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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 49, número 1 (2008)
Dedicado a la memoria de Mischa Cotlar.
Mischa Cotlar, in memoriam (19132007).
PDF

ixi 
Bifurcation theory applied to the analysis of power systems.
Gustavo Revel, Diego M. Alonso, and Jorge L. Moiola
PDF
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 3bus 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 BogdanovTakens codimensiontwo 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.

114 
Finite element approximation of the vibration problem
for a Timoshenko curved rod.
E. Hernández, E. Otárola, R. Rodríguez, and F. Sanhueza
PDF
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.

1528 
Iterated Aluthge transforms: a brief survey.
Jorge Antezana, Enrique R. Pujals, and Demetrio Stojanoff
PDF
Given an r × r complex matrix T,
if T = UT is the polar
decomposition of T, then the Aluthge transform is defined by
Δ(T) = T^{1/2} U T^{1/2}.
Let Δ^{n}(T) denote the ntimes iterated
Aluthge transform of T,
i.e. Δ^{0}(T) = T
and Δ^{n}(T) =
Δ(Δ^{n−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
{Δ^{n}(T)}_{n∈N}
converges for every r × r matrix T.
This result was conjectured by Jung, Ko and Pearcy in 2003.

2941 
Regular optimal control problems with quadratic
final penalties.
Vicente Costanza
PDF

4356 
Some aspects of the history of applied mathematics
in Argentina.
Pablo Miguel Jacovkis
PDF
In this paper we shall briefly describe some aspects of the history,
evolution and problems of applied mathematics in Argentina.

5769 
PoissonLie Tduality and integrable systems.
H. Montani
PDF
We describe a hamiltonian approach to PoissonLie Tduality
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.

7182 
The duality between algebraic posets and bialgebraic
frames: a lattice theoretic perspective.
James B. Hart and Constantine Tsinakis
PDF
This paper sets two goals. The first is to present algebraists with a
purely ordertheoretic derivation of the adjunction between the category
DCPO
of DCPOs (directed complete posets) and the category
Frm of frames. This
adjunction restricts to several Stonetype dualities which are wellknown 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.

8398 
On the notion of bandlimitedness and its generalizations.
Ahmed I. Zayed
PDF
In this survey article we introduce the PaleyWiener space of
bandlimited functions PW_{ω}, 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 PaleyWiener space, we construct a subspace of
vectors PW_{ω}(D) in a Hilbert space H using a selfadjoint
operator D. We then show that the space PW_{ω}(D) has similar
properties to those of the space PW_{ω}.
The paper is concluded with an application to show how to apply the
abstract results to integral transforms associated with singular SturmLiouville
problems.

99109 
Saturated neighbourhood models of monotonic modal logics.
Sergio Arturo Celani
PDF
In this paper we shall introduce the notions of pointclosed, point
compact, and msaturated monotonic neighbourhood models. We will give
some characterizations, and we will prove that the ultrafilter extension and
the valuation extension of a model are msaturated.

111121 
The nhomology of representations.
Tim Bratten
PDF
The nhomology groups of a gmodule 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 nhomology groups and a survey of some developments, with a
particular emphasis on results pertaining to the problem of caculating nhomology
groups.

123135 
Volumen 49, número 2 (2008)
On the life and work of Mischa Cotlar.
Cora Sadosky
PDF

iiv 
Matrix spherical functions and orthogonal polynomials:
an instructive example.
I. Pacharoni
PDF
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.

115 
Minimal Hermitian matrices with fixed entries
outside the diagonal.
E. Andruchow, L. E. MataLorenzo, A. Mendoza,
L. Recht, and A. Varela
PDF
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.

1728 
Weighted inequalities for generalized fractional operators.
María Silvina Riveros
PDF
In this note we present weighted Coifman type estimates, and twoweight
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.

2938 
Restriction of the Fourier transform.
Marta Urciuolo
PDF
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.

3944 
Quaternions and octonions in mechanics.
Aroldo Kaplan
PDF

4553 
A model for the thermoelastic behavior of a
jointlegbeam system for space applications.
E. M. Cliff, Z. Liu, and R. D. Spies
PDF
RigidizableInflatable (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
trussstructures because of the efficiency they offer in packaging
during boosttoorbit. 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 PDEODE
system. Wellposedness and stability results are shown and analyzed.

5566 
Admissible restriction of holomorphic discrete series
for exceptional groups.
Jorge Vargas
PDF
In this note, we give results about the restriction of a holomorphic
discrete series of an exceptional simple Lie real group to a subgroup.

6780 
Best local approximations by abstract norms with
nonhomogeneous dilations.
Norma Yanzón and Felipe Zó
PDF
We introduce a concept of best local approximation using abstract
norms and nonhomogeneous dilations. The asymptotic behavior of the
normalized error function as well as the limit of some net of best approximation
polynomials P_{ε} as ε → 0 are studied.

8196 
Hypergeometric functions and binomials.
Alicia Dickenstein
PDF
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.

97110 
The problem of entanglement of quantum states.
G. A. Raggio
PDF
We give a brief and incomplete survey of the problem of entanglement
of states of composite quantum systems.

111119 
A survey on hyperKähler with torsion geometry.
M. L. Barberis
PDF
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 hyperKähler 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.

121131 
The Hilbert transform and scattering.
Cora Sadosky
PDF
Through the prism of abstract scattering, and the invariant forms
acting in them, we discuss the Hilbert transform in weighted L^{p} spaces in one
and several dimensions.

133142 
Erratum to "Some aspects of the history of applied
mathematics in Argentina", vol. 49, no. 1, 2008, pág. 5769.
Pablo Miguel Jacovkis
PDF

143 
2007/ LVII Reunión anual de Comunicaciones Científicas
de la Unión Matemática Argentina y XXX Reunión de Educación Matemática.
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145147 
