hex splines a novel spline family for hexagonal lattices this paper proposes a new family of bivariate nonseparable splines called hex splines especially designed for hexagonal lattices the starting point of the construction is the indicator function of the voronoi cell which is used to define in a natural way the first order hex spline higher order hex splines are obtained by successive convolutions a mathematical analysis of this new bivariate spline family is presented in particular we derive a closed form for a hex spline of arbitrary order we also discuss important properties such as their fourier transform and the fact they form a riesz basis we also highlight the approximation order for conventional rectangular lattices hex splines revert to classical separable tensor product b splines finally some prototypical applications and experimental results demonstrate the usefulness of hex splines for handling hexagonally sampled data

counting real zeros of analytic functions satisfying linear ordinary differential equations abstract we suggest an explicit procedure to establish upper bounds for the number of real zeros of analytic functions satisfying linear ordinary differential equations with meromorphic coefficients if the equation formula has no singular points in a small neighborhooduof a real segmentk all the coefficientsaj t have absolute value aonuanda0 t 1 then any solution of this equation may have no more than a zeros onk where u k is a geometric constant depending only onkandu if the principal coefficienta0 t is nonconstant but its modulus is at leasta 0 somewhere onk then the number of real zeros onkof any solution analytic inu does not exceed a a with some u k

speech intelligibility as a function of the number of channels of stimulation for signal processors using sine wave and noise band outputs vowels consonants and sentences were processed through software emulations of cochlear implant signal processors with 2 9 output channels the signals were then presented as either the sum of sine waves at the center of the channels or as the sum of noise bands the width of the channels to normal hearing listeners for identification the results indicate as previous investigations have suggested that high levels of speech understanding can be obtained using signal processors with a small number of channels the number of channels needed for high levels of performance varied with the nature of the test material for the most difficult material vowels produced by men women and girls no statistically significant differences in performance were observed when the number of channels was increased beyond 8 for the least difficult material sentences no statistically significant differences in performance were observed when the number of channels was increased beyond 5 the nature of the output signal noise bands or sine waves made only a small difference in performance the mechanism mediating the high levels of speech recognition achieved with only few channels of stimulation may be the same one that mediates the recognition of signals produced by speakers with a high fundamental frequency i e the levels of adjacent channels are used to determine the frequency of the input signal the results of an experiment in which frequency information was altered but temporal information was not altered indicates that vowel recognition is based on information in the frequency domain even when the number of channels of stimulation is small

the importance for speech intelligibility of random fluctuations in steady background noise spectrally shaped steady noise is commonly used as a masker of speech the effects of inherent random fluctuations in amplitude of such a noise are typically ignored here the importance of these random fluctuations was assessed by comparing two cases for one speech was mixed with steady speech shaped noise and n channel tone vocoded a process referred to as signal domain mixing sdm this preserved the random fluctuations of the noise for the second the envelope of speech alone was extracted for each vocoder channel and a constant was added corresponding to the root mean square value of the noise envelope for that channel this is referred to as envelope domain mixing edm it removed the random fluctuations of the noise sinusoidally modulated noise and a single talker were also used as backgrounds with both sdm and edm speech intelligibility was measured for n 12 19 and 30 with the target to background ratio fixed at 7 db for sdm performance was best for the speech background and worst for the steady noise for edm this pattern was reversed intelligibility with steady noise was consistently very poor for sdm but near ceiling for edm demonstrating that the random fluctuations in steady noise have a large effect

parallelization of the lyapunov constants and cyclicity for centers of planar polynomial vector fields christopher in 2006 proved that under some assumptions the linear parts of the lyapunov constants with respect to the parameters give the cyclicity of an elementary center this paper is devote to establish a new approach namely parallelization to compute the linear parts of the lyapunov constants more concretely it is showed that parallelization computes these linear parts in a shorter quantity of time than other traditional mechanisms to show the power of this approach we study the cyclicity of the holomorphic center iz z 2 z 3 z n under general polynomial perturbations of degree n for n 13 we also exhibit that from the point of view of computation among the hamiltonian time reversible and darboux centers the holomorphic center is the best candidate to obtain high cyclicity examples of any degree for n 4 5 13 we prove that the cyclicity of the holomorphic center is at least n 2 n 2 this result give the highest lower bound for m 6 m 7 m 13 among the existing results where m n is the maximum number of limit cycles bifurcating from an elementary monodromic singularity of polynomial systems of degree n as a direct corollary we also obtain the highest lower bound for the hilbert numbers h 6 40 h 8 70 and h 10 108 because until now the best result was h 6 39 h 8 67 and h 10 100

center conditions rigidity of logarithmic differential equations abstract in this paper we prove that any degree d deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again this is a generalization of ilyashenko s result on hamiltonian differential equations the main tools are picard lefschetz theory of a polynomial with complex coefficients in two variables specially the gusein zade a campo s theorem on calculating the dynkin diagram of the polynomial and the action of gauss manin connection on the so called brieskorn lattice petrov module of the polynomial we will also generalize j p francoise recursion formula and condition for a polynomial which is a product of lines in a general position some applications on the cyclicity of cycles and the bautin ideals will be given

efficient algorithms for computing the 2 d hexagonal fourier transforms in this paper representations of the two dimensional 2 d signals are presented that reduce the computation of 2 d discrete hexagonal fourier transforms 2 d dhfts the representations are based on the concept of the covering that reveals the mathematical structure of the transforms specifically a set of unitary paired transforms is derived that splits the 2 d dhft into a number of smaller one dimensional 1 d dfts examples for the 8 spl times 4 and 16 spl times 8 hexagonal lattices are described in detail the number of multiplications required for computing the 8 spl times 4 and 16 spl times 8 point dhfts are equal 20 and 136 respectively in the general n spl ges 8 case the number of multiplications required to compute the 2n spl times n point dhft by the paired transforms equals n sup 2 log n 1 n

geometric transformations on the hexagonal grid the hexagonal grid has long been known to be superior to the more traditional rectangular grid system in many aspects in image processing and machine vision related fields however systematic developments of the mathematical backgrounds for the hexagonal grid are conspicuously lacking the purpose of this paper is to study geometric transformations on the hexagonal grid formulations of the transformation matrices are carried out in a symmetrical hexagonal coordinate frame a trio of new trigonometric functions are defined in this paper to facilitate the rotation transformations a fast algorithm for rounding an arbitrary point to the nearest hexagonal grid point is also presented

the infinitesimal 16th hilbert problem in the quadratic case let h x y be a real cubic polynomial with four distinct critical values in a complex domain and let x h h y frac partial partial x h x frac partial partial y be the corresponding hamiltonian vector field we show that there is a neighborhood of x h in the space of all quadratic plane vector fields such that any x has at most two limit cycles

design and evaluation of more accurate gradient operators on hexagonal lattices digital two dimensional images are usually sampled on square lattices while the receptors of the human eye are following a hexagonal structure it is the main motivation for adopting hexagonal lattices the fundamental operation in many image processing algorithms is to extract the gradient information as such various gradient operators have been proposed for square lattices and have been thoroughly optimized accurate gradient operators for hexagonal lattices have however not been researched well enough while the distance between neighbor pixels is constant we therefore derive consistent gradient operators on hexagonal lattices and compare them with the existing optimized filters on square lattices the results show that the derived filters on hexagonal lattices achieve a better signal to noise ratio than those on square lattices results on artificial images also show that the derived filters on hexagonal lattices outperform the square ones with respect to accuracy of gradient intensity and orientation detection

bifurcations of certain family of planar vector fields tangent to axes abstract the topological versality of the family v x x 1 x y y y 2 ax by cy 2 of vector fields on the plane is proven the asymptotic formulas of the bifurcational curves are given the proofs rely on an analysis of the limit cycles and the non abelian integrals along irrational curves

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

the transverse dynamics of a holomorphic flow on considere un champ vectoriel polynomial homogene p z dans c n 1 les solutions du systeme d equations differentielles dz i dt p i z t c i 0 n feuillette c n 1 par des courbes holomorphes ayant des singularites le long du lieu commun p i z 0 on definit la notion de dynamique transverse du feuilletage

benefit of high rate envelope cues in vocoder processing effect of number of channels and spectral region in cochlear implants or vocoder simulations of cochlear implants the transmission of envelope cues at high rates related to voice fundamental frequency f0 may be limited by the widths of the filters used to form the channels and or by the cutoff frequency flp of the low pass filters used for envelope extraction the effect of varying flp in tone and noise vocoders was investigated for channel numbers n from 6 to 18 as n increased the widths of the channels decreased the value of flp was 45hz envelope or e filter or 180hz pitch or p filter the following combinations of cutoff frequencies were used for channels below and above 1500hz respectively ee pe ep and pp results from a competing talker task showed that the tone vocoder led to better intelligibility than the noise vocoder the pp condition led to the best intelligibility and the ee condition to the worst for n 6 intelligibility was better for condition pe than for condition ep for n 18 the reverse was true the results

novel reversible integer fourier transform with control bits this paper presents a novel concept of the reversible integer discrete fourier transform ridft of order 2r r 2 when the transform is split by the paired representation into a minimum set of short transforms i e transforms of orders 2k k r by means of the paired transform the signal is represented as a set of short signals which carry the spectral information of the signal at specific and disjoint sets of frequencies the paired transform based fast fourier transform fft involves a few operations of multiplication that can be approximated by integer transforms examples of 1 point transforms with one control bit are described control bits allow us to invert such approximations two control bits are required to perform the 8 point ridft and 12 or even 8 bits for the 16 point ridft of real inputs the proposed forward and inverse ridfts are fast and the computational complexity of these transforms is comparative with the complexity of the fft the 8 point direct and inverse ridfts are described in detail

liouvillian first integrals of differential equations liouvillian functions are functions that are built up from rational functions using exponentiation integration and algebraic functions we show that if a system of differential equations has a generic solution that satisfies a liouvillian relation that is there is a liouvillian function of several variables vanishing on the curve defined by this solution then the system has a liouvillian first integral that is a nonconstant liouvillian function that is constant on solution curves in some nonempty open set we can refine this result in special cases to show that the first integral must be of a very special form

on the determination of functions from their integral values along certain manifolds when one integrates a function of two variables x y a point function f p in the plane subject to suitable regularity conditions along an arbitrary straight line g then one obtains in the integral values f g a line function in part a of the present paper the problem which is solved is the inversion of this linear functional transformation that is the following questions are answered can every line function satisfying suitable regularity conditions be regarded as constructed in this way if so is f uniquely known from f and how can f be calculated in part b a solution of the dual problem of calculating a line function f g from its point mean values f p is solved in a certain sense finally in part c certain generalizations are discussed prompted by consideration of non euclidean manifolds as well as higher dimensional spaces the treatment of these problems themselves of interest gains enhanced importance through the numerous relationships that exist between this topic and the theory of logarithmic and newtonian potentials these are mentioned at appropriate places in the text

a unified treatment of cooley tukey algorithms for the evaluation of the multidimensional dft in this paper the cooley tukey fast fourier transform fft algorithm is generalized to the multidimensional case in a natural way which allows for the evaluation of discrete fourier transforms of rectangularly or hexagonally sampled signals or of signals which are sampled on an arbitrary periodic grid in either the spatial or fourier domain this general algorithm incorporates both the traditional rectangular row column and vector radix algorithms as special cases this fft algorithm is shown to result from the factorization of an integer matrix for each factorization of that matrix a different algorithm can be developed this paper presents the general algorithm discusses its computational efficiency and relates it to existing multi dimensional fft algorithms

contribution of temporal fine structure information and fundamental frequency separation to intelligibility in a competing speaker paradigm the speech reception threshold srt for identifying a target speaker in a background speaker was measured as a function of the difference f0sep in fundamental frequency f0 between the two speakers the amount of original temporal fine structure tfs information in the mixed signals was manipulated by tone vocoding channels above a certain cutoff channel co when the natural variations in f0 of both speakers were preserved the srt did not decrease with increasing f0sep indicating that short term differences in f0 can allow perceptual segregation of two speakers even when their f0s cross when f0 variations were removed from both speakers increasing f0sep led to decreased better srts the decrease was greater for unprocessed signals than for fully tone vocoded signals however the decrease was similar for unprocessed signals and for signals with original tfs below 1600 hz suggesting that most of the benefit from increasing f0 difference depends on the use of tfs information at lower frequenci

polynomial systems a lower bound for the hilbert numbers let h n be the maximum possible number of limit cycles of systems dot x p x y dot y q x y where p and q are polynomials of degree at most n we are concerned with the rate of growth of h n as n increases it is known that h n geq kn 2 for some constant k in this paper we show that h n grows at least as rapidly as n 2 log n

on local behavior of holomorphic functions along complex submanifolds of ℂ n in this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of n as a corollary we present multi dimensional generalizations of an important result of coman and poletsky on bernstein type inequalities on transcendental curves in 2

algebraic signal processing theory 2 d spatial hexagonal lattice we develop the framework for signal processing on a spatial or undirected 2 d hexagonal lattice for both an infinite and a finite array of signal samples this framework includes the proper notions of z transform boundary conditions filtering or convolution spectrum frequency response and fourier transform in the finite case the fourier transform is called discrete triangle transform like the hexagonal lattice this transform is nonseparable the derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced namely we construct the proper signal models given by polynomial algebras bottom up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory these signal models in turn then provide all the basic signal processing concepts the framework developed in this paper is related to mersereau s early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete fourier transform a fact that will be made rigorous in this paper

local bifurcations and a survey of bounded quadratic systems abstract this paper presents a survey of the known results for bounded quadratic systems as well as a study of the local bifurcations that occur at critical points of such systems it is shown that the only finite codimension bifurcations that occur at a critical point of a bounded quadratic system are the saddle node and the hopf takens bifurcations of codimensions 1 and 2 and the bogdanov takens bifurcations of codimensions 2 and 3 furthermore it is shown that whenever a bounded quadratic system has one of these critical points then a full generic unfolding of the critical point exists in the class of bounded quadratic systems finally we give a complete list of those limit periodic sets whose finite cyclicity still needs to be established in order to obtain the existence of a finite upper bound for the number of limit cycles that can occur in a bounded quadratic system

on the number of channels needed to understand speech recent studies have shown that high levels of speech understanding could be achieved when the speech spectrum was divided into four channels and then reconstructed as a sum of four noise bands or sine waves with frequencies equal to the center frequencies of the channels in these studies speech understanding was assessed using sentences produced by a single male talker the aim of experiment 1 was to assess the number of channels necessary for a high level of speech understanding when sentences were produced by multiple talkers in experiment 1 sentences produced by 135 different talkers were processed through n 2 n 16 number of channels synthesized as a sum of n sine waves with frequencies equal to the center frequencies of the filters and presented to normal hearing listeners for identification a minimum of five channels was needed to achieve a high level 90 of speech understanding asymptotic performance was achieved with eight channels at least for the speech material used in this study the outcome of experiment 1 demonstrated that the number of channels needed to reach asymptotic performance varies as a function of the recognition task and or need for listeners to attend to fine phonetic detail in experiment 2 sentences were processed through 6 and 16 channels and quantized into a small number of steps the purpose of this experiment was to investigate whether listeners use across channel differences in amplitude to code frequency information particularly when speech is processed through a small number of channels for sentences processed through six channels there was a significant reduction in speech understanding when the spectral amplitudes were quantized into a small number 8 of steps high levels 92 of speech understanding were maintained for sentences processed through 16 channels and quantized into only 2 steps the findings of experiment 2 suggest an inverse relationship between the importance of spectral amplitude resolution number of steps and spectral resolution number of channels

the recognition of sentences in noise by normal hearing listeners using simulations of cochlear implant signal processors with 6 20 channels sentences were processed through simulations of cochlear implant signal processors with 6 8 12 16 and 20 channels and were presented to normal hearing listeners at 2 db s n and at 2 db s n the signal processing operations included bandpass filtering rectification and smoothing of the signal in each band estimation of the rms energy of the signal in each band computed every 4 ms and generation of sinusoids with frequencies equal to the center frequencies of the bands and amplitudes equal to the rms levels in each band the sinusoids were summed and presented to listeners for identification at issue was the number of channels necessary to reach maximum performance on tests of sentence understanding at 2 db s n the performance maximum was reached with 12 channels of stimulation at 2 db s n the performance maximum was reached with 20 channels of stimulation these results in combination with the outcome that in quiet asymptotic performance is reached with five channels of stimulation demonstrate that more channels are needed in noise than in quiet to reach a high level of sentence understanding and that as the s n becomes poorer more channels are needed to achieve a given level of performance

the importance of temporal fine structure information in speech at different spectral regions for normal hearing and hearing impaired subjects speech reception thresholds srts were measured for target and competing speech signals processed to contain variable amounts of temporal fine structure tfs information signals were filtered into 30 1 erb n wide channels where erb n refers to the bandwidth of normal auditory filters which were either tone vocoded preserving temporal envelope information extracted using the hilbert transform or left unprocessed containing both tfs and envelope information improvements in srt were compared when tfs was progressively introduced starting with the high or low frequency channels the results suggest some redundancy in the tfs information across frequency regions in a second experiment the signal was divided into five 6 erb n wide spectral regions four of which were tone vocoded the remaining region was either absent creating a spectral notch or was present and unprocessed srts were measured for normal hearing and hearing impaired subjects conditions where all channels were vocoded or unprocessed were also included normal hearing subjects benefited similarly when tfs information was added to each region suggesting that tfs information is important over a wide frequency range hearing impaired subjects benefited less although the benefit varied across subjects benefit from tfs information in speech was correlated with a psychophysical measure of tfs sensitivity obtained at two center frequencies

fast algorithms for the multidimensional discrete fourier transform in this paper the prime factor algorithm for the evaluation of a one dimensional discrete fourier transform is generalized to the evaluation of multidimensional discrete fourier transforms defined on arbitrary periodic sampling lattices it is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete fourier transform as a sidelight to the derivation of the algorithm a chinese remainder theorem is derived for integer lattices

entropie geometrique des feuilletages on definit et on etudie l entropie geometrique d un feuilletage generalisant directement l entropie topologique d un flot

transform based image enhancement algorithms with performance measure this paper presents a new class of the frequency domain based signal image enhancement algorithms including magnitude reduction log magnitude reduction iterative magnitude and a log reduction zonal magnitude technique these algorithms are described and applied for detection and visualization of objects within an image the new technique is based on the so called sequency ordered orthogonal transforms which include the well known fourier hartley cosine and hadamard transforms as well as new enhancement parametric operators a wide range of image characteristics can be obtained from a single transform by varying the parameters of the operators we also introduce a quantifying method to measure signal image enhancement called eme this helps choose the best parameters and transform for each enhancement a number of experimental results are presented to illustrate the performance of the proposed algorithms

2 d and 1 d multipaired transforms frequency time type wavelets a concept of multipaired unitary transforms is introduced these kinds of transforms reveal the mathematical structure of fourier transforms and can be considered intermediate unitary transforms when transferring processed data from the original real space of signals to the complex or frequency space of their images considering paired transforms we analyze simultaneously the splitting of the multidimensional fourier transform as well as the presentation of the processed multidimensional signal in the form of the short one dimensional 1 d signals that determine such splitting the main properties of the orthogonal system of paired functions are described and the matrix decompositions of the fourier and hadamard transforms via the paired transforms are given the multiplicative complexity of the two dimensional 2 d 2 sup r spl times 2 sup r point discrete fourier transform by the paired transforms is 4 sup r 2 r 7 3 8 3 12 r 3 which shows the maximum splitting of the 5 d fourier transform into the number of the short 1 d fourier transforms the 2 d paired transforms are not separable and represent themselves as frequency time type wavelets for which two parameters are united frequency and time the decomposition of the signal is performed in a way that is different from the traditional haar system of functions

computer assisted techniques for the verification of the chebyshev property of abelian integrals abstract we develop techniques for the verification of the chebyshev property of abelian integrals these techniques are a combination of theoretical results analysis of asymptotic behavior of wronskians and rigorous computations based on interval arithmetic we apply this approach to tackle a conjecture formulated by dumortier and roussarie in f dumortier r roussarie birth of canard cycles discrete contin dyn syst 2 2009 723 781 which we are able to prove for q 2

importance of tonal envelope cues in chinese speech recognition recent studies have shown that temporal waveform envelope cues can provide significant information for english speech recognition this study investigated the use of temporal envelope cues in a tonal language mandarin chinese in this study the speech was divided into several frequency analysis bands the amplitude envelope was extracted from each band by half wave rectification and low pass filtering and was used to modulate a noise of the same bandwidth as the analysis band these manipulations preserved temporal and amplitude cues in each frequency band but removed the spectral detail within each band chinese vowels consonants tones and sentences were identified by 12 native chinese speaking listeners with 1 2 3 and 4 noise bands the results showed that the recognition score of vowels consonants and sentences increased monotonically with the number of bands a pattern similar to that observed in english speech recognition in contrast tones were consistently recognized at about 80 correct level independent of the number of bands this high level of tone recognition produced a significant difference in the open set sentence recognition between chinese 11 0 and english 2 9 for the one band condition where no spectral information was available the data also revealed that with primarily temporal cues the falling rising tone tone 3 and the falling tone tone 4 were more easily recognized than the flat tone tone 1 and the rising tone tone 2 this differential pattern in tone recognition resulted in a similar pattern in word recognition words having either tone 3 or 4 were more likely to be recognized while words having tone 1 and 2 were not the quantitative role of tones in chinese speech recognition was further explored using a power function model and found to play a significant role in relating phoneme recognition to sentence recognition

genericity conditions for finite cyclicity of elementary graphics abstract in this paper we explore the khovanskii method for proving the finite cyclicity of elementary graphics and how it can be applied in practice the genericity conditions needed in that case form a proper subset of the usual methods moreover some of the conditions are non intrinsic and can be artificially created by action of the automorphism groups preserving the normal forms near the singularities and their action on regular transitions hence we introduce an extension of the method which treats the usual functional pfaffian systems together with the admissible changes of coordinates in the functional equations

centennial history of hilbert s 16th problem the second part of hilbert s 16th problem deals with polynomial differential equations in the plane it remains unsolved even for quadratic polynomials there were several attempts to solve it that failed yet the problem inspired significant progress in the geometric theory of planar differential equations as well as bifurcation theory normal forms foliations and some topics in algebraic geometry the dramatic history of the problem as well as related developments are presented below 1 the problem and its counterparts what may be said about the number and location of limit cycles of a planar polynomial vector field of degree n the limit cycle is an isolated closed orbit of a vector field this second part of hilbert s 16th problem appears to be one of the most persistent in the famous hilbert list h second only to the riemann function conjecture traditionally hilbert s question is split into three each one requiring a stronger answer problem 1 is it true that a planar polynomial vector field has but a finite number of limit cycles problem 2 is it true that the number of limit cycles of a planar polynomial vector field is bounded by a constant depending on the degree of the polynomials only the bound on the number of limit cycles in problem 2 is denoted by h n and known as the hilbert number linear vector fields have no limit cycles hence h 1 0 it is still unknown whether or not h 2 exists problem 3 give an upper bound for h n a solution to any of these problems implies a solution for the previous ones only the first problem is solved now the positive answer was established in e92 i91 there are analytic counterparts of problems 1 and 2 received by the editors december 2001 2000 mathematics subject classification primary 34cxx 34mxx 37f75

the construction of low dispersive fdtd on hexagon based on the sampling theorem with arbitrary geometry the spatial discretization can be carried out on hexagonal lattices grids instead of rectangular lattices in the two dimensional case with the concept of the directional derivative in aid a new finite difference time domain fdtd method based on hexagonal lattices h fdtd is introduced the coefficients of the h fdtd method are chosen with aim to obtain the low numerical dispersion final numerical experiment shows that the numerical anisotropy of the h fdtd method is lower than that of the conventional yee fdtd method based on rectangular lattices r fdtd in addition some numerical examples are provided to verify its good performance on the low numerical anisotropy

the effect of smoothing filter slope and spectral frequency on temporal speech information it is known that information contained within the filter skirts can provide cues important to speech intelligibility however the role of filter slope during temporal smoothing has received little attention in experiment 1 smoothing filter slope angle was found to have a large effect on the intelligibility of sentences represented by three amplitude modulated sinusoids in experiment 2 the use of temporal cues above 16hz was examined across various regions of the spectrum when increases in rate were presented to individual spectral bands intelligibility only increased when presented in the higher spectral region this result suggests a greater reliance on higher rate cues in this region however intelligibility was greatest when these cues were distributed across the spectrum indicating that their effective use is not restricted solely to this region

method of paired transforms for reconstruction of images from projections discrete model an effective method of discrete image reconstruction from its projections is introduced the method is based on the vector and paired representations of the two dimensional 2d image with respect to the 2d discrete fourier transform such representations yield algorithms for image reconstruction by a minimal number of attenuation measurements in certain projections the proposed algorithms are described in detail for an n spl times n image when n 2 sup r r 1 the inverse formulas for image reconstruction are given the efficiency of the algorithms is expressed in the fact that they require a minimal number of multiplications or can be implemented without such at all the problem of discrete image reconstruction is also considered in three dimensional 3d space namely on the 3d torus where the reconstruction is performed by means of the nonlinear projections that are integral over 3d spirals on the torus

hilbert s 16th problem for quadratic vector fields abstract we discuss here a systematic approach towards a positive answer to hilbert s 16th problem for quadratic systems namely the existence of a uniform bound for the number of limit cycles of a quadratic system the method is the following describe the limit periodic sets surrounding the origin in a family of quadratic vector fields and prove that they have finite cyclicity in this paper we give the list of all graphics and degenerate graphics that should be considered and describe their general features we also indicate how to find or where to find concrete examples of these limit periodic sets

features of stimulation affecting tonal speech perception implications for cochlear prostheses tone languages differ from english in that the pitch pattern of a single syllable word conveys lexical meaning in the present study dependence of tonal speech perception on features of the stimulation was examined using an acoustic simulation of a cis type speech processing strategy for cochlear prostheses contributions of spectral features of the speech signals were assessed by varying the number of filter bands while contributions of temporal envelope features were assessed by varying the low pass cutoff frequency used for extracting the amplitude envelopes ten normal hearing native mandarin chinese speakers were tested when the low pass cutoff frequency was fixed at 512 hz consonant vowel and sentence recognition improved as a function of the number of channels and reached plateau at 4 to 6 channels subjective judgments of sound quality continued to improve as the number of channels increased to 12 the highest number tested tone recognition i e recognition of the four mandarin tone patterns depended on both the number of channels and the low pass cutoff frequency the trade off between the temporal and spectral cues for tone recognition indicates that temporal cues can compensate for diminished spectral cues for tone recognition and vice versa an additional tone recognition experiment using syllables of equal duration showed a marked decrease in performance indicating that duration cues contribute to tone recognition a third experiment showed that recognition of processed fm patterns that mimic mandarin tone patterns was poor when temporal envelope and duration cues were removed

use of high rate envelope speech cues and their perceptually relevant dynamic range for the hearing impaired the ability of hearing impaired hi listeners to use high rate envelope information in a competing talker situation was assessed in experiment 1 signals were tone vocoded and the cutoff frequency fc of the envelope extraction filter was either 50 hz e filter or 200 hz p filter the channels for which the p or e filter was used were varied intelligibility was higher with the p filter regardless of whether it was used for low or high center frequencies performance was best when the p filter was used for all channels experiment 2 explored the dynamic range over which hi listeners made use of high rate cues in each channel of a vocoder the envelope extracted using fc 16 hz was replaced by the envelope extracted using fc 300 hz either at the peaks or valleys with a parametrically varied switching threshold for a target to background ratio of 5 db changes in speech intelligibility occurred mainly when the switching threshold was between 8 and 8 db relative to the channel root mean square level this range is similar in width to but about 3 db higher in absolute level than that found for normal hearing listeners despite the reduced dynamic range of the hi listeners

effects of spectral smearing and temporal fine structure degradation on speech masking release this study assessed the effects of spectral smearing and temporal fine structure tfs degradation on masking release mr the improvement in speech identification in amplitude modulated compared to steady noise observed for normal hearing listeners syllables and noise stimuli were processed using either a spectral smearing algorithm or a tone excited vocoder the two processing schemes simulated broadening of the auditory filters by factors of 2 and 4 simulations of the early stages of auditory processing showed that the two schemes produced comparable excitation patterns however fundamental frequency f0 information conveyed by tfs was degraded more severely by the vocoder than by the spectral smearing algorithm both schemes reduced mr but for each amount of spectral smearing the vocoder produced a greater reduction in mr than the spectral smearing algorithm consistent with the effects of each scheme on f0 representation moreover the effects of spectral smearing on mr produced by the two schemes were different for manner and voicing finally mr data for listeners with moderate hearing loss were well matched by mr data obtained for normal hearing listeners with vocoded stimuli suggesting that impaired frequency selectivity alone may not be sufficient to account for the reduced mr observed for hearing impaired listeners