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

otoacoustic emissions from normal hearing and hearing impaired subjects distortion product responses distortion product otoacoustic emissions dpoae were measured in normal hearing and hearing impaired human subjects analyses based on decision theory were used to evaluate dpoae test performance specifically relative operating characteristic roc curves were constructed and the areas under these curves were used to estimate the extent to which normal and impaired ears could be correctly identified by these measures dpoae amplitude and dpoae noise measurements were able to distinguish between normal and impaired subjects at 4000 8000 and to a lesser extent at 2000 hz the ability of these measures to distinguish between groups decreased however as frequency and audiometric criterion used to separate normal and hearing impaired ears decreased at 500 hz performance was no better than chance regardless of the audiometric criterion for normal hearing cumulative distributions of misses hearing impaired ears incorrectly identified as normal hearing and false alarms normal hearing ears identified as hearing impaired were constructed and used to evaluate test performance for a range of hit rates i e the percentage of correctly identified hearing impaired ears depending on the desired hit rate criterion values of 5 to 12 db spl for dpoae amplitudes and 8 to 15 db for dpoae noise accurately distinguished normal hearing ears from those with thresholds greater than 20 db hl for the two frequencies at which performance was best 4000 and 8000 hz it would appear that dpoae measurements can be used to accurately identify the presence of high frequency hearing loss but are not accurate predictors of hearing status at lower frequencies at least for the conditions of the present measurements

hybrid measurement of auditory steady state responses and distortion product otoacoustic emissions using an amplitude modulated primary tone a maximum auditory steady state response assr amplitude is yielded when the assr is elicited by an amplitude modulated tone f c with a fixed modulation frequency f m 40 hz whereas the maximum distortion product otoacoustic emission dpoae level is yielded when the dpoae is elicited using a fixed frequency ratio of the primary tones f2 f1 1 2 when eliciting the dpoae and assr by the same tone pair optimal stimulation is present for either dpoae or assr and thus adequate simultaneous dpoae assr measurement is not possible across test frequency f2 or f c respectively the purpose of the present study was to determine whether the assr and dpoae can be measured simultaneously without notable restrictions using a dpoae stimulus setting in which one primary tone is amplitude modulated a dpoae of frequency 2f1 f2 and assr of modulation frequency 41 hz were measured in ten normal hearing subjects at a test frequency between 0 5 and 8 khz f2 f c the decrease in the dpoae level and the loss in assr amplitude during hybrid mode stimulation amounted on average to only 2 60 db standard deviation sd 1 38 db and 1 83 db sd 2 38 db respectively these findings suggest simultaneous dpoae and assr measurements to be feasible across all test frequencies when using a dpoae stimulus setting where the primary tone f2 is amplitude modulated

on the minimum time function and the minimum energy problem a nonlinear case abstract for a semilinear control system in general banach spaces we prove results on exact and approximate controllability regularity of the minimum time function connections between the minimum time function and the minimum energy

a classification of one dimensional cellular automata using infinite computations this paper proposes an application of the infinite unit axiom and grossone introduced by yaroslav sergeyev see sergeyev 2003 2009 2013 2008 2008 15 19 to classify one dimensional cellular automata whereby each class corresponds to a different and distinct dynamical behavior the forward dynamics of a cellular automaton map are studied via defined classes using these classes along with the infinite unit axiom and grossone the number of configurations that equal those of a given configuration in some finite central window under an automaton map can now be computed hence a classification scheme for one dimensional cellular automata is developed whereby determination in a particular class is dependent on the number of elements in their respective forward iteration classes

hearing threshold estimation using concurrent measurement of distortion product otoacoustic emissions and auditory steady state responses both distortion product otoacoustic emissions dpoaes and auditory steady state responses assrs provide frequency specific assessment of hearing however each method suffers from some restrictions hearing losses above 50 db hl are not quantifiable using dpoaes and their performance at frequencies below 1 khz is limited but their recording time is short in contrast assrs are a time consuming method but have the ability to determine hearing thresholds in a wider range of frequencies and hearing losses thus recording dpoaes and assrs simultaneously at their adequate frequencies and levels could decrease the overall test time considerably the goal of the present study was to develop a parameter setting and test protocol to measure dpoaes and assrs binaurally and simultaneously at multiple frequencies ten normal hearing and 23 hearing impaired subjects participated in the study the interaction of both responses when stimulated simultaneously at frequencies between 0 25 and 6 khz was examined two limiting factors need to be kept frequency distance between assr carrier frequency f c and dpoae primary tone f 2 needs to be at least 1 5 octaves and dpoaes may not be measured if the assr stimulus level is 70 db spl or above there was a significant correlation between pure tone and dpoae assr thresholds in sensorineural hearing loss ears

effects of ear canal standing waves on measurements of distortion product otoacoustic emissions at frequencies above 3 khz standing waves in the ear canal complicate calibration of stimulus sound pressure levels spls for measurements of distortion product otoacoustic emissions dpoaes in the literature two stimulus presentation strategies have been used for dpoae measurements in the in the ear adjustment strategy the voltage command to the speakers is adjusted to maintain a constant stimulus spl across frequency at the dpoae measurement microphone in the iso voltage strategy the voltage presented to the speakers is held constant across frequency on the basis of the assumption that the frequency response of the speakers is approximately flat at the eardrum in the average human ear canal because of standing wave effects there are large systematic but idiosyncratic differences of stimulus spl between the two strategies dpoae versus frequency functions dpoae audiograms obtained using both stimulus presentation strategies in the same ears are presented the differences of sti

necessary and sufficient conditions for viability for semilinear differential inclusions given a set a in a banach space x we define the tangent set and the quasi tangent set to k atc g k concepts more general than the one of tangent vector introduced by bouligand 1930 and severi 1931 both notions prove very suitable in the study of viability problems referring to differential inclusions namely we establish several new necessary and even necessary and sufficient conditions for viability referring to both differential inclusions and semilinear evolution inclusions conditions expressed in terms of the tangency concepts introduced

interpretation of percolation in terms of infinity computations abstract in this paper a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use cantor s ideas and describes infinite and infinitesimal numbers in accordance with the principle the part is less than the whole it gives a possibility to work with finite infinite and infinitesimal quantities numerically by using a new kind of a computer the infinity computer introduced recently in 18 the new approach does not contradict cantor in contrast it can be viewed as an evolution of his deep ideas regarding the existence of different infinite numbers in a more applied way site percolation and gradient percolation have been studied by applying the new computational tools it has been established that in an infinite system the phase transition point is not really a point as with respect of traditional approach in light of new arithmetic it appears as a critical interval rather than a critical point depending on microscope we use this interval could be regarded as finite infinite and infinitesimal short interval using new approach we observed that in vicinity of percolation threshold we have many different infinite clusters instead of one infinite cluster that appears in traditional consideration

on the bellman equation for the minimum time problem in infinite dimensions we consider the time optimal control problem for a semilinear parabolic control system where the target is the closed ball with center 0 and radius rgeq0 in a hilbert space x in particular we allow the origin of x to be the target using an appropriate kruzkov type transformation we give an existence and uniqueness result for the associated hamilton jacobi bellman equation even when the reachable set is not the whole space

minimum time and minimum energy for linear control systems abstract in this paper we give estimates concerning regularity properties of the minimum time function and the minimum norm controls involving the controllability function given by the observability inequalities we further study the continuity of the minimum time function in two variables the initial point and the radius of the ball that limits the control we prove a maximum principle for both time and norm optimal control problems

computing truth values in the topos of infinite peirce s α existential graphs abstract we present here an approach to the analysis of the truth values of peirce s graphs without the restriction of finite number of elements cuts and characters on the sheet of assertion we show that the ensuing structure in which such graphs are objects constitutes a topos while the computation of the truth value of a graph in the topos can be an infinite process we show that using the concept of grossone the subobject classifier of the topos allows to determine a truth value for each graph

an application of grossone to the study of a family of tilings of the hyperbolic plane abstract in this paper we look at the improvement of our knowledge on a family of tilings of the hyperbolic plane which is brought in by the use of sergeyev s numeral system based on grossone see 17 18 19 it appears that the information we can get by using this new numeral system depends on the way we look at the tilings the ways are significantly different but they confirm some results which were obtained in the traditional but constructive frame and allow us to obtain an additional precision with respect to this information

numerical point of view on calculus for functions assuming finite infinite and infinitesimal values over finite infinite and infinitesimal domains abstract the goal of this paper consists of developing a new more physical and numerical in comparison with standard and non standard analysis approaches point of view on calculus with functions assuming infinite and infinitesimal values it uses recently introduced infinite and infinitesimal numbers being in accordance with the principle the part is less than the whole observed in the physical world around us these numbers have a strong practical advantage with respect to traditional approaches they are representable at a new kind of a computer the infinity computer able to work numerically with all of them an introduction to the theory of physical and mathematical continuity and differentiation including subdifferentials for functions assuming finite infinite and infinitesimal values over finite infinite and infinitesimal domains is developed in the paper this theory allows one to work with derivatives that can assume not only finite but infinite and infinitesimal values as well it is emphasized that the newly introduced notion of the physical continuity allows one to see the same mathematical object as a continuous or a discrete one in dependence on the wish of the researcher i e as it happens in the physical world where the same object can be viewed as a continuous or a discrete in dependence on the instrument of the observation used by the researcher connections between pure mathematical concepts and their computational realizations are continuously emphasized through the text numerous examples are given

regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type under suitable controllability and smoothness assumptions the minimum time function t x of a semilinear control system is proved to be locally lipschitz continuous and semiconcave on the controllable set these properties are then applied to derive optimality conditions relating optimal trajectories to the superdifferential of t

lexicographic multi objective linear programming using grossone methodology theory and algorithm abstract numerous problems arising in engineering applications can have several objectives to be satisfied an important class of problems of this kind is lexicographic multi objective problems where the first objective is incomparably more important than the second one which in its turn is incomparably more important than the third one etc in this paper lexicographic multi objective linear programming lmolp problems are considered to tackle them traditional approaches either require solution of a series of linear programming problems or apply a scalarization of weighted multiple objectives into a single objective function the latter approach requires finding a set of weights that guarantees the equivalence of the original problem and the single objective one and the search of correct weights can be very time consuming in this work a new approach for solving lmolp problems using a recently introduced computational methodology allowing one to work numerically with infinities and infinitesimals is proposed it is shown that a smart application of infinitesimal weights allows one to construct a single objective problem avoiding the necessity to determine finite weights the equivalence between the original multi objective problem and the new single objective one is proved a simplex based algorithm working with finite and infinitesimal numbers is proposed implemented and discussed results of some numerical experiments are provided

regularity of the minimum time function and minimum energy problems the linear case we prove new results on the continuity properties and on reachable sets of the minimum time function associated with a linear dynamical system in a separable hilbert space h part of the results are new also in the finite dimensional case the regularity results are stated thanks to the result we obtain on the connection between the minimum time function and the minimum energy

nonlinear programming and grossone quadratic programing and the role of constraint qualifications abstract a novel and interesting approach to infinite and infinitesimal numbers was recently proposed in a series of papers and a book by sergeyev this novel numeral system is based on the use of a new infinite unit of measure the number grossone indicated by the numeral the number of elements of the set in of natural numbers based on the use of de cosmis and de leone 2012 have then proposed a new exact differentiable penalty function for constrained optimization problems in this paper these results are specialized to the important case of quadratic problems with linear constraints moreover the crucial role of constraint qualification conditions well know in constraint minimization literature is also discussed with reference to the new proposed penalty function

optimal feedback controls for a class of nonlinear distributed parameter systems it is shown that the optimal controls for a distributed control problem governed by semilinear parabolic equations can be expressed in feedback form the corresponding hamilton jacobi equation is studied and applications to infinite time horizon and time optimal control problems are given some extensions to control problems governed by parabolic variational inequalities are indicated also

computing sums of conditionally convergent and divergent series using the concept of grossone abstract let a1 a2 be a numerical sequence as the main task of the paper we consider the classical problem of computing the sum n 1 a n when the series is either conditionally convergent or divergent we demonstrate that the concept of grossone recently proposed by sergeyev can be useful in both computing this sum and studying properties of summation methods we also consider the problem of choosing the upper limit in the sum if we wish to replace the infinity sign with a grossone based quantity finally we discuss some properties of prime numbers in the grossone universe and make an attempt of analyzing the celebrated euler s product formula

usage of infinitesimals in the menger s sponge model of porosity abstract the present work concerns the calculation of the infinitesimal porosity by using the menger s sponge model this computation is based on the grossone theory considering the pore volume estimation for the menger s sponge and afterwards the classical definition of the porosity given by the ratio between the volume of voids and the total volume voids plus solid phase the aim is to investigate the different solutions given by the standard characterization of the porosity and the grossone theory without the direct estimation of the fractal dimension once the utility of this procedure had been clarified the focus moves to possible practical applications in which infinitesimal parts can play a fundamental role the discussion on this matter still remains open

approximation of time optimal controls for heat equations with perturbations in the system potential in this paper we study a certain approximation property for a time optimal control problem of the heat equation with l infty potential we prove that the optimal time and the optimal control to the same time optimal control problem for the heat equation where the potential has a small perturbation are close to those for the original problem we also verify that for the heat equation with a small perturbation in the potential one can construct a new time optimal control problem which has the same target as that of the original problem but has a different control constraint bound from that of the original problem such that the new and the original problems share the same optimal time and meanwhile the optimal control of the new problem is close to that of the original one the main idea to approach such approximation is an appropriate use of an equivalence theorem of minimal norm and minimal time control problems for the heat equations under consideration this theorem was first established by wa

on strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions abstract the implementation of global optimization algorithms using the arithmetic of infinity is considered a relatively simple version of implementation is proposed for the algorithms that possess the introduced property of strong homogeneity it is shown that the p algorithm and the one step bayesian algorithm are strongly homogeneous

simultaneous latency estimations for distortion product otoacoustic emissions and envelope following responses the purpose of this research was to simultaneously estimate processing delays in the cochlea and brainstem using the same acoustic stimuli apparent latencies were estimated from ear canal measurements of 2f1 f2 distortion product otoacoustic emissions dpoaes and scalp recordings of the f2 f1 envelope following response efr the stimuli were equal level tone pairs 65db spl with the upper tone f2 set at either 900 or 1800hz to fix the initiation site of the dpoae and efr the frequency of f1 was swept continuously between frequency limits chosen to keep the efr response between 150 and 170hz the average dpoae latencies were 9 6 and 6 2ms for f2 900 and 1800hz and the corresponding efr latencies were 12 4 and 8 8ms in a control condition a third suppressor tone was added near the dpoae response frequency to evaluate whether the potential source at fdp was contributing significantly to the measured emission dpoae latency is the sum of both inward and outward cochlear delays the efr apparent la

characterization of lyapunov pairs in the nonlinear case and applications abstract the paper presents a characterization of the lyapunov pairs for a general initial value problem with a possibly multivalued m accretive operator on an arbitrary banach space by means of the contingent derivative related to the operator the proof is based on tangency and flow invariance arguments combined with a priori estimates and approximation the abstract results are applied to obtain precise a priori estimates for the mild solutions they readily lead to the existence of global solutions and various controllability properties important lyapunov pairs are pointed out in connection with specific problems

further efforts to predict pure tone thresholds from distortion product otoacoustic emission input output functions recently boege and janssen j acoust soc am 111 1810 1818 2002 fit linear equations to distortion product otoacoustic emission dpoae input output i o functions after the dpoae level in db spl was converted into pressure in pa significant correlations were observed between these dpoae thresholds and audiometric thresholds the present study extends their work by 1 evaluating the effect of frequency 2 determining the behavioral thresholds in those conditions that did not meet inclusion criteria and 3 including a wider range of stimulus levels dpoae i o functions were measured in as many as 278 ears of subjects with normal and impaired hearing nine f2 frequencies 500 to 8000 hz in 12 octave steps were used l2 ranged from 10 to 85 db spl 5 db steps and l1 was set according to the equation l1 0 4l2 39 db kummer et al j acoust soc am 103 3431 3444 1998 for l2 levels up to 65 db spl beyond which l1 l2 for the same conditions as those used by boege and janssen we o

evolution equations on locally closed graphs and applications abstract let x be a banach space let a d a x x be the infinitesimal generator of a c 0 semigroup let i be a nonempty bounded interval and let k i x be a given multi valued function by using the concept of a quasi tangent set introduced by c rj necula vrabie o c rj m necula i i vrabie necessary and sufficient conditions for viability for a semilinear differential inclusions trans amer math soc 361 2009 343 390 o c rj m necula i i vrabie viability invariance and applications north holland a mathematics studies vol 207 elsevier 2007 and using a tangency condition expressed in the terms of this concept we establish a necessary and sufficient condition for mild viability referring to evolution inclusions of the form u t a u t f t u t where f is a multi function defined on the graph of k as applications we deduce a sufficient condition for null controllability and a comparison result for semilinear evolution inclusions

the sierpinski curve viewed by numerical computations with infinities and infinitesimals abstract the sierpinski curve is one of the most known space filling curves and one with the highest number of applications we present a recently proposed computational methodology based on the infinite quantity called grossone to investigate the behavior of two different constructions of the sierpinski curve we emphasize that adopting this point of view we have infinitely many sierpinski curves depending contrarily to traditional analysis on each specific starting configuration of particular interest are some power series expansions in the new infinitesimal quantities emerging from the study of the considered curves

counting systems and the first hilbert problem the first hilbert problem is studied in this paper by applying two instruments a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets several counting systems are taken into consideration it is emphasized in the paper that different mathematical languages can describe mathematical objects in particular sets and the number of their elements with different accuracies the traditional and the new approaches are compared and discussed

the use of grossone in mathematical programming and operations research the concepts of infinity and infinitesimal in mathematics date back to anciens greek and have always attracted great attention very recently a new methodology has been proposed by sergeyev 10 for performing calculations with infinite and infinitesimal quantities by introducing an infinite unit of measure expressed by the numeral grossone an important characteristic of this novel approach is its attention to numerical aspects in this paper we will present some possible applications and use of in operations research and mathematical programming in particular we will show how the use of can be beneficial in anti cycling procedure for the well known simplex method for solving linear programming problems and in defining exact differentiable penalty functions in nonlinear programming