quadratic higher order criteria for iterative blind separation of a mimo convolutive mixture of sources this paper deals with the problem of source separation in the case when the observations result from a multiple input multiple output convolutive mixing system in a blind framework higher order contrast functions have been proved to be efficient for extracting sources inspired by a semiblind approach we propose new contrast functions for blind signal separation that make use of reference signals the main advantage of this approach consists in the quadratic form of these criteria the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available the separation of the other sources from the mixture is then carried out by an iterative deflation method furthermore these contrasts are shown to be valid for both independent identically distributed i i d and non i i d source signals the performance offered by these criteria is investigated through simulations they appear as very appealing tools compared with some classical contrast functions

common fixed point theorems for contractive maps two common fixed point theorems have been proved by using minimal type commutativity and contractive conditions the last theorem extends known results on compatible maps to a wider class of mappings

some consequences of masser s counting theorem on elliptic curves we use masser s counting theorem to prove a lower bound for the canonical height in powers of elliptic curves we also prove the galois case of the elliptic lehmer problem combining kummer theory and masser s result with bounds on the rank and torsion of some groups of rational points on an elliptic curve

mesures et equidistribution sur les espaces de berkovich the proof by ullmo and zhang of bogomolov s conjecture about points of small height in abelian varieties made a crucial use of an equidistribution property for small points in the associated complex abelian variety we study the analogous equidistribution property at p adic places our results can be conveniently stated within the framework of the analytic spaces defined by berkovich the first one is valid in any dimension but is restricted to algebraic metrics the second one is valid for curves but allows for more general metrics in particular to the normalized heights with respect to dynamical systems

note on common fixed points under strict contractive conditions the first error occurs in lines 4 7 on page 329 which claim that the inequality d f u ff u max d gu gf u k d f u gu d ff u gf u 2 k d ff u gu d f u gf u 2 kd f u ff u leads to a contradiction however this inequality does not lead to a contradiction unless condition ii is slightly modified to overcome this problem we replace the condition ii of theorem 2 1 by d f x fy max d gx gy k d f x gx d fy gy 2 d fy gx d f x gy 2 1 k 2 ii with the above modification the theorem can be proved along the similar lines as given in the original one with minor changes in accordance with the replaced condition ii

a generalization of the banach contraction principle one of the most fundamental fixed point theorems is banach s contraction principle of which the following conjecture is a generalization generalized banach contraction conjecture gbcc let t be a self map of a complete metric space x d and let 0 m 1 let j be a positive integer assume that for each pair x y x min d tkx tky 1 k j md x y then t has a fixed point unlike banach s original theorem the case j 1 the above hypothesis does not compel t to be continuous in this paper we use a density argument coupled with ramsey s theorem from combinatorics to establish the gbcc for arbitrary j without the assumption of continuity it is known that the case j 3 includes instances where t is not continuous at any nonisolated point of x the arguments are constructive and may be useful in establishing other fixed point theorems without appealing to the axiom of choice

unbiased efficient estimator of the fourth order cumulant for random zero mean non i i d signals particular case of ma stochastic process non gaussian processes may require not only the information provided by first two moments but also that given by the higher order statistics in particular by the third and fourth order moments or cumulants this paper addresses a fourth order cumulant estimation problem for real discrete time random non i i d signal that can be approximated as an ma stochastic process an unbiased estimator is proposed studied and compared to two other frequently used estimators of the fourth order cumulant natural estimator and fourth k statistics statistical comparative studies are undertaken from both bias and mse points of view for different distribution laws and ma filters algorithms aiming to reduce computational complexity of the proposed estimator as well as that of the fourth k statistics bias are also provided

common fixed point theorems under strict contractive conditions in menger spaces abstract the main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property e a in menger probabilistic metric spaces as applications we obtain the corresponding common fixed point theorems under strict contractive in metric spaces

common fixed points under strict contractive conditions abstract the aim of the present paper is to obtain common fixed point theorems under strict contractive conditions by using a minimal commutativity condition our results extend the recent results due to pant 1998 j math anal appl 226 251 258 1999 soochow j math 25 37 42

the estimation of the fourth order cumulant for dependent data consistency and asymptotic normality let xi be a stationary dependent random process with finite eight order moments for broad classes of processes mixing and strongly mixing we obtain the convergence in probability with sharp rates of the estimate of the fourth order cumulant from n observations xi i 1 n we also establish the asymptotic distribution of the estimation error the asymptotic expression of the variance is explicitly specified

on generalizations of the meir keeler type contraction maps in 1969 meir and keeler 29 obtained a remarkable generalization of the banach contraction principle since then there have appeared a number of generalizations of their result in 1981 the second author and bae 33 extended the meir keeler theorem to two commuting maps by adopting jungck s method this influenced many authors and consequently a number of new results in this line followed recent works of sessa and others 46 47 contain common fixed point theorems of four maps satisfying certain contractive type conditions in the present paper we give a new result which encompasses most of such generalizations of the meir keeler theorem further our result also includes many other generalizations of the banach contraction principle some authors have obtained their results on 2 metric spaces however 2 metric versions are easily obtained from metric ones by an obvious

fixed point theorems for families of weakly non expansive maps abstract in this paper we present some fixed point theorems for families of weakly non expansive maps under some relatively weaker and more general conditions our results generalize and improve several results due to jungck g jungck fixed points via a generalized local commutativity int j math math sci 25 8 2001 497 507 jachymski j jachymski a generalization of the theorem by rhoades and watson for contractive type mappings math japon 38 6 1993 1095 1102 guo c guo an extension of fixed point theorem of krasnoselski chinese j math p o c 21 1 1993 13 20 rhoades b e rhoades a comparison of various definitions of contractive mappings trans amer math soc 226 1977 257 290 and others

coincidence and fixed points in symmetric spaces under strict contractions abstract some common fixed point theorems due to aamri and el moutawakil m aamri d el moutawakil some new common fixed point theorems under strict contractive conditions j math anal appl 270 2002 181 188 and pant and pant r p pant v pant common fixed points under strict contractive conditions j math anal appl 248 2000 327 332 proved for strict contractive mappings in metric spaces are extended to symmetric semi metric spaces under tight conditions some related results are derived besides discussing illustrative examples which establish the utility of results proved in this note

a complete comparison of 25 contraction conditions abstract in this paper we establish a comparison of the 25 contraction conditions considered in a previous paper of rhoades 16 thus completing the comparison first made in a systematic way in that paper

coincidence and fixed points for hybrid strict contractions abstract we define the property e a for single valued and multivalued mappings and introduce the notion of t weak commutativity for a hybrid pair f t of single valued and multivalued maps we obtain some coincidence and fixed point theorems for this class of maps and derive as application an approximation theorem

identification and deconvolution of multichannel linear non gaussian processes using higher order statistics and inverse filter criteria this paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple input multiple output mimo system given only the measurements of the vector output of the system the system is assumed to be driven by a temporally i i d and spatially independent non gaussian vector sequence which is not observed an iterative inverse filter criteria based approach is developed using the third order or the fourth order normalized cumulants of the inverse filtered data at zero lag stationary points of the proposed cost functions are investigated the approach is input iterative i e the input sequences are extracted and removed one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed the strong consistency of the proposed approach is also briefly discussed computer simulation examples are presented to illustrate the proposed approaches

some new common fixed point theorems under strict contractive conditions the main purpose of this paper is to give some new common fixed point theorems under strict contractive conditions for mappings satisfying a new property

small height and infinite nonabelian extensions let e be an elliptic curve defined over q without complex multiplication the field f generated over q by all torsion points of e is an infinite nonabelian galois extension of the rationals which has unbounded wild ramification above all primes we prove that the absolute logarithmic weil height of an element of f is either zero or bounded from below by a positive constant depending only on e we also show that the neron tate height has a similar gap on e f and use this to determine the structure of the group e f

unbiased adaptive estimations of the fourth order cumulant for real random zero mean signal in this paper a consistent efficient estimator of the fourth order cumulant for real discrete time random i i d at least up to order 8 zero mean signal is proposed in both batch and adaptive versions in batch version the proposed estimator is not only consistent but also unbiased and efficient the systematical theoretical and experimental studies with comparisons between the proposed estimator and three other estimators of the fourth order cumulant the natural or the traditional one the trivial unbiased estimator for the known power case and the fourth k statistics are undertaken for both normal and uniform processes then the adaptive versions of the estimators all except the fourth k statistics are given and studied in detail the convergence in mean and the convergence in mean square analyses are performed for them first theoretically then empirically finally the whole set of analyses carried out for both batch and adaptive versions shows that from many points of view the proposed estimator is interesting for use in versatile signal processing applications especially in real time and short term ones