topological degree theory and fixed point theorems in fuzzy normed space abstract in this paper the leray schauder topological degree theory is developed in a fuzzy normed space since the linear topology on this fuzzy normed space is not necessarily locally convex and since each menger probabilistic normed space can be considered as a special fuzzy normed space the degree theory in this paper is different from the degree theory in locally convex linear topological space presented by nagumo amer j math 73 1951 497 511 and it also is an extension of the degree theory in menger probabilistic normed space studied by zhang and chen appl math mech 10 6 1989 477 486 applying this degree theory some fixed point theorems for operators are given in fuzzy normed spaces and some former corresponding results are extended and improved

hadamard products of linear spaces abstract we describe properties of hadamard products of algebraic varieties we show any hadamard power of a line is a linear space and we construct star configurations from products of collinear points tropical geometry is used to find the degree of hadamard products of other linear spaces

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

matroid configurations and symbolic powers of their ideals star configurations are certain unions of linear subspaces of projective space that have been studied extensively we develop a framework for studying a substantial gen eralization which we call matroid configurations whose ideals generalize stanley reisner ideals of matroids such a matroid configuration is a union of complete intersections of a fixed codimension relating these to the stanley reisner ideals of matroids and using methods of liaison theory allows us in particular to describe the hilbert function and minimal generators of the ideal of what we call a hypersurface configuration we also establish that the symbolic powers of the ideal of any matroid configuration are cohen macaulay as applications we study ideals coming from certain complete hypergraphs and ideals derived from tetrahedral curves we also consider waldschmidt constants and resurgences in particular we determine the resurgence of any star configuration and many hypersurface configurations previously the only non trivial cases for which the resurgence was known were certain monomial ideals and ideals of finite sets of points finally we point out a connection to secant varieties of varieties of reducible forms

on zwicker tones and musical pitch in the likely absence of phase locking corresponding to the pitcha it was assessed whether zwicker tones zts an auditory afterimage produced by a band stop noise have a musical pitch first stage i musically trained subjects adjusted the frequency level and decay time of an exponentially decaying diotic sinusoid to sound similar to the zt they perceived following the presentation of diotic broadband noise for various band stop positions next stage ii subjects adjusted a sinusoid in frequency and level so that its pitch was a specified musical interval below that of either a preceding zt or a preceding sinusoid and so that it was equally loud for each subject the reference sinusoid corresponded to their adjusted sinusoid from stage i subjects selected appropriate frequency ratios for zts although the standard deviations of the adjustments were larger for the zts than for the equally salient sinusoids by a factor of 1 0 2 2 experiments with monaural stimuli led to similar results although the pitch of the zts could differ for monaural and diotic presentation of the zt exciting noise the results suggest that a weak musical pitch may exist in the absence of phase locking in the auditory nerve to the frequency corresponding to the pitch or harmonics thereof at the time of the percept

fuzzy bounded linear operators in felbin s type fuzzy normed linear spaces in this paper definitions of strongly fuzzy bounded linear operator and weakly fuzzy bounded linear operators are given and the idea of their fuzzy norms are introduced the concept of fuzzy dual spaces are introduced and the hahn banach theorem is established in fuzzy setting

fuzzy real numbers abstract the paper gives a contribution to the study of fuzzy real numbers continuing that in eklund and gahler 1988 gahler and gahler 1992 and gahler 1992 we start with investigating algebraic properties using two types of decompositions of fuzzy numbers and the notions of fuzzy norm of symmetric difference and of supplements of fuzzy numbers by means of these notions two special fuzzy metrics on the fuzzy real line are given the fuzzy distance function d and the extended fuzzy distance function d the main interest concerns fuzzy topological properties of the fuzzy real line in particular there are studied the fuzzy topologies t t d and t d t is closely related to the fuzzy topology of hutton s fuzzy unit interval and t d and t d are canonically generated by the fuzzy metrics d and d respectively

betti numbers of symmetric shifted ideals abstract we introduce a new class of monomial ideals which we call symmetric shifted ideals symmetric shifted ideals are fixed by the natural action of the symmetric group and within the class of monomial ideals fixed by this action they can be considered as an analogue of stable monomial ideals within the class of monomial ideals we show that a symmetric shifted ideal has linear quotients and compute its equivariant graded betti numbers as an application of this result we obtain several consequences for graded betti numbers of symbolic powers of defining ideals of star configurations

star configurations on generic hypersurfaces let f be a homogeneous polynomial in s c x0 xn our goal is to understand a particular polynomial decomposition of f geometrically we wish to determine when the hypersurface defined by f in pn contains a star configuration to solve this problem we use techniques from commutative algebra and algebraic geometry to reduce our question to computing the rank of a matrix

perceptual separation of concurrent speech sounds absence of across frequency grouping by common interaural delay three experiments and a computational model explored the role of within channel and across channel processes in the perceptual separation of competing complex broadband sounds which differed in their interaural phase spectra in each experiment two competing vowels whose first and second formants were represented by two discrete bands of noise were presented concurrently for identification experiments 1 and 2 showed that listeners were able to identify the vowels accurately when each was presented to a different ear but were unable to identify the vowels when they were presented with different interaural time delays itds i e listeners could not group the noisebands in different frequency regions with the same itd and thereby separate them from bands in other frequency regions with a different itd experiment 3 demonstrated that while listeners were unable to exploit a difference in interaural delay between the pairs of noisebands listeners could identify a vowel defined by interaurally decorrelated noisebands when the other two noisebands were interaurally correlated a computational model based upon that of durlach j acoust soc am 32 1075 1076 1960 showed that the results of these and other experiments can be interpreted in terms of a within channel mechanism which is sensitive to interaural decorrelation thus the across frequency integration which occurs in the lateralization of complex sounds may play little role in segregating concurrent sounds

linear subspaces symbolic powers and nagata type conjectures abstract inspired by results of guardo van tuyl and the second author for lines in p 3 we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r dimensional planes in p n for n 2 r 1 these considerations lead to new conjectures that suggest that the well known conjecture of nagata for points in p 2 is not an exotic statement but rather a manifestation of a much more general phenomenon which seems to have been overlooked so far

evolutions symbolic squares and fitting ideals given a reduced local algebra t over a suitable ring or field k we study the question of whether there are nontrivial algebra surjections r t which induce isomorphisms r k t t k such maps called evolutions arise naturally in the study of hecke algebras as they implicitly do in the recent work of wiles taylor wiles and flach we show that the existence of non trivial evolutions of an algebra t can be characterized in terms of the symbolic square of an ideal defining t we give a characterization of the symbolic square in terms of fitting ideals using this and other techniques we show that certain classes of reduced algebras codimension 2 cohen macaulay codimension 3 gorenstein licci algebras in general and some others admit no nontrivial evolutions on the other hand we give examples showing that non trivial evolutions of reduced cohenmacaulay algebras of codimension 3 do exist in every positive characteristic

integration of monaural and binaural evidence of vowel formants the intelligibility of speech is sustained at lower signal to noise ratios when the speech has a different interaural configuration from the noise this paper argues that the advantage arises in part because listeners combine evidence of the spectrum of speech in the across frequency profile of interaural decorrelation with evidence in the across frequency profile of intensity to support the argument three experiments examined the ability of listeners to integrate and segregate evidence of vowel formants in these two profiles in experiment 1 listeners achieved accurate identification of the members of a small set of vowels whose first formant was defined by a peak in one profile and whose second formant was defined by a peak in the other profile this result demonstrates that integration is possible experiment 2 demonstrated that integration is not mandatory insofar as listeners could report the identity of a vowel defined entirely in one profile despite the presence of a competing vowel in the other profile the presence of the competing vowel reduced accuracy of identification however showing that segregation was incomplete experiment 3 demonstrated that segregation of the binaural vowel in particular can be increased by the introduction of an onset asynchrony between the competing vowels the results of experiments 2 and 3 show that the intrinsic cues for segregation of the profiles are relatively weak overall the results are compatible with the argument that listeners can integrate evidence of spectral peaks from the two profiles

dichotic pitches as illusions of binaural unmasking ii the fourcin pitch and the dichotic repetition pitch the predictions of three models are compared with respect to existing experimental data on the perception of the fourcin pitch fp and the dichotic repetition pitch drp each model generates a central spectrum cs which is examined for peaks at frequencies consistent with the perceived pitches a modified equalization cancellation me c model of binaural unmasking culling and summerfield j acoust soc am 98 785 797 1995 generates a cs which reflects the degree of interaural decorrelation present in each frequency channel this model accounts for the perceived frequencies of fps but produces no output for drp stimuli a restricted equalization cancellation re c model bilsen and goldstein j acoust soc am 55 292 296 1974 sums the time varying excitation in corresponding frequency channels without equalization to form a cs a central activity pattern cap model raatgever and bilsen j acoust soc am 80 429 441 1986 generates a cs by scanning an interaural cross correlation matrix across frequency the re c and cap models yield inaccurate predictions of the perceived frequencies of fps but predict the occurrence of the drp and its correct pitch the complementary predictions of the me c model compared to the re c and cap models together with the evidence that the fp is clearly audible for the majority of listeners while the drp is faintly heard by a minority of listeners suggest that the me c model provides the best available account of the fp and that the drp is produced by a separate mechanism

suggested formulae for calculating auditory filter bandwidths and excitation patterns recent estimates of auditory filter shape are used to derive a simple formula relating the equivalent rectangular bandwidth erb of the auditory filter to center frequency the value of the auditory filter bandwidth continues to decrease as center frequency decreases below 500 hz a formula is also given relating erb rate to frequency finally a method is described for calculating excitation patterns from filter shapes

temporal pitch perception and the binaural system two experiments examined the relationship between temporal pitch and more generally rate perception and auditory lateralization both used dichotic pulse trains that were filtered into the same high 3900 5400 hz frequency region in order to eliminate place of excitation cues in experiment 1 a 1 s periodic pulse train of rate fr was presented to one ear and a pulse train of rate 2fr was presented to the other in the synchronous condition every other pulse in the 2fr train was simultaneous with a pulse in the opposite ear in each trial subjects concentrated on one of the two binaural images produced by this mixture they matched its perceived location by adjusting the interaural level difference ild of a bandpass noise and its rate pitch was then matched by adjusting the rate of a regular pulse train the results showed that at low fr e g 2 hz subjects heard two pulse trains of rate fr one in the higher rate ear and one in the middle of the head at higher fr 25 hz subjects hea

some fixed point theorems in fuzzy normed linear spaces in this paper the concepts of sectional fuzzy continuous mappings l fuzzy compact sets asymptotic fuzzy normal structure and strong uniformly convex fuzzy normed linear spaces have been introduced schauder type and other fixed point theorems have been established in fuzzy normed linear spaces

a central spectrum theory of binaural processing evidence from dichotic pitch a theory is presented that describes the binaural processing of interaural time or phase differences it is an elaboration of the central spectrum concept for the explanation of dichotic pitch phenomena f a bilsen pitch of noise signals evidence for a central spectrum j acoust soc am 61 150 161 1977 the generation is postulated for central activity patterns cap due to binaural interaction from these caps the central processor selects specific spectral information that constitutes the information for lateralization dichotic pitch binaural masking etc here a strategy is assumed to be based on central spectra cs rather than on interaural cross correlation for the calculation of the central activity patterns a number of assumptions have been introduced the peripheral filters are supposed to be infinitesimally narrow the analog filter outputs from corresponding filters at both ears are thought to interact by means of a linear delay and add mechanism the squared output power

fuzzy bounded linear operators in this paper a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types strong and weak of fuzzy bounded linear operators are defined relation between fuzzy continuity and fuzzy boundedness is studied definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed the hahn banach theorem the open mapping theorem the closed graph theorem and the uniform boundedness principle theorem are established

a comparative study of fuzzy norms on a linear space in this paper a comparative study among several types of fuzzy norms on a linear space defined by various authors has been made and it is shown that broadly they may be classified into two types one of which is katsaras s type and the other is felbin s type

dichotic pitches as illusions of binaural unmasking i huggins pitch and the binaural edge pitch the two most salient dichotic pitches the huggins pitch hp and the binaural edge pitch bep are produced by applying interaural phase transitions of 360 and 180 degrees respectively to a broadband noise this paper examines accounts of these pitches concentrating on a central activity pattern cap model and a modified equalization cancellation me c model the cap model proposes that a dichotic pitch is heard at frequency f when an individual across frequency scan in an interaural cross correlation matrix contains a sharp peak at f the me c model proposes that a dichotic pitch is heard when a plot of interaural decorrelation against frequency contains a peak at f the predictions of the models diverge for the bep at very narrow transition bandwidths the me c model predicts that salience is sustained while the cap model predicts that salience declines and that the dominant percept is of the in phase segment of the noise experiment 1 showed that the salience of the bep was sustained at the narrowest bandwidths that could be generated 0 5 of the transition frequency experiment 2 confirmed that the pitch of a bep produced by a 0 5 transition bandwidth was close to the frequency of the transition band experiment 3 showed that pairs of simultaneous narrow 180 degree transitions whose frequencies corresponded to vowel formants were perceived as the intended vowels moreover the same vowels were perceived whether the in phase portion of the noise lay between the two transition frequencies or on either side of them in contrast different patterns of identification responses were made to diotic band pass and band stop noises whose cutoff frequencies corresponded to the same formants thus the vowel identification responses made to the dichotic stimuli were not based on hearing the in phase portions of the noise as formants these results are not predicted by the cap model but are consistent with the me c model it is argued that the me c model provides a more coherent and parsimonious account of many aspects of the hp and the bep than do alternative models

on the first infinitesimal neighborhood of a linear configuration of points in p2 abstract we consider the following open questions fix a hilbert function h that occurs for a reduced zero dimensional subscheme of p 2 among all subschemes x with hilbert function h what are the possible hilbert functions and graded betti numbers for the first infinitesimal neighborhood z of x i e the double point scheme supported on x is there a minimum h min and maximum h max such function the numerical information encoded in h translates to a type vector which allows us to find unions of points on lines called linear configurations with hilbert function h we give necessary and sufficient conditions for the hilbert function and graded betti numbers of the first infinitesimal neighborhoods of all such linear configurations to be the same even for those h for which the hilbert functions or graded betti numbers of the resulting double point schemes are not uniquely determined we give one depending only on h that does occur we prove the existence of h max in general and discuss h min our methods include liaison techniques

detection of static and dynamic changes in interaural correlation this study examines the relation between a static and a dynamic measure of interaural correlation discrimination 1 the just noticeable difference jnd in interaural correlation and 2 the minimum detectable duration of a fixed interaural correlation change embedded within a single noise burst of a given reference correlation for the first task jnds were obtained from reference interaural correlations of 1 1 and from 0 interaural correlation in either the positive or negative direction for the dynamic task duration thresholds were obtained for a brief target noise of 1 1 and 0 interaural correlation embedded in reference marker noise of 1 1 and 0 interaural correlation performance with a reference interaural correlation of 1 was significantly better than with a reference correlation of 1 similarly when the reference noise was interaurally uncorrelated discrimination was significantly better for a target correlation change towards 1 than towards 1 thus for both static and dynamic tasks interaural correlation discrimination in the positive range was significantly better than in the negative range using the two measures the length of a binaural temporal window was estimated its equivalent rectangular duration erd was approximately 86 ms and independent of the interaural correlation configuration

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

fixed point theorems for fuzzy mappings in this paper some results on fixed point theorems for contractive type fuzzy mappings and nonexpansive fuzzy mappings are obtained which are extensions of the results of bose and mukherjee and that of bose and sahani

symbolic powers of monomial ideals and vertex cover algebras abstract we introduce and study vertex cover algebras of weighted simplicial complexes these algebras are special classes of symbolic rees algebras we show that symbolic rees algebras of monomial ideals are finitely generated and that such an algebra is normal and cohen macaulay if the monomial ideal is squarefree for a simple graph the vertex cover algebra is generated by elements of degree 2 and it is standard graded if and only if the graph is bipartite we also give a general upper bound for the maximal degree of the generators of vertex cover algebras

binaural models and the strength of dichotic pitches modern physiologically based models of the binaural system incorporate internal delay lines in the pathways from left and right peripheries to central processing nuclei different binaural models for the formation of dichotic pitch employ these delay lines in different ways consequently the different models make different predictions for the relative strengths of dichotic pitches made with particular phase conditions the differences are magnified for dichotic pitches at low frequencies where especially long delay lines may be required data from four low frequency pitch strength experiments on pure tone like dichotic pitches two on huggins pitch and two on binaural coherence edge pitch are consistent with models of the equalization cancellation type and not consistent with the central activity pattern model

pitch shifts of mistuned partials a time domain model mistuning one partial of a complex harmonic tone makes that partial easier to hear as a tone separate from the complex at the same time two pitch shifts may be observed first the low pitch of the complex is shifted in the direction of the mistuning as if it were pulled by the partial second the mistuning of the partial is perceptually exaggerated as if the pitch of the partial were pushed away from the harmonic series defined by the complex this paper shows how the latter effect can emerge within a hypothetical neural circuit the circuit involves a gating neuron fed by three pathways one direct and excitatory and the other two delayed and inhibitory the neuron responds to any excitatory input spike unless it is accompanied by an inhibitory input spike on either delayed input thus acting as a kind of anticoincidence counter the first delay is fixed and tuned to the period of the background harmonic complex its purpose is to weaken correlates of in tune components and allow the mistuned partial to stand out the second delay is variable and used to estimate the period of the mistuned partial by searching for a minimum output as a function of delay with an appropriate choice of parameters the estimate is subject to shifts that are of the same sign as the mistuning and that peak at about 4 mistuning and decrease beyond as observed experimentally

a common fixed point theorem in fuzzy metric spaces abstract in this note jungck s common fixed point theorem is generalized to fuzzy metric spaces grabiec 2 proved the contraction principle in the setting of fuzzy metric spaces introduced by kramosil and michalek 5 this note offers a generalization of jungck s theorem 3 in the setting of a fuzzy metric space in the following text the preliminaries are collected

chudnovsky s conjecture for very general points in pkn abstract we prove a long standing conjecture of chudnovsky for very general and generic points in p k n where k is an algebraically closed field of characteristic zero and for any finite set of points lying on a quadric without any assumptions on k we also prove that for any homogeneous ideal i in the homogeneous coordinate ring r k x 0 x n chudnovsky s conjecture holds for large enough symbolic powers of i

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

the lateralization of simple dichotic pitches a simple dichotic pitch arises when a single narrow band possesses a different interaural configuration from a surrounding broadband noise whose interaural configuration is uniform and correlated such pitches were created by interaurally decorrelating a narrow band experiment 1 or by giving a narrow band a different interaural time difference from the noise experiment 2 using an adaptive forced choice procedure listeners adjusted the interaural intensity difference of pointers to match their lateralization to that of the dichotic pitches the primary determinants of lateralization were the interaural configuration of the broadband noise experiment 1 the center frequency of the narrow band experiment 1 and its interaural configuration experiment 2 the ability of two computational models to predict these results was evaluated a version of the central spectrum model j raatgever and f a bilsen j acoust soc am 80 429 441 1986 incorporating realistic frequency selectivity accounted for the main results of experiment 1 but not experiment 2 a new reconstruction comparison model accounted for the main results of both experiments to accommodate the variables shown to influence lateralization this model segregates evidence of the dichotic pitch from the noise reconstructs the cross correlogram of the noise and compares it with the cross correlogram of the original stimulus

star configurations in pn abstract star configurations are certain unions of linear subspaces of projective space they have appeared in several different contexts the study of extremal hilbert functions for fat point schemes in the plane the study of secant varieties of some classical algebraic varieties the study of the resurgence of projective schemes in this paper we study some algebraic properties of the ideals defining star configurations including getting partial results about hilbert functions generators and minimal free resolutions of the ideals and their symbolic powers we also show that their symbolic powers define arithmetically cohen macaulay subschemes and we obtain results about the primary decompositions of the powers of the ideals as an application we compute the resurgence for the ideal of the codimension n 1 star configuration in p n in the monomial case i e when the number of hyperplanes is n 1

on fixed point theorems of gregori and sapena using the theory of countable extension of a t norm we prove in this paper that the fixed point theorem of gregori and sapena holds under more general conditions

effects of contralateral presentation and of interaural time differences in segregating a harmonic from a vowel the extent to which the 500 hz component of a steady state vowel contributed to its phonemic category was measured by estimating the position of the i e phoneme boundary along a first formant f1 continuum shifts in the phoneme boundary were calibrated against shifts produced by physical changes in the level of the 500 hz component when the 500 hz component was presented contralateral to the rest of the vowel the phoneme boundary changed by an amount equivalent to a physical reduction in the level of the component of about 5 db experiment 1 however giving the 500 hz component an interaural time difference itd of 666 s and the remainder of the vowel an itd of 666 s did not reduce the component s contribution to vowel quality experiment 2 placing the 500 hz component of the vowel in a sequence of 500 hz tones substantially reduced the contribution of the 500 hz component the contribution was further reduced by giving both the tone sequence and the component an itd of 666 s and the re

supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings this paper generalizes a classical result about the space of bounded closed sets with the hausdorff metric and establishes the completeness of cb x with respect to the completeness of the metric space x where cb x is the class of fuzzy sets with nonempty bounded closed a cut sets equipped with the supremum metric d which takes the supremum on the hausdorff distances between the corresponding a cut sets in addition some common fixed point theorems for fuzzy mappings are proved and two examples are given to illustrate the validity of the main results in fixed point theory

fixed point theorems for fuzzy mappings in quasi metric spaces we obtain fixed point theorems for fuzzy mappings in smyth complete and left k complete quasi metric spaces respectively well known theorems are special cases of our results

fixed point theorems on fuzzy normed linear spaces in this paper definitions of strongly fuzzy convergent sequence l fuzzy weakly convergent sequence and l fuzzy weakly compact set are given in a fuzzy normed linear space the concepts of fuzzy normal structure fuzzy non expansive mapping uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non expansive mappings are proved