Revista de la
Unión Matemática Argentina

Volumen 49, número 1 (2008)

Dedicado a la memoria de Mischa Cotlar.
Mischa Cotlar, in memoriam (1913-2007).
Bifurcation theory applied to the analysis of power systems. Gustavo Revel, Diego M. Alonso, and Jorge L. Moiola

In this paper, several nonlinear phenomena found in the study of power system networks are described in the context of bifurcation theory. Toward this end, a widely studied 3-bus power system model is considered. The mechanisms leading to static and dynamic bifurcations of equilibria as well as a cascade of period doubling bifurcations of periodic orbits are investigated. It is shown that the cascade verifies the Feigenbaum's universal theory. Finally, a two parameter bifurcation analysis reveals the presence of a Bogdanov-Takens codimension-two bifurcation acting as an organizing center for the dynamics. In addition, evidence on the existence of a complex global phenomena involving homoclinic orbits and a period doubling cascade is included.

Finite element approximation of the vibration problem for a Timoshenko curved rod. E. Hernández, E. Otárola, R. Rodríguez, and F. Sanhueza

The aim of this paper is to analyze a mixed finite element method for computing the vibration modes of a Timoshenko curved rod with arbitrary geometry. Optimal order error estimates are proved for displacements and rotations of the vibration modes, as well as a double order of convergence for the vibration frequencies. These estimates are essentially independent of the thickness of the rod, which leads to the conclusion that the method is locking free. A numerical test is reported in order to assess the performance of the method.

Iterated Aluthge transforms: a brief survey. Jorge Antezana, Enrique R. Pujals, and Demetrio Stojanoff

Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then the Aluthge transform is defined by

Δ(T) = |T|1/2 U |T|1/2.

Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e. Δ0(T) = T and Δn(T) = Δ(Δn−1(T)), n ∈ N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {Δn(T)}nN converges for every r × r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003.

Regular optimal control problems with quadratic final penalties. Vicente Costanza
Some aspects of the history of applied mathematics in Argentina. Pablo Miguel Jacovkis

In this paper we shall briefly describe some aspects of the history, evolution and problems of applied mathematics in Argentina.

Poisson-Lie T-duality and integrable systems. H. Montani

We describe a hamiltonian approach to Poisson-Lie T-duality based on the geometry of the underlying phases spaces of the dual sigma and WZW models. Duality is fully characterized by the existence of a hamiltonian action of a Drinfeld double Lie group on the cotangent bundle of its factors and the associated equivariant momentum maps. The duality transformations are explicitly constructed in terms of these actions. It is shown that compatible integrable dynamics arise in a general collective form.

The duality between algebraic posets and bialgebraic frames: a lattice theoretic perspective. James B. Hart and Constantine Tsinakis

This paper sets two goals. The first is to present algebraists with a purely order-theoretic derivation of the adjunction between the category DCPO of DCPOs (directed complete posets) and the category Frm of frames. This adjunction restricts to several Stone-type dualities which are well-known and of considerable interest to computer scientists. The second goal is to describe the object classes of these subdualities in terms familiar to algebraists, thereby making a large body of literature about them more accessible.

On the notion of bandlimitedness and its generalizations. Ahmed I. Zayed

In this survey article we introduce the Paley-Wiener space of bandlimited functions PWω, and review some of its generalizations. Some of these generalizations are new and will be presented without proof because the proofs will be published somewhere else.

Guided by the role that the differentiation operator plays in some of the characterizations of the Paley-Wiener space, we construct a subspace of vectors PWω(D) in a Hilbert space H using a self-adjoint operator D. We then show that the space PWω(D) has similar properties to those of the space PWω.

The paper is concluded with an application to show how to apply the abstract results to integral transforms associated with singular Sturm-Liouville problems.

Saturated neighbourhood models of monotonic modal logics. Sergio Arturo Celani

In this paper we shall introduce the notions of point-closed, point- compact, and m-saturated monotonic neighbourhood models. We will give some characterizations, and we will prove that the ultrafilter extension and the valuation extension of a model are m-saturated.

The n-homology of representations. Tim Bratten

The n-homology groups of a g-module provide a natural and fruitful extension of the concept of highest weight to the representation theory of a noncompact reductive Lie group. In this article we give an introduction to the n-homology groups and a survey of some developments, with a particular emphasis on results pertaining to the problem of caculating n-homology groups.


Volumen 49, número 2 (2008)

On the life and work of Mischa Cotlar. Cora Sadosky
Matrix spherical functions and orthogonal polynomials: an instructive example. I. Pacharoni

In the scalar case, it is well known that the zonal spherical functions of any compact Riemannian symmetric space of rank one can be expressed in terms of the Jacobi polynomials. The main purpose of this paper is to revisit the matrix valued spherical functions associated to the complex projective plane to exhibit the interplay among these functions, the matrix hypergeometric functions and the matrix orthogonal polynomials. We also obtain very explicit expressions for the entries of the spherical functions in the case of 2 × 2 matrices and exhibit a natural sequence of matrix orthogonal polynomials, beyond the group parameters.

Minimal Hermitian matrices with fixed entries outside the diagonal. E. Andruchow, L. E. Mata-Lorenzo, A. Mendoza, L. Recht, and A. Varela

We survey some results concerning the problem of finding the complex hermitian matrix or matrices of least supremum norm with variable diagonal. Some qualitative general results are given and more specific descriptions are shown for the 3 × 3 case. We also comment some results and examples concerning this approximation problem.

Weighted inequalities for generalized fractional operators. María Silvina Riveros

In this note we present weighted Coifman type estimates, and two-weight estimates of strong and weak type for general fractional operators. We give applications to fractional operators given by an homogeneous function, and by a Fourier multiplier. The complete proofs of these results appear in the work [5] done jointly with Ana L. Bernardis and María Lorente.

Restriction of the Fourier transform. Marta Urciuolo

This paper contains a brief survey about the state of progress on the restriction of the Fourier transform and its connection with other conjectures. It contains also a description of recent related results that we have obtained.

Quaternions and octonions in mechanics. Aroldo Kaplan
A model for the thermoelastic behavior of a joint-leg-beam system for space applications. E. M. Cliff, Z. Liu, and R. D. Spies

Rigidizable-Inflatable (RI) materials offer the possibility of deployable large space structures (C.H.M. Jenkins (ed.), Gossamer Spacecraft: Membrane and Inflatable Structures Technology for Space Applications, Progress in Aeronautics and Astronautics, 191, AIAA Pubs., 2001) and so are of interest in applications where large optical or RF apertures are needed. In particular, in recent years there has been renewed interest in inflatablerigidizable truss-structures because of the efficiency they offer in packaging during boost-to-orbit. However, much research is still needed to better understand dynamic response characteristics, including inherent damping, of truss structures fabricated with these advanced material systems. One of the most important characteristics of such space systems is their response to changing thermal loads, as they move in and out of the Earth's shadow. We study a model for the thermoelastic behavior of a basic truss componentconsisting of two RI beams connected through a joint subject to solar heating. Axial and transverse motions as well as thermal response of the beams with thermoelastic damping are taking into account. The model results in a couple PDE-ODE system. Well-posedness and stability results are shown and analyzed.

Admissible restriction of holomorphic discrete series for exceptional groups. Jorge Vargas

In this note, we give results about the restriction of a holomorphic discrete series of an exceptional simple Lie real group to a subgroup.

Best local approximations by abstract norms with non-homogeneous dilations. Norma Yanzón and Felipe Zó

We introduce a concept of best local approximation using abstract norms and non-homogeneous dilations. The asymptotic behavior of the normalized error function as well as the limit of some net of best approximation polynomials Pε as ε → 0 are studied.

Hypergeometric functions and binomials. Alicia Dickenstein

We highlight the role of primary decomposition of binomial ideals in a commutative polynomial ring, in the description of the holonomicity, the holonomic rank, and the shape of solutions of multivariate hypergeometric differential systems of partial differential equations.

The problem of entanglement of quantum states. G. A. Raggio

We give a brief and incomplete survey of the problem of entanglement of states of composite quantum systems.

A survey on hyper-Kähler with torsion geometry. M. L. Barberis

Manifolds with special geometric structures play a prominent role in some branches of theoretical physics, such as string theory and supergravity. For instance, it is well known that supersymmetry requires target spaces to have certain special geometric properties. In many cases these requirements can be interpreted as restrictions on the holonomy group of the target space Riemannian metric. However, in some cases, they cannot be expressed in terms of the Riemannian holonomy group alone and give rise to new geometries previously unknown to mathematicians. An example of this situation is provided by hyper-Kähler with torsion (or HKT) metrics, a particular class of metrics which possess a compatible connection with torsion whose holonomy lies in Sp(n).

A survey on recent results on HKT geometry is presented.

The Hilbert transform and scattering. Cora Sadosky

Through the prism of abstract scattering, and the invariant forms acting in them, we discuss the Hilbert transform in weighted Lp spaces in one and several dimensions.

Erratum to "Some aspects of the history of applied mathematics in Argentina", vol. 49, no. 1, 2008, pág. 57-69. Pablo Miguel Jacovkis

2007/ LVII Reunión anual de Comunicaciones Científicas de la Unión Matemática Argentina y XXX Reunión de Educación Matemática.