from the restricted to the full three body problem the three body problem with all the classical integrals fixed and all the symmetries removed is called the reduced three body problem we use the methods of symplectic scaling and reduction to show that the reduced planar or spatial three body problem with one small mass is to the first approximation the product of the restricted three body problem and a harmonic oscillator this allows us to prove that many of the known results for the restricted problem have generalizations for the reduced three body problem for example all the non degenerate periodic solutions generic bifurcations hamiltonian hopf bifurcations bridges and natural centers known to exist in the restricted problem can be continued into the reduced three body problem the classic normalization calculations of deprit and deprit bartholome show that there are two dimensional kam invariant tori near the lagrange point in the restricted problem with the above result this proves that there are three dimensional kam invariant tori near the lagrange point in the reduced three body problem

simulation of the effects of loudness recruitment and threshold elevation on the intelligibility of speech in quiet and in a background of speech these experiments simulated the threshold elevation and loudness recruitment associated with three different types of cochlear hearing loss moderate flat condition r2 severe flat condition r3 and moderate to severe sloping condition rx this was done to allow an examination of the effects of these factors on the intelligibility of speech in isolation from other factors that are normally associated with cochlear hearing loss such as reduced frequency selectivity the simulation was performed by splitting the input signal into 13 frequency bands and processing the envelope in each band so as to create loudness sensations in a normal ear that would resemble those produced in an impaired ear with recruitment the bands were then recombined all tests were performed using subjects with normal hearing for speech in quiet simulation of hearing loss produced a reduction in the ability to understand low level speech however speech at sufficiently high levels was highly intelligible in all conditions linear amplification according to the national acoustic laboratory nal prescription gave high intelligibility for speech at normal conversational levels for speech presented at a fixed input level of 65 db spl against a background of a single competing talker simulation of hearing loss produced substantial decrements in performance the speech to background ratios in conditions r2 and rx had to be 11 13 db higher than in the control condition unprocessed stimuli to achieve similar levels of performance linear amplification according to the nal prescription improved performance markedly for the conditions simulating flat losses but was less effective for the condition simulating a sloping loss this indicates that threshold elevation combined with recruitment produces a loss of intelligibility for speech in the presence of a single competing talker that is only partly compensated by linear amplification of the type typically used in hearing aids

central configurations of the n body problem via equivariant morse theory in this paper we use the equivariant morse theory to give an estimate of the minimal number of central configurations in the n body problem in 3 in the case of equal masses we prove that the planar central configurations are saddle points for the potential energy from this we deduce the presence of non planar central configurations for every n 4

linear instability of relative equilibria for n body problems in the plane abstract following smale we study simple symmetric mechanical systems of n point particles in the plane in particular we address the question of the linear and spectral stability properties of relative equilibria which are special solutions of the equations of motion our main result is a sufficient condition to detect spectral hence linear instability namely we prove that if the morse index of an equilibrium point with even nullity is odd then the associated relative equilibrium is spectrally unstable the proof is based on some refined formulae for computing the spectral flow as a notable application of our theorem we examine two important classes of singular potentials the homogeneous one with 0 2 which includes the gravitational case and the logarithmic one we also establish for the homogeneous potential an inequality which is useful to test the spectral instability of the associated relative equilibrium

effects of level and frequency on the detection of decrements and increments in sinusoids thresholds for the detection of decrements in level of sinusoidal signals were measured as a function of decrement duration level 25 40 55 and 70 db spl and frequency 250 1000 and 4000 hz in eleven normally hearing subjects thresholds for detecting a brief increment in level were also measured the sinusoids were presented in a background noise intended to mask spectral splatter associated with the decrement or increment performance tended to worsen with decreasing frequency for all decrement durations and for increment detection performance also worsened with decreasing level the results were analyzed using a model consisting of a compressive nonlinearity a sliding temporal integrator and a decision device the analysis indicated that the worsening in performance with decreasing frequency and decreasing level can be attributed partly to increases in the equivalent rectangular duration erd of the temporal integrator but mainly to changes in the efficiency of the detection process following the temporal integrator at lower frequencies and levels a larger change is required at the output of the integrator for threshold to be reached at each frequency the erd was relatively invariant with level for levels more than about 20 db above the absolute threshold

maslov type indices and linear stability of elliptic euler solutions of the three body problem in this paper we use the central configuration coordinate decomposition to study the linearized hamiltonian system near the 3 body elliptic euler solutions then using the maslov type omega index theory of symplectic paths and the theory of linear operators we compute the omega indices and obtain certain properties of linear stability of the euler elliptic solutions of the classical three body problem

finding einstein solvmanifolds by a variational method we use a variational approach to prove that any nilpotent lie algebra having a codimension one abelian ideal and anyone of dimension leq 5 admits a rank one solvable extension which can be endowed with an einstein left invariant riemannian metric a curve of 8 dimensional einstein solvmanifolds is also given

phoneme recognition as a function of the number of auditory filter outputs it has been proposed that listeners take advantage of brief coups d oeil when processing speech in noise these glimpses can be characterized both in time and frequency the obligatory role of the auditory filters in determining the nature of any further processing suggests that the frequency extent of a glimpse should be equivalent to that of an auditory filter accordingly it is hypothesized that the spectral characteristics of glimpses primarily relate to the available number of auditory channels the present study investigated the number of auditory filter outputs needed to identify phonemes in quiet stimuli were first restricted to 80 8000 hz and then split into 30 contiguous auditory filter width bands normal hearing listeners were presented with n bands whose spectral location was selected randomly from trial to trial no signal was presented in the other bands consistent with previous studies performance gradually increased with the number of bands an asymptote was reached with 24 and 16 bands for vowels and consonants respectively while high levels of speech understanding are typically observed with as few as 4 channels of spectral information our results indicate that accurate phoneme recognition requires combination of a much larger number of auditory filter outputs

equivariant morse theory for flows and an application to the n body problem a l aide de l indice de conley et de la cohomologie equivariante on deduit certaines inegalites de type morse pour un flot equivariant par rapport a l action d un groupe topologique compact

geometric norm equality related to the harmonicity of the poisson kernel for homogeneous siegel domains in this paper we present a geometric norm equality involving an admissible linear form for the shilov boundary of a homogeneous siegel domain d we prove that the validity of this norm equality is equivalent to the symmetry of d and the reduction of essentially to the koszul form this in particular reveals a geometric reason that the poisson kernel is annihilated by the laplace beltrami operator if and only if d is symmetric a theorem due to hua look koranyi and xu

masking of speech by amplitude modulated noise abstract the degree of masking of human speech by environmental noise may be influenced by amplitude variations in the noise the listener s condition with respect to age and auditory function may affect his sensitivity to such noise also fatigue effects are possible after prolonged exposure to masking noise these aspects have been tested in the present study the results show that in general amplitude modulation of a masking noise reduces its speech masking effect as compared to unmodulated noise of the same r m s sound level and spectrum age did not affect the release of masking found in am noise however hearing impaired listeners obtained much less release of speech masking than those with normal hearing small but statistically significant fatigue effects were found after up to 60 min exposure to noise at 60 db spl the speech to noise ratio needed for 30 correct speech recognition was significantly affected by both age and hearing loss

persistence of lagrange invariant tori at tangent degeneracy abstract in the present paper without russmann s nondegenderate condition we show the persistence of kam invariant tori using this theorem we obtain the persistence of invariant tori for degenerate systems rising from restricted three body problems especially for lagrange equilibrium position l2 with certain degeneracy

linear stability of the elliptic lagrangian triangle solutions in the three body problem abstract this paper concerns the linear stability of the well known periodic orbits of lagrange in the three body problem given any three masses there exists a family of periodic solutions for which each body is at the vertex of an equilateral triangle and travels along an elliptic kepler orbit reductions are performed to derive equations which determine the linear stability of the periodic solutions these equations depend on two parameters the eccentricity e of the orbit and the mass parameter 27 m1m2 m1m3 m2m3 m1 m2 m3 2 a combination of numerical and analytic methods is used to find the regions of stability in the e plane in particular using perturbation techniques it is rigorously proven that there are mass values where the truly elliptic orbits are linearly stable even though the circular orbits are not

trace formula for linear hamiltonian systems with its applications to elliptic lagrangian solutions in the present paper we build up trace formulas for both the linear hamiltonian systems and sturm liouville systems the formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the hessian of the action functional a natural application is to study the non degeneracy of linear hamiltonian systems precisely by the trace formula we can give an estimation for the upper bound such that the non degeneracy preserves moreover we could estimate the relative morse index by the trace formula consequently a series of new stability criteria for the symmetric periodic orbits is given as a concrete application the trace formula is used to study the linear stability of elliptic lagrangian solutions of the classical planar three body problem which depends on the mass parameter beta in 0 9 and the eccentricity e in 0 1 based on the trace formula we estimate the stable region and hyperbolic region of the elliptic lagrangian solutions

comet like periodic orbits in the n body problem abstract take any nonresonant relative equilibrium solution of the n body problem then there is a periodic solution of the n 1 body problem where n of the particles remain close to the relative equilibrium solution and the remaining particle is close to a circular orbit of the kepler problem encircling the center of mass of the n particle system

representations of the affine transformation groups acting simply transitively on siegel domains let g be the split solvable lie group acting simply transitively on a siegel domain d we consider irreducible unitary representations of g realized on hilbert spaces of holomorphic functions on d we determine all such hilbert spaces by connecting them with positive riesz distributions on the dual cone and describe them through the fourier laplace transform moreover we classify the representations of g by making use of the orbit method

finiteness of central configurations of five bodies in the plane we prove there are finitely many isometry classes of planar central configurations also called relative equilibria in the newtonian 5 body problem except perhaps if the 5 tuple of positive masses belongs to a given codimension 2 subvariety of the mass space

noncompact homogeneous einstein manifolds attached to graded lie algebras in this paper we study the nilradicals of parabolic subalgebras of semisimple lie algebras and the natural one dimensional solvable extensions of them we investigate the structures curvatures and einstein conditions of the associated nilmanifolds and solvmanifolds we show that our solvmanifold is einstein if the nilradical is two step new examples of einstein solvmanifolds with three step and four step nilradicals are also given

asymptotic expansions and hua harmonic functions on bounded homogeneous domains let d be a homogeneous siegel domain of type ii we prove that every bounded hua harmonic function f on d is pluriharmonic the proof is based on asymptotic expansion of f

inequalities defining orbit spaces the orbit space of a representation of a compact lie group has a natural semialgebraic structure we describe explicit ways of finding the inequalities defining this structure and we give some applications

morse index and stability of elliptic lagrangian solutions in the planar three body problem abstract we illustrate a new way to study the stability problem in celestial mechanics in this paper using the variational nature of elliptic lagrangian solutions in the planar three body problem we study the relation between morse index and its stability via maslov type index theory of periodic solutions of hamiltonian system for elliptic lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the morse index which is the key to understand the stability problem as a special case we provide a criterion to spectral stability of relative equilibrium

determinant type differential operators on homogeneous siegel domains abstract we study the differential operators whose symbols are determinant type polynomials associated to homogeneous cones in connection with unitary representations of the split solvable lie group acting simply transitively on a siegel domain

ricci soliton homogeneous nilmanifolds we study a notion weakening the einstein condition on a left invariant riemannian metric g on a nilpotent lie groupn we consider those metrics satisfying ric g ci d for some c in mathbb r and some derivationd of the lie algebra mathfrak n ofn where ric g denotes the ricci operator of n g this condition is equivalent to the metric g to be a ricci soliton we prove that a ricci soliton left invariant metric on n is unique up to isometry and scaling the following characterization is also given n g is a ricci soliton if and only if n g admits a metric standard solvable extension whose corresponding standard solvmanifold s tilde g is einstein this gives several families of new examples of ricci solitons by a variational approach we furthermore show that the ricci soliton homogeneous nilmanifolds n g are precisely the critical points of a natural functional defined on a vector space which contains all the homogeneous nilmanifolds of a given dimension as a real algebraic set

psychoacoustic and phonetic temporal processing in normal and hearing impaired listeners four measures of auditory temporal processing were obtained from 16 normals and 16 individuals with a hearing loss of heterogeneous origin these measures were 1 temporal integration the difference in detection thresholds between signals of 10 and 1000 ms duration which was determined to provide an estimate of the ability to integrate energy over time 2 gap detection the shortest duration of silence between two noise bursts that can be discriminated from an uninterrupted noise 3 temporal difference limen the increment in duration necessary to detect a difference in the duration of a noise burst 4 gap difference limen the increment in duration necessary to detect a difference in the duration of a silent interval between two noise bursts each measure was obtained for stimuli centered both at 500 and at 4000 hz using a three alternative forced choice procedure in addition measures of identification and discrimination were obtained for two sets of synthetic speech syllables varying chiefly in a temporal parameter voice onset time from ba to pa and from bi to pi finally speech identification in noise was measured with the faaf test most of the hearing impaired listeners displayed poorer temporal analysis than the normals on all of the psychoacoustical tasks regardless of whether the two groups were compared at similar sound pressure levels or at similar sensation levels although the hearing impaired listeners displayed a reduction in the ability to discriminate subphonemic cues for the voiced voiceless distinction their identification of that distinction in stop consonants appeared to be normal the hearing impaired group made about twice as many errors as did the normals on each of the consonant features of place manner and voicing when identifying speech in noise increased temporal difference limen and longer gap detection thresholds were found to correlate significantly with reduced speech intelligibility in noise even when the effects of the pure tone threshold loss were partialed out

speech reception by listeners with real and simulated hearing impairment effects of continuous and interrupted noise the effects of audibility and age on masking for sentences in continuous and interrupted noise were examined in listeners with real and simulated hearing loss the absolute thresholds of each of ten listeners with sensorineural hearing loss were simulated in normal hearing listeners through a combination of spectrally shaped threshold noise and multi band expansion for octave bands with center frequencies from 0 25 8 khz each individual hearing loss was simulated in two groups of three normal hearing listeners an age matched and a non age matched group the speech to noise ratio s n for 50 correct identification of hearing in noise test hint sentences was measured in backgrounds of continuous and temporally modulated 10 hz square wave noise at two overall levels for unprocessed speech and for speech that was amplified with the nal rp prescription the s n in both continuous and interrupted noise of the hearing impaired listeners was relatively well simulated in both groups of normal hearing listeners thus release from masking the difference in s n obtained in continuous versus interrupted noise appears to be determined primarily by audibility minimal age effects were observed in this small sample observed values of masking release were compared to predictions derived from intelligibility curves generated using the extended speech intelligibility index esii rhebergen et al 2006 j acoust soc am 120 3988 3997

growth of masking as a measure of response growth in hearing impaired listeners growth of masking functions were obtained from 19 normal and 5 hearing impaired listeners using a simultaneous masking paradigm when masker and probe frequency are identical the slope of masking approximates 1 0 for both normal hearing and impaired listeners for masker frequencies less than or greater than probe frequency the slopes for impaired listeners are shallower than those of normals these findings are consistent with previously reported physiological data single fiber rate versus level and ap masking functions for animals with induced cochlear lesions results are discussed in terms of a potential masking technique to estimate the growth of response in normal and impaired ears

morse theory and relative equilibria in the planar n vortex problem morse theoretical ideas are applied to the study of relative equilibria in the planar n vortex problem for the case of positive circulations we prove that the morse index of a critical point of the hamiltonian restricted to a level surface of the angular impulse is equal to the number of pairs of real eigenvalues of the corresponding relative equilibrium periodic solution the morse inequalities are then used to prove the instability of some families of relative equilibria in the four vortex problem with two pairs of equal vorticities we also show that for positive circulations relative equilibria cannot accumulate on the collision set

multiscale kam theorem for hamiltonian systems abstract in this paper we study the persistence of invariant tori in nearly integrable multiscale hamiltonian systems with highorder degeneracy in the integrable part such hamiltonian systems arise naturally in planar and spatial lunar problems of celestial mechanics for which the persistence problem connects closely to the stability of the systems we introduce multiscale nondegenerate condition and multiscale diophantine condition comparable to the usual diophantine condition using quasilinear kam method we prove a multiscale kam theorem

psychometric functions for gap detection in a yes no procedure to examine models of temporal resolution and to investigate the decision processes underlying the detection of a brief pause in a bandpass noise psychometric functions for gap detection were measured at octave frequencies from 0 25 to 8 khz three normal listeners were tested using a constant stimulus procedure with a cued yes no paradigm the minimum detectable gap mdg estimated from the midpoint of the psychometric functions decreased systematically with increasing frequency the slopes of the psychometric functions generally increased as the test frequency increased up to 2 khz but remained constant at the higher frequencies two models were investigated an energy detector model and a loudness detector model both consisted of auditory filtering a nonlinearity and short term integration in the energy detector model the nonlinearity was a square law in the loudness detector model it was a compressive power law using the usual gaussian approximations the energy detector model fails at low fr

versal normal form of the hamiltonian function of the restricted problem of three bodies near l 4 abstract when one studies matrices depending on parameters the transformation into jordan canonical form can become singular when multiple eigenvalues occur the versal normal form for a matrix was introduced by arnol d 1971 in order to overcome this difficulty unfortunately no method was given on how to construct this transformation for a special class of matrices we describe a simple procedure to accomplish this task we use the one to one resonance at the lagrangian triangular equilibrium point in the restricted problem of three bodies as an example to demonstrate our method we then extend the idea of versal normal form to higher order terms in the hamiltonian function after performing this normalization we are able to analyze the behavior of the periodic orbits near the equilibrium point

the deterioration of hearing with age frequency selectivity the critical ratio the audiogram and speech threshold the frequency selectivity of the auditory system was measured by masking a sinusoidal signal 0 5 2 0 or 4 0 khz or a filtered speech signal with a wideband noise having a notch or stopband centered on the signal as the notch was widened performance improved for both types of signal but the rate of improvement decreased as the age of the 16 listeners increased from 23 to 75 years indicating a loss in frequency selectivity with age auditory filter shapes derived from the tone in noise data show a that the passband of the filter broadens progressively with age and b that the dynamic range of the filter ages like the audiogram that is the range changes little with age before 55 but beyond this point there is an accelerating rate of loss the speech experiment shows comparable but smaller effects the filter width measurements show that the critical ratio is a poor estimator of frequency selectivity because it confounds the tuning of the system with the efficiency of the signal detection and speech processing mechanisms that follow the filter an alternative one point measure of frequency selectivity which is both sensitive and reliable is developed via the filter shape model of masking

symmetric trajectories for the 2n body problem with equal masses we consider the problem of 2n bodies of equal masses in mathbb r 3 for the newtonian like weak force potential r and we prove the existence of a family of collision free nonplanar and nonhomographic symmetric solutions that are periodic modulo rotations in addition the rotation number with respect to the vertical axis ranges in a suitable interval these solutions have the hip hop symmetry a generalization of that introduced in 19 for the case of many bodies and taking account of a topological constraint the argument exploits the variational structure of the problem and is based on the minimization of lagrangian action on a given class of paths

the topology of reduces phase spaces of the motion of vortices on a sphere abstract the motion of point vortices in a perfect incompressible fluid on a two dimensional sphere can be represented by a hamiltonian flow which is invariant under the action of the special orthogonal group so 3 following the reduction method of marsden and weinstein this motion can be described by hamiltonian flows on reduced phase spaces some topological invariants of these reduced phase spaces are calculated for suitable vorticities the results obtained can be used to give lower bounds on numbers of relative equilibria of the original system

the berezin transform and invariant differential operators the berezin calculus is important to quantum mechanics creation annihilation operators and operator theory toeplitz operators we study the basic berezin transform linking the contravariant and covariant symbol for all bounded symmetric domains and express it in terms of invariant differential operators

equivalence of linear stabilities of elliptic triangle solutions of the planar charged and classical three body problems in this paper we prove that the linearized system of elliptic triangle homographic solution of planar charged three body problem can be transformed to that of the elliptic equilateral triangle solution of the planar classical three body problem consequently the results of martinez sama and simo 2006 15 and results of hu long and sun 2014 6 can be applied to these solutions of the charged three body problem to get their linear stability

gap detection in normal and hearing impaired listeners temporal resolution estimated by measuring the minimum detectable gap t msec separating two successive signals was assessed in five normal hearing and five cochlear impaired listeners the signals were octave band noises 400 800 hz 800 1600 hz and 2000 4000 hz presented in a background of continuous broadband notched noise that was applied to eliminate unwanted spectral cues temporal resolution in all listeners showed systematic improvement with an increase in octave band center frequency resolution in the hearing impaired subjects was significantly poorer than normal regardless of whether the comparisons were made at equal sound pressure level or at equal sensation level

sentence reception in noise from one versus two sources effects of aging and hearing loss sentence reception thresholds srts and babble detection thresholds bdts were measured for signals presented from loudspeakers located at 0 deg and 90 deg azimuth in addition the s b ratios necessary to achieve srt in the presence of a 12 talker babble were determined under three conditions in which the speech and babble were presented from the same or spatially separated loudspeakers in the first experiment normal hearing subjects were tested on two occasions the results were highly reliable with standard errors of the test retest differences of less than 1db for all conditions in the second experiment srts bdts and s b ratios were measured for three normal hearing groups 39 40 54 and 55 years and for a fourth group with presbycusis 55 years presbycusics had higher srts and bdts than all other groups regardless of age and the oldest normals had higher thresholds than younger subjects presbycusics required higher s b ratios than any of the normal groups and the oldest normal group needed a higher s b ratio compared to the youngest group all groups demonstrated a significant advantage in s b ratio when the sentences and babble sources were spatially separated compared to when they were presented from the same loudspeaker there was no significant difference in the magnitude of advantage due to spatial separation of speech and noise between the normal groups regardless of age but the presbycusics had significantly smaller advantages than all normals these findings suggest that aging alone does not impair the ability to take advantage of the spatial separation of speech and noise and that the speech reception problems of aging individuals involve various components that depend upon the nature of the listening task

on central configurations this paper concerns an old problem which arose in celestial mechanics and has since taken on a life of its own the probem of central configurations of the n body problem

parabolic subgroups of semisimple lie groups and einstein solvmanifolds in this paper we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple lie algebras these solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type we show that the ricci curvatures of our solvmanifolds coincide with the restrictions of the ricci curvatures of the ambient symmetric spaces consequently all of our solvmanifolds are einstein which provide a large number of new examples of noncompact homogeneous einstein manifolds we also show that our solvmanifolds are minimal but not totally geodesic submanifolds of symmetric spaces

hill type formula for hamiltonian system with lagrangian boundary conditions abstract in this paper we build up hill type formula for linear hamiltonian systems with lagrangian boundary conditions which include standard neumann dirichlet boundary conditions such a kind of boundary conditions comes from the n reversible symmetry periodic orbits in n body problem naturally where n is an anti symplectic orthogonal matrix with n 2 i the hill type formula connects the infinite determinant of the hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions consequently we derive the krein type trace formula and give nontrivial estimation for the eigenvalue problem combined with the maslov type index theory we give some new stability criteria for the n reversible symmetry periodic solutions of hamiltonian systems as an application we study the linear stability of elliptic relative equilibria in planar 3 body problem

index iteration theories for periodic orbits old and new abstract in this paper we give a survey of the index iteration theories developed for periodic solution orbits of hamiltonian systems in treating various problems from 1950s up to now including some recent developments and some of their applications to periodic solution problems

on solvable lie groups of negative ricci curvature we study solvable lie groups which admit a left invariant metric of strictly negative ricci curvature we obtain necessary and sufficient conditions of the existence of such a metric for lie groups the nilradical of whose lie algebra is either abelian or heisenberg or standard filiform and discuss some open questions

simulation of the effect of threshold elevation and loudness recruitment combined with reduced frequency selectivity on the intelligibility of speech in noise the effect of loudness recruitment and threshold elevation together with reduced frequency selectivity have been simulated to examine the combined effect of the two major consequences of cochlear hearing loss on the intelligibility of speech in speech shaped noise in experiment 1 four conditions were simulated a moderate flat loss with auditory filters broadened by a factor of three b3r2 a moderate to severe sloping loss with auditory filters broadened by a constant factor of three b3rx and these conditions with linear amplification applied prior to the simulation processing b3r2 b3rx for conditions b3r2 and b3rx performance was markedly worse than for a control condition normal hearing condition r1 tested in a previous study for conditions b3r2 and b3rx linear amplification improved performance considerably however performance remained below that for condition r1 by between 5 and 19 in experiment 2 the broadening of the auditory filters was made more realistic by making it a function of the absolute threshold at the center frequency of the auditory filter three different hearing losses were simulated a moderate to severe sloping loss with variable broadening of the auditory filters bxrx the same moderate to severe sloping loss with linear amplification bxrx and the same broadening of the auditory filters but without the simulation of loudness recruitment and threshold elevation bx for condition bxrx performance was markedly worse than in condition r1 while performance in condition bx was somewhat worse than for condition r1 for condition bxrx linear amplification according to the nal procedure improved performance to a large extent but it remained worse than for condition r1 the results are consistent with previous evidence indicating that only part of the decrease of performance produced by actual cochlear hearing loss can be compensated by conventional linear hearing aids

temporal modulation transfer functions for listeners with real and simulated hearing loss a functional simulation of hearing loss was evaluated in its ability to reproduce the temporal modulation transfer functions tmtfs for nine listeners with mild to profound sensorineural hearing loss each hearing loss was simulated in a group of three age matched normal hearing listeners through spectrally shaped masking noise or a combination of masking noise and multiband expansion tmtfs were measured for both groups of listeners using a broadband noise carrier as a function of modulation rate in the range 2 to 1024 hz the tmtfs were fit with a lowpass filter function that provided estimates of overall modulation depth sensitivity and modulation cutoff frequency although the simulations were capable of accurately reproducing the threshold elevations of the hearing impaired listeners they were not successful in reproducing the tmtfs on average the simulations resulted in lower sensitivity and higher cutoff frequency than were observed in the tmtfs of the hearing impaired listeners discrepancies in performance between listeners with real and simulated hearing loss are possibly related to inaccuracies in the simulation of recruitment

existence and non existence of homogeneous einstein metrics on demontre un theoreme d existence general pour des metriques d einstein homogenes et on presente des espaces homogenes compacts simplement connexes qui ne portent pas une metrique d einstein homogene

morse theory for symmetric functionals on the sphere and an application to a bifurcation problem abstract this paper uses conley s index to study the cortical points of a function f on a finite dimensional sphere in presence of a symmetry group the authors prove a theorem which leads to a lower bound on the number of critical points of f when the group is finite even if the action is not free this investigation has been motivated by the following bifurcation problem au lambda where a is a variational g equivariant operator an estimated on the number of branches bifurcating from an eigenvalue of a 0 is given author

comparisons of frequency selectivity in simultaneous and forward masking for subjects with unilateral cochlear impairments two experiments are described in which frequency selectivity was estimated in simultaneous and forward masking for each ear of subjects with moderate 25 60 db hl unilateral cochlear hearing losses in both experiments the signal level was fixed for a given ear and type of masking simultaneous or forward and the masker level was varied to determine threshold using an adaptive two alternative forced choice procedure in experiment i the masker was a noise with a spectral notch centered at the signal frequency either 1 0 or 1 5 khz threshold was determined as a function of notch width signal levels were chosen so that the noise level required at threshold for a notch width of zero was similar for the normal and impaired ear of each subject in both simultaneous and forward masking the function relating threshold to notch width had a steeper slope for the normal ear than for the impaired ear of each subject for the normal ears these functions were steeper in forward masking than in simultaneous masking this difference was interpreted as resulting from suppression for the impaired ears significant differences in the same direction were observed for three of the five subjects but the differences were smaller in experiment ii psychophysical tuning curves ptcs were determined in the presence of a fixed notched noise centered at the signal frequency 1 0 khz for the normal ears the ptcs were sharper in forward masking than in simultaneous masking for the impaired ears the ptcs were similar in simultaneous and forward masking but those in forward masking tended to be sharper at masker frequencies far removed from the signal frequency overall the results suggest that suppression is reduced but not completely absent in cases of moderate cochlear hearing loss

temporal resolution in sensorineural hearing impaired listeners temporal masking curves were obtained from 12 normal hearing and 16 hearing impaired listeners using 200 ms 1000 hz pure tone maskers and 20 ms 1000 hz fixed level probe tones for the delay times used here 40 ms temporal masking curves obtained from both groups can be well described by an exponential function with a single level independent time constant for each listener normal hearing listeners demonstrated time constants that ranged between 37 and 67 ms with a mean of 50 ms most hearing impaired listeners with significant hearing loss at the probe frequency demonstrated longer time constants range 58 114 ms than those obtained from normal hearing listeners time constants were found to grow exponentially with hearing loss according to the function 52e0 011 hl when the slope of the growth of masking is unity the longest individual time constant was larger than normal by a factor of 2 3 for a hearing loss of 52 db the steep slopes of the growth of masking functions typically observed

structure of manifolds of nonpositive curvature clearly 1 rank m dim m we may regard rank m as a measurement of the flatness of m since a parallel field x along yv and perpendicular to yv is a jacobi field if and only if the sectional curvatures of the planes i t a x t are zero for all t e r in particular m is flat if rank m dim m hence a compact surface of nonpositive curvature has rank one unless it is a torus or a klein bottle it also follows that rank m1 x m2 rank ml rank m2 finally it is important that the definition of rank m above coincides with the usual one if m is locally symmetric

pitch discrimination and phase sensitivity in young and elderly subjects and its relationship to frequency selectivity frequency difference limens for pure tones dlfs and for complex tones dlcs were measured for four groups of subjects young normal hearing young hearing impaired elderly with near normal hearing and elderly hearing impaired the auditory filters of the subjects had been measured in earlier experiments using the notched noise method for center frequencies fc of 100 200 400 and 800 hz the dlfs for both impaired groups were higher than for the young normal group at all fc s 50 4000 hz the dlfs at a given fc were generally only weakly correlated with the sharpness of the auditory filter at that fc and some subjects with broad filters had near normal dlfs at low frequencies some subjects in the elderly normal group had very large dlfs at low frequencies in spite of near normal auditory filters these results suggest a partial dissociation of frequency selectivity and frequency discrimination of pure tones the dlcs for the two impaired groups were higher than those for the young normal group at all fundamental frequencies fo tested 50 100 200 and 400 hz the dlcs for the elderly normal group were intermediate at fo 50 hz dlcs for a complex tone containing only low harmonics 1 5 were markedly higher than for complex tones containing higher harmonics for all subject groups suggesting that pitch was conveyed largely by the higher unresolved harmonics for the elderly impaired group and some subjects in the elderly normal group dlcs were larger for a complex tone with lower harmonics 1 12 than for tones without lower harmonics 4 12 and 6 12 for fo s up to 200 hz some elderly normal subjects had markedly larger than normal dlcs in spite of near normal auditory filters the dlcs tended to be larger for complexes with components added in alternating sine cosine phase than for complexes with components added in cosine phase phase effects were significant for all groups but were small for the young normal group the results are not consistent with place based models of the pitch perception of complex tones rather they suggest that pitch is at least partly determined by temporal mechanisms

elliptic relative equilibria in the n body problem a planar central configuration of the n body problem gives rise to a solution where each particle moves on a specific keplerian orbit while the totality of the particles move on a homothety motion if the keplerian orbit is elliptic then the solution is an equilibrium in pulsating coordinates so we call this solution an elliptic relative equilibrium the totality of such solutions forms a four dimensional symplectic subspace and we give a symplectic coordinate system which is adapted to this subspace and its symplectic complement in our coordinate system the linear variational equations of such a solution decouple into three subsystems one subsystem simply gives the motion of the center of mass another is kepler s problem and the third determines the nontrivial characteristic multipliers using these coordinates we study the linear stability of the elliptic relative equilibrium defined by the equilateral triangular central configuration of the three body problem we reproduce the analytic studies of g roberts we also study the linear stability of the four and five body problem where three or four bodies of unit mass are at the vertices of a equilateral triangle or

morse index and linear stability of the lagrangian circular orbit in a three body type problem via index theory it is well known that the linear stability of the lagrangian elliptic solutions in the classical planar three body problem depends on a mass parameter and on the eccentricity e of the orbit we consider only the circular case e 0 but under the action of a broader family of singular potentials homogeneous potentials for alpha in 0 2 and the logarithmic one it turns out indeed that the lagrangian circular orbit persists also in this more general setting we discover a region of linear stability expressed in terms of the homogeneity parameter and the mass parameter then we compute the morse index of this orbit and of its iterates and we find that the boundary of the stability region is the envelope of a family of curves on which the morse indices of the iterates jump in order to conduct our analysis we rely on a maslov type index theory devised and developed by y long x hu and s sun a key role is played by an appropriate index theorem and by some precise computations of suitable maslov type indices

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

a characterization of bounded symmetric domains by curvature this paper will prove that a bounded homogeneous domain is symmetric if and only if in the bergman metric all sectional curvatures are nonpositive introduction it is well known that a bounded symmetric domain has nonpositive sectional curvature in the bergman metric this paper is devoted to the converse namely that a bounded homogeneous domain equivalently homogeneous siegel domain which has nonpositive sectional curvature in the bergman metric must be a symmetric domain the proof uses the techniques of normal j algebras 13 as well as results of vinberg 16 17 the first author 1 3 and indirectly dorfmeister 5 6 the body of the paper is in two sections in the first we derive certain relations between the dimensions of the root spaces in an irreducible normal j algebra which in the presence of the additional curvature assumption show the equality of the dimensions of all root spaces corresponding to certain roots for which no multiple is a root and the equality of the dimensions of all root spaces corresponding to roots which are half of another root in the second section we show that the first dimension result implies that the cone of the corresponding siegel domain is self dual while the two dimension results together imply that the domain is quasi symmetric the proof is then finished because 3 a quasi symmetric domain with nonpositive sectional curvature in the bergman metric is known to be symmetric we remark that some of the subsidiary results mentioned above are not essentially new however for consistency of presentation it is necessary to have them in the language of normal jalgebras and for that reason they are included there is also overlap here with work of zelow lundquist 21 1 throughout this paper s j will denote a normal j algebra with admissible form w this means that s is a finite dimensional real split solvable lie algebra with almost complex structure j s s such that x y j jx y j x jy jx jy and w is a linear form on s such that the bilinear form o jx y is symmetric positive definite and j invariant note that the assumption that s is real split was incorrectly omitted in 2 let n s s and let a be the orthogonal complement of n in s by the basic structure theorem of pyatetskii shapiro 13 a is a commutative received by the editors july 13 1981 1980 mathematics subiect classification primary 32mi0 53c30 1983 american mathematical society 0002 9947 82 000 0759 09 00