Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 24 num. 3 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<b><b>UNE PROPRIÉTÉ DU GROUPE Á 168 ÉLÉMENTS</b></b>]]> Let e be an affine space of dimension n over a field <img width=30 height=16 id="_x0000_i1026" src="http:/fbpe/img/proy/v24n3/img01-05.jpg">the affine group of e, G the corresponding linear group. To each point <img width=40 height=15 id="_x0000_i1027" src="http:/fbpe/img/proy/v24n3/img01-03.jpg">corresponds a section <img width=60 height=17 id="_x0000_i1028" src="http:/fbpe/img/proy/v24n3/img01-01.jpg">of the canonical map <img width=50 height=16 id="_x0000_i1029" src="http:/fbpe/img/proy/v24n3/img01-02.jpg">to the linear map <img width=50 height=21 id="_x0000_i1030" src="http:/fbpe/img/proy/v24n3/img01-04.jpg">corresponds the affine map <img width=25 height=23 id="_x0000_i1031" src="http:/fbpe/img/proy/v24n3/img01-06.jpg">wich has <img width=15 height=19 id="_x0000_i1032" src="http:/fbpe/img/proy/v24n3/img01-07.jpg">as associated linear map and a as fixed point. We proove that every section is of this type, except in the only one case where K = F2 and n = 3 <![CDATA[<b>OCCUPATION TIMES SEQUENCES AND</b> <b>MARTINGALES OF SIMPLE RANDOM</b><b> </b><b>WALKS ON THE REAL LINE</b>]]> Given a simple random walk on the real line , we consider the sequences of occupation times on states and associate to them martingales defined by the moments of first order of this random walk. We deduce by this way recurrent relations for the expectations of the occupation times in states before a given time , and then remarkable identities for the expectations of the absolute values of the random walk <![CDATA[<b>FIXED POINTS OF A FAMILY OF</b> <b>EXPONENTIAL MAPS</b>]]> We consider the family of functions ¦l(z) = exp(ilz), l real. With the help of MATLAB computations, we show ¦l has a unique attracting fixed point for several values of l. We prove there is no attracting periodic orbit of period n ³ 2 <![CDATA[<b>THE NATURAL VECTOR BUNDLE OF THE</b> <b>SET OF MULTIVARIATE DENSITY</b><b> </b><b>FUNCTIONS</b><b> </b>]]> We find a description of the set of multivariate density functions with given marginals and introduce an associated vector bundle. The interest for the probability theory is restricted to the nonnegative elements in the sets of the derived vector bundle. The fiber is the space of all correlation measures among a multivariate density function and its unidimensional marginals <![CDATA[<b>TOPOLOGICAL CLASSIFICATION OF COMPACT SURFACES WITH NODES OF GENUS 2</b>]]> We associate to each Riemann or Klein surface with nodes a graph that classifies it up homeomorphism. We obtain that, for surfaces of genus two, there are 7 topological types of stable Riemann surfaces, 33 topological types of stable Klein surfaces and 35 topological types of symmetric stable Riemann surfaces (this last type of surfaces corresponds to the new surfaces appearing in the compactification of the Moduli space of real algebraic curves, see [Se] and [Si] <![CDATA[<b>AN IMPROVEMENT OF J</b>: <b>RIVERA-LETELIER RESULT ON WEAK HYPERBOLICITY ON PERIODIC ORBITS FOR POLYNOMIALS</b>]]> We prove that for f : <img border=0 width=50 height=19 id="_x0000_i1026" src="http:/fbpe/img/proy/v24n3/img06-01.jpg">a rational mapping of the Riemann sphere of degree at least 2 and W a simply connected immediate basin of attraction to an attracting fixed point, if |(f n)'(p)| ³ Cn³+x for constants x > 0, C > 0 all positive integers n and all repelling periodic points p of period n in Julia set for f , then a Riemann mapping R : <img border=0 width=50 height=18 id="_x0000_i1027" src="http:/fbpe/img/proy/v24n3/img06-02.jpg">extends continuously to <img border=0 width=20 height=18 id="_x0000_i1028" src="http:/fbpe/img/proy/v24n3/img06-03.jpg">and FrW is locally connected. This improves a result proved by J. Rivera-Letelier for W the basin of infinity for polynomials, and 5 + x rather than 3 + x. <![CDATA[<b>COUNTABLE S</b><b><sup>*</sup></b><b>-COMPACTNESS IN</b> <b>L-SPACES</b><b> </b>]]> In this paper, the notions of countable S*-compactness is introduced in L-topological spaces based on the notion of S*-compactness. An S*-compact L-set is countably S*-compact. I¦ L = [0, 1], then countable strong compactness implies countable S*-compactness and countable S*-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S*-compact L-set and a closed L-set is countably S*-compact. The continuous image of a countably S*-compact L-set is countably S*-compact. A weakly induced L-space (X, T ) is countably S*-compact if and only if (X, [T]) is countably compact