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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 54, número 1 (2013)
Published online: June 25, 2013
The N_{0}^{1}matrix completion problem.
GuFang Mou and TingZhu Huang
PDF
An n × n matrix is
called an N_{0}^{1}matrix if all its
principal minors are nonpositive and each entry is nonpositive.
In this paper, we study general combinatorially symmetric partial
N_{0}^{1}matrix completion problems and
prove that a combinatorially symmetric partial
N_{0}^{1}matrix with all specified off
diagonal entries negative has an
N_{0}^{1}matrix completion if the graph
of its specified entries is an undirected cycle or a 1chordal
graph.

114 
Differentiability and best local approximation.
Héctor H. Cuenya and Claudia N. Rodriguez
PDF
In this paper we give sufficient conditions
over the differentiability of a function to assure existence of
the best local approximant in L^{p}spaces,
0 < p ≤ ∞. These conditions are weaker than
those given in previous papers. For p = 2 we show that,
in a certain way, they are also necessary. In addition, we
characterize the best local approximant.

1525 
On mixed brightnessintegrals.
ChangJian Zhao
PDF
We establish the greatest upper bound for the product of the
ith brightnessintegrals of a convex body and its polar
dual. Further, the greatest upper bound for the product of the
brightnessintegrals of order p of a convex body and its
polar dual is also given.

2734 
A combinatorial identity and applications.
Mariano Ferrari and Pablo A. Panzone
PDF
An identity for the finite sum $\sum_1^N\frac{z^n}{q^nr}$ is given. Related
sums (or series) were studied by Scherk, Clausen, Ramanujan, Shanks, Andrews,
and others. We use such identity to give new formulas for
$\sum_1^\infty\frac{z^n}{q^nr}$, the Riemann zeta function and the
Euler–Mascheroni constant. An irrationality result is also proved.

3542 
Global controllability of the 1D Schrödinger–Poisson equation.
Mariano De Leo, Constanza Sánchez Fernández de la Vega, and Diego Rial
PDF
This paper is concerned with both the local and global internal controllability
of the 1D Schrödinger–Poisson equation
$iu_t(x,t)=u_{xx}+V(u)\,u$,
which arises in quantum semiconductor models. Here $V(u)$ is a
Hartreetype nonlinearity stemming from the coupling with the 1D
Poisson equation, which includes the socalled doping profile or
impurities. More precisely, it is shown that for both
attractive and repulsive selfconsistent potentials —depending on
the balance between the total charge and the impurities— this
problem is globally internal controllable in a suitable Sobolev space.

4354 
Uniform distribution modulo one of some sequences concerning
the Euler function.
Mehdi Hassani
PDF
In this paper, we follow the recent method in the theory of
uniform distribution, developed by J.M. Deshouillers and H.
Iwaniec, to prove uniform distribution modulo one of various
sequences involving the Euler function, together with some
generalizations.

5568 
Translations, normattaining functionals, and elements of minimum norm.
Francisco Javier GarcíaPacheco
PDF
In this paper we continue a work that James started in 1971 about
normattaining functionals on noncomplete normed spaces by
proving that every functional on a normed space is normattaining
if and only if every proper, closed, convex subset with nonempty
interior can be translated to have a nonzero, minimumnorm
element. We also study this type of spaces when they are
noncomplete. Finally, we consider translations and elements of
maximum norm.

6982 
Maximal operators associated with generalized Hermite polynomial and
function expansions.
Liliana Forzani, Emanuela Sasso, and Roberto Scotto
PDF
We study the weak and strong type boundedness of maximal
heat–diffusion operators associated with the system of
generalized Hermite polynomials and with two different systems of
generalized Hermite functions. We also give a necessary
background to define Sobolev spaces in this context.

83107 
Volumen 54, número 2 (2013)
Published online: December 21, 2013
Sequential entry in onetoone matching markets.
Beatriz Millán
PDF
We study in onetoone matching markets a process of sequential
entry, in which participants enter in the market one at a time,
in some arbitrary given order. We identify a large family of
orders (optimal orders) which converge to the optimal stable
matching.

114 
Metallic structures on Riemannian manifolds.
CristinaElena Hreţcanu and Mircea Crasmareanu
PDF
Our aim in this paper is to focus on some
applications in differential geometry of the metallic means
family (a generalization of the golden mean) and generalized
Fibonacci sequences, using a class of polynomial structures
defined on Riemannian manifolds. We search for properties of the
induced structure on a submanifold by metallic Riemannian
structures and we find a necessary and sufficient condition for a
submanifold to be also a metallic Riemannian manifold in terms of
invariance. Also, the totally geodesic, minimal and respectively
totally umbilical hypersurfaces in metallic Riemannian manifolds
are analyzed and the Euclidean space and its hypersphere is
treated as example.

1527 
Multiplication of crowns.
P. J. Witbooi
PDF
It is known that the only finite topological spaces that are
Hspaces are the discrete spaces. For a finite poset which is
weakly equivalent to an Hspace, a generalized multiplication may
be found after suitable subdivision. In this paper we construct
minimal models of the kfold generalised multiplications of
circles in the category of relational structures, including poset
models. In particular, we obtain higher dimensional analogues of
a certain ternary multiplication of crowns [Hardie and Witbooi,
Topology Appl. 154 (2007), no. 10, 20732080].

2936 
On Cremona transformations of P^{3} which factorize in a minimal form.
Ivan Pan
PDF
We consider Cremona transformations of the complex projective
space of dimension 3 which factorize as a product of two
elementary links of type II, without small contractions,
connecting two Fano 3folds. We show there are essentially eight
classes of such transformations and give a geometric description
of elements in each of these classes.

3758 
On Tauberian conditions for (C, 1) summability of integrals.
Ümit Totur and İbrahim Çanak
PDF
We investigate some Tauberian conditions in terms of the general
control modulo of the oscillatory behavior of integer order of
continuous real functions on [0, ∞) for (C, 1) summability
of integrals. Moreover, we obtain a Tauberian theorem for a real
bounded function on [0, ∞).

5965 
Graph painting and the Borelde Siebenthal property.
ChingI Hsin
PDF
In this article, we consider graph painting and introduce the
Borelde Siebenthal property. We study this property on graphs of type E.
We also study its applications in Hermitian symmetric spaces and hyperbolic
KacMoody Lie algebras.

6773 
A historical review of the classifications of Lie algebras.
L. Boza, E. M. Fedriani, J. Núñez, and Á. F. Tenorio
PDF
The problem of Lie algebras’ classification, in their different
varieties, has been dealt with by theory researchers since the
early 20th century. This problem has an intrinsically infinite
nature since it can be inferred from the results obtained that
there are features specific to each field and dimension. Despite
the hundreds of attempts published, there are currently fields
and dimensions in which only partial classifications of some
families of algebras of low dimensions have been obtained. This
article intends to bring some order to the achievements of this
prolific line of research so far, in order to facilitate future
research.

7599 
On connectedness via a sequential method.
Hüseyin Çakallı and Osman Mucuk
PDF
Recently, the first author has introduced a concept of
Gsequential connectedness in the sense that a nonempty
subset A of a Hausdorff topological group X is
Gsequentially connected if the only subsets of A
which are both Gsequentially open and
Gsequentially closed are A and the empty set ∅.
In this paper we investigate further properties of
Gsequential connectedness and obtain some interesting
results.

101109 
Two classes of slant surfaces in the nearly Kähler six sphere.
K. Obrenović and S. Vukmirović
PDF
In this paper we find examples of slant surfaces in the nearly
Kähler six sphere. First, we characterize twodimensional small
and great spheres which are slant. Their description is given in
terms of the associative 3form in Im O. Later on, we
classify the slant surfaces of S^{6} which are
orbits of a maximal torus in G_{2}. Among them we
find a one parameter family of minimal orbits with arbitrary
slant angle.

111121 
