there also exist correspondences between arbitrary solutions of any two such hierarchies is presented a full account of these results appears elsewhere 12 13

the initial value problem for the sequence of generalized korteweg de vries equations on considere le probleme aux valeurs initiales pour l equation u t g m u x k m u m 1

application of the extended homotopy perturbation method to a kind of nonlinear evolution equations based on the homotopy perturbation method we propose a new extended homotopy perturbation method we apply the method to solve a kind of nonlinear evolution equations with the help of the symbolic computation system maple the success of the paper lies on the fact that we do not conform to the traditional homotopy mode but construct a new homotopy of the given equations the results reveal that we can obtain the approximation solution of a kind of nonlinear evolution equations

the korteweg de vries hierarchy and long water waves by using the multiple scale method with the simultaneous introduction of multiple times we study the propagation of long surface waves in a shallow inviscid fluid as a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion we show that the korteweg de vries hierarchy equations do play a role in the description of such waves finally we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by kodama and taniuti

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

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave