w2 p estimates for fully nonlinear elliptic equations with oblique boundary conditions abstract we study fully nonlinear elliptic equations with oblique boundary conditions we obtain a global w 2 p estimate n 0 p for viscosity solutions of such problems when the boundary of the domain is in c 2 for every 0 1

generalized information entropy analysis of financial time series abstract generalized information entropy has been widely applied to analyzing complex systems in this paper we propose the weighted multiscale renyi permutation entropy mswrpe based on the weight assigned to each vector as a novel technique to consider the amplitude information renyi permutation entropy rpe has a parameter q for non extensivity compared to shannon permutation entropy pe hence we speculate that rpe has a better sensitivity to patterns extracted from signals containing amplitude information and a better robustness to noise compared to pe firstly we perform the multiscale renyi permutation entropy msrpe and mswrpe methods on synthetic data we find that mswrpe suits better signals containing considerable amplitude information and is successful to consider the multiple time scales inherent in the financial systems the finding is also verified in four different stock markets then we make a comparison between mswrpe and weighted multiscale permutation entropy mswpe on different stock markets the conclusion is that the mswrpe method has a better characterization than mswpe for q 1 different markets have the same law on mswrpe while hsi can be distinguished from the other markets for q 1 which is more obvious when m 7

evidence for two discrete sources of 2f1 f2 distortion product otoacoustic emission in rabbit i differential dependence on stimulus parameters the results of studies of the physiological vulnerability of distortion product otoacoustic emissions dpoaes suggest that the dpoae at 2f1 f2 in vertebrate ears is generated by more than one source the principal aims of the present study were to provide independent evidence for the existence of more than one dpoae source and to determine the contributions of each to the ear canal 2f1 f2 signal to accomplish these aims specific stimulus parameters were separately and systematically varied to provide detailed parametric information regarding 2f1 f2 dpoae amplitude and phase in normal ears of awake rabbits the findings indicate that two discrete sources demonstrating differential dependence on stimulus parameters dominate the generation of the 2f1 f2 dpoae one source of distortion is dominant above 60 70 db spl at moderate primary frequency separations and at all stimulus levels when the primary tones are closely spaced the other source is dominant below 60 70 db spl at moderate primary frequency

the mathematical analysis of the structure of some songs abstract the mathematical structures of six songs were studied by treating them as complex systems the studies were based on i scattering diagram ii spiral structure iii graph theory and animal diagrams and iv entropy and organization in i the fractal dimension and the radius of gyration was determined for each melody in ii it was shown that the total number of notes used in a song display a spiral which can be expressed by a mathematical equation in iii the animal diagram was obtained by using the pathways between the consecutive notes of the song a ratio defined as the number of edges to the total number of unit edge for the animal diagram was used as a parameter to characterize a melody in iv the entropy the maximum entropy and the negentropy or the organization of the songs were determined in addition the rate of change of organization of the songs was also determined

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

intensive entropic non triviality measure abstract we discuss a way of characterizing probability distributions complementing that provided by the celebrated notion of information measure with reference to a measure of complexity that we call a nontriviality measure our starting point is the lmc measure of complexity advanced by lopez ruiz et al phys lett a 209 1995 321 and its analysis by anteneodo and plastino phys lett a 223 1997 348 an improvement of some of their troublesome characteristics is thereby achieved basically we replace the euclidean distance to equilibrium by the jensen shannon divergence the resulting measure turns out to be i an intensive quantity and ii allows one to distinguish between different degrees of periodicity we apply the cured measure to the logistic map so as to clearly exhibit its advantages

characterization of time series via renyi complexity entropy curves abstract one of the most useful tools for distinguishing between chaotic and stochastic time series is the so called complexity entropy causality plane this diagram involves two complexity measures the shannon entropy and the statistical complexity recently this idea has been generalized by considering the tsallis monoparametric generalization of the shannon entropy yielding complexity entropy curves these curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature here we further explore these complexity entropy curves in the context of the renyi entropy which is another monoparametric generalization of the shannon entropy by combining the renyi entropy with the proper generalization of the statistical complexity we associate a parametric curve the renyi complexity entropy curve with a given time series we explore this approach in a series of numerical and experimental applications demonstrating the usefulness of this new technique for time series analysis we show that the renyi complexity entropy curves enable the differentiation among time series of chaotic stochastic and periodic nature in particular time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points whereas curves related to chaotic phenomena have a negative curvature finally periodic time series are represented by vertical straight lines

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

characterizing time series via complexity entropy curves the search for patterns in time series is a very common task when dealing with complex systems this is usually accomplished by employing a complexity measure such as entropies and fractal dimensions however such measures usually only capture a single aspect of the system dynamics here we propose a family of complexity measures for time series based on a generalization of the complexity entropy causality plane by replacing the shannon entropy by a monoparametric entropy tsallis q entropy and after considering the proper generalization of the statistical complexity q complexity we build up a parametric curve the q complexity entropy curve that is used for characterizing and classifying time series based on simple exact results and numerical simulations of stochastic processes we show that these curves can distinguish among different long range short range and oscillating correlated behaviors also we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed we further test this technique in experimental scenarios related to chaotic laser intensity stock price sunspot and geomagnetic dynamics confirming its usefulness finally we prove that these curves enhance the automatic classification of time series with long range correlations and interbeat intervals of healthy subjects and patients with heart disease

complexity entropy causality plane a useful approach for distinguishing songs nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies this is particularly true when dealing with music databases in this context it is essential to have techniques and tools able to discriminate properties from these massive sets in this work we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure building up the complexity entropy causality plane the results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs additionally we believe that the here reported method may be applied in practical situations since it is simple robust and has a fast numerical implementation

self similarity of the 1 f noise called music abstract suggestions have been made that computer musicians should attempt to compose fractal music and questions have been raised whether there is such a thing as fractal music voss and clark observed that music is scaling or 1 f noise as analyzed on the basis of the amplitude loudness of the audio signals they failed to find a fractal distribution of acoustic frequencies music notes in music analyzing bach s and mozart s compositions we have shown that the incidence of the frequency intervals or of the changes of acoustic frequency has a fractal geometry fractal phenomena are characterized by scale independency the purpose of this investigation is to demonstrate the self similarity of music and to explore its implications

the calderon zygmund property for quasilinear divergence form equations over reifenberg flat domains abstract the results by palagachev 2009 3 regarding global holder continuity for the weak solutions to quasilinear divergence form elliptic equations are generalized to the case of nonlinear terms with optimal growths with respect to the unknown function and its gradient moreover the principal coefficients are discontinuous with discontinuity measured in terms of small b m o norms and the underlying domain is supposed to have fractal boundary satisfying a condition of reifenberg flatness the results are extended to the case of parabolic operators as well

correlations in a mozart s music score k 73x with palindromic and upside down structure abstract in this work we study long range correlations in a scherzo duetto di mozart score k 73x for two violins this is a fascinating piece as the second violin part is upside down on the same sheet below the first violin and some parts are like a palindrome given such ingenious structure it is expected the existence of long range correlations in the score structure in order to quantify long range correlations we considered the music score as a sequence of integer numbers each of them corresponding to last common denominator units of note by using detrended fluctuation analysis dfa correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note the following conclusions can be drawn from the analysis a for about 10 25 neighbor note distances correlations are similar to 1 f noise this is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1 f noise b as the neighbor note distance increases the long range correlations decays continuously for some score sections the music score behaves like non correlated i e purely random noise summing up the results show that the studied mozart s score contains a certain degree of correlation for relatively small note distances and becomes close to non correlated behavior for long note distances we considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins interestingly for relatively small neighbor note distances a scaling behavior similar to that found for individual violins is also displayed in some sense this is an expression of the specific structure palindromes plus upside down construction used by mozart in the composition of this music score although we focused on a particular high art music score our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques

global morrey regularity of strong solutions to the dirichlet problem for elliptic equations with discontinuous coefficients abstract well posedness is proved in the space w2 p w1 p0 for the dirichlet problem equation omitted if the principal coefficients aij x of the uniformly elliptic operator belong to vmo l

hessian estimates in weighted lebesgue spaces for fully nonlinear elliptic equations abstract we prove global regularity in weighted lebesgue spaces for the viscosity solutions to the dirichlet problem for fully nonlinear elliptic equations as a consequence regularity in morrey spaces of the hessian is derived as well

global holder continuity of weak solutions to quasilinear divergence form elliptic equations abstract we derive global holder regularity for the w 0 1 2 weak solutions to the quasilinear uniformly elliptic equation div a i j x u d j u a i x u a x u d u 0 over a c 1 smooth domain r n n 2 the nonlinear terms are all of caratheodory type with coefficients a i j x u belonging to the class vmo of functions with vanishing mean oscillation with respect to x while a i x u and a x u d u exhibit controlled growths with respect to u and the gradient du

weighted regularity estimates in orlicz spaces for fully nonlinear elliptic equations abstract in this paper we develop a global w 2 p estimate for the viscosity solution of the dirichlet problem of fully nonlinear elliptic equations f d 2 u d u u x f x in u 0 on to a more general function space given an n function and a muckenhoupt weight w we prove that if f belongs to the associated weighted orlicz space l w then d 2 u l w and u satisfies a global w w 2 estimate under a minimal regularity requirement on f in the variable x and a basic geometric assumption on the correct condition on the couple and w is also addressed this result generalizes the w 2 p estimate caffarelli 1989 escauriaza 1993 winter 2009 of calderon and zygmund as well as an analogous one byun et al 2016 in the weighted l p setting

lp λ regularity for fully nonlinear elliptic equations abstract we establish the variable exponent morrey spaces l p estimate to the dirichlet problem for fully nonlinear elliptic equations on a c 1 1 bounded domain for variable exponents p and

weighted permutation entropy based on different symbolic approaches for financial time series abstract in this paper we introduce weighted permutation entropy wpe and three different symbolic approaches to investigate the complexities of stock time series containing amplitude coded information and explore the influence of using different symbolic approaches on obtained wpe results we employ wpe based on symbolic approaches to the us and chinese stock markets and make a comparison between the results of us and chinese stock markets three symbolic approaches are able to help the complexity containing in the stock time series by wpe method drop whatever the embedding dimension is the similarity between these stock markets can be detected by the wpe based on binary coding method while the difference between them can be revealed by the wpe based on method max min method the combinations of the symbolic approaches method and max min method and wpe method are capable of reflecting the multiscale structure of complexity by different time delay and analyze the differences between complexities of stock time series in more detail and more accurately furthermore the correlations between stock markets in the same region and the similarities hidden in the s p500 and dji shangzheng and shencheng are uncovered by the comparison of the wpe based on binary coding method of six stock markets

generalized entropy plane based on large deviations theory for financial time series abstract complexity entropy causality plane analysis and large deviations spectrums theory are proposed to study time series the entropy plane analysis depicts the complexity of a system in two dimensional plane while large deviations theory shows the spectral structure of time series in the way of multifractal in this paper we combine the characteristics of these two popular methods and propose a generalized entropy plane model based on the large deviation theory the methodology is applied to both synthetic data and financial markets we discuss the impact of the parameters on the results in detail besides the modified model can distinguish different time series meanwhile we compare our results with the original complexity entropy causality plane and large deviations spectrums and the consistency of these results is confirmed the method can provide abundant dynamical properties of complex systems

generalized entropy plane based on permutation entropy and distribution entropy analysis for complex time series abstract entropy is an accessible way to work as a measure of the irregularity and the uncertainty between the predicting knowledge and the given time series statistical complexity measure scm combining shannon entropy and the extensive jensen shannon divergence provides important additional information regarding the peculiarities of the underlying probability distribution not already detected by the entropy in this paper we extend the traditional complexity entropy causality plane which applies the diagram of scm versus normalized shannon entropy to two generalized complexity entropy plane based on permutation entropy pe and permuted distribution entropy pedisen moreover as the important extension of the shannon entropy the tsallis entropy and renyi entropy are used to construct the plane we discuss the parameter selection for the pe plane and pedisen plane respectively outlier detection is recently a heated point focusing on discovering patterns that occur infrequently in the time series in data mining however there exists few entropy plane based methods in outlier detection we apply the proposed procedure to the real world data for outlier detection it turns out that the generalized entropy plane is robust to the type of original series and is efficient for detecting outliers

distortion product otoacoustic emission 2 f1 f2 amplitude as a function of f2 f1 frequency ratio and primary tone level separation in human adults and neonates distortion product otoacoustic emission dpoae 2 f1 f2 amplitude is dependent upon both the frequency ratio and level separation of the eliciting primary tones in adults it has been established that on average a f2 f1 ratio of 1 22 is optimal for evoking the most robust dpoae dpoae amplitude is systematically reduced when f2 f1 ratio is either increased or decreased thus forming a bandpass function harris et al 1989 the frequency ratio function dpoae amplitude f2 f1 ratio is thought to reflect the filtering properties of the cochlea allen and fahey 1993 brown et al 1993 primary tone level separation also influences dpoae amplitude with a 10 to 15 db level difference between the primary tones l1 l2 typically generating largest amplitude in adults equivalent studies have not been conducted in neonates the present study evoked the 2 f1 f2 dpoae in adults term and premature neonates to define the optimal f2 f1 ratio and l1 l2 level separation and to investigate the filtering prope

the behavior of the acoustic distortion product 2f1 f2 from the human ear and its relation to auditory sensitivity the acoustic intermodulation distortion product 2f1 f2 adp was measured in human subjects to investigate 1 the dependence of adp level on stimulus parameters and 2 the relationship between adp level and auditory sensitivity the frequency ratio f2 f1 at which adp level is maximal varies only slightly across frequency and subjects the average optimal ratio is 1 225 beyond the maximum the adp level declines with increasing f2 f1 ratio at rates of up to 250 db oct as the level of one stimulus is increased relative to the other the adp grows saturates and in most cases shows a bendover maximum distortion is generated when l 1 exceeds l 2 growth rate and saturation point are dependent on which stimulus is incremented and on the level of the stationary stimulus with optimal stimulus parameters levels below 60 db spl l 1 greater than l 2 by 15 db f2 f1 1 225 adp levels are commonly 30 db below l 2 patterns of adp level across frequency vary between subjects but are repeatable within each subject as the frequency of one or both of the stimuli is varied changes in adp level exhibit a broadly featured pattern with a fine structure superimposed upon it this fine structure was compared with the features in the stimulus frequency emission spectrum in one subject with appropriate stimulus parameters half of our subjects show a statistically significant correlation across frequency between adp level and auditory sensitivity at the corresponding f1 frequency our results suggest that with low levels of stimulation adp measurements could form the basis of an objective measure of cochlear function in human subjects

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

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

quasilinear elliptic equations with vmo coefficients strong solvability and uniqueness in sobolev space w2 cl are proved for the dirichlet problem a j x u djju b x u du 0 a e i2 u p on d l it is assumed that the coefficients of the quasilinear elliptic operator satisfy caratheodory s condition the a i s are vmo functions with respect to x and structure conditions on b are required the main results are derived by means of the aleksandrov pucci maximum principle and leray schauder s fixed point theorem via a priori estimate for the 7 2 norm of the gradient

the influence of systematic primary tone level variation l2 l1 on the acoustic distortion product emission 2f1 f2 in normal human ears the purpose of the present study was to determine the effect of primary tone level variation l2 l1 on the amplitude of distortion product otoacoustic emissions dpoaes the dpoae at the frequency 2f1 f2 f2 f1 was measured in 20 ears of ten normally hearing subjects acoustic distortion products were generated by primaries f1 and f2 with geometric mean frequencies of 1 2 and 4 khz the f2 f1 ratios were 1 25 1 khz 1 23 2 khz and 1 21 4 khz the primary tone level l1 was kept constant at either 65 or 75 db spl while the second primary tone level l2 was varied between 20 and 90 db spl in 5 db steps the level differences l2 l1 generating maximal dpoae amplitudes depended on l1 and on the geometric mean frequency of f1 and f2 there were large interindividual differences overall the l2 l1 evoking maximal mean dpoae amplitudes was 10 db for geometric mean frequencies of 1 and 2 khz with both l1 65 db spl and l1 75 db spl for 4 khz l2 l1 was 5 db with l1 65 db spl and 0 db with l1 75 db sp

applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients the paper concerns dirichlet s problem for second order quasilinear non divergence form elliptic equations with discontinuous coefficients we start with suitable structure growth and regularity conditions ensuring solvability of the problem under consideration fixing then a solution u 0 such that the linearized at u 0 problem is non degenerate we apply the implicit function theorem as a result we get that for all small perturbations of the coefficients there exists exactly one solution u u 0 which depends smoothly in w 2 p with p larger than the space dimension on the data for that no structure and growth conditions are needed and the perturbations of the coefficients can be general l functions of the space variable x moreover we show that the newton iteration procedure can be applied in order to obtain a sequence of approximate in w 2 p solutions for u 0

the maximum principle for viscosity solutions of fully nonlinear second order partial differential equations we prove that viscosity solutions in w1 of the second order fully nonlinear equation f d2u du u 0 are unique when i f is degenerate elliptic and decreasing in u or ii f is uniformly elliptic and nonincreasing in u we do not assume that f is convex the method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions respectively this method is completely different from that used in lions 8 9 for second order problems with f convex in d 2 u and from that used by crandall lions 3 and crandall evans lions 2 for fully nonlinear first order problems

gas liquid two phase flow structure in the multi scale weighted complexity entropy causality plane abstract the multi scale weighted complexity entropy causality plane ms wcecp is proposed for characterizing the physical structure of complex system firstly we use the method to investigate typical nonlinear time series compared with the multi scale complexity entropy causality plane ms cecp the ms wcecp can not only uncover the dynamic information loss of complex system with the increase of scale but also can characterize the complexity of nonlinear dynamic system in particular the algorithm of ms wcecp performs strong anti noise ability then we calculate the ms wcecp for the conductance fluctuating signals measured from vertical upward gas liquid two phase flow experiments in a small diameter pipe the results demonstrate that the ms wcecp is a useful approach for exploring the stability and complexity in gas liquid two phase flows

universality in the tail of musical note rank distribution abstract although power laws have been used to fit rank distributions in many different contexts they usually fail at the tails languages as sequences of symbols have been a popular subject for ranking distributions and for this purpose music can be treated as such here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution which arises in the ranking of multiplicative stochastic processes the parameters a and b are obtained for classical jazz and rock music revealing interesting features specially we have obtained a clear trend in the values of the parameters for major and minor tonal modes finally we discuss the distribution of notes for each octave and its connection with the ranking of the notes

comparison of nine methods to estimate ear canal stimulus levels the reliability of nine measures of the stimulus level in the human ear canal was compared by measuring the sensitivity of behavioral hearing thresholds to changes in the depth of insertion of an otoacoustic emission probe four measures were the ear canal pressure the eardrum pressure estimated from it and the pressure measured in an ear simulator with and without compensation for insertion depth the remaining five quantities were derived from the ear canal pressure and the thevenin equivalent source characteristics of the probe forward pressure initial forward pressure the pressure transmitted into the middle ear eardrum sound pressure estimated by summing the magnitudes of the forward and reverse pressure integrated pressure and absorbed power two sets of behavioral thresholds were measured in 26 subjects from 0 125 to 20 khz with the probe inserted at relatively deep and shallow positions in the ear canal the greatest dependence on insertion depth was for transmitted pressure and absorbed power the measures with the least dependence on insertion depth throughout the frequency range best performance included the depth compensated simulator eardrum forward and integrated pressures among these forward pressure is advantageous because it quantifies stimulus phase

local holder regularity of the gradients for the elliptic p x laplacian equation abstract in this paper we obtain the interior holder regularity of the gradients of weak solutions for the elliptic p x laplacian equation div a u u p x 2 2 a u div f p x 2 f under some proper assumptions on the holder continuous functions p f and a

solvability of uniformly elliptic fully nonlinear pde we get existence uniqueness and non uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the hamilton jacobi bellman isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness some of our results are new even for equations in divergence form

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

on viscosity solutions of fully nonlinear equations with measurable ingredients we study fully nonlinear uniformly elliptic equations with measurable ingredients caffarelli s recent work on w2 p estimates for viscosity solutions has led to significant progress in this area here we present a unified treatment of this theory based on an appropriate notion of viscosity solution for instance it is shown that strong solutions are viscosity solutions that viscosity solutions are twice differentiable a e and that the pointwise derivatives satisfy the equation a e an important consequence of our approach is the possibility of passage to various kinds of limits in fully nonlinear equations this extends results of this type due to evans and krylov our work is to some extent expository the main purpose being to provide an easily accessible set of tools and techniques to study equations with measurable ingredients 1996 john wiley sons inc

multifractal analyses of music sequences multifractal analysis is applied to study the fractal property of music in this paper a method is proposed to transform both the melody and rhythm of a music piece into individual sets of distributed points along a one dimensional line the structure of the musical composition is thus manifested and characterized by the local clustering pattern of these sequences of points specifically the local holder exponent and the multifractal spectrum are calculated for the transformed music sequences according to the multifractal formalism the observed fluctuations of the holder exponent along the music sequences confirm the non uniformity feature in the structures of melodic and rhythmic motions of music our present result suggests that the shape and opening width of the multifractal spectrum plot can be used to distinguish different styles of music in addition a characteristic curve is constructed by mapping the point sequences converted from the melody and rhythm of a musical work into a two dimensional graph each different pieces of music has its own unique characteristic curve this characteristic curve which also exhibits a fractal trait unveils the intrinsic structure of music

generalized statistical complexity measures geometrical and analytical properties abstract we discuss bounds on the values adopted by the generalized statistical complexity measures m t martin et al phys lett a 311 2003 126 p w lamberti et al physica a 334 2004 119 introduced by lopez ruiz et al phys lett a 209 1995 321 and shiner et al phys rev e 59 1999 1459 several new theorems are proved and illustrated with reference to the celebrated logistic map

comparing the optimal signal conditions for recording cubic and quadratic distortion product otoacoustic emissions odd and even order distortion products dps evoked by two primary tones f1 f2 f1 f2 represent different aspects of cochlear nonlinearity the cubic and quadratic difference tones cdt 2f1 f2 and qdt f2 f1 are prominent representatives of the odd and even dps distortion product otoacoustic emissions dpoaes were measured within a primary level l1 l2 space over a wide range of f2 f1 ratios to compare the optimal signal conditions for these dps for cdt the primary level difference decreased as l1 increased with a rate proportional to the f2 f1 ratio moreover the optimal ratio increased with l1 a set of two formulas is proposed to describe the optimal signal conditions however for a given level of a primary increasing the other tone level could maximize the qdt amplitude the frequency ratio at the maximal qdt was about 1 3 and quite constant across different primary levels a notch was found in the qdt amplitude at the f2 f1 ratio of about 1 22 1 25 these opposite behaviors suggest that the optimal recording conditions are different for cdt and qdt due to the different aspects in the cochlear nonlinearity optimizing the dpoae recordings could improve the reliability in clinical or research practices

quasilinear parabolic operators with discontinuous ingredients let q 0 t r n 1 be a cylinder of height t 0 and c1 1 smooth base unique strong solvability in the sobolev spaces wq2 1 q q n 2 is proved for oblique derivative boundary value problem for quasilinear nondivergence form strictly parabolic equation with vanishing mean oscillation coefficients ut aij x t u diju f x t u du a e in q where aij and f are caratheodory s functions an essential step of our investigations is deriving of suitable a priori estimates for the solution and its spatial gradient which makes possible the application of leray schauder s fixed point theorem

on the regularity theory of fully nonlinear parabolic equations ii recently m crandall and p l lions 3 developed a very successful method for proving the existence of solutions of nonlinear second order partial differential equations their method called the theory of viscosity solutions also applies to fully nonlinear equations in which even the second order derivatives can enter in nonlinear fashion solutions produced by the viscosity method are guaranteed to be continuous but not necessarily smooth here we announce smoothness results for viscosity solutions our methods extend those of 1 we obtain krylov safonov i e c estimates 8 c 1 schauder c and w estimates for viscosity solutions of uniformly parabolic equations in general form the results can be viewed as a priori estimates on the classical c solutions our method produces in particular regularity results for a broad new array of nonlinear heat equations including the bellman equation 6

lorentz estimates for fully nonlinear parabolic and elliptic equations abstract we prove an interior lorentz estimate of the hessian of strong solutions to fully nonlinear parabolic equations u t f d 2 u x t f x t and elliptic equations f d 2 u x f x respectively here we assume that the associated nonlinearities satisfy uniformly parabolic condition or ellipticity certain growth condition and the r vanishing condition we establish lorentz estimates for such fully nonlinear equations based on the approach of the large m inequality principle introduced by acerbi mingione

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

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

nondivergence elliptic and parabolic problems with irregular obstacles we prove the natural weighted calderon and zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irregular obstacles we also obtain morrey regularity results for the hessian of the solutions and holder continuity of the gradient of the solutions

2 solvability of the dirichlet problem for nondivergence elliptic equations with vmo coefficients we prove a well posedness result in the class w 2 p w 0 1 p for the dirichlet problem lu f a e in u 0 on we assume the coefficients of the elliptic nondivergence form equation that we study are in vmo l

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

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

permutation information theory approach to unveil delay dynamics from time series analysis in this paper an approach to identify delay phenomena from time series is developed we show that it is possible to perform a reliable time delay identification by using quantifiers derived from information theory more precisely permutation entropy and permutation statistical complexity these quantifiers show clear extrema when the embedding delay of the symbolic reconstruction matches the characteristic time delay s of the system numerical data originating from a time delay system based on the well known mackey glass equations operating in the chaotic regime were used as test beds we show that our method is straightforward to apply and robust to additive observational and dynamical noise moreover we find that the identification of the time delay is even more efficient in a noise environment our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity

fractal geometry of music abstract music critics have compared bach s music to the precision of mathematics what mathematics and what precision are the questions for a curious scientist the purpose of this short note is to suggest that the mathematics is at least in part mandelbrot s fractal geometry and the precision is the deviation from a log log linear plot

music walk fractal geometry in music abstract in this study sequences of musical notes from various pieces of music are converted into one variable random walks here termed music walks quantitative measurements of the properties of each musical composition are then performed by applying hurst exponent and fourier spectral analyses on these music walk sequences our results show that music shares the similar fractal properties of a fractional brownian motion fbm that is music displays an anti persistent trend in its tone changes melody over decades of musical notes and music sequence exhibits generally the 1 f type spectrum fractal property with apparently two different values in two different temporal scales