on formal variational calculus of higher dimensions abstract based upon the definition of variational derivatives presented by galindo and martinez alonso a series of formulae on formal variational calculus of higher dimensions is developed

invariance principles for partial sum processes and empirical processes indexed by sets let x j j q be independent identically formed random elements with values in a banach spaceb indexed byq tuples of positive integers we obtain the almost sure approximation as well as the approximation in probability of the partial sum process sum limits j in na x j a in a by a partial sum process sum limits j in na y j a in a asn uniformly over all setsa in a certain class a of subsets of theq dimensional unit cube here y j j q are independent identically distributed gaussian random variables these results are then applied to obtain the approximation of empirical processes over sets and indexed by sets by gaussian partial sum processes indexed by sets

lateralization of complex binaural stimuli a weighted image model this article describes a new model that predicts the subjective lateral position of bandpass stimuli it is assumed as in other models that stimuli are bandpass filtered and rectified and that the rectified outputs of filters with matching center frequencies undergo interaural cross correlation the model specifies and utilizes the shape and location of assumed patterns of neural activity that describe the cross correlation function individual modes of this function receive greater weighting if they are straighter describing consistent interaural delay over frequency and or more central describing interaural delays of smaller magnitude this weighting of straightness and centrality is used by the model to predict the perceived laterality of several types of low frequency bandpass stimuli with interaural time delays and or phase shifts including bandpass noise amplitude modulated stimuli with time delayed envelopes and bandpass filtered clicks this model is compared to other theories that describe lateralization in terms of the relative contributions of information in the envelopes and fine structures of binaural stimuli

pfaffianization of the two dimensional toda lattice pfaffianization procedure due to hirota and ohta is applied to the two dimensional toda lattice as a result a pfaffianized version of the two dimensional toda lattice is found

coupling integrable couplings and bi hamiltonian structure associated with the boiti pempinelli tu hierarchy a kind of new lie algebra is introduced whose corresponding loop algebra is followed to define from which two isospectral problems are established whose compatibility condition gives rise to a coupling integrable coupling of the boiti pempinelli tu bpt hierarchy by making use of the quadratic form identity its bi hamiltonian structure is obtained finally we reduce the coupling integrable coupling to obtain two integrable couplings of the bpt hierarchy furthermore the well known mkdv equation and a new coupled equation with two dependent variables are produced respectively

the generalized fractional trace variational identity and fractional integrable couplings of kaup newell hierarchy starting from fractional isospectral problems and general bilinear forms the generalized fractional trace identity is presented then a new explicit lie algebra is introduced for which the fractional integrable couplings of kaup newell hierarchy are derived furthermore we obtained the fractional hamiltonian structures of the fractional integrable couplings of kaup newell hierarchy the methods derived by us can be generalized to other fractional integrable couplings

lateralization predictions for high frequency binaural stimuli the position variable model r m stern jr and h s colburn j acoust soc am 64 127 140 1978 g d shear and r m stern j acoust soc am suppl 1 81 s27 1987 is extended to describe the subjective lateral position of amplitude modulated tones and bandpass noise as well as other complex stimuli that are presented within spectral regions at which the binaural system appears to be unable to make use of cycle by cycle interaural temporal differences predictions of the model are based on the centroid of the cross correlation of the hypothetical auditory nerve response to the stimuli which is either calculated using analytical techniques or simulated numerically the model of auditory nerve activity which is typically used to describe the response to stimuli at lower frequencies also extracts envelopes of higher frequency stimuli as discussed previously by colburn and esquissaud this information appears to be useful in predicting the lateral position of such high frequency stimuli p

a central spectrum theory of binaural processing evidence from dichotic pitch a theory is presented that describes the binaural processing of interaural time or phase differences it is an elaboration of the central spectrum concept for the explanation of dichotic pitch phenomena f a bilsen pitch of noise signals evidence for a central spectrum j acoust soc am 61 150 161 1977 the generation is postulated for central activity patterns cap due to binaural interaction from these caps the central processor selects specific spectral information that constitutes the information for lateralization dichotic pitch binaural masking etc here a strategy is assumed to be based on central spectra cs rather than on interaural cross correlation for the calculation of the central activity patterns a number of assumptions have been introduced the peripheral filters are supposed to be infinitesimally narrow the analog filter outputs from corresponding filters at both ears are thought to interact by means of a linear delay and add mechanism the squared output power

additive versus multiplicative combination of differences of interaural time and intensity predictions of the position variable model r m stern jr and h s colburn j acoust soc am 64 127 140 1978 are compared to the observed lateralization of bandpass noise as a joint function of differences of interaural time intensity and phase itd iid and ipd respectively t n buell and c trahiotis j acoust soc am 90 2266 a 1991 this presentation is primarily concerned with the effect of iids on the lateralization of bandpass noise it is shown that the multiplicative intensity weighting function that had been a feature of all previous implementations of the position variable model is fundamentally unable to describe the data of buell and trahiotis it is argued that the form of these data suggests that the effects of iid must be introduced in an additive fashion at a more central level after image position is estimated on the basis of timing information alone such a model provides a very good description of the buell and trahiotis data as well as the results of severa

a similar extension of the wki hierarchy its hamiltonian structure and the associated finite dimensional hamiltonian system abstract an isospectral problem and a similar extension of the wadati konno ichikawa hierarchy are proposed by using the trace identity it is shown that the hierarchy of equations possesses a bi hamiltonian structure the eigenvalue problem is nonlinearized to a finite dimensional hamiltonian system under a constraint between the potentials and the eigenfunctions

solitary waves of the generalized kdv equation with distributed delays abstract in this paper we study an integro differential equation based on the generalized kdv equation with a convolution term which introduces a time delay in the nonlinearity special attention is paid to the existence of solitary wave solutions motivated by m j ablowitz h seger soliton and inverse scattering transform siam philadelphia 1981 c k r t jones geometrical singular perturbation theory in r johnson ed dynamical systems in lecture notes in math vol 1609 springer new york 1995 t ogawa travelling wave solutions to perturbed korteweg de vries equations hiroshima math j 24 1994 401 422 we prove using the linear chain trick and geometric singular perturbation analysis that the solitary wave solutions persist when the average delay is suitably small for a special convolution kernel

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

canonical structure of soliton equations i abstract the canonical structure of the nonlinear evolution equations in 1 1 dimensions solvable in terms of an n n inverse scattering problem is discussed the simplest form of the scattering problems that is those containing the spectral parameter linearly is considered it applies to most of the known soliton equations like the korteweg de vries eq the sine gordon eq and the boussinesq eq discussion of various possible reductions of the number of dependent variables by imposing constraints consistent with the hamiltonian flows is given together with the canonical structure of the reduced systems a direct proof of the involutive character of the infinite number of conserved quantities is given for the general case as well as the reduced case the relation between the conserved quantities and symmetry transformations lie backlund transformations becomes very simple in this framework

on the backlund transformation and hamiltonian properties of superevaluation equations backlund and darboux backlund transformations are deduced for the superevaluation equations recently deduced by kupershmidt b kuperschmidt a super k dv equation an integrable system preprint utsi tullahoma 1984 phys lett a 102 213 1983 j phys a 17 l 863 1984 and gurses h gurses and o oguz phys lett a 108 437 1985 by a extension of the technique of bpt m boiti f pempinelli and g z tu nuovo cimento b 79 231 1984 to anticommuting variables the bi hamiltonian structure and hence the form of the recursion operator for the lie backlund symmetry for such equations are deduced incidentally some explicit forms of the lie backlund symmetry are also deduced

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

some algebro geometric solutions for the coupled modified kadomtsev petviashvili equations arising from the neumann type systems a treatment is described for getting some algebro geometric solutions of the coupled modified kadomtsev petviashvili cmkp equations and a hierarchy of 1 1 dimensional integrable nonlinear evolution equations inlees by using the neumann type systems through three steps i according to the nonlinearization of lax pair the cmkp equations and the 1 1 dimensional inlees are reduced to a family of compatible neumann type systems on a symplectic submanifold whose involutive solutions give rise to the finite parametric solutions of the inlees in both 2 1 and 1 1 dimensions ii from the holomorphic differentials and the abel map on a hyperelliptic curve of riemman surface the abel jacobi variables are introduced to straighten out the neumann type flows the 1 1 and 2 1 dimensional flows giving the abel jacobi solutions iii based on the riemann theorem and the trace formulas the jacobi inversion is applied to the straightened flows for getting some new algebro geometric solutions of the cmkp equations and the 1 1 dimensional integrable hierarchy

nonlinearization of the 3 3 matrix eigenvalue problem related to coupled nonlinear schrodinger equations abstract the nonlinearization method is extended to the investigation of coupled nonlinear schrodinger equations associated with a 3 3 matrix eigenvalue problem from which a new finite dimensional hamiltonian system is obtained by nonlinearization of the eigenvalue problem and its adjoint one a scheme for generating involutive systems of conserved integrals is proposed by which the finite dimensional hamiltonian system is further proved to be completely integrable in the liouville sense

a powerful approach to generate new integrable systems in this paper an effective algorithm to generate integrable systems is given as a result many new integrable equations are derived in a systematic way

solitary wave solutions to the generalized coupled mkdv equation with multi component using the darboux matrix method the multi solitary wave solutions of the generalized coupled mkdv equation with multi component are obtained the obtained solution formulas provide us with a comprehensive approach to construct exact solutions for the generalized coupled mkdv equation by some basic solutions of the boiti and tu spectral problem

lateral position based models of interaural discrimination this letter investigates the hypothesis that lateral position is the only cue available for interaural discrimination experiments using 500 hz stimuli the discussion of this hypothesis is in the context of comparisons of the experimental data to predictions of the position variable model of binaural interaction the model predicts the mean and variance of the subjective lateral position of stimuli used in the discrimination experiments assuming that discrimination performance is based on optimal processing of this subjective position to the extent that the laterality predictions of the model are accurate data that are inconsistent with its predictions would also be problematical for any model based on the subjective laterality of a single binaural image the predictions at least qualitatively describe much of the observed experimental data including a number of results that have not been addressed by any previous theory nevertheless the observed performance is significantly better than the corresponding predictions for three types of experiments in which the utility of the position cue has been eliminated by experimental design we believe that our results indicate that changes in lateral position are the primary cue in most interaural discrimination experiments but that secondary attributes of the perceptual images can be useful when performance based on position alone would be poor

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

single and multi solitary wave solutions to a class of nonlinear evolution equations abstract in this paper an effective discrimination algorithm is presented to deal with equations arising from physical problems the aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations many examples are given to illustrate the algorithm at the same time some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations such as camassa holm equation kolmogorov petrovskii piskunov equation and so on then a direct constructive method called multi auxiliary equations expansion method is described to derive the multi solitary wave solutions of nonlinear evolution equations finally a class of novel multi solitary wave solutions of the 2 1 dimensional asymmetric version of the nizhnik novikov veselov equation are given by three direct methods the algorithm proposed in this paper can be steadily applied to some other nonlinear problems

approximation of rectangular sums of b valued random variables given independent identically distributed random variables xn n q indexed by q tuples of positive integers and taking values in a separable banach space b we approximate the rectangular sums sum limits m leqq n x m n in mathbb n q by a brownian sheet we obtain the corresponding result for random variables with values in a separable hilbert space h while assuming an optimal moment condition generalized versions of the functional law of the iterated logarithm are thus derived

on a new hierarchy of hamiltonian soliton equations a method is suggested for studying the hamiltonian structure of the nonlinear partial differential equations that can be solved by the use of the spectral transform soliton equations the method is applied to a new hierarchy of n 1 coupled partial differential equations related to a schrodinger like spectral problem it is shown that these soliton equations are integrable hamiltonian equations with commuting flows for n 1 and n 2 a miura like transformation is computed and the corresponding modified equations are explicitly given

on liouville integrability of zero curvature equations and the yang hierarchy sufficient conditions for a zero curvature equation ut vx u v 0 being liouville integrable are investigated in the case that the equation is integrable an explicit formula of the poisson bracket h lambda h mu for hamiltonians h is proposed the yang hierarchy is derived and shown to be liouville integrable

backlund transformations related to the kaup newell spectral problem abstract a hierarchy of isospectral deformation equations related to the kaup newell spectral problem is obtained the generalized gauge transformations of the eigenmatrix of the spectral problem are used to generate backlund and self backlund transformations in a special case the backlund transformation of the null solution for all the equations in the hierarchy has been explicitly solved

soliton solutions and a backlund transformation for a generalized nonlinear schrodinger equation with variable coefficients from optical fiber communications under investigation in this paper is a generalized nonlinear schrodinger model with variable dispersion nonlinearity and gain loss which could describe the propagation of optical pulse in inhomogeneous fiber systems by employing the hirota method one and two soliton solutions are obtained with the aid of symbolic computation furthermore a general formula which denotes multi soliton solutions is given some main properties of the solutions are discussed simultaneously as one important property of nonlinear evolution equation the backlund transformation in bilinear form is also constructed which is helpful on future research and as far as we know is firstly proposed in this paper

a generalized fractional kn equation hierarchy and its fractional hamiltonian structure a generalized hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders we construct the generalized fractional trace identity through the riemann liouville fractional derivative an example of the fractional kn soliton equation hierarchy and hamiltonian structure is presented which is a new integrable hierarchy and possesses hamiltonian structure