Current volume
Past volumes
19521968 Revista de la Unión Matemática Argentina y de la Asociación Física Argentina
19441951 Revista de la Unión Matemática Argentina; órgano de la Asociación Física Argentina
19361944

Volumen 53, número 1 (2012)
Published online: June 15, 2012
Conjuntos suma pequeños en grupos hamiltonianos.
Wilson F. Mutis, Fernando A. Benavides, and John H. Castillo
PDF
Given a group (G, ·) and positive integers
r, s ≤ G, we denote with μ_{G} (r,s) the
least possible size of the sumsets
AB = {a · b : a ∈ A and b ∈ B},
where A, B run over all subsets
of G, such that A = r and B = s.
Let H = Q × (Z/2Z)^{k} × C be a Hamiltonian group, where k
is a nonnegative integer, Q is the quaternion group of 8 elements and C is a cyclic group of odd
order. We present an explicit formula for μ_{H}(r,s).

19 
Approximation in weighted L^{p} spaces.
Ali Guven
PDF
The Lipschitz classes Lip(α, p, w),
0 < α ≤ 1 are defined for the weighted Lebesgue
spaces L^{p}_{w} with Muckenhoupt weights, and the degree of
approximation by matrix transforms of
f ∈ Lip (α, p, w) is estimated by n^{−α}.

1123 
Boundedness of the fractional maximal operator
on variable exponent Lebesgue spaces: A short proof.
Osvaldo Gorosito, Gladis Pradolini and Oscar Salinas
PDF
We give a simple proof of the boundedness of
the fractional maximal operator providing in this way an alternative
approach to the one given by C. Capone, D. Cruz Uribe and A. Fiorenza
in The fractional maximal operator and fractional integrals on variable
L^{p} spaces, Rev. Mat. Iberoam. 23 (2007), no. 3, 743770.

2527 
On the nonuniqueness of conformal metrics
with prescribed scalar and mean curvatures on compact manifolds with boundary.
Gonzalo García and Jhovanny Muñoz
PDF
For a compact Riemannian manifold (M^{n},g)
with boundary and dimension n, with n ≥ 2, we study
the existence of metrics in the conformal class of g with scalar
curvature R_{g} and mean curvature h_{g} on the boundary.
In this paper we find sufficient and necessary conditions for
the existence of a smaller metric g' < g with curvatures
R_{g'} = R_{g} and h_{g'} = h_{g}.
Furthermore, we establish the uniqueness of such a metric g'
in the conformal class of the metric g when R_{g} ≥ 0.

2942 
Strongly transitive geometric spaces: Applications to hyperrings.
S. Mirvakili and B. Davvaz
PDF
In this paper, we determine two families R and G
of subsets of a hyperring R and sufficient conditions such that two
geometric spaces (R, R) and (R, G) are strongly transitive.
Moreover, we prove that the relations Γ and α are strongly regular
equivalence relations on a hyperfield or a hyperring such that (R, +)
has an identity element.

4353 
Dualistic structures on Kähler manifolds.
Adara M. Blaga
PDF
Affine connections compatible with a symplectic structure are defined and conditions
for two compatible connections on a Kähler manifold to form a dualistic structure are given. The
special symplectic case is detailed.

5560 
Semiconvergence analysis of the inexact Uzawa
method for singular saddle point problems.
JianLei Li and TingZhu Huang
PDF
Recently, various Uzawa methods were proposed based on different matrix splitting
for solving nonsingular saddle point problems, and the necessary and sufficient condition of the
convergence for those Uzawa methods were derived. Motivated by their results, in this paper we
give the semiconvergence analysis of the inexact Uzawa method which is applied to solve singular
saddle point problems under certain conditions.

6170 
Haar type bases in Lorentz spaces via extrapolation.
Luis Nowak
PDF
In this note we consider Haar type systems as unconditional bases for Lorentz spaces
defined on spaces of homogeneous type. We also give characterizations of these spaces in terms
of the Haar coefficients. The basic tools are the Rubio de Francia extrapolation technique and
the characterization of weighted Lebesgue spaces with Haar bases.

7183 
A graph theoretical model for the total balancedness of combinatorial games.
M. Escalante, V. Leoni and G. Nasini
PDF
In this paper we present a model for the study of the total balancedness of packing
and covering games, concerning some aspects of graph theory. We give an alternative proof of van
Velzen’s characterization of totally balanced covering games. We introduce new types of graph
perfection, which allows us to give another approach to the open problem of characterizing totally
balanced packing games.

8592 
Inequalities for norms on products of star ordered operators.
Cristina Cano, Irene Mosconi and Susana Nicolet
PDF
The aim of this paper is to relate the star order
in operators in a Hilbert space with certain norm inequalities.
We are showing inequalities of the type ‖BXA‖_{2}
≤ ‖XBA‖_{2}
(or ‖BXA_{2}‖ ≥ ‖XBA‖_{2}),
which are already known under the assumption that A = ψ(B), with ψ
a positive increasing (or decreasing, respectively) function defined
on the spectrum of B. In this work, we will study this type of
inequalities with the hypothesis that A ≤^{∗} B, where
A ≤^{∗} B if A^{∗}A = B^{∗}A and
AA^{∗} = BA^{∗}.

93100 
HájekRényi inequality for dependent random
variables in Hilbert space and applications.
Yu Miao
PDF
In this paper, we obtain some HájekRényi inequalities
for sequences of Hilbert valued random variables which are associated,
negatively associated and φmixing. As applications, we give some almost
sure convergence theorems for these dependent sequences in Hilbert space.
These results extend and improve some wellknown results.

101112 
Erratum to the paper “On semisimple Hopf algebras
with few representations of dimension greater than one”,
Rev. Un. Mat. Argentina, vol. 51 no. 2, 2010, 91105.
V. A. Artamonov
PDF

113 
Volumen 53, número 2 (2012)
Published online: November 21, 2012
On barycentric constants.
Florian Luca, Oscar Ordaz, and María Teresa Varela
PDF
Let G be an abelian group with n elements.
Let S be a sequence of elements of G,
where the repetition of elements is allowed. Let S be the cardinality,
or the length of S. A sequence S ⊆ G with S ≥ 2
is barycentric or has a barycentricsum if it contains one element
a_{j} such that
Σ_{ai ∈ S}a_{i}
= Sa_{j}.
This paper is a survey on the following three barycentric constants:
the kbarycentric Olson constant BO(k, G), which is
the minimum positive integer t ≥ k ≥ 3 such
that any subset of t elements of G contains a barycentric subset with k elements, provided such
an integer exists; the kbarycentric Davenport constant BD(k, G),
which is the minimum positive integer t such that any subsequence of
t elements of G contains a barycentric subsequence with k
terms; the barycentric Davenport constant BD(G), which is the
minimum positive integer t ≥ 3
such that any subset of t elements of G contains a barycentric subset.
New values and bounds on the above barycentric constants when
G = Z_{n} is the group of integers modulo n are also given.

112 
Examples of homogeneous manifolds with uniformly bounded metric projection.
Eduardo Chiumiento
PDF
Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by
L^{p}(M)_{sh} the skewHermitian part of the noncommutative
L^{p} space associated with (M,τ). Let
1 < p < ∞, z ∈ L^{p}(M)_{sh} and S
be a real closed subspace of L^{p}(M)_{sh}.
The metric projection Q : L^{p}(M)_{sh} → S
is defined for every z ∈ L^{p}(M)_{sh}
as the unique operator Q(z) ∈ S such that
z − Q(z)_{p} =
min_{y∈S} z − y_{p}.
We show the relation between metric projection and metric geometry of homogeneous spaces
of the unitary group U_{M} of M, endowed with a Finsler
quotient metric induced by the pnorms
of τ, x_{p} = τ(x^{p})^{1/p}, p
an even integer. The problem of finding minimal curves in such homogeneous
spaces leads to the notion of uniformly bounded metric projection. Then we
show examples of metric projections of this type.

1323 
Some results on O^{∗}groups.
Sebahattin Ikikardes and Recep Sahin
PDF
A compact Klein surface with boundary of algebraic genus g ≥ 2
has at most 12(g−1) automorphisms. When a surface attains
this bound, it has maximal symmetry, and the group of
automorphisms is then called an M^{∗}group. If a finite group
G of odd order acts on a bordered Klein surface X of algebraic
genus g ≥ 2, then G ≤ 3(g − 1). If G
acts with the largest possible order 3(g − 1), then G
is called an O^{∗}group. In this paper, using the results about
some normal subgroups of the extended modular group Γ,
we obtain some results about O^{∗}groups. Also, we give the
relationships between O^{∗}groups and M^{∗}groups.

2530 
A remark on prime repunits.
Pablo A. Panzone
PDF
A formula for the generating function of prime repunits is given in terms of a Lambert
series using S. Golomb’s formula.

3135 
On Inull lie algebras.
L. Magnin
PDF
We consider the class of complex Lie algebras for which the Koszul
3form is zero, and prove that it contains all quotients of Borel
subalgebras, or of their nilradicals, of finite dimensional complex
semisimple Lie algebras. A list of KacMoody types for indecomposable
nilpotent complex Lie algebras of dimension ≤ 7 is given.

3758 
An elementary proof of the continuity from
L^{2}_{0}(Ω) to
H^{1}_{0}(Ω)^{n}
of Bogovskii’s right inverse of the divergence.
Ricardo G. Durán
PDF
The existence of right inverses of the divergence as an operator
from H^{1}_{0}(Ω)^{n} to
L^{2}_{0}(Ω) is a problem that has been widely
studied because of its importance in the analysis of the classic
equations of fluid dynamics. When Ω is a bounded domain which
is starshaped with respect to a ball B, a right inverse given
by an integral operator was introduced by Bogovskii, who also
proved its continuity using the CalderónZygmund theory of
singular integrals.
In this paper we give an alternative elementary proof of the
continuity using the Fourier transform. As a consequence, we
obtain estimates for the constant in the continuity in terms of
the ratio between the diameter of Ω and that of B. Moreover,
using the relation between the existence of right inverses of
the divergence with the Korn and improved Poincaré inequalities, we
obtain estimates for the constants in these two inequalities.
We also show that one can proceed in the opposite way, that is,
the existence of a continuous right inverse of the divergence, as well
as estimates for the constant in that continuity, can be obtained
from the improved Poincaré inequality. We give an interesting
example of this situation in the case of convex domains.

5978 
On Hamilton circuits in Cayley digraphs over
generalized dihedral groups.
Adrián Pastine and Daniel Jaume
PDF
In this paper we prove that given a generalized dihedral group
D_{H} and a generating subset S,
if S ∩ H = ∅ then the Cayley digraph
Cay(D_{H}, S) is Hamiltonian. The proof we
provide is via a recursive algorithm that produces a Hamilton
circuit in the digraph.

7987 
On completeness of integral manifolds of nullity distributions.
Carlos Olmos and Francisco Vittone
PDF
We give a conceptual proof of the fact that if M is a
complete submanifold of a space form, then the maximal integral
manifolds of the nullity distribution of its second fundamental
form through points of minimal index of nullity are complete.

8990 
The finite model property for the variety of
Heyting algebras with successor.
J.L. Castiglioni and H.J. San Martín
PDF
The finite model property of the variety of Salgebras was
proved by X. Caicedo using Kripke model techniques of the associated
calculus. A more algebraic proof, but still strongly
based on Kripke model ideas, was given by Muravitskii. In this article
we give a purely algebraic proof for the finite model property which
is strongly based on the fact that for every element x in a
Salgebra the interval [x, S(x)] is a
Boolean lattice.

9196 
Further results on semisimple Hopf algebras of
dimension p^{2}q^{2}.
Jingcheng Dong and Li Dai
PDF
Let p, q be distinct prime numbers, and k an
algebraically
closed field of characteristic 0. Under certain restrictions on
p, q, we discuss the structure of semisimple Hopf algebras
of dimension p^{2}q^{2}. As an
application, we obtain the
structure theorems for semisimple Hopf algebras of dimension
9q^{2} over k. As a byproduct, we also prove
that odddimensional
semisimple Hopf algebras of dimension less than 600 are of
Frobenius type.

97112 
