Revista de la
Unión Matemática Argentina

Volumen 54, número 1 (2013)

Published online: June 25, 2013
The N01-matrix completion problem. Gu-Fang Mou and Ting-Zhu Huang
An n × n matrix is called an N01-matrix if all its principal minors are non-positive and each entry is non-positive. In this paper, we study general combinatorially symmetric partial N01-matrix completion problems and prove that a combinatorially symmetric partial N01-matrix with all specified off- diagonal entries negative has an N01-matrix completion if the graph of its specified entries is an undirected cycle or a 1-chordal graph.
Differentiability and best local approximation. Héctor H. Cuenya and Claudia N. Rodriguez
In this paper we give sufficient conditions over the differentiability of a function to assure existence of the best local approximant in Lp-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.
On mixed brightness-integrals. Chang-Jian Zhao
We establish the greatest upper bound for the product of the i-th brightness-integrals of a convex body and its polar dual. Further, the greatest upper bound for the product of the brightness-integrals of order p of a convex body and its polar dual is also given.
A combinatorial identity and applications. Mariano Ferrari and Pablo A. Panzone
An identity for the finite sum $\sum_1^N\frac{z^n}{q^n-r}$ 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 $\sum_1^\infty\frac{z^n}{q^n-r}$, the Riemann zeta function and the Euler–Mascheroni constant. An irrationality result is also proved.
Global controllability of the 1D Schrödinger–Poisson equation. Mariano De Leo, Constanza Sánchez Fernández de la Vega, and Diego Rial
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 Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which includes the so-called doping profile or impurities. More precisely, it is shown that for both attractive and repulsive self-consistent potentials —depending on the balance between the total charge and the impurities— this problem is globally internal controllable in a suitable Sobolev space.
Uniform distribution modulo one of some sequences concerning the Euler function. Mehdi Hassani
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.
Translations, norm-attaining functionals, and elements of minimum norm. Francisco Javier García-Pacheco
In this paper we continue a work that James started in 1971 about norm-attaining functionals on non-complete normed spaces by proving that every functional on a normed space is norm-attaining if and only if every proper, closed, convex subset with non-empty interior can be translated to have a non-zero, minimum-norm element. We also study this type of spaces when they are non-complete. Finally, we consider translations and elements of maximum norm.
Maximal operators associated with generalized Hermite polynomial and function expansions. Liliana Forzani, Emanuela Sasso, and Roberto Scotto
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.

Volumen 54, número 2 (2013)

Published online: December 21, 2013
Sequential entry in one-to-one matching markets. Beatriz Millán
We study in one-to-one 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.
Metallic structures on Riemannian manifolds. Cristina-Elena Hreţcanu and Mircea Crasmareanu
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.
Multiplication of crowns. P. J. Witbooi
It is known that the only finite topological spaces that are H-spaces are the discrete spaces. For a finite poset which is weakly equivalent to an H-space, a generalized multiplication may be found after suitable subdivision. In this paper we construct minimal models of the k-fold 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, 2073-2080].
On Cremona transformations of P3 which factorize in a minimal form. Ivan Pan
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 3-folds. We show there are essentially eight classes of such transformations and give a geometric description of elements in each of these classes.
On Tauberian conditions for (C, 1) summability of integrals. Ümit Totur and İbrahim Çanak
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, ∞).
Graph painting and the Borel-de Siebenthal property. Ching-I Hsin
In this article, we consider graph painting and introduce the Borel-de Siebenthal property. We study this property on graphs of type E. We also study its applications in Hermitian symmetric spaces and hyperbolic Kac-Moody Lie algebras.
A historical review of the classifications of Lie algebras. L. Boza, E. M. Fedriani, J. Núñez, and Á. F. Tenorio
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.
On connectedness via a sequential method. Hüseyin Çakallı and Osman Mucuk
Recently, the first author has introduced a concept of G-sequential connectedness in the sense that a non-empty subset A of a Hausdorff topological group X is G-sequentially connected if the only subsets of A which are both G-sequentially open and G-sequentially closed are A and the empty set ∅. In this paper we investigate further properties of G-sequential connectedness and obtain some interesting results.
Two classes of slant surfaces in the nearly Kähler six sphere. K. Obrenović and S. Vukmirović
In this paper we find examples of slant surfaces in the nearly Kähler six sphere. First, we characterize two-dimensional small and great spheres which are slant. Their description is given in terms of the associative 3-form in Im O. Later on, we classify the slant surfaces of S6 which are orbits of a maximal torus in G2. Among them we find a one parameter family of minimal orbits with arbitrary slant angle.