Scielo RSS <![CDATA[Revista de la Unión Matemática Argentina]]> vol. 50 num. 1 lang. en <![CDATA[SciELO Logo]]> <![CDATA[Roque Scarfiello (1916-2008)]]> <![CDATA[A description of hereditary skew group algebras of Dynkin and Euclidean type]]> In this work we study the skew group algebra &Lambda;[G] when G is a finite group acting on &Lambda; whose order is invertible in &Lambda;. Here, we assume that &Lambda; is a finite-dimensional algebra over an algebraically closed field k. The aim is to describe all possible actions of a finite abelian group on an hereditary algebra of finite or tame representation type, to give a description of the resulting skew group algebra for each action and finally to determinate their representation type. <![CDATA[A Compact trace theorem for domains with external cusps]]> This paper deals with the compact trace theorem in domains <img width=31 height=13 src="../../../../../img/revistas/ruma/v50n1/1a030x.png"><img width=19 height=14 src="../../../../../img/revistas/ruma/v50n1/1a031x.png">with external cusps. We show that if the power sharpness of the cusp is bellow a critical exponent, then the trace operator <img width=158 height=20 src="../../../../../img/revistas/ruma/v50n1/1a032x.png">exists and it is compact. <![CDATA[Simultaneous approximation by a new sequence of Szãsz-beta type operators]]> In this paper, we study some direct results in simultaneous approximation for a new sequence of linear positive operators <img width=86 height=19 src="../../../../../img/revistas/ruma/v50n1/1a040x.png">of Szãsz-Beta type operators. First, we establish the basic pointwise convergence theorem and then proceed to discuss the Voronovaskaja-type asymptotic formula. Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated. <![CDATA[Amalgamation Property in Quasi-Modal algebras]]> In this paper we will give suitable notions of Amalgamation and Super-amalgamation properties for the class of quasi-modal algebras introduced by the author in his paper Quasi-Modal algebras. <![CDATA[The subvariety of Q-Heyting algebras generated by chains]]> The variety <img width=28 height=14 src="../../../../../img/revistas/ruma/v50n1/1a061x.png">of Heyting algebras with a quantifier [14] corresponds to the algebraic study of the modal intuitionistic propositional calculus without the necessity operator. This paper is concerned with the subvariety <img border=0 width=10 height=12 src="../../../../../img/revistas/ruma/v50n1/1a062x.png">of <img border=0 width=28 height=14 src="../../../../../img/revistas/ruma/v50n1/1a063x.png">generated by chains. We prove that this subvariety is characterized within <img border=0 width=28 height=14 src="../../../../../img/revistas/ruma/v50n1/1a064x.png">by the equations <img border=0 width=163 height=19 src="../../../../../img/revistas/ruma/v50n1/1a065x.png">and <img border=0 width=175 height=19 src="../../../../../img/revistas/ruma/v50n1/1a066x.png">. We investigate free objects in <img border=0 width=10 height=12 src="../../../../../img/revistas/ruma/v50n1/1a067x.png">. <![CDATA[Approximation degree for generalized integral operators]]> Very recently Jain et al. [4] proposed generalized integrated Baskakov operators <img width=124 height=19 src="../../../../../img/revistas/ruma/v50n1/1a070x.png">and estimated some approximation properties in simultaneous approximation. In the present paper we establish the rate of convergence of these operators and its Bezier variant, for functions which have derivatives of bounded variation. <![CDATA[Exponents of Modular Reductions of Families of Elliptic Curves]]> For some natural families of elliptic curves we show that "on average" the exponent of the point group of their reductions modulo a prime <img width=10 height=12 src="../../../../../img/revistas/ruma/v50n1/1a080x.png">grows as <img width=48 height=19 src="../../../../../img/revistas/ruma/v50n1/1a081x.png">. <![CDATA[Exponential families of minimally non-coordinated graphs]]> A graph G is coordinated if, for every induced subgraph H of G, the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques of H with a common vertex. In a previous work, coordinated graphs were characterized by minimal forbidden induced subgraphs within some classes of graphs. In this note, we present families of minimally non-coordinated graphs whose cardinality grows exponentially on the number of vertices and edges. Furthermore, we describe some ideas to generate similar families. Based on these results, it seems difficult to find a general characterization of coordinated graphs by minimal forbidden induced subgraphs. <![CDATA[Functional versions of the Caristi-Kirk theorem]]> Many functional versions of the Caristi-Kirk fixed point theorem are nothing but logical equivalents of the result in question. <![CDATA[Hecke operators on cohomology]]> Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operators are introduced includes the group cohomology of discrete subgroups of a semisimple Lie group, the de Rham cohomology of locally symmetric spaces, and the cohomology of symmetric spaces with coefficients in a system of local groups. We construct canonical isomorphisms among such cohomology groups and discuss the compatibility of the Hecke operators with respect to those canonical isomorphisms. <![CDATA[Weak type (1, 1) of maximal operators on metric measure spaces]]> A discretization method for the study of the weak type (1, 1) for the maximal of a sequence of convolution operators on <img width=21 height=13 src="../../../../../img/revistas/ruma/v50n1/1a122x.png">has been introduced by Miguel de Guzmán and Teresa Carrillo, by replacing the integrable functions by finite sums of Dirac deltas. Trying to extend the above mentioned result to integral operators defined on metric measure spaces, a general setting containing at once continuous, discrete and mixed contexts, a caveat comes from the result in On restricted weak type (1, 1); the discrete case (Akcoglu M.; Baxter J.; Bellow A.; Jones R., Israel J. Math. 124 (2001), 285-297). There a sequence of convolution operators in <img width=39 height=20 src="../../../../../img/revistas/ruma/v50n1/1a124x.png">is constructed such that the maximal operator is of restricted weak type (1, 1), or equivalently of weak type (1, 1) over finite sums of Dirac deltas, but not of weak type (1, 1). The purpose of this note is twofold. First we prove that, in a general metric measure space with a measure that is absolutely continuous with respect to some doubling measure, the weak type (1, 1) of the maximal operator associated to a given sequence of integral operators is equivalent to the weak type (1, 1) over linear combinations of Dirac deltas with positive integer coefficients. Second, for the non-atomic case we obtain as a corollary that any of these weak type properties is equivalent to the weak type (1, 1) over finite sums of Dirac deltas supported at different points. <![CDATA[Formulas for the Euler-Mascheroni constant]]> We give several integral representations for the Euler-Mascheroni constant using a combinatorial identity for <img width=119 height=27 src="../../../../../img/revistas/ruma/v50n1/1a130x.png">. The derivation of this combinatorial identity is done in an elemental way. <![CDATA[2008 / LVIII Reunión anual de Comunicaciones Científicas de la Unión Matemática Argentina y XXXI Reunión de Educación Matemática]]> We give several integral representations for the Euler-Mascheroni constant using a combinatorial identity for <img width=119 height=27 src="../../../../../img/revistas/ruma/v50n1/1a130x.png">. The derivation of this combinatorial identity is done in an elemental way.