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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 56, número 1 (2015)
Published online: June 24, 2015
Luis Amadeo Piovan, 19592015.
Pablo A. Panzone
PDF

iii 
Quasilinear eigenvalues.
Julián Fernández Bonder, Juan P. Pinasco, and Ariel M. Salort
PDF
We review and extend some well known results for
the eigenvalues of the Dirichlet $p$Laplace operator to a more general
class of monotone quasilinear elliptic operators. As an application we
obtain some homogenization results for nonlinear eigenvalues.

125 
Three dimensional real Lie bialgebras.
Marco A. Farinati and A. Patricia Jancsa
PDF
By different methods, we classify the real three dimensional Lie bialgebras and
give their automorphism groups; in case of coboundary Lie bialgebras, the
corresponding coboundaries $r\in\Lambda ^2\mathfrak{g}$ are listed.

2762 
Computation of the canonical lifting via division polynomials.
Altan Erdoğan
PDF
We study the canonical lifting of ordinary elliptic curves over the
ring of Witt vectors. We prove that the canonical lifting is compatible with
the base field of the given ordinary elliptic curve which was first proved in
Finotti, J. Number Theory 130 (2010), 620638. We also give some results
about division polynomials of elliptic curves defined over the ring of Witt
vectors.

6371 
Local bounds, Harnack's inequality and Hölder continuity for divergence type
elliptic equations with nonstandard growth.
Noemi Wolanski
PDF
We obtain a Harnack type inequality for solutions to elliptic
equations in divergence form with nonstandard $p(x)$type growth. A model
equation is the inhomogeneous $p(x)$Laplacian. Namely,
\[
\Delta_{p(x)}u:=\operatorname{div}\big(\nabla u^{p(x)2}\nabla u\big)=f(x)\quad\text{in }\Omega,
\]
for which we prove Harnack's inequality when $f\in L^{q_0}(\Omega)$ if
$\max\{1,\frac N{p_1}\} < q_0\le \infty$. The constant in Harnack's inequality
depends on $u$ only through $\u^{p(x)}\_{L^1(\Omega)}^{p_2p_1}$.
Dependence of the constant on $u$ is known to be necessary in the case of
variable $p(x)$. As in previous papers, logHölder continuity on the exponent
$p(x)$ is assumed.
We also prove that weak solutions are locally bounded and Hölder continuous
when $f\in L^{q_0(x)}(\Omega)$ with $q_0\in C(\Omega)$ and $\max\{1,\frac
N{p(x)}\} < q_0(x)$ in $\Omega$.
These results are then generalized to elliptic equations
\[
\operatorname{div} A(x,u,\nabla u)=B(x,u,\nabla u)
\]
with $p(x)$type growth.

73105 
A note on the reversibility of the elementary cellular automaton with rule number 90.
A. Martín del Rey
PDF
The reversibility properties of the elementary cellular automaton with
rule number 90 are studied. It is shown that the cellular automaton
considered is not reversible when periodic boundary conditions are
considered, whereas when null boundary conditions are stated, the
reversibility appears when the number of cells of the cellular space is
even. The DETGTRI algorithm is used to prove these statements.
Moreover, the explicit expressions of inverse cellular automata of
reversible ones are computed.

107125 
Volumen 56, número 2 (2015)
Published online: December 1, 2015
Inequalities for submanifolds of a Riemannian manifold of nearly quasiconstant curvature with a semisymmetric nonmetric connection.
Pan Zhang, Xulin Pan, and Liang Zhang
PDF
By using two new algebraic lemmas we obtain Chen’s inequalities
for submanifolds of a Riemannian manifold of nearly quasiconstant curvature
endowed with a semisymmetric nonmetric connection. Moreover, we correct
a result of C. Özgür and A. Mihai’s paper (Chen inequalities for submanifolds
of real space forms with a semisymmetric nonmetric connection, Canad.
Math. Bull. 55 (2012), 611622).

119 
Semislant lightlike submanifolds of indefinite Kaehler manifolds.
S. S. Shukla and Akhilesh Yadav
PDF
We introduce the notion of semislant lightlike submanifolds of indefinite
Kaehler manifolds giving a characterization theorem with some nontrivial
examples of such submanifolds. Integrability conditions of distributions
D_{1}, D_{2} and Rad TM on semislant lightlike submanifolds of indefinite
Kaehler manifolds have been obtained. We also obtain necessary and sufficient
conditions for foliations determined by the above distributions to be totally
geodesic.

2137 
Prime ideals of skew PBW extensions.
Oswaldo Lezama, Juan Pablo Acosta, and Milton Armando Reyes Villamil
PDF
We describe the prime ideals of some important classes of skew
PBW extensions, using the classical technique of extending and contracting
ideals. Skew PBW extensions include as particular examples Weyl algebras,
enveloping algebras of finitedimensional Lie algebras (and their quantizations),
Artamonov quantum polynomials, diffusion algebras, and Manin algebra
of quantum matrices, among many others.

3955 
The quasistate space of a $C^*$algebra is a
topological quotient of the representation space.
Sergio A. Yuhjtman
PDF
We show that for any $C^*$algebra $A$, a sufficiently large Hilbert space
$H$ and a unit vector $\xi \in H$, the natural application $\operatorname{rep}(A\mathrm{:}H)
\xrightarrow{\theta_\xi} Q(A)$, $\pi \mapsto \langle \pi()\xi,\xi \rangle$
is a topological quotient, where $\operatorname{rep}(A\mathrm{:}H)$ is the space of representations
on $H$ and $Q(A)$ the set of quasistates, i.e. positive linear functionals
with norm at most $1$. This quotient might be a useful tool in the
representation theory of $C^*$algebras. We apply it to give an
interesting proof of Takesaki–Bichteler duality for $C^*$algebras which
allows to drop a hypothesis.

5765 
A generalized version of Fubini's theorem on $C_{a,b}[0,T]$ and
applications
.
Il Yong Lee, Hyun Soo Chung, and Seung Jun Chang
PDF
We define a transform with respect to the Gaussian process, the
$\diamond$product and the first variation on function space. We then establish
a generalized Fubini theorem rather than the Fubini theorem introduced in H. S.
Chung, J. G. Choi and S. J. Chang,
Banach J. Math. Anal. 7 (2013), 173185. Also, we examine the
various relationships of the transform with respect to the Gaussian
process, the $\diamond$product and the first variation for functionals on
function space.

6783 
Detection of the torsion classes in the Brieskorn modules of homogeneous polynomials.
Khurram Shabbir
PDF
Let $f\in \mathbb{C}[X_1,\dots, X_n]$ be a homogeneous polynomial
and $B(f)$ be the corresponding Brieskorn module, which is the
quotient of the polynomial ring by some specific $\mathbb{C}$vector
space and it has a $\mathbb{C}[t]$module structure. The main
results detect torsion classes in the Brieskorn module using
explicit computations with differential forms. We compute the
torsion of the Brieskorn module $B(f)$ for two variables in case of
nonisolated singularities and show that torsion order is at most
$1$. In addition, we find some interesting families in which $B(f)$
is torsion free even in case of nonisolated singularities. We
exhibit several examples to compute the monomial basis for $B(f)$
and the construction of torsion elements for $n > 2$.

8594 
Some results on spectral distances of graphs.
Irena M. Jovanović
PDF
Spectral distances of graphs related to some graph operations and
modifications are considered. We show that the spectral distance between two
graphs does not depend on their common eigenvalues, up to multiplicities. The
spectral distance between some graphs with few distinct eigenvalues is computed
and due to the results obtained one of the previously posed conjectures
related to the Aspectral distances of graphs has been disproved. In order
to investigate the cospectrality for special classes of graphs, we computed
spectral distances and distance related graph parameters on several specially
constructed sets of graphs.

95117 
Planar normal sections of focal manifolds of isoparametric hypersurfaces in spheres.
Cristián U. Sánchez
PDF
The present paper contains some results about the algebraic sets
of planar normal sections associated to the focal manifolds of homogeneous
isoparametric hypersurfaces in spheres. With the usual identification of the
tangent spaces to the focal manifold with subspaces of the tangent spaces
to the isoparametric hypersurface, it is proven that the algebraic set of planar
normal sections of the focal manifold is contained in that of the original
hypersurface.

119133 
