development of a glottal area index that integrates glottal gap size and open quotient because voice signals result from vocal fold vibration perceptually meaningful vibratory measures should quantify those aspects of vibration that correspond to differences in voice quality in this study glottal area waveforms were extracted from high speed videoendoscopy of the vocal folds principal component analysis was applied to these waveforms to investigate the factors that vary with voice quality results showed that the first principal component derived from tokens without glottal gaps was significantly p 0 01 associated with the open quotient oq the alternating current ac measure had a significant effect p 0 01 on the first principal component among tokens exhibiting glottal gaps a measure ac oq defined as the ratio of ac to oq was proposed to combine both amplitude and temporal characteristics of the glottal area waveform for both complete and incomplete glottal closures analyses of glide phonations in which quality varied continuously from breathy to pressed showed that the ac oq measure was able to characterize the corresponding continuum of glottal area waveform variation regardless of the presence or absence of glottal gaps

knots and links in steady solutions of the euler equation given any possibly unbounded locally nite link we show that there exists a smooth dieomorphism transforming this link into a set of stream or vortex lines of a vector eld that solves the steady incompressible euler equation in r 3 furthermore the dieomorphism can be chosen arbitrarily close to the identity in any c r norm

existence of knotted vortex tubes in steady euler flows we prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible euler equation in mathbb r 3 more precisely given a finite collection of possibly linked and knotted disjoint thin tubes in mathbb r 3 we show that they can be transformed with a c m small diffeomorphism into a set of vortex tubes of a beltrami field that tends to zero at infinity the structure of the vortex lines in the tubes is extremely rich presenting a positive measure set of invariant tori and infinitely many periodic vortex lines the problem of the existence of steady knotted thin vortex tubes can be traced back to lord kelvin

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

beltrami fields with nonconstant proportionality factor we consider the question raised by enciso and peralta salas arch ration mech anal 220 1 243 260 2016 what nonconstant functions f can occur as the proportionality factor for a beltrami field mathbf u on an open subset u subset mathbb r 3 we also consider the related question for any such f how large is the space of associated beltrami fields by applying cartan s method of moving frames and the theory of exterior differential systems we are able to improve upon the results given in peralta salas 2016 in particular the answer to the second question depends crucially upon the geometry of the level surfaces of f we conclude by giving a complete classification of beltrami fields that possess either a translation symmetry or a rotation symmetry

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

dissipative continuous euler flows we show the existence of continuous periodic solutions of the 3d incompressible euler equations which dissipate the total kinetic energy

existence of solution for m point boundary value problems of second order differential systems with impulses with the help of the coincidence degree continuation theorem we get a general theorem concerning the existence of solution of the m point boundary value problems for second order differential systems with impulses we also give a definition of autonomous curvature bound set relative to this m point boundary value problems and by using this definition and the above existence theorem we obtain some simple existence conditions of solution for these boundary value problems in particular when the impulses are absent our results can be applied to study the usual m point boundary value problems at resonance

variability in the relationships among voice quality harmonic amplitudes open quotient and glottal area waveform shape in sustained phonation increases in open quotient are widely assumed to cause changes in the amplitude of the first harmonic relative to the second h1 h2 which in turn correspond to increases in perceived vocal breathiness empirical support for these assumptions is rather limited and reported relationships among these three descriptive levels have been variable this study examined the empirical relationship among h1 h2 the glottal open quotient oq and glottal area waveform skewness measured synchronously from audio recordings and high speed video images of the larynges of six phonetically knowledgeable vocally healthy speakers who varied fundamental frequency and voice qualities quasi orthogonally across speakers and voice qualities oq the asymmetry coefficient and fundamental frequency accounted for an average of 74 of the variance in h1 h2 however analyses of individual speakers showed large differences in the strategies used to produce the same intended voice qualities thus h1 h2 can be predicted with good overall accuracy but its relationship to phonatory characteristics appears to be speaker dependent

dissipative euler flows with onsager critical spatial regularity for any 0 we show the existence of continuous periodic weak solutions v of the euler equations that do not conserve the kinetic energy and belong to the space lt1 cx1 3 e namely x v x t is e holder continuous in space at a e time t and the integral t 1 3 edt is finite a well known open conjecture of l onsager claims that such solutions exist even in the class lt cx1 3 e 2016 wiley periodicals inc

beltrami fields with a nonconstant proportionality factor are rare we consider the existence of beltrami fields with a nonconstant proportionality factor f in an open subset u of mathbb r 3 by reformulating this problem as a constrained evolution equation on a surface we find an explicit differential equation that f must satisfy whenever there is a nontrivial beltrami field with this factor this ensures that there are no nontrivial regular solutions for an open and dense set of factors f in the c k topology k geqq 7 in particular there are no nontrivial beltrami fields whenever f has a regular level set diffeomorphic to the sphere this provides an explanation of the helical flow paradox of morgulis et al commun pure appl math 48 571 582 1995

on stationary solutions of two dimensional euler equation we study the geometry of streamlines and stability properties for steady state solutions of the euler equations for an ideal fluid

on the collapse of tubes carried by 3d incompressible flows we define the notion of a regular tube and prove that a regular tube convected by a 3d incompressible flow cannot collapse to zero thickness in finite time

divergence free fields energy and asymptotic crossing number in more than one context the equations of classical physics lead to a closed 2 form co on 3 dimensional space which is a conserved quantity in the sense that it pulls back under time evolution in the physics literature co is written as a divergence free vector field w appendix a describes two settings in which a divergence free w is conserved or frozen one is the magnetic field in ideal magneto hydrodynamics and the other is curl velocity in incompressible inviscid fluid flow if ht denotes the transport diffeomorphisms of a moving fluid in which the field is imbedded with ho id wt denotes the field in the fluid at time t and x0 is the space variable at time t 0 then

local representation and construction of beltrami fields ii solenoidal beltrami fields and ideal mhd equilibria abstract object of the present paper is the local theory of solution for steady ideal euler flows and ideal mhd equilibria the present analysis relies on the lie darboux theorem of differential geometry and the local theory of representation and construction of beltrami fields developed in sato and yamada 2019 a theorem for the construction of harmonic orthogonal coordinates is proved using such coordinates families of solenoidal beltrami fields with different topologies are obtained in analytic form existence of global solenoidal beltrami fields satisfying prescribed boundary conditions while preserving the local representation is considered it is shown that only singular solutions are admissible an explicit example is given in a spherical domain and a theorem on existence of singular solutions is proven local conditions for existence of solutions and local representation theorems are derived for generalized beltrami fields ideal mhd equilibria and general steady ideal euler flows the theory is applied to construct analytic examples

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

effects of spectral slope on perceived breathiness in vowels previous studies have indicated that breathiness is correlated with changes in spectral slope as well as aspiration noise klatt klatt analysis synthesis and perception of voice quality variations among female and male talkers j acoust soc am 87 820 857 1990 in a recent study shrivastav and pinero shrivastav pinero effect of aspiration noise and spectral slope on perceived breathiness in vowels j acoust soc am 117 2622 2005 observed that varying spectral slope resulted in minimal changes on the perceived breathiness for synthetic vowels however the stimuli tested in this experiment included a relatively narrow range of spectral slope variation the goal of the present experiment was to verify the role of spectral slope on the perception of breathiness by testing stimuli that had a wider range of variation in spectral slope ten voices 5 male and 5 female were synthesized using a klatt synthesizer each of these was manipulated to generate two continua varying in the

euler equations on homogeneous spaces and virasoro orbits abstract we show that the following three systems related to various hydrodynamical approximations the korteweg de vries equation the camassa holm equation and the hunter saxton equation have the same symmetry group and similar bihamiltonian structures it turns out that their configuration space is the virasoro group and all three dynamical systems can be regarded as equations of the geodesic flow associated to different right invariant metrics on this group or on appropriate homogeneous spaces in particular we describe how arnold s approach to the euler equations as geodesic flows of one sided invariant metrics extends from lie groups to homogeneous spaces we also show that the above three cases describe all generic bihamiltonian systems which are related to the virasoro group and can be integrated by the translation argument principle they correspond precisely to the three different types of generic virasoro orbits finally we discuss interrelation between the above metrics and kahler structures on virasoro orbits as well as open questions regarding integrable systems corresponding to a finer classification of the orbits

the beltrami spectrum for incompressible fluid flows recently v yakhot s orszag and their co workers have suggested that turbulent flows in various regions of space organize into a coherent hierarchy of weakly interacting superimposed approximate beltrami flows a mathematical framework is developed here to study organized beltrami hierarchies in a systematic fashion this framework is applied to several important classes of examples with universal beltrami hierarchies an analysis of the persistence of such beltrami hierarchies is also presented for general solutions of the navier stokes equations

on the existence of force free magnetic fields with small nonconstant α in exterior domains the existence of force free magnetic fields in the exterior domain of some compact simply connected surface s is proved via an iteration scheme the iteration starts with an arbitrary exterior vacuum field which contains flux tubes originating and ending on s at one cross section of such a flux tube with s an arbitrary function is prescribed for small values of in the holder norm 1 0 1 the iteration is shown to converge to a force free field with the prescribed values of in a flux tube which is close to the vacuum flux tube and 0 outside the force free field is close in the holder norm 1 to the starting vacuum field in particular it has the same field line topology the same boundary values on s and satisfies the same decay conditions in spatial infinity it is in general three dimensional and requires no continuous symmetries

two dimensional magnetohydrodynamic equilibria with prescribed topology we establish existence of weak solutions to the equilibrium equations of magnetohydrodynamics with prescribed topology this is carried out in two settings in the first we consider the variational problem of minimizing total energy in a torus under the assumption of axisymmetry and prescription of mass and flux profiles existence of weak solutions implies that the prescription of topology is a natural constraint both the compressible and incompressible cases are considered in the second setting we adapt examples of b c low and r wolfson 13 and j j aly and t amari 1 2 3 associated with parker s explanation of the extreme heating of the solar corona and other solar phenomena existence of solutions with fixed topology is a first crucial step in rigorously examining the relationship between topology and the existence of current sheets we use a decomposition introduced in 8 9 11 that captures much of the topology of level sets for certain classes of sobolev functions this decomposition is preserved under weak limits and so is useful for prescribing topological constraints the approach is especially suited to the use of domain deformations 2000 john wiley sons inc

measures of phonation type in hmong this study examines measures of glottal flow for vowels of hmong a southeast asian language which uses breathy and normal phonation contrastively a software inverse filter was used to recover glottal airflow from oral airflow recordings properties of glottal flow measured in the time domain were glottal pulse symmetry and relative closed phase duration in the frequency domain measures of spectral tilt and the amplitude difference between f0 and h2 were applied to discrete fourier transforms dfts of the glottal flow waveforms spectral tilt could not be reliably measured for many tokens for the other measures values were available for all tokens and were compared across phonation types flow pulse symmetry is not significantly different for breathy and normal voice vowels on the other hand prominence of the fundamental relative to the second harmonic is a very significant correlate of the breathy normal distinction as is the relative closed phase duration these results are considered in light of an existing model of the voice source

compressible helical flows helical beltrami flow with nonuniform coefficient is considered for the case of compressible fluid and a class of exact solutions is proposed a paradox of helical flow is discussed and the compressibility is considered as a possible resolution of the paradox examples with different symmetries are given for the compressible helical flow and in particular the generalization of the abc arnold beltrami childress flow for the compressible case is proposed 1995 john wiley sons inc

local representation and construction of beltrami fields abstract a beltrami field is an eigenvector of the curl operator beltrami fields describe steady flows in fluid dynamics and force free magnetic fields in plasma turbulence by application of the lie darboux theorem of differential geometry we prove a local representation theorem for beltrami fields we find that locally a beltrami field has a standard form amenable to an arnold beltrami childress flow with two of the parameters set to zero furthermore a beltrami flow admits two local invariants a coordinate representing the physical plane of the flow and an angular momentum like quantity in the direction across the plane as a consequence of the theorem we derive a method to construct beltrami fields with given proportionality factor this method based on the solution of the eikonal equation guarantees the existence of beltrami fields for any orthogonal coordinate system such that at least two scale factors are equal we construct several solenoidal and non solenoidal beltrami fields with both homogeneous and inhomogeneous proportionality factors

beltrami fields with hyperbolic periodic orbits enclosed by knotted invariant tori abstract we prove that there exist beltrami fields in euclidean space with sharp decay at infinity which have a prescribed set of invariant tori possibly knotted or linked that enclose an arbitrarily large number of hyperbolic periodic orbits these hyperbolic orbits are cablings over the core curve of each torus moreover the domain bounded by each invariant torus is covered by an almost full measure set of invariant tori we show that an analogous result holds for high frequency beltrami fields on the flat torus t 3

analytic smoothing of geometric maps with applications to kam theory we show that finitely differentiable diffeomorphisms which are either symplectic volume preserving or contact can be approximated with analytic diffeomorphisms that are respectively symplectic volume preserving or contact we prove that the approximating functions are uniformly bounded on some complex domains and that the rate of convergence in cr norms of the approximation can be estimated in terms of the size of such complex domains and the order of differentiability of the approximated function as an application to this result we give a proof of the existence the local uniqueness and the bootstrap of regularity of kam tori for finitely differentiable symplectic maps the symplectic maps considered here are not assumed either to be written in action angle variables or to be perturbations of integrable systems our main assumption is the existence of a finitely differentiable parameterization of a maximal dimensional torus that satisfies a non degeneracy condition and that is approximately invariant the symplectic volume preserving and contact forms are assumed to be analytic

solutions of lidstone bvps for higher order impulsive differential equations abstract in this paper the lidstone boundary value problems for 2 n order impulsive differential equation x 2 n t f t x t x t x 2 n 1 t 0 t 1 x i s k i i k x s k x 2 n 1 s k i 1 2 n 1 k 1 p with one of following boundary conditions x 2 i 0 x 2 i 1 0 i 0 n 1 and x 2 i 1 0 x 2 i 1 0 i 0 n 1 are considered sufficient conditions which guarantee the existence of at least one solution for these problems are established the results are new examples illustrate our main results

a variational principle for three dimensional water waves over beltrami flows abstract we consider steady three dimensional gravity capillary water waves with vorticity propagating on water of finite depth we prove a variational principle for doubly periodic waves with relative velocities given by beltrami vector fields under general assumptions on the wave profile

the euler equations as a differential inclusion we propose a new point of view on weak solutions of the euler equations describing the motion of an ideal incompressible fluid in r n with n 2 we give a reformulation of the euler equations as a differential inclusion and in this way we obtain transparent proofs of several celebrated results of v scheffer and a shnirelman concerning the non uniqueness of weak solutions and the existence of energy decreasing solutions our results are stronger because they work in any dimension and yield bounded velocity and pressure