Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 27 num. 2 lang. es <![CDATA[SciELO Logo]]> <![CDATA[0N CHARACTERIZATION OF RIEMANNIAN MANIFOLDS]]> This survey, present some results about characterization of Riemannian manifolds by using notions of convexity. The first part deals with immersed manifolds and the second part gives a characterization for the Euclidean space and for the Euclidean sphere. <![CDATA[CHARACTERIZATION OF LALLEMENT ORDER ON A REGULAR SEMIGROUP]]> In this paper a study of properties of the Mitsch order relation ’µ’on a regular semigroup and Nambooripads order <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img01.JPG" alt="http:/fbpe/img/proy/v27n2/img01.JPG">on any arbitrary regular semigroup is made. Mainly a characterization of Lallement order on a regular semigroup is obtained. The necessary and sufficient condition for the restriction of Lallement order ’λ ’ to B(S) to be usual order on an orthodox semigroup is also obtained. <![CDATA[AN ABSTRACT ORLICS: PETTIS THEOREM AND APPLICATIONS]]> In this paper we establish two abstract versions of the classical Orlicz-Pettis Theorem for multiplier convergent series. We show that these abstract results yield known versions of the Orlicz-Pettis Theorem for locally convex spaces as well as versions for operator valued series. We also give applications to vector valued measures and spaces of continuous functions. <![CDATA[EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN <img width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG">]]> Let Q : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img03.JPG" alt="http:/fbpe/img/proy/v27n2/img03.JPG">be a symmetric and positive semi-definite linear operator and f j : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img04.JPG" alt="http:/fbpe/img/proy/v27n2/img04.JPG">(j = 1, 2, ...) be real functions so that, f j(0) = 0 and, for every x = (x1, x2, ....) <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img05.JPG" alt="http:/fbpe/img/proy/v27n2/img05.JPG"><img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">, it holds that f (x) := (f1(x1), f2(x2), ...) <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img05.JPG" alt="http:/fbpe/img/proy/v27n2/img05.JPG"><img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">. Sufficient conditions for the existence of non-trivial solutions to the semilinear problem Qx = f (x) are provided. Moreover, if G is a group of orthogonal linear automorphisms of <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">which commute with Q, then such sufficient conditions ensure the existence of non-trivial solutions which are invariant under G. As a consequence, sufficient conditions to ensure solutions of nonlinear partial difference equations on finite degree graphs with vertex set being either finite or infinitely countable are obtained. We consider adaptations to graphs of both Matukuma type equations and Helmholtz equations and study the existence of their solutions. <![CDATA[FUNCTIONS OF BOUNDED (φ, ρ) MEAN OSCILLATION]]> In this paper we extend a result of Garnett and Jones to the case of spaces of homogeneous type. <![CDATA[A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES]]> Algebraic systems with partial operations have different ways to interpret equality between two terms of the language. A strong identity is a formula which says that two terms are equal in the algebra if the existence of one of them implies the existence of the other one and in the case of existence their values are equal. A class of partial algebras defined by a set of strong identities is called a strong variety. In the characterization of strong varieties in the case of partial algebras by means of a Birkhoff-type theorem there appeared a new concept, regularity of partial homomorphisms and partial subalgebras. Here we define and study these operators from two different perspectives. Firstly, in their relation with other well known concecpts of partial homomorphisms and partial subalgebras, as well as with the po-monoid of Pigozzi for the H, S and P operators. Secondly, in regard to the preservation of the different types of formulae that represent equality in the case of partial algebras for these operators. Finally, we give a characterization of the strong varieties as classes closed under regular homomorphisms, regular subalgebras, direct products and that satisfy a closure condition.