comparison theorems for the matrix riccati equation on deduit une inegalite matricielle a partir d une inegalite differentielle on utilise ce resultat pour deduire des inegalites pour les solutions d equations de riccati matricielles

immersions of compact riemannian manifolds into a ball of a complex space form there are some classical theorems on non immersibility of compact riemannian manifolds with sectional curvature bounded from above given by tompkins o neill chern kuiper and moore see 3 pages 221 226 more recently attention has been paid to the case of immersions into a geodesic ball of a simply connected space form and some conditions of non immersibility in such a ball have been proved in particular estimates for the mean curvature of a complete immersion into a geodesic ball have been obtained by jorge and xavier 11 and a corresponding rigidity theorem for compact hypersurfaces has been proved by markvorsen 14 in this paper we give the kahler analogs of the theorems of jorge and xavier only for the compact case and markvorsen and get some other new results for the kahler case that have no riemannian analog in order to state our results we shall introduce some notation and terminology given a real number let us consider the functions

cyclic differential equations and period three solutions of differential delay equations where g c is a given function ni are integers and a is a real parameter such equations have been considered in several papers for instance 2 5 6 it has become apparent that it is important to be able to show that 0 1 has no nontrivial periodic solutions of certain periods for example the global hopf bifurcation theorem as developed by alexander and yorke for ordinary differential equations and later extended to functional differential equations 12 6 1 gives relatively little information about 0 i if one does not know that 0 1 has no nontrivial solutions of certain periods a well known result see lemma 4 1 in 21 asserts that eq 0 i can have no nonconstant periodic solutions of period 2 in this paper we show that for certain classes of g 0 1 can have no nonconstant periodic solutions of period 3 the general idea that periodic solutions of 0 1 of period n n an integer satisfy an associated system of ordinary differential equations has been used before see 141 and lemma 4 1 of 121 however in our case we deal with a system of three first order odes instead of two odes as in lemma4 1 of 121

temporal integration of loudness measured using categorical loudness scaling and matching procedures temporal integration of loudness of 1 khz tones with 5 and 200 ms durations was assessed in four subjects using two loudness measurement procedures categorical loudness scaling cls and loudness matching cls provides a reliable and efficient procedure for collecting data on the temporal integration of loudness and previously reported nonmonotonic behavior observed at mid sound pressure level levels is replicated with this procedure stimuli that are assigned to the same category are effectively matched in loudness allowing the measurement of temporal integration with cls without curve fitting interpolation or assumptions concerning the form of the loudness growth function

on stable complete minimal hypersurfaces in r n 1 abstract by using the interior curvature estimate and gromov s compactness theorem we prove that a stable complete minimal hypersurface in rn l with finite total scalar curvature must be a hyperplane this extends the result obtained by p b rard in remarques sur l quation de j simons pitman monographs surveys pure appl math vol 52 1991 pp 47 57

spectral loudness summation shortcomings of current standards there are two competing national standards for the calculation of loudness of steady sounds din 45631 and ansi s3 4 their different concepts of critical bands lead to different predictions for broadband sounds as that discrepancy is neither constant nor linear but highly frequency dependent the present study investigates spectral loudness summation in three frequency regions at various levels and using two different methods the results show that both algorithms overestimate loudness however din 45631 comes closer to the subjective evaluations and often falls within their interquartile range the overestimation by the standards is particularly large in the frequency range from 2 to 5 khz

multiplicity results of periodic solutions for a class of second order delay differential systems abstract this paper is concerned with the periodic boundary value problem 1 u t u t f t u t a e t 0 2 u 0 u 2 u 0 u 2 0 where 0 is a given constant r is a parameter the variational principle is given and some multiplicity results of periodic solutions of 1 are obtained directly via variational methods

an estimate for the curvature of bounded submanifolds 1 statement of the result all manifolds considered in this paper shall be connected of class c smooth and dimension at least 2 im mersions will also be smooth and of codimension at least 1 if m and m are riemannian manifolds and p m m is an isometric immersion with the property that sp m lies in a ball we intend to estimate the supremum of the sectional curvature k of m in terms of the sectional curvature k of m and the radius of the ball this is our result theorem a let ml be a complete riemannian manifold whose scalar curvature is bounded below let m q be a riemannian manifold with q c n 1 and bx a closed normal ball in mt4 q of radius x sup pose sp m j m q is an isometric immersion with the property that

the extension problem of the mean curvature flow i we show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in mathbb r 3

loudness recalibration as a function of level recent research on loudness has focused on contextual effects on loudness both assimilation and recalibration the current experiments examined loudness recalibration marks j exp psychol 20 382 396 1994 in the first experiment an adaptive tracking procedure was used to measure loudness recalibration as a function of standard and recalibration tone level the standard tone frequencies were 500 and 2500 hz and the levels were 80 70 60 and 40 db spl and threshold seventeen db of loudness recalibration was obtained combined over both frequencies in the 60 db spl condition this amount of loudness recalibration while substantial is still less than that obtained by marks 22 db using the method of paired comparisons the second experiment sought to duplicate marks earlier experiment marks j exp psychol 20 382 396 1994 experiment 2 the results of this experiment 21 db were almost identical to those obtained by marks the results of experiment 1 indicate that loudness recalibration is maximum when the recalibration tone is moderately louder than the subsequent standard tones relatively little loudness recalibration is exhibited when the standard tone level equals the recalibration tone level in addition there is no loudness recalibration at threshold the tracking procedure also identified that the onset of loudness recalibration is very rapid the difference between the maximum loudness recalibration obtained at each frequency 11 db at 500 hz 6 db at 2500 hz suggests that loudness recalibration is dependent upon the frequency of the standard tone

a first eigenvalue estimate for minimal hypersurfaces on obtient une borne inferieure pour la premiere valeur propre d une hypersurface orientable compacte plongee de facon minimale dans une variete orientable compacte a courbure de ricci positive

nontrivial periodic solutions for delay differential systems via morse theory abstract the existence of the nontrivial periodic solutions to the system of delay differential equations 1 1 x t f x t is investigated where x r n f c r n r n we prove several new existence results via morse theory and the galerkin methods

multiplicity results of periodic solutions for systems of first order delay differential equation abstract this paper is concerned with the periodic solutions of the following delay non autonomous systems 1 u t f t u t r where r 0 f c r 1 r n r n satisfies f t r z f t z for all z r n some multiplicity results of periodic solutions of 1 are obtained via variational methods

compactness of self shrinkers in r3 with fixed genus abstract we prove the compactness of self shrinkers in r 3 with bounded entropy and fixed genus as a corollary we show that numbers of ends of such surfaces are uniformly bounded by the entropy and genus

inequivalent complexity criteria for free boundary minimal surfaces abstract we obtain a series of results in the global theory of free boundary minimal surfaces which in particular provide a rather complete picture for the way different complexity criteria such as area topology and morse index compare beyond the regime where effective estimates are at disposal

minimal hypersurfaces and bordism of positive scalar curvature metrics let y g be a compact riemannian manifold of positive scalar curvature psc it is well known due to schoen yau that any closed stable minimal hypersurface of y also admits a psc metric we establish an analogous result for stable minimal hypersurfaces with free boundary furthermore we combine this result with tools from geometric measure theory and conformal geometry to study psc bordism for instance assume y 0 g 0 and y 1 g 1 are closed psc manifolds equipped with stable minimal hypersurfaces x 0 subset y 0 and x 1 subset y 1 under natural topological conditions we show that a psc bordism z bar g y 0 g 0 rightsquigarrow y 1 g 1 gives rise to a psc bordism between x 0 and x 1 equipped with the psc metrics given by the schoen yau construction

harmonic maps from degenerating riemann surfaces we study harmonic maps from degenerating riemann surfaces with uniformly bounded energy and show the so called generalized energy identity we find conditions that are both necessary and sufficient for the compactness in w 1 2 and c 0 modulo bubbles of sequences of such maps

recent advances about the uniqueness of the slowly oscillating periodic solutions of wright s equation abstract an old conjecture in delay equations states that wright s equation y t y t 1 1 y t r has a unique slowly oscillating periodic solution sops for every parameter value 2 we reformulate this conjecture and we use a method called validated continuation to rigorously compute a global continuous branch of sops of wright s equation using this method we show that a part of this branch does not have any fold point partially answering the new reformulated conjecture

global bifurcation of periodic solutions to some autonomous differential delay equations we are concerned with slowly oscillating periodic solutions of the parametrized differential delay equation x xdot t email protected x t 1 l 0 where is an odd continuous and nonlinear function satisfying email protected x 0 for all x 0 due to the oddness of we can identify odd harmonic periodic solutions having the period t with other solutions of the periods 2t t 2 from this observation and a result of nussbaum we obtain the existence of periodic solutions with a period close to 2 moreover we can reach conclusions about a secondary bifurcation of periodic solutions we present a combination of a galerkin scheme with a continuation method which yields a feasable numerical procedure for the effective computation and continuation of periodic solutions we report the results of an extensive case study for the nonlinearities x x 1 x p p 1 for p 8 we show many different continua of periodic solutions which are either disjoint or bifurcating from continua of periodic solutions that contain a higher symmetry for p 1 and l p 2 it is known that periodic solutions are unique we discuss two homotopies linking the cases p 8 and p 1 which exhibit very different transitions from multiplicity to uniqueness of solutions

a potential carry over effect in the measurement of induced loudness reduction the majority of studies on induced loudness reduction ilr use an experimental paradigm that results in an underestimation of the amount of ilr most of those studies utilize loudness matches between tones of two different frequencies a test tone and a comparison tone with experimental condition and without baseline condition an inducer tone at the test frequency the change in level of the comparison tone between the baseline and experimental conditions is the amount of ilr in those experiments the level of the comparison tone in the baseline condition tends to be substantially higher often about 10db than in the experimental condition because of this level difference exposure to the baseline condition immediately prior to the experimental condition causes unintended ilr for the comparison tone in this study the delay between the baseline and experimental conditions was varied and it was determined that the amount of ilr is underestimated by about 30 and the variability is increased when

symmetric functional differential equations and neural networks with memory we establish an analytic local hopf bifurcation theorem and a topological global hopf bifurcation theorem to detect the existence and to describe the spatial temporal pattern the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry we apply these general results to obtain the coexistence of multiple large amplitude wave solutions for the delayed hopfield cohen grossberg model of neural networks with a symmetric circulant connection matrix

effect of adaptive psychophysical procedure on loudness matches large variability in equal loudness matches has been observed across studies the purpose of the present study was to gain insight into the extent to which this variability results from differences in psychophysical procedures and or differences among listeners four adaptive two interval two alternatives forced choice procedures were used to obtain equal loudness matches between 5 and 200 ms 1 khz tones as a function of level for each of six normal listeners the procedures differed primarily in the sequence in which the stimuli were presented the variations tested were the ordering of stimuli by amplitude across blocks of trials both increasing and decreasing amplitudes randomizing the order across those blocks and randomizing the order within blocks the random within block procedure which sought to randomize any intertrial information yielded a significantly greater amount of temporal integration than the other three procedures the results show significant differences in temporal integration

loudness enhancement induced loudness reduction in disguise l two opposite sequential loudness effects concern the effect of a stronger tone 1 on the loudness of a subsequent weaker tone 2 as assessed by loudness matches with tone 3 loudness enhancement is reported when tone 1 precedes tone 2 by 50 to 100 ms loudness recalibration or induced loudness reduction is obtained for delays of about 1 s this letter argues that what appears as an enhancement of tone 2 s loudness is in fact an induced reduction of tone 3 s loudness which occurs because tones 1 and 3 are at the same frequency preliminary experiments support this analysis

multiplicity results for periodic solutions to delay differential equations via critical point theory abstract by the critical point theory we study the existence and multiplicity of periodic solutions to the following system of delay differential equations x t f x t r where x r n f c r n r n and r 0 is a given constant a sufficient condition on the existence and multiplicity of periodic solutions for eq is obtained to the authors knowledge this is the first time the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly

special lagrangian cones we study special lagrangian cones in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i with isolated singularities especially the case n 3 our main result constructs an infinite family of special lagrangian cones in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i each of which has a toroidal link we obtain a detailed geometric description of these tori we prove a regularity result for special lagrangian cones in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i with a spherical link any such cone must be a plane we also construct a one parameter family of asymptotically conical special lagrangian submanifolds from any special lagrangian cone

tracking the time to recovery after induced loudness reduction l in induced loudness reduction ilr a strong tone causes the loudness of a subsequently presented weak tone to decrease the aim of the experiment was to determine the time required for loudness to return to its initial level after ilr twenty four subjects were exposed to 5 10 20 or 40 brief bursts of 2500 hz pure tones at 80 db spl inducers and then tested in a series of paired comparison trials subjects compared the loudness of a weak target 2500 hz at 60 db spl to the loudness of a comparison tone at 500 hz previously judged to match the target the comparison task was repeated until the two tones were again judged equally loud the results showed that a recovery after ilr is a relatively long process with a time scale of minutes and b recovery time increased approximately 20 s with each doubling of the number of inducers

minimal hypersurfaces with bounded index we prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index and volume if the ambient dimension is greater than three in a riemannian manifold m n g 3 le n le 7 can degenerate loosely speaking our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces up to controlled errors several compactness finiteness theorems follow from our local picture

a test of the equal loudness ratio hypothesis using cross modality matching functions this study tests the equal loudness ratio hypothesis florentine et al j acoust soc am 99 1633 1644 1996 which states that the loudness ratio between equal spl long and short tones is independent of spl the amount of temporal integration i e the level difference between equally loud short and long sounds is maximal at moderate levels therefore the equal loudness ratio hypothesis predicts that the loudness function is shallower at moderate levels than at low and high levels equal loudness matches and cross modality string length matches were used to assess the form of the loudness function for 5 and 200 ms tones at 1 khz and the loudness ratio between them results from nine normal listeners show that 1 the amount of temporal integration is largest at moderate levels in agreement with previous studies and 2 the loudness functions are shallowest at moderate levels for eight of the nine listeners the loudness ratio between the 200 and 5 ms tones is approximately constant except at

smooth bifurcation of symmetric periodic solutions of functional differential equations with odd f c r in contrast to the one dimensional ordinary differential equation this equation can have periodic solutions as the example i t 7r 2 x t 1 with solutions x t z sin rc 2 t z 0 shows numerical bifurcation diagrams e g 6 143 indicate a complicated structure of the period solutions depending on the delay parameter u one finds various intersecting smooth curves one task of mathematics is to prove the existence of periodic solutions in this paper we are mainly interested in symmetric periodic solutions i e solutions x of c which fultil the symmetry property

triply periodic constant mean curvature surfaces abstract given a closed flat 3 torus n for each h 0 and each non negative integer g we obtain area estimates for closed surfaces with genus g and constant mean curvature h embedded in n this result contrasts with the theorem of traizet 31 who proved that every flat 3 torus admits for every positive integer g with g 2 connected closed embedded minimal surfaces of genus g with arbitrarily large area

min max theory and the willmore conjecture in 1965 t j willmore conjectured that the integral of the square of the mean curvature of a torus immersed in r 3 is at least 2 2 we prove this conjecture using the min max theory of minimal surfaces

induced loudness reduction as a function of exposure time and signal frequency induced loudness reduction ilr is the decline in the loudness of a weaker tone induced by a preceding stronger tone in this study we investigate how ilr depends on exposure time and signal frequency for 12 listeners successive magnitude estimation was used to measure the loudness of 70 db spl test tones presented with and without preceding 80 db spl inducer tones at the same frequency experiment 1 measured the evolution of ilr over time at 0 5khz the results suggest that ilr may begin after a single inducer presentation and increases over at least 2 to 3min as the inducer and test tones are repeated every few seconds following the cessation of the inducer the recovery of loudness is slow and still incomplete after 1min experiment 2 extended the measurements to additional signal frequencies the results show that the amount of ilr and its evolution over time are approximately the same at frequencies from 0 5 to 8khz similarly loudness matching showed no effect of frequency on ilr which avera

curvature estimates for surfaces with bounded mean curvature estimates for the norm of the second fundamental form a play a crucial role in studying the geometry of surfaces in r3 in fact when a is bounded the surface cannot bend too sharply in this paper we prove that for an embedded geodesic disk with bounded l2 norm of a a is bounded at interior points provided that the w 1 p norm of its mean curvature is sufficiently small p 2 in doing this we generalize some renowned estimates on a for minimal surfaces

a modified prony algorithm for exponential function fitting a modification of the classical technique of prony for fitting sums of exponential functions to data is considered the method maximizes the likelihood for the problem unlike the usual implementation of prony s method which is not even consistent for transient signals proves to be remarkably effective in practice and is supported by an asymptotic stability result novel features include a discussion of the problem parametrization and its implications for consistency the asymptotic convergence proofs are made possible by an expression for the algorithm in terms of circulant divided difference operators

qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area we prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed riemannian manifolds in terms of their index and area restricting to the case where the hypersurface has dimension less than seven in particular we prove that if we are given a sequence of closed minimal hypersurfaces of bounded area and index the total curvature along the sequence is quantised in terms of the total curvature of some limit surface plus a sum of total curvatures of complete properly embedded minimal hypersurfaces in euclidean space all of which are finite thus we obtain qualitative control on the topology of minimal hypersurfaces in terms of index and area as a corollary

the space of minimal embeddings of a surface into a three dimensional manifold of positive ricci curvature in this paper we obtain a curvature estimate for embedded minimal surfaces in a three dimensional manifold of positive ricci curvature in terms of the geometry of the ambient manifold and the genus of the minimal surface it should be mentioned that there are two main points in our result one is the absence of a stability assumption and the other is the requirement of being embedded most known curvature estimates require the stability assumption and once the stability assumption is dropped many of these known results cease to be valid see ss and an for another example of a curvature estimate without the assumption of stability the embeddedness condition is rather subtle because of the way it enters in our proof our proof depends on the eigenvalue estimate and the area bound due to the first author and wang cw which require embeddedness in an essential way present knowledge indicates that closed embedded minimal surfaces in s 3 are rare while immersed surfaces are more plentiful for example only a finite number of minimal embeddings of a given genus are known on the other hand otsuki o constructed infinitely many immersed minimal tori with arbitrarily large area we obtain the curvature estimate indirectly by proving the smooth compactness theorem theorem 1 theorem 1 has many interesting consequences it shows that the set of conformal structures that can be realized on a minimal embedding in s 3 is a compact subset of the moduli space this is in contrast with the result of bryant b who showed that every riemann surface is conformally and minimally immersed in s 4 in view of our compactness result and the scarcity of examples it is very tempting to conjecture that there are only finitely many embedded minimal surfaces up to rigid motion in s 3 for each fixed genus throughout this paper manifold means manifold without boundary unless explictly stated otherwise when we say a sequence m i of surfaces converges to a

circulant matrices and differential delay equations on etudie les solutions periodiques non triviales de familles parametrisees d equations differentielles a retard

equal loudness level contours for pure tones equal loudness level contours provide the foundation for theoretical and practical analyses of intensity frequency characteristics of auditory systems since 1956 equal loudness level contours based on the free field measurements of robinson and dadson br j appl phys 7 166 181 1956 have been widely accepted however in 1987 some questions about the general applicability of these contours were published h fastl and e zwicker fortschritte der akustik daga 87 pp 189 193 1987 as a result a new international effort to measure equal loudness level contours was undertaken the present paper brings together the results of 12 studies starting in the mid 1980s to arrive at a new set of contours the new contours estimated in this study are compared with four sets of classic contours taken from the available literature the contours described by fletcher and munson j acoust soc am 5 82 108 1933 exhibit some overall similarity to our proposed estimated contours in the mid frequency range up to 60 phons the contours described by robinson and dadson exhibit clear differences from the new contours these differences are most pronounced below 500 hz and the discrepancy is often as large as 14 db

on the radial behavior of minimal surfaces and the uniqueness of their tangent cones suppose v is an m 1 dimensional minimal surface in r containing 0 as an isolated singular point what can one say about the structure of v near o this question initiated the present investigation and in certain special cases has a satisfactory answer 1 if one of the tangent cones to v at 0 is of the form 0 m where m is an m dimensional minimal submanifold of s and if also for each jacobi normal vectorfield z of m in sn 1 there is a one parameter family of minimal surfaces in s 1 having velocity z at m then 0 m is the unique tangent cone to v at 0 with v converging to 0 m for small radii r with rate rx it 0 2 in case m is the cartesian product of two standard spheres of appropriate radii then each jacobi vectorfield on m arises from isometric motions of sn 1 and the jacobi vectorfield hypothesis in 1 is satisfied this is shown in chapter 6 the uniqueness of tangent cones to one dimensional stationary varifolds with positive densities was shown in aa and the uniqueness of tangent cones to certain two dimensional area minimizing singular surfaces in r3 was shown by j taylor in tj1i tj2 tj3 also b white has shown such uniqueness for area minimizing hypersurfaces mod 4 in space dimen

the space of embedded minimal surfaces of fixed genus in a 3 manifold i estimates off the axis for disks this paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed riemannian 3 manifold the key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in r3 with the flat metric this study is undertaken here and completed in cm6 these local results are then applied in cm7 where we describe the general structure of fixed genus surfaces in 3 manifolds there are two local models for embedded minimal disks by an embedded disk we mean a smooth injective map from the closed unit ball in r2 into r3 one model is the plane or more generally a minimal graph the other is a piece of a helicoid in the first four papers of this series we will show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multi valued graph this will be done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase to prove that such a disk

on large volume preserving stable cmc surfaces in initial data sets let m g be a complete 3 dimensional asymptotically flat manifold with everywhere positive scalar curvature we prove that given a compact subset k subset m all volume preserving stable constant mean curvature surfaces of sufficiently large area will avoid k this complements the results of g huisken and s t yau and of j qing and g tian on the uniqueness of large volume preserving stable constant mean curvature spheres in initial data sets that are asymptotically close to schwarzschild with mass m gt 0 the analysis in g huisken and s t yau and in j qing and g tian takes place in the asymptotic regime of m here we adapt ideas from the minimal surface proof of the positive mass theorem by r schoen and s t yau and develop geometric properties of volume preserving stable constant mean curvature surfaces to handle surfaces that run through the part of m that is far from euclidean

an inequality between the exterior diameter and the mean curvature of bounded immersions this paper is a natural outgrowth of 9 where the problem of studying the boundedness properties of complete minimal surfaces in 1r was approached via the consideration of a certain gradient flow after the completion of 9 it was soon realized that the basic technique lemma 3 below could be successfully employed to study boundedness of arbitrary complete submanifolds in this regard the method can be used to prove the following three theorems

homoclinic orbits for nonlinear difference equations containing both advance and retardation in this paper we discuss how to use the critical point theory to study the existence of a nontrivial homoclinic orbit for nonlinear difference equations containing both advance and retardation without any periodic assumptions moreover if the nonlinearity is an odd function the existence of an unbounded sequence of homoclinic orbits is obtained

an introduction to induced loudness reduction induced loudness reduction ilr is a phenomenon by which a preceding higher level tone an inducer tone reduces the loudness of a lower level tone a test tone the strength of this effect depends on a number of parameters reviewed here some of the implications of ilr on loudness data are presented via the analysis of several studies in which ilr likely resulted in otherwise unexplained biases in data sets these results serve as examples of the pervasiveness of ilr in loudness measurements and indicate that it is necessary to consider ilr when designing any psychoacoustical experiment in which level varies