Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 32 num. 2 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<b>Caracterisation des classes de (</b><strong><i>≤</i></strong><b> 3)-hypomorphie</b><strong> </strong><b>a l'aide d'interdits</b>]]> G. Lopez a démontré la(≤6)-reconstructibilitédes relationsbi-naires finies (1972) (voir [1] et [2]) résolvant ainsi un probleme de Roland Fraissé (voir[3]). Sa preuve repose sur la notion de classe de difference. Depuis, la notion de classe de difference est un outil ma-jeur dans bien des travaux en reconstruction et demi-reconstruction notammenten[4], [5] et [6]etpermet dedefinir la notion de classe d'hypomorphie. La caracterisation des classes de (≤k)-hypomorphie finies, pour k≥6, a été obtenue par Hagendorf et Lopez en 1994 (voir [4]). La caracterisation des classes de (≤4)-hypomorphie finies a ete obtenue par G. Lopez et C. Rauzy (1992) (voir [6]). Ensuite, celle des classes de (≤5)-hypomorphie finies a etetrouvee par Y. Boudabbous (2000) (voir [7]). Dans cet article nous obtenons une caracterisation, par interdits, des classes de (≤3)-hypomorphie finies, puis infinies dans un prochain article. Ces deux articles sont resumes en [8]. La reconstruction infinie a ete en particulier etudiee en [4], [9] et [11]. D'autres utilisations des classes de difference ou des liens avec elles se trouvent par exemple dans [12] a [21]. <![CDATA[<b>On square sum graphs</b>]]> A (p, q)-graph G is said to be square sum, if there exists a bijection f : V(G) - {0,1, 2,...,p - 1} such that the induced function f * : E(G) - N given by f * (uv) = (f (u))² + (f (v))² for every uv G E(G) is injective. In this paper we initiate a study on square sum graphs and prove that trees, unicyclic graphs, mCn,m > 1,cycle with a chord, the graph obtained by joining two copies of cycle Cn by a path Pk and the graph defined by path union of k copies of Cn, when the path Pn = P2 are square sum. <![CDATA[<b>The Nemytskii operator on bounded </b>ö<b>-variation in the mean spaces</b>]]> We introduce the notion of bounded Ö-variation in the sense of LÖ-norm. We obtain a Riesz type result for functions of bounded Ö-variation in the mean. We also show that if the Nemytskii operator act on the bounded Ö-variation in the mean spaces into itself and satisfy some Lipschitz condition there exist two functions g and h belonging to the bounded Ö-variation in the mean space such that f (t,y) = g(t)y + h(t),t ∈ [0, 2ð], y ∈ R. <![CDATA[<b>The stability of fuzzy approximately Jordan</b> <b>mappings</b>]]> In this paper we introduce the concept of fuzzy approximately Jordan mappings in fuzzy algebras, and study some of their basic properties. The main purpose of this paper is to study the stability of fuzzy approximately Jordan mappings in fuzzy algebras. <![CDATA[<b>Some new generalized I-convergent difference sequence spaces defined by a sequence of moduli</b>]]> In this articlewe introduce the sequence space <img src="http:/fbpe/img/proy/v32n2/art5.1.jpg" name="_x0000_i1028" width=82 height=20 id="_x0000_i1028">and <img src="http:/fbpe/img/proy/v32n2/art5.2.jpg" name="_x0000_i1027" width=83 height=20 id="_x0000_i1027">for the of sequence of modulii F = (/¾) and given some inclusion relations. These results here proved are analogus to those by M.Aiyub [1](Global Journal of Science Frontier Research Mathematics and Decision Sciences 12(9)(2012),32-36). <![CDATA[<b>An approximation formula for n!</b>]]> We prove the following very accurate approximation formula for the factorial function: <img src="http:/fbpe/img/proy/v32n2/art6.1.jpg" name="_x0000_i1029" width=383 height=46 id="_x0000_i1029"> This gives better results than the following approximation formula <img src="http:/fbpe/img/proy/v32n2/art6.2.jpg" name="_x0000_i1028" width=455 height=49 id="_x0000_i1028"> which is established by the author [5] and C. Mortici [16] independently, and gives similar results with <img src="http:/fbpe/img/proy/v32n2/art6.3.jpg" name="_x0000_i1027" width=369 height=48 id="_x0000_i1027"> which is established by C. Mortici in his very new paper [8]. <![CDATA[<b>Edge Detour Monophonic Number of a Graph</b>]]> For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G) .We determine bounds for it and characterize graphs which realize these bounds. Also, certain general properties satisfied by an edge detour monophonic set are studied. It is shown that for positive integers a, b and c with 2 ≤ a ≤ c, there exists a connected graph G such that m(G) = a, m!(G) = b and edm(G) = c,where m(G) is the monophonic number and m! (G) is the edge monophonic number of G. Also, for any integers a and b with 2 ≤ a ≤ b, there exists a connected graph G such that dm(G) = a and edm(G)= b,where dm(G) is the detour monophonic number of a graph G.