eigenvalue estimates for schrodinger operators with complex potentials we discuss properties of eigenvalues of non self adjoint schrodinger operators with complex valued potential v among our results are estimates of the sum of powers of imaginary parts of eigenvalue

pure tone threshold estimation from extrapolated distortion product otoacoustic emission i o functions in normal and cochlear hearing loss ears a new method for direct pure tone threshold estimation from input output functions of distortion product otoacoustic emissions dpoaes in humans is presented previous methods use statistical models relating dpoae level to hearing threshold including additional parameters e g age or slope of dpoae i o function here we derive a dpoae threshold from extrapolated dpoae i o functions directly cubic 2 f1 f2 distortion products and pure tone threshold at f2 were measured at 51 frequencies between f2 500 hz and 8 khz at up to ten primary tone levels between l2 65 and 20 db spl in 30 normally hearing and 119 sensorineural hearing loss ears using an optimized primary tone level setting l1 0 4l2 39 db that accounts for the nonlinear interaction of the two primaries at the dpoae generation site at f2 the pressure of the 2 f1 f2 distortion product pdp is a linear function of the primary tone level l2 linear regression yields correlation coefficients higher than 0 8 in the majority of the dpoae i o functions

bounds on complex eigenvalues and resonances we obtain bounds on the complex eigenvalues of non self adjoint schrodinger operators with complex potentials and also on the complex resonances of self adjoint schrodinger operators our bounds are compared with numerical results and are seen to provide useful information

multistep numerical integrators for time dependent vibrating systems abstract by means of the weighted residual method a general form of linear multistep methods is developed for time dependent vibrating systems and a feasible two step method is then obtained finally two examples are analyzed to show its applications to the initial value problems of time dependent systems and the steady state solution of periodically time dependent ones to the authors knowledge this is the first time that numerical methods for direct integration of the motion equations of time dependent vibrating systems have been deeply investigated

numerical analysis of dynamic problems an alternative integration abstract several applications of the well known fourth order runge kutta r k method for the time integration of the equations of motion in structural dynamics are presented the numerical solutions are compared with the analytical solution in order to examine the solution behaviour on successively refined meshes an interesting merit of the method lies in the fact that it can be implemented on personal computers

mechanism for bandpass frequency characteristic in distortion product otoacoustic emission generation it is commonly observed that the levels of the 2f1 f2 and the other mf1 nf2 m n 1 integer distortion product otoacoustic emissions dpoaes initially increase in level for fixed f2 as f1 f2 starting at f1 f2 and then begin to decrease when these dpoae levels are plotted as a function of either the distortion product frequency fdp or f2 f1 the curve has an approximate bandpass shape it has been hypothesized that this effect is due to 1 a second filter 2 suppression of distortion generation by the primary tones 3 reemission of distortion products from the distortion product place on the basilar membrane 4 the presence of an even order nonlinearity and 5 cancellation of the dpoae due to the vector addition of multiple sources of distortion product in this study distortion products were produced with f1 sweep conditions where there would be minimal vector cancellation of multiple dpoae sources it was observed that under this condition there is no or minimal bandpass shape of the dpo

a note on eigenvalue bounds for schrodinger operators abstract we obtain a new bound on the location of eigenvalues for a non self adjoint schrodinger operator with complex valued potentials by obtaining a weighted l 2 estimate for the resolvent of the laplacian

distortion product otoacoustic emission input output characteristics in normal hearing and hearing impaired human ears dpoae input output i o functions were measured at 7f2 frequencies 1 to 8 khz f2 f1 1 22 over a range of levels 5 to 95 db spl in normal hearing and hearing impaired human ears l1 l2 was level dependent in order to produce the largest 2f1 f2 responses in normal ears system distortion was determined by collecting dp data in six different acoustic cavities these data were used to derive a multiple linear regression model to predict system distortion levels the model was tested on cochlear implant users and used to estimate system distortion in all other ears at most but not all f2 s measurements in cochlear implant ears were consistent with model predictions at all f2 frequencies the ears with normal auditory thresholds produced i o functions characterized by compressive nonlinear regions at moderate levels with more rapid growth at low and high stimulus levels as auditory threshold increased dpoae threshold increased accompanied by dpoae amplitude reductions notably over the range of levels where normal ears showed compression the slope of the i o function was steeper in impaired ears the data from normal hearing ears resembled direct measurements of basilar membrane displacement in lower animals data from ears with hearing loss showed that the compressive region was affected by cochlear damage however responses at high levels of stimulation resembled those observed in normal ears

a simple criterion for the existence of nonreal eigenvalues for a class of 2d and 3d pauli operators abstract in this work we investigate the discrete spectrum generated by complex matrix valued perturbations for a class of 2d and 3d pauli operators with nonconstant magnetic fields we establish a simple criterion for the potentials to produce discrete spectrum near the low ground energy of the operators moreover in case of creation of nonreal eigenvalues this criterion specifies also their location

eigenvalue bounds for schrodinger operators with complex potentials iii laptev and safronov conjectured that any non positive eigenvalue of a schrodinger operator v in l 2 r with complex potential has absolute value at most a constant times v 2 2 for 0 2 in dimension 2 we prove this conjecture for radial potentials if 0 2 and we almost disprove it for general potentials if 1 2 2 in addition we prove various bounds that hold in particular for positive eigenvalues

eigenvalue bounds for dirac and fractional schrodinger operators with complex potentials abstract we prove lieb thirring type bounds for fractional schrodinger operators and dirac operators with complex valued potentials the main new ingredient is a resolvent bound in schatten spaces for the unperturbed operator in the spirit of frank and sabin 11

development of f2 f1 ratio functions in humans otoacoustic emissions oaes presumably represent active processes within the cochlea fundamental to frequency selectivity in peripheral auditory function maturation of the cochlear amplifier vis a vis frequency encoding or selectivity has yet to be fully characterized in humans the purpose of this study was to further investigate the maturation of features of the f2 f1 frequency ratio distortion product oae amplitude x f2 f1 ratio presumed to reflect cochlear frequency selectivity a cross sectional multivariate study was completed comparing three age groups pre term infants term infants and young adult subjects frequency ratio functions were analyzed at three f2 frequencies 2000 4000 and 6000 hz an analysis included an estimation of the optimal ratio or and a bandwidth like measure q3 analysis revealed significant interactions of age x frequency x gender for optimal ratio and a significant interaction of age x frequency for q3 consistent and statistically significant differences for

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

locus of generation for the 2 f1 f2 vs 2 f2 f1 distortion product otoacoustic emissions in normal hearing humans revealed by suppression tuning onset latencies and amplitude correlations the present study used distortion product otoacoustic emission dpoae suppression tuning curves stcs dpoae onset latencies ols and dpoae amplitude correlations to investigate the locus of generation of the 2 f1 f2 dpoae versus the 2 f2 f1 dpoae in humans the results of the tuning study revealed that for the 2 f1 f2 dpoae the tips of the stcs tuned consistently below the geometric mean gm frequency of the primary tones in contrast for the 2 f2 f1 dpoae stcs tuned above the gm of the primaries with 50 of the tip frequencies at or above the 2 f2 f1 frequency place when the average ratio of the 2 f2 f1 to the 2 f1 f2 tip frequencies was computed a factor of 1 44 provided an estimate of the frequency shift needed to align the two dpoae generation sites other results showed that ols for the 2 f2 f1 dpoae were uniformly shorter than those for the 2 f1 f2 with differences at the low frequencies amounting to as much as 6 7 ms further for both dpoaes curves describing latency decreases as

pseudomodes for schrodinger operators with complex potentials abstract for one dimensional schrodinger operators with complex valued potentials we construct pseudomodes corresponding to large pseudoeigenvalues we develop a first systematic non semi classical approach which results in a substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials including discontinuous ones applications of the present results to higher dimensional schrodinger operators are also discussed

accumulation of complex eigenvalues of a class of analytic operator functions for analytic operator functions we prove accumulation of branches of complex eigenvalues to the essential spectrum moreover we show minimality and completeness of the corresponding system of eig

a further look at newmark houbolt etc time stepping formulae this paper looks at some well known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved new forms are given of the general three parameter method introduced by zienkiewicz 1 some new one step methods are introduced these are of great practical importance because of the ease with which the size of time step can be changed

uniform resolvent estimates and absence of eigenvalues for lame operators with complex potentials abstract we consider the 0 order perturbed lame operator v x it is well known that if one considers the free case namely v 0 the spectrum of is purely continuous and coincides with the non negative semi axis the first purpose of the paper is to show that at least in part this spectral property is preserved in the perturbed setting precisely developing a suitable multipliers technique we will prove the absence of point spectrum for lame operator with potentials which satisfy a variational inequality with suitable small constant we stress that our result also covers complex valued perturbation terms moreover the techniques used to prove the absence of eigenvalues enable us to provide uniform resolvent estimates for the perturbed operator under the same assumptions about v

sources of variability in distortion product otoacoustic emissions the goal of this study was to determine the extent to which the variability seen in distortion product otoacoustic emissions dpoaes among ears with normal hearing could be accounted for several factors were selected for investigation including behavioral threshold differences in middle ear transmission characteristics either in the forward or the reverse direction and differences in contributions from the distortion and reflection sources these variables were assessed after optimizing stimulus parameters for individual ears at each frequency a multiple linear regression was performed to identify whether the selected variables either individually or in combination explained significant portions of variability in dpoae responses behavioral threshold at the f2 frequency and behavioral threshold squared at that same frequency explained the largest amount of variability in dpoae level compared to the other variables the combined model explained a small but significant amount of variance in dpoae level at five frequencies a large amount of residual variability remained even at frequencies where the model accounted for significant amounts of variance

the use of distortion product otoacoustic emission suppression as an estimate of response growth distortion product otoacoustic emission dpoae levels in response to primary pairs f2 2 or 4 khz l2 ranging from 20 to 60 db spl l1 0 4l2 39 db were measured with and without suppressor tones f3 which varied from 1 octave below to 12 octave above f2 in normal hearing subjects suppressor level l3 varied from 5 to 85 db spl dpoae levels were converted into decrements by subtracting the level in the presence of the suppressor from the level in the absence of a suppressor dpoae decrement vs l3 functions showed steeper slopes when f3 f2 this pattern is similar to other measurements of response growth such as direct measures of basilar membrane motion single unit rate level functions suppression of basilar membrane motion and discharge rate suppression from lower animals as l2 increased the l3 necessary to maintain 3 db of suppression increased at a rate of about 1 db db when f3 was approximately equal to f2 but increased more slowly when f3 f2 functions r

restriction theorems for orthonormal functions strichartz inequalities and uniform sobolev estimates we generalize the theorems of stein tomas and strichartz about surface restrictions of fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions we deduce the corresponding strichartz bounds for solutions to schr odinger equations up to the endpoint thereby solving an open problem of frank lewin lieb and seiringer we also prove uniform sobolev estimates in schatten spaces extending the results of kenig ruiz and sogge we finally provide applications of these results to a limiting absorption principle in schatten spaces to the well posedness of the hartree equation in schatten spaces to lieb thirring bounds for eigenvalues of schr odinger operators with complex potentials and to schatten properties of the scattering matrix

distortion product otoacoustic emission measured with continuously varying stimulus level distortion product otoacoustic emissions dpoae are measured by stimulating the ear with two simultaneous tones a novel method for measuring dpoaes has been developed in which the tone levels vary continuously instead of in discrete steps varying the tone levels continuously may offer advantages for characterizing dpoae level as a function of stimulus level for equivalent primary levels dpoae levels measured with the continuous level method were the same as levels obtained with the discrete level method thus validating the new method continuous level measurements were used to determine the optimal l1 for each l2 in individual subjects n 20 at f2 1 2 4 and 8 khz by using a lissajous path that covered a wide range of stimulus levels the optimal l1 defined as the l1 that resulted in the largest dpoae for each l2 varied across subjects and across frequency the optimal difference between l1 and l2 decreased with increasing l2 at all frequencies and increased with frequency when l2 was low whe

schrodinger operators with slowly decaying potentials several recent papers have obtained bounds on the distribution of eigenvalues of non self adjoint schrodinger operators and resonances of self adjoint operators in this paper we describe two new methods of obtaining such bounds when the potential decays more slowly than previously permitted

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

resolvent estimates and bounds on eigenvalues for dirac operators on the half line estimates for the eigenvalues of non self adjoint 1d dirac operators considered on the half line are obtained in terms of the l p norms of the potentials the proofs are based on the resolvent est

large time asymptotics of solutions to the kramers fokker planck equation with a short range potential in this work we use a scattering method to study the kramers fokker planck equation with a potential whose gradient tends to zero at the infinity for short range potentials in dimension three we show that complex eigenvalues do not accumulate at low energies and obtain the low energy resolvent asymptotics this combined with high energy pseudospectral estimates valid in more general situations gives the large time asymptotics of solutions in weighted l 2 spaces

spectral instability for some schrodinger operators we show that the condition numbers of isolated eigenvalues of typical non self adjoint differential operators such as the harmonic oscillator may be extremely large we describe a stable procedure for computing the condition numbers for schrodinger operators in one dimension and apply it to the complex resonances of a typical operator with a dilation analytic potential

analytic continuation and resonance free regions for sturm liouville potentials with power decay the analytic continuation of the jost solution into a sector of the unphysical sheet is established for analytic potentials with power decay the method also yields resonance free regions which in the case of super exponential decay are confirmed to be the best possible of their kind by the known asymptotic distribution of resonances

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

dependence of distortion product otoacoustic emissions on primary levels in normal and impaired ears i effects of decreasing l2 below l1 the 2f1 f2 distortion product otoacoustic emission dpoae is evoked by two primary tones of frequencies f1 f2 and levels l1 and l2 previous reports indicate that decreasing l2 below l1 l2 can 1 increase dpoae amplitude in normal ears and 2 increase the degree to which dpoae amplitudes are reduced by cochlear trauma although both of these factors could be advantageous for clinical applications of dpoaes neither has been explored in detail in the present study 2f1 f2 dpoae amplitude frequency functions were collected from normal and impaired ears of rabbits and humans with l1 l2 and with l2 l1 at each of three values of l1 in rabbits controlled tonal or noise overexposures were used to produce permanent reductions of dpoae amplitudes comparison of pre and postexposure dpoae amplitude frequency functions demonstrated that the frequency specific reductions of dpoaes were enhanced by decreasing l2 below l1 in humans dpoae amplitude frequency functions obtained with the various l1 and l2 c

level dependence of the nonlinear distortion component of distortion product otoacoustic emissions in humans distortion product otoacoustic emissions dpoaes emerge when presenting two primary tones with different frequencies f1 and f2 to the cochlea and are commonly used in diagnosis and research to evaluate the functional state of the cochlea optimal primary tone stimulus levels accounting for the different level dependencies of the traveling wave amplitudes of the two primary tones near the f2 tonotopic place on the basilar membrane are often used to maximize dpoae amplitudes however parameters defining the optimal levels can be affected by wave interference between the nonlinear distortion and coherent reflection components of the dpoae here the components were separated in the time domain using a pulsed stimulus paradigm and optimal levels determined based on the amplitude dependence of the nonlinear distortion components on primary tone stimulus levels level parameters yielding maximum dpoae amplitudes were derived for six normal hearing adults and compared to data recorded with continuous two tone stimulation the level parameters resulting from analysis of the nonlinear distortion components show dependence on stimulus frequency and small standard deviations dpoae input output functions derived for optimal levels exhibit larger slopes wider dynamic range and less variability across subjects than those derived for conventional stimulus and analysis conditions potentially increasing their reliability and sensitivity for assessing cochlea function

influence of primary frequencies ratio on distortion product otoacoustic emissions amplitude i intersubject variability and consequences on the dpoae gram distortion product otoacoustic emissions dpoaes are used widely in humans to assess cochlear function the standard procedure consists of recording the 2f1 f2 dpoae amplitude as a function of the f2 frequency using a fixed f2 f1 ratio dpoae gram close to 1 20 dpoae amplitude as recorded in the dpoae gram shows a wide range of values in normal hearing subjects which can impair the predictive value of the dpoae gram for hearing thresholds this study is aimed at comparing intersubject variability in 2f1 f2 dpoae amplitude according to three paradigms a fixed f2 f1 ratio such as the dpoae gram a variable ratio dpoae gram f2 f1 adapted to frequency and an optimum dpoae gram where the f2 f1 is adapted both to subject and frequency the 2f1 f2 dpoae amplitude has been investigated on 18 normally hearing subjects at ten different f2 frequencies from 0 75 to 6 khz using an f2 fixed f1 sweep paradigm and allowed to define for each frequency the f2 f1 ratio giving the greatest 2f1 f2 dpoae amplitude or optimum ratio results showed a large intersubject variability of the optimum ratio especially at frequencies below 1 5 khz and a significant decrease of the optimum ratio with frequency the optimum dpoae gram was underestimated by up to 5 8 db on average up to 14 9 db for an individual subject by the fixed ratio dpoae gram and by up to 3 db on average up to 10 6 db for an individual subject by the variable ratio dpoae gram intersubject variability was slightly but significantly reduced in the optimum dpoae gram versus the fixed ratio dpoae gram lastly correlations between tone burst evoked otoacoustic emission tboae amplitudes and maximum dpoae amplitudes were significantly greater than correlations between tboae amplitudes and fixed ratio dpoae amplitudes

is it necessary to penalize impulsive noise 5 db due to higher risk of hearing damage it is studied whether the 5 db penalty for impulsiveness established by iso 1999 1990 accounts for a higher risk of noise induced hearing loss a total of 16 normal hearing human subjects were exposed for 10 min to two types of binaural industrial recordings 1 a continuous broad band noise normalized to lex 8 h 80 dba and 2 the combination of the previous stimulus with an impulsive noise normalized to lex 8 h 75 5db penalty 80 dba peak level 117 dbc and repetition rate of 0 5 impacts per second distortion product otoacoustic emissions dpoaes were measured in a broad frequency range before and in the following 90 min after the exposure the group results show that the continuous exposure had a bigger impact on dpoae levels with a maximum dpoae shift of approximately 5 db in the frequency range of 2 3 15 khz during the first 10 min of the recovery no evident dpoae shift is seen for the impulsive continuous stimulus the results indicate that the penalty overestimated the effects on dp

improved eigenvalue bounds for schrodinger operators with slowly decaying potentials we extend a result of davies and nath j comput appl math 148 1 1 28 2002 on the location of eigenvalues of schrodinger operators with slowly decaying complex valued potentials to higher dimensions in this context we also discuss various examples related to the laptev and safronov conjecture laptev and safronov in commun math phys 292 1 29 54 2009

level dependence of distortion product otoacoustic emissions measured at high frequencies in humans given that high frequency hearing is most vulnerable to cochlear pathology it is important to characterize distortion product otoacoustic emissions dpoaes measured with higher frequency stimuli in order to utilize these measures in clinical applications the purpose of this study was to explore the dependence of dpoae amplitude on the levels of the evoking stimuli at frequencies greater than 8 khz and make comparisons with those data that have been extensively measured with lower frequency stimuli to accomplish this dpoae amplitudes were measured at six different f2 frequencies 2 5 10 12 14 and 16 khz with a frequency ratio f2 f1 of 1 2 at five fixed levels 30 to 70 db spl of one primary either f1 or f2 while the other primary was varied in level 30 to 70 db spl generally the level separation between the two primary tones l1 l2 generating the largest dpoae amplitude referred to as the optimal level separation decreased as the level of the fixed primary increased additional

interpretation of distortion product otoacoustic emission measurements i two stimulus tones the interpretation of common but poorly understood observed characteristics of distortion product emissions is assisted by the development of a simple model this model essentially includes only saturation of the cochlear amplifier with emissions arising naturally from the same nonlinear processes which cause the saturation the model provides useful physical explanations of emission behavior particularly considered as a function of the stimulus intensities of the two primaries i e behavior with fixed stimulus frequencies it is assumed that emission generation consists of two main components which are always present in the total emission but which most often have approximately opposite i e canceling phases one component arises in a small region centered about the peak of the emission generation function while the other arises from the region basal to this peak at low stimulus levels with normal cochlear amplifier operation the peak of the emission generation function is sharp so the emission from the peak region dominates the total emission this peak emission has typically been characterized as the active emission at high stimulus levels where saturation is important or at all levels when the gain of the cochlear amplifier is reduced the summed basal component dominates the total emission the characteristics of this basal emission are similar to and continuous with the characteristics of the truly passive emission i e the emission observed when the cochlear amplifier gain is identically zero under circumstances when the emissions from the peak and basal components are approximately equal there is seen a sharp notch characteristic of phase cancellation the simple model produces emission distributions as a function of independent variation of the two stimulus amplitudes which are in good agreement with observation it is shown that the furosemide assay provides a good estimate of cochlear amplifier gain when a correction factor of about 10 db is added however when using two stimulus tones neither absolute emission amplitudes or emission input output functions or the furosemide assay can adequately distinguish between cases of moderate versus poor cochlear amplifier dysfunction when the cochlear amplifier gains are in the range from about half normal to zero