reduced contribution of a nonsimultaneous mistuned harmonic to residue pitch ciocca and darwin v ciocca and c j darwin j acoust soc am 105 2421 2430 1999 reported that the shift in residue pitch caused by mistuning a single harmonic the fourth out of the first 12 was the same when the mistuned harmonic was presented after the remainder of the complex as when it was simultaneous even though subjects were asked to ignore the pure tone percept the present study tried to replicate this result and investigated the role of the presence of the nominally mistuned harmonic in the matching sound subjects adjusted a matching sound so that its pitch equaled that of a subsequent 90 ms complex tone 12 harmonics of a 155 hz f0 whose mistuned 3 third harmonic was presented either simultaneously with or after the remaining harmonics in experiment 1 the matching sound was a harmonic complex whose third harmonic was either present or absent in experiments 2a and 2b the target and matching sound had nonoverlapping spectra pitch shifts were reduced both when the mistuned component was nonsimultaneous and when the third harmonic was absent in the matching sound the results indicate a shorter than originally estimated time window for obligatory integration of nonsimultaneous components into a virtual pitch

pitch strength of regular interval click trains with different length runs of regular intervals click trains were generated with first and second order statistics following kaernbach and demany j acoust soc am 104 2298 2306 1998 first order intervals are between successive clicks while second order intervals are those between every other click click trains were generated with a repeating alternation of fixed and random intervals which produce a pitch at the reciprocal of the duration of the fixed interval the intervals were then randomly shuffled and compared to the unshuffled alternating click trains in pitch strength comparison experiments in almost all comparisons for the first order interval stimuli the shuffled interval click trains had a stronger pitch strength than the unshuffled interval click trains the shuffled interval click trains only produced stronger pitches for second order interval stimuli when the click trains were unfiltered several experimental conditions and an analysis of runs of regular and random intervals in these click trains suggest that the auditory system is sensitive to runs of regular intervals in a stimulus that contains a mix of regular and random intervals these results indicate that fine structure regularity plays a more important role in pitch perception than randomness and that the long term autocorrelation function or spectra of these click trains are not good predictors of pitch strength

one dimensional schrodinger operators with singular potentials a schwartz distributional formulation using an extension of the hormander product of distributions we obtain an intrinsic formulation of one dimensional schrodinger operators with singular potentials this formulation is entirely defined in terms of standard schwartz distributions and does not require as some previous approaches the use of more general distributions or generalized functions we determine in the new formulation the action and domain of the schrodinger operators with arbitrary singular boundary potentials we also consider the inverse problem and obtain a general procedure for constructing the singular pseudo potential that imposes a specific set of local boundary conditions this procedure is used to determine the boundary operators for the complete four parameter family of one dimensional schrodinger operators with a point interaction finally the and potentials are studied in detail and the corresponding schrodinger operators are shown to coincide with the norm resolvent limit of specific sequences of schrodinger operators with regular potentials

spatial dynamics of an epidemic model with nonlocal infection abstract nonlocal infection plays an important role in epidemic spread which can reflect the real rules of infectious disease to understand its mechanism on disease transmission we construct an epidemic model with nonlocal delay and logistic growth the turing space for the emergence of stationary pattern is determined by series of inequations by mathematical analysis moreover we use the multi scale analysis to derive the amplitude equation and obtain rich pattern structures by controlling the variation of the delay parameter as the increase of delay parameter the degree of pattern isolation increase as well as the density of the infected population decrease which prohibits the propagation of the disease in space the results systematically reveal the impact of nonlocal delay on the spread of infectious diseases and provide some new theoretical supports for controlling the spread of infectious diseases

an example of unitary equivalence between self adjoint extensions and their parameters abstract the spectral problem for self adjoint extensions is studied using the machinery of boundary triplets for a class of symmetric operators having weyl functions of a special type we calculate explicitly the spectral projections in the form of operator valued integrals this allows one to give a constructive proof of the fact that in certain intervals the resulting self adjoint extensions are unitarily equivalent to the parameterizing boundary operator acting in a smaller space and one is able to provide an explicit form for the associated unitary transform applications to differential operators on metric graphs and to direct sums are discussed

a new class of solvable models in quantum mechanics describing point interactions on the line the authors provide a detailed analysis of properties of the schrodinger operator in l2 r which formally can be written as d2 dx2 sigma y in gamma nu y delta y where delta is the derivative of dirac s delta function and y contained in implied by r is discrete this model allows for an explicit calculation of spectral properties special emphasis is given to the periodic case y z nu nu j j in z where the spectrum and the density of states are explicitly computed also the spectrum for a half crystal is given the authors study in detail spectral consequences when various defects and impurities are added to the periodic case

spectral theory of semibounded sturm liouville operators with local interactions on a discrete set we study the hamiltonians hx q with type point interactions at the centers xk on the positive half line in terms of energy forms we establish analogs of some classical results on operators hq d2 dx2 q with locally integrable potentials q lloc1 r in particular we prove that the hamiltonian hx q is self adjoint if it is lower semibounded this result completes the previous results of brasche perturbation of schrodinger hamiltonians by measures selfadjointness and semiboundedness j math phys 26 621 1985 on lower semiboundedness also we prove the analog of molchanov s discreteness criteria birman s result on stability of a continuous spectrum and investigate discreteness of a negative spectrum in the recent paper kostenko a and malamud m 1 d schrodinger operators with local point interactions on a discrete set j differ equations 249 253 2010 it was shown that the spectral properties of hx hx 0 correlate with the corresponding spectral properties of a certain clas

a unitary model of pitch perception a model of the mechanism of residue pitch perception is revisited it is evaluated in the context of some new empirical results and it is proposed that the model is able to reconcile a number of differing approaches in the history of theories of pitch perception the model consists of four sequential processing stages peripheral frequency selectivity within channel half wave rectification and low pass filtering within channel periodicity extraction and cross channel aggregation of the output the pitch percept is represented by the aggregated periodicity function using autocorrelation as the periodicity extraction method and the summary autocorrelation function sacf as the method for representing pitch information it is shown that the model can simulate new experimental results that show how the quality of the pitch percept is influenced by the resolvability of the harmonic components of the stimulus complex these include i the pitch of harmonic stimuli whose components alternate in phase ii the increased frequency difference limen of tones consisting of higher harmonics and iii the influence of a mistuned harmonic on the pitch of the complex as a function of its harmonic number to accommodate these paradigms it was necessary to compare stimuli along the length of the sacf rather than relying upon the highest peak alone these new results demonstrate that the model responds differently to complexes consisting of low and high harmonics as a consequence it is not necessary to postulate two separate mechanisms to explain different pitch percepts associated with resolved and unresolved harmonics

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

traveling waves in a nonlocal dispersal sirh model with relapse this paper is concerned with traveling wave solutions of a nonlocal dispersal susceptibleinfectiveremovalhealing for short sirh model with relapse it is found that the existence and nonexistence of traveling waves of the system are not only determined by the critical wave speed c but also by the basic reproduction number r0 of the corresponding system of ordinary differential equations more precisely we use schauders fixed point theorem to obtain the existence of traveling waves for r0 1 and c c and the nonexistence of traveling waves for r0 1 and 0

spectral theory of schrodinger operators with infinitely many point interactions and radial positive definite functions abstract a number of results on radial positive definite functions on r n related to schoenberg s integral representation theorem are obtained they are applied to the study of spectral properties of self adjoint realizations of two and three dimensional schrodinger operators with countably many point interactions in particular we find conditions on the configuration of point interactions such that any self adjoint realization has purely absolutely continuous non negative spectrum we also apply some results on schrodinger operators to obtain new results on completely monotone functions

spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity abstract this paper is concerned with the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity we first prove that the traveling wave solution with critical minimal speed c c decays exponentially as while other traveling wave solutions with c c do not decay exponentially as then the monotonicity and uniqueness up to translation of traveling wave solution with critical minimal speed is established finally we prove that the critical minimal wave speed c coincides with the asymptotic speed of spread

metastability and stability of patterns in a convolution model for phase transitions where e is a small positive parameter and f is bistable having only three zeros 1 a 1 and is balanced i e r 1 1 f u du 1 4 0 see fig 1 for a typical initial datum j which crosses a several times at the beginning the solution evolves as if the diffusion term euxx were not there and in the time scale o ej n ej the solution gets close to 1 or 1 in intervals separated by thin layers of thickness at the order of o ej n ej 17 28 at this moment a spatial pattern is generated it persists on a time scale o ece but is eventually destroyed typically u x t 1 u x t 1 uniformly for x on 1 20 1 as t 1 it is possible that u x t converges to a or a nonconstant steady state as t 1 but this is an unlikely event because all these steady states are unstable 16 27 research supported in part by the national science foundation and bor leqsf

dominance region for pitch effects of duration and dichotic presentation the dominance region dr for pitch was determined for 16 and 200 ms complex tones containing the first seven harmonics of a fundamental frequency f0 of 250 hz a tone was presented with one of the harmonics mistuned upwards or downwards by 3 followed 500 ms later by a perfectly harmonic tone of the same duration listeners adjusted the f0 of the harmonic tone so that its pitch matched that of the mistuned complex in experiment 1 stimuli were presented monaurally the dr was significantly higher in harmonic number for the short than for the long duration the overall sum of the pitch shifts produced by all harmonics was significantly larger for the short than for the long duration presumably due to stronger perceptual fusion for the former in experiment 2 the mistuned harmonic was presented only contralaterally to the remainder of the complex a similar shift in the dr with duration was observed although the pitch shifts were smaller than for monaural presentation there was no significant effect of duration on the overall pitch shifts the results are discussed in terms of pattern recognition and autocorrelation models of pitch perception and a role of attention in pitch matching is suggested

traveling waves for a nonlocal dispersal sir model with delay and external supplies this paper is concerned with the existence nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed sir model with constant external supplies and holling ii incidence rate we find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c but also by the so called basic reproduction number r 0 of the corresponding reaction system that is we establish the existence of traveling waves for r 0 1 and each wave speed c c and the nonexistence for r 0 1 and any 0 c c or r 0 1 we also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed biologically speaking the longer the latency of infection in a vector is the slower the disease spreads

invasion traveling wave solutions of a predator prey system abstract this paper is concerned with the traveling wave solutions of a predator prey system in which intra specific conflictions are involved by using the comparison principle and the asymptotic speed of spreading the existence nonexistence and minimal wave speed of non negative traveling wave solutions are established such a traveling wave solution can model the spatial temporal process where the predator invades the territory of the prey and they eventually coexist

an exactly solvable periodic schrodinger operator the authors explicitly determine the band spectrum of a periodically strongly singular schrodinger operator in l2 r associated with the differential expression d2 dx2 s2 1 4 cos2 x s 2 1 4 sin2 x x epsilon r x epsilon pi z 2 0 s s 1 the corresponding density of states is calculated analytically

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

on the unitary equivalence of absolutely continuous parts of self adjoint extensions the classical weyl von neumann theorem states that for any self adjoint operator a0 in a separable hilbert space h there exists a non unique hilbert schmidt operator c c such that the perturbed operator a0 c has purely point spectrum we are interesting whether this result remains valid for non additive perturbations by considering the set exta of self adjoint extensions of a given densely defined symmetric operator a in h and some fixed a0 a0 exta we show that the ac parts a ac and a0ac of a a exta and a0 are unitarily equivalent provided that the resolvent difference ka a i 1 a0 i 1 is compact and the weyl function m of the pair a a0 admits weak boundary limits m t w limy 0m t iy for a e t r this result generalizes the classical kato rosenblum theorem moreover it demonstrates that for such pairs a a0 the weyl von neumann theorem is in general not true in the class exta

one dimensional schrodinger operators with δ interactions on cantor type sets we introduce a novel approach for defining a interaction on a subset of the real line of lebesgue measure zero which is based on sturm liouville differential expression with measure coefficients this enables us to establish basic spectral properties e g self adjointness lower semiboundedness and spectral asymptotics of hamiltonians with interactions concentrated on sets of complicated structures

a nonlocal diffusion model of a single species with age structure abstract using theory of fourier transformation dirac function and von foerster rule with nonlocal diffusion operator we derive a single species population model with two age stages juvenile and mature which includes nonlocal dispersal both in diffusion and reaction we found that the nonlocal reaction kernel function for mature population depends on the kernel function of diffusion for two age stages this model takes the local diffusion model with only laplacian operator or laplacian operator combining with convection operator as particular examples the existence uniqueness positivity and boundedness of initial value problem are also investigated in the present article as a new model its dynamics is worthy to be explored in the future work

traveling waves in a delayed sir model with nonlocal dispersal and nonlinear incidence this paper is concerned with traveling waves of a delayed sir model with nonlocal dispersal and a general nonlinear incidence the existence and nonexistence of traveling waves of the system are established respectively by schauder s fixed point theorem and two sided laplace transform it is also shown that the spread speed c is influenced by the dispersal rate of the infected individuals and the delay

reduced contribution of a nonsimultaneous mistuned harmonic to residue pitch the role of harmonic number listeners adjusted a matching sound so that its pitch equaled that of a subsequent 90 ms complex tone 12 harmonics of a 155 hz f0 whose mistuned harmonic 3 was presented either simultaneously with or after the other harmonics the third or the fourth harmonic was mistuned for both harmonics pitch shifts were significantly smaller when the mistuned harmonic was presented after rather than simultaneously with the remainder of the target complex and when the component corresponding to the mistuned harmonic was absent as opposed to present from the matching sound presenting the mistuned component after the remainder of the complex generally reduced the pitch shifts more for the third than for the fourth harmonic the nonsimultaneous presentation reduced shifts by a factor of 2 8 third and 1 7 fourth in the presence and 6 4 third and 1 9 fourth in the absence of the nominally mistuned harmonic from the matching sound the results are discussed in terms of an analytical listening and matching strategy that results in larger pitch shifts for a nonsimultaneous mistuned harmonic that has an octave or double octave relationship to the f0 than for one that does not without it necessarily being temporally integrated into the residue pitch of the complex

on the spectral theory of gesztesy seba realizations of 1 d dirac operators with point interactions on a discrete set abstract we investigate spectral properties of gesztesy seba realizations d x and d x of the 1 d dirac differential expression d with point interactions on a discrete set x x n n 1 r here n n 1 and n n 1 r the gesztesy seba realizations d x and d x are the relativistic counterparts of the corresponding schrodinger operators h x and h x with and interactions respectively we define the minimal operator d x as the direct sum of the minimal dirac operators on the intervals x n 1 x n then using the regularization procedure for direct sum of boundary triplets we construct an appropriate boundary triplet for the maximal operator d x in the case d x inf x i x j i j 0 it turns out that the boundary operators b x and b x parameterizing the realizations d x and d x are jacobi matrices these matrices substantially differ from the ones appearing in spectral theory of schrodinger operators with point interactions we show that certain spectral properties of the operators d x and d x correlate with the corresponding spectral properties of the jacobi matrices b x and b x respectively using this connection we investigate spectral properties self adjointness discreteness absolutely continuous and singular spectra of gesztesy seba realizations moreover we investigate the non relativistic limit as the velocity of light c most of our results are new even in the case d x 0

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

traveling waves in a delayed sir epidemic model with nonlinear incidence we study the traveling waves of a diffusive sir epidemic model with a general nonlinear incidence we obtain the threshold dynamics for spatial spread of the disease we show that c is the minimum wave speed for the existence of traveling wave solutions we establish the existence and non existence of traveling wave solutions for a diffusive sir model with a general nonlinear incidence the existence proof is shown by introducing an auxiliary system applying schauder s fixed point theorem and then a limiting argument the nonexistence proof is obtained by two sided laplace transform when the speed is less than the critical velocity numerical simulations support the theoretical results we also point out the effects of the delay and the diffusion rate of the infective individuals on the spreading speed

spectral enclosures for non self adjoint extensions of symmetric operators abstract the spectral properties of non self adjoint extensions a b of a symmetric operator in a hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding weyl functions these extensions are given in terms of abstract boundary conditions involving an in general non symmetric boundary operator b in the abstract part of this paper sufficient conditions for sectoriality and m sectoriality as well as sufficient conditions for a b to have a non empty resolvent set are provided in terms of the parameter b and the weyl function special attention is paid to weyl functions that decay along the negative real line or inside some sector in the complex plane and spectral enclosures for a b are proved in this situation the abstract results are applied to elliptic differential operators with local and non local robin boundary conditions on unbounded domains to schrodinger operators with potentials of complex strengths supported on unbounded hypersurfaces or infinitely many points on the real line and to quantum graphs with non self adjoint vertex couplings

mixed types of waves in a discrete diffusive epidemic model with nonlinear incidence and time delay abstract in this paper we investigate the traveling wave solutions of a discrete diffusive epidemic model with nonlinear incidence and time delay employing the method of upper and lower solutions schauder s fixed point theorem and a limiting approach we prove the existence of bounded super critical and critical traveling wave solutions moreover we obtain the positiveness and asymptotic boundary of the traveling wave solutions which guarantee that the traveling wave solutions are non trivial the existence results show that the traveling waves are mixed of front type and pulse type by way of contradiction and two sided laplace transform we derive the non existence of non trivial positive and bounded traveling wave solutions it is the first time to apply the method of upper and lower solutions together with schauder s fixed point theorem and two sided laplace transform to investigate the existence and non existence of traveling wave solutions for discrete diffusive epidemic models respectively

traveling waves in a bio reactor model with stage structure abstract in this paper the existence and non existence of traveling wave solutions are established for a bio reactor model with stage structure the method to prove the existence of wave solutions is to construct an invariant cone of initial functions defined in a large but bounded domain to apply a fixed point theorem on this cone and then extend to the unbounded spatial domain r by a limiting argument

generalized resolvents and the boundary value problems for hermitian operators with gaps a hermitian operator a with gaps j j 1 j m is studied the self adjoint extensions which put exactly kj eigenvalues into each gap j j in particular for kj 0 1 j m the extensions preserving the gaps are described in terms of boundary conditions the generalized resolvents of the extensions with the indicated properties are described also a solvability criterion and description of all the solutions of the hamburger moment problem with supports in r j 1m j j are obtained in terms of the nevanlinna matrix

relative dominance of individual partials in determining the pitch of complex tones these experiments were conducted to determine the dominance of each partial in determining the residue pitch of a complex tone subjects were required to make pitch matches to a complex tone which had one partial slightly mistuned from its correct harmonic value the shift in residue pitch was measured as a function of the frequency shift of the harmonic for each harmonic in turn for mistunings up to 2 3 the shift in residue pitch was approximately a linear function of the shift in the harmonic but for greater mistunings the shift in residue pitch was reduced the degree to which a given harmonic can influence residue pitch gives a measure of the dominance of that harmonic the dominant harmonics were always contained within the lowest six harmonics for fundamental frequencies of 100 200 and 400 hz but there were marked individual differences in the exact distribution of dominance across harmonics the level of a harmonic relative to adjacent harmonics can have a significant effect on its dominance the implications of the results for theories of pitch perception are discussed

stability of traveling waves of a diffusive susceptible infective removed sir epidemic model this paper is concerned with the stability and uniqueness of traveling waves of a delayed diffusive susceptible infective removed sir epidemic model we first prove the exponential stability of traveling waves by using the weighted energy method where the traveling waves are allowed to be non monotone then we establish the exact asymptotic behavior of traveling waves at by using ikehara s theorem finally the uniqueness of traveling waves is proved by the stability result of traveling waves

boundary relations and their weyl families the concepts of boundary relations and the corresponding weyl families are introduced let s be a closed symmetric linear operator or more generally a closed symmetric relation in a hilbert space h let h be an auxiliary hilbert space let graphics and let jh be defined analogously a unitary relation g from the krein space h 2 j h to the kre in space h 2 j h is called a boundary relation for the adjoint s if ker gamma s the corresponding weyl family m lambda is de ned as the family of images of the defect subspaces n over cap lambda lambda is an element of c r under gamma here gamma need not be surjective and is even allowed to be multi valued while this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex hilbert space h and the class of unitary relations gamma h 2 j h h 2 j h it also generalizes the notion of so called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems moreover these new notions yield for instance the following realization theorem every h valued maximal dissipative for lambda is an element of c holomorphic family of linear relations is the weyl family of a boundary relation which is unique up to unitary equivalence if certain minimality conditions are satisfied further connections between analytic and spectral theoretical properties of weyl families and geometric properties of boundary relations are investigated and some applications are given

entire solutions in nonlocal dispersal equations with bistable nonlinearity abstract we consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one dimensional spatial domain a two dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed furthermore we show that such an entire solution is unique up to space time translations and liapunov stable a key idea is to characterize the asymptotic behaviors of the solutions as t in terms of appropriate subsolutions and supersolutions we have to emphasize that a lack of regularizing effect occurs

on a nonlocal equation arising in population dynamics we study a one dimensional nonlocal variant of fisher s equation describing the spatial spread of a mutant in a given population and its generalization to the so called monostable nonlinearity the dispersion of the genetic characters is assumed to follow a nonlocal diffusion law modelled by a convolution operator we prove that as in the classical local problem there exist travelling wave solutions of arbitrary speed beyond a critical value and also characterize the asymptotic behaviour of such solutions at infinity our proofs rely on an appropriate version of the maximum principle qualitative properties of solutions and approximation schemes leading to singular limits

temporal dynamics of pitch strength in regular interval noises the pitch strength of rippled noise and iterated rippled noise has recently been fitted by an exponential function of the height of the first peak in the normalized autocorrelation function j acoust soc am 100 3329 3335 1996 the current study compares the pitch strengths and autocorrelation functions of rippled noise rn and another regular interval noise aabb rn is generated by delaying a copy of a noise sample and adding it to the undelayed version aabb with the same pitch is generated by taking a sample of noise a with the same duration as the rn delay and repeating it to produce aa and then concatenating many of these once repeated sequences to produce aabbccdd the height of the first peak h1 in the normalized autocorrelation function of aabb is 0 5 identical to that of rn the current experiments show the following 1 aabb and rn can be discriminated when the pitch is less than about 250 hz 2 for these low pitches the pitch strength of aabb is greater than that for rn

epidemic waves of a spatial sir model in combination with random dispersal and non local dispersal abstract in this paper a spatial sir model in combination with random dispersal and non local dispersal is proposed we establish the existence and non existence of the traveling wave solutions connecting the disease free equilibrium and the endemic equilibrium for the model the main difficulties lie in the fact that the semiflow generated here does not admit the order preserving property and the solutions lack of regularity we use a proper iteration scheme to construct a pair of upper and lower solutions and then apply the schauder s fixed point theorem polar coordinates transform to study the threshold dynamics of the model that is we show that if the basic reproduction number of the model r 0 1 there is a positive constant critical number c such that for each c c the model admits a non trivial and positive traveling wave with wave speed c and if r 0 1 and 0

travelling waves of a diffusive kermack mckendrick epidemic model with non local delayed transmission we obtain full information about the existence and non existence of travelling wave solutions for a general class of diffusive kermack mckendrick sir models with non local and delayed disease transmission we show that this information is determined by the basic reproduction number of the corresponding ordinary differential model and the minimal wave speed is explicitly determined by the delay such as the latent period and non locality in disease transmission and the spatial movement pattern of the infected individuals the difficulty is the lack of order preserving property of the general system and we obtain the threshold dynamics for spatial spread of the disease by constructing an invariant cone and applying schauder s fixed point theorem

on the relative influence of individual harmonics on pitch judgment spectral weighting functions were estimated in a pitch comparison task to assess the relative influence of individual harmonics on listeners pitch judgment the stimuli were quasi harmonic complex tones composed of the first 12 components with fundamental frequencies ranging from 100 to 800 hz on each stimulus presentation the frequency of each harmonic was randomly jittered by a small amount the perceptual weight for each harmonic was calculated as the correlation coefficient between the binary responses of the listener and the frequency jitters for that harmonic although in general the present results conform to previous ones showing the predominant role of several low ranked harmonics discrepancies exist in details contrary to some previous reports that the dominant harmonics were of fixed harmonic ranks regardless of their frequencies the current results showed that the dominant harmonics were best described as close to a fixed absolute frequency of 600 hz

pitch of iterated rippled noise iterated rippled noise irn stimuli are generated by a cascade of delay d gain g and add networks the matched pitch of irn stimuli was determined as a function of the type of network used to generate irn stimuli the delay d 2 4 and 8 ms the number of iterations n 1 2 3 4 6 8 of the delay and add networks and whether the delayed noise was added g 1 to or subtracted g 1 from the undelayed noise the matched pitch of irn stimuli did not depend on the type of network when g 1 addition the matched pitch did not depend on the number of stages of iterations n and was always equal to the reciprocal of the delay 1 d when g 1 subtraction the match pitch depended on n when n 1 the matched pitch of irn stimuli was ambiguous having two pitches in the region of 1 d 10 when n 8 the match pitch was equal to 1 2d this change in the pitch occurred between n 2 and 6 the results are discussed in terms of spectral and temporal models of complex pitch processing a temporal model based on autocorrelation was able to provide quantitative predictions for the pitch of these irn stimuli however a spectral type of model can also account for the pitch of these irn stimuli

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

traveling waves in a nonlocal dispersal sir model with critical wave speed abstract this paper is concerned with the existence of traveling waves for a nonlocal dispersal kermack mckendrick epidemic model as we know due to the semiflow generated by the model does not have the order preserving property and the solutions lack of regularity it is difficult to investigate traveling waves with the critical wave speed furthermore the nonlocal dispersal and bilinear incidence bring additional difficulties to get the boundedness of traveling waves in the present paper we overcome these difficulties to obtain the boundedness of traveling waves by analysis technique firstly and then prove the existence of traveling waves under the critical wave speed

1 d schrodinger operators with local point interactions on a discrete set abstract spectral properties of 1 d schrodinger operators h x d 2 d x 2 x n x n x x n with local point interactions on a discrete set x x n n 1 are well studied when d inf n k n x n x k 0 our paper is devoted to the case d 0 we consider h x in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding weyl functions we show that the spectral properties of h x like self adjointness discreteness and lower semiboundedness correlate with the corresponding spectral properties of certain classes of jacobi matrices based on this connection we obtain necessary and sufficient conditions for the operators h x to be self adjoint lower semibounded and discrete in the case d 0 the operators with type interactions are investigated too the obtained results demonstrate that in the case d 0 as distinguished from the case d 0 the spectral properties of the operators with and type interactions are substantially different

δ interaction as a limit of a thin neumann waveguide with transversal window abstract we consider a waveguide like domain consisting of two thin straight tubular domains connected through a tiny window the perpendicular size of this waveguide is of order e under the assumption that the window is appropriately scaled we prove that the neumann laplacian on this domain converges in a kind of norm resolvent sense as e 0 to a one dimensional schrodinger operator corresponding to a interaction of a non negative strength we estimate the rate of this convergence also we prove the convergence of spectra

searching for the time constant of neural pitch extraction multichannel auditory models have been repeatedly used to explain many aspects of human pitch perception among the most successful ones are models where pitch is estimated based on an analysis of periodicity in the simulated auditory nerve firing this periodicity analysis is typically implemented as a running autocorrelation i e the autocorrelation is calculated within a temporal window which is shifted along the time axis the window was suggested to have an exponential decay with time constant estimates between 1 5 and 100 ms the window length determines the minimal integration time of pitch extraction the present experiments are designed to quantify the temporal window of pitch extraction using regular interval noises rins rins were generated by concatenating equal duration noise samples which produce a pitch corresponding to the reciprocal of the sample duration when the samples are identical periodic noise when the samples are independent the stimulus is gaussian noise and produces no pitch using rin stimuli where periodic portions interchange with aperiodic portions it is shown that the temporal window of pitch extraction cannot be modeled using a single time constant but that the size of the temporal window depends on the pitch itself

spherical schrodinger operators with δ type interactions we investigate spectral properties of spherical schrodinger operators also known as bessel operators with point interactions concentrated on a discrete set we obtain necessary and sufficient conditions for these hamiltonians to be self adjoint lower semibounded and also we investigate their spectra we also extend the classical bargmann estimate to such hamiltonians in certain cases we express the number of negative eigenvalues explicitly by means of point interactions and the corresponding intensities we apply our results to schrodinger operators in l2 rn with a singular interaction supported by an infinite family of concentric spheres

one dimensional schrodinger operators with interactions singular on a discrete set on etudie le caractere auto adjoint des operateurs de schrodinger sur y u j i x j y j ou on suppose y j x j 1

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

sturm liouville boundary value problems with operator potentials and unitary equivalence consider the minimal sturm liouville operator a amin generated by the differential expression a d2dt2 t in the hilbert space l2 r h where t t 0 in h we investigate the absolutely continuous parts of different self adjoint realizations of a in particular we show that dirichlet and neumann realizations ad and an are absolutely continuous and unitary equivalent to each other and to the absolutely continuous part of the krein realization moreover if inf ess t inf t then the part a acea ad of any self adjoint realization a of a is unitarily equivalent to ad in addition we prove that the absolutely continuous part a ac of any realization a is unitarily equivalent to ad provided that the resolvent difference a i 1 ad i 1 is compact the abstract results are applied to elliptic differential expressions in the half space