Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 20 num. 2 lang. en <![CDATA[SciELO Logo]]> <![CDATA[PRESERVING FUZZY SG-CLOSED SETS]]> In this paper we consider new weak and stronger forms of fuzzy irresolute and fuzzy semi-closure via the concept Fsg-closed sets which we call Fap-irresolute maps, Fap-semi-closed maps and contra-fuzzy irresolute and we use it to obtain several results in the literature concerning the preservation of fuzzy sg-closed sets and to abtain also a characterization of fuzzy semi-T1/2 spaces <![CDATA[BOUNDS FOR CONFORMAL AUTOMOMORPHISMS OF RIEMANN SURFACES WITH CONDITION (A)]]> In this note we consider a class of groups of conformal automorphisms of closed Riemann surfaces containing those which can be lifted to some Schottky uniformization. These groups are those which satisfy a necessary condition for the Schottky lifting property. We find that all these groups have upper bound 12(g - 1), where g <FONT FACE=Symbol>&sup3;</FONT> 2 is the genus of the surface. We also describe a sequence of infinite genera g1< g2 < ... for which these upper bound is attained. Also lower bounds are found, for instance, (i ) 4(g+1) for even genus and 8(g - 1) for odd genus. Also, for cyclic groups in such a family sharp upper bounds are given <![CDATA[SEPARATION PROBLEM FOR STURM-LIOUVILLE EQUATION WITH OPERATOR COEFFICIENT]]> Let H be a separable Hilbert Space. Denote by H1 = L2(a,b; H) the set of function defned on the interval a < chi < b (<FONT FACE=Symbol>&frac34;</FONT><FONT FACE=Symbol>¥</FONT> <FONT FACE=Symbol>a < c</FONT> < b <FONT FACE=Symbol>&pound;</FONT><FONT FACE=Symbol>¥</FONT>) whose values belong to H strongly measurable [12] and satisfying the condition If the inner product of function <FONT FACE=Symbol>&brvbar;</FONT>(chi) and g(chi) belonging to H1 is defined by then H1 forms a separable Hilbert space. We study separation problem for the operator formed by <FONT FACE=Symbol>&frac34;</FONT> y"+ Q (chi) y Sturm-Liouville differential expression in L2(<FONT FACE=Symbol>&frac34;</FONT> <FONT FACE=Symbol>¥</FONT>, <FONT FACE=Symbol>¥</FONT>; H) space has been proved where Q (chi) in an operator which transforms at H in value of chi,,self-adjoint, lower bounded and its inverse is complete continous <![CDATA[ATTRACTORS POINTS IN THE AUTOSUBSTITUTION]]> Recently an operation of graphs called substitution has been incorporated. In an informal way, the substitution consists in the replacement of a vertex for a graph. This new graph is characterized through a function (of substitution) that it could be self definable. The substitution of each vertex of a graph G, through injectives functions of substitution, by the same G graph will be called autosubstitution and denoted by G(G). If X represents the class of all the simple and finite graphs and w is an application of X in X, defined by w (G) = G (G), then it is interest in studying the dynamic properties of w and the construction of some algorithms that they permit the generating of fractal images. In function of the above-mentioned it is proposed to analyze the autosubstitution for graphs simple and finite. Framed in the area of the Graph Dynamics, inside the area of the Graph Theory, the present work will use, preferably, simple and finite graph <![CDATA[RIGID SPHERICAL HYPERSURFACES IN C<SUP>2</SUP>]]> In this paper we describe explicity one class of real-analytic hipersurfaces in C² rigid and spherical at the origin <![CDATA[TOPOLOGIES POLAIRES COMPATIBLES AVEC UNE DUALITÉ SÉPARANTE SUR UN CORPS VALUÉ NON-ARCHIMÉDIEN]]> In this paper, we deal with polar topologies in separated dual pair (X, Y) of vector spaces over a non-archimedean valued field. We study compatible polar topologies, and we give some results characterizing specific subsets of X related to these topologies, especially if the field K is spherically complete or the compatible topology is polar or strongly polar. Furthermore, we investigate some topological properties in the duality (X, Y) such as barreldness and reflexivity <![CDATA[A GLIDING HUMP PROPERTY AND BANACH-MACKEY SPACES]]> We consider the Banach-Mackey property for pairs of vector spaces E and E' which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and anoter measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given