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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 57, número 1 (2016)
Published online: June 28, 2016
A note on the classification of gamma factors.
Román Sasyk
PDF
One of the earliest invariants introduced in the study of finite von
Neumann algebras is the property Gamma of Murray and von Neumann. The
set of separable $\operatorname{II}_1$ factors can be split in two
disjoint subsets: those that have the property Gamma and those that do
not have it, called full factors by Connes. In this note we prove that
it is not possible to classify separable $\operatorname{II}_1$ factors
satisfying the property Gamma up to isomorphism by a Borel measurable
assignment of countable structures as invariants. We also show that the
same holds true for the full $\operatorname{II}_1$ factors.

17 
An approximation formula for EulerMascheroni's constant.
Pablo A. Panzone
PDF
A fast approximation formula for Euler–Mascheroni's constant based on
a certain integral due to Peter Borwein is given. This asymptotic
formula for $\gamma$ involves harmonic numbers, $\ln2$ and rational
numbers whose denominators are powers of $2$.

922 
Geometric properties of neutral signature metrics on
$4$dimensional nilpotent Lie groups.
Tijana Šukilović
PDF
The classification of left invariant metrics of neutral signature on
the $4$dimensional nilpotent Lie groups is presented. Their geometry
is extensively studied with special emphasis on the holonomy groups and
projective equivalence. Additionally, we focus our attention on the
Walker metrics. They appear as the underlying structure of metrics on
the nilpotent Lie groups with degenerate center. Finally, we give
complete description of the isometry groups.

2347 
Conjugacy classes of extended generalized Hecke groups.
Bilal Demir, Özden Koruoğlu, and Recep Sahin
PDF
Generalized Hecke groups $H_{p,q}$ are generated by $X(z)=(z\lambda
_{p})^{1}$ and $Y(z)=(z+\lambda _{q})^{1}$, where $\lambda
_{p}=2\cos \frac{\pi }{p}$ , $\lambda _{q}=2\cos \frac{\pi }{q}$, $p,q$
are integers such that $2\leq p\leq q$, $p+q > 4$. Extended generalized
Hecke groups $\overline{H}_{p,q}$ are obtained by adding the reflection
$R(z)=1/\overline{z}$ to the generators of generalized Hecke groups
$H_{p,q}$. We determine the conjugacy classes of the torsion elements
in extended generalized Hecke groups $\overline{H}_{p,q}$.

4956 
Best simultaneous approximation on small regions by rational functions.
H. H. Cuenya, F. E. Levis, and A. N. Priori
PDF
We study the behavior of best simultaneous $(l^q,L^p)$approximation by
rational functions on an interval, when the measure tends to zero. In addition,
we consider the case of polynomial approximation on a finite union of
intervals. We also get an interpolation result.

5770 
Null helix and $k$type null slant helices in $\mathbb{E}_{1}^{4}$.
Jinhua Qian and Young Ho Kim
PDF
We study the null helix and $k$type null slant helices in $4$dimensional
Minkowski space $\mathbb{E}_{1}^{4}$ and characterize them in terms of the null
curvature, null torsion and structure functions. Some null helices and $k$type
null slant helices are presented by solving special differential equations.

7183 
Singular integral operators, John–Nirenberg
inequalities and Triebel–Lizorkin type spaces on weighted
Lebesgue spaces with variable exponents.
KwokPun Ho
PDF
We establish the boundedness of singular integral operators, the
Fefferman–Stein inequality and the John–Nirenberg inequalities on weighted
Lebesgue spaces with variable exponents by using the extrapolation theorem.
Moreover, as a consequence of the extrapolation theorem, we have the
Fefferman–Stein vectorvalued inequalities on weighted Lebesgue spaces, and
hence we use it to study the weighted Triebel–Lizorkin spaces with variable
exponent.

85101 
Another proof of characterization of BMO via Banach function spaces.
Mitsuo Izuki
PDF
Our aim is to give a characterization of the BMO norm via Banach function
spaces based on the Rubio de Francia algorithm. Our proof is different from the
one by Ho [Atomic decomposition of Hardy spaces and characterization of BMO via
Banach function spaces, Anal. Math. 38 (2012), 173–185].

103109 
On rooted directed path graphs.
Marisa Gutiérrez and Silvia Tondato
PDF
An asteroidal triple is a stable set of three vertices such that
each pair is connected by a path avoiding the neighborhood of the
third vertex. An asteroidal quadruple is a stable set of four
vertices such that any three of them is an asteroidal triple.
Two non adjacent vertices are linked by a special connection if
either they have a common neighbor or they are the endpoints of
two vertexdisjoint chordless paths satisfying certain technical
conditions.
Cameron, Hoàng, and Lévêque [DIMAP Workshop on Algorithmic Graph
Theory, 67–74, Electron. Notes Discrete Math., 32, Elsevier,
2009] proved that if a pair of
non adjacent vertices are linked by a special connection then in
any directed path model $T$ the subpaths of $T$ corresponding to
the vertices forming the special connection have to overlap and
they force $T$ to be completely directed in one direction between
these vertices. Special connections along with the concept of
asteroidal quadruple play an important role to study rooted
directed path graphs, which are the intersection graphs of
directed paths in a rooted directed tree.
In this work we define other special connections; these special
connections along with the ones defined by Cameron, Hoàng, and Lévêque
are nine in total, and we prove that every one forces $T$ to be
completely directed in one direction between these vertices. Also, we
give a characterization of rooted directed path graphs whose rooted
models cannot be rooted on a bold maximal clique. As a byproduct of
our result, we build new forbidden induced subgraphs for rooted
directed path graphs.

111144 
Volumen 57, número 2 (2016)
Published online: December 5, 2016
Multiparameter quantum groups, bosonizations and cocycle deformations.
Gastón Andrés García
PDF
$\def\lieg{\mathfrak{g}}
\def\QEA{U_{\mathbf{q}}(\lieg_{A})}
\def\U{{\mathcal U}}
\def\D{{\mathcal D}}
\def\red{\mathrm{red}}$The multiparameter quantized enveloping algebras $\QEA$
constructed by Pei, Hu and Rosso
[Quantum affine algebras, extended affine Lie algebras, and their
applications, 145–171, Amer. Math. Soc., Providence, 2010]
are presented as the pointed Hopf algebras
$\widetilde{\U}(\D_{\red},\ell)$ defined by Andruskiewitsch and Schneider
[Ann. of Math. (2) 171 (2010), 375–417].
The result is applied to show that under a certain assumption $\QEA$
depends, up to cocycle deformation, on only one parameter in each
connected component of the associated Dynkin diagram. In the special case
that $\mathfrak{g}_{A}$ is simple, this was already shown by
Pei, Hu and Rosso
in an alternative way.

123 
The moduli space of principal Spin bundles.
Álvaro Antón Sancho
PDF
We study the geometry of the moduli space of principal Spin bundles through the
study of the subvarieties of fixed points of automorphisms of finite order
coming from outer automorphisms of the structure group. We describe the
nonstable and the singular locus of the moduli space, prove that nonstable
bundles are singular points, and identify the fixed points, in the case of
$M(\operatorname{Spin}(8,\mathbb{C}))$, in the stable or strictly polystable
locus of the moduli space.

2551 
Inequalities for generalized $\delta$Casorati
curvatures of submanifolds in real space forms endowed with a
semisymmetric metric connection.
Jae Won Lee, Chul Woo Lee, and Dae Won Yoon
PDF
We study two sharp inequalities involving the instrinsic
scalar curvature and extrinsic generalized normalized $\delta$Casorati
curvature of submanifolds of real space forms endowed with a semisymmetric
metric connection, which are the generalization of some recent results
related to the Casorati curvature for submanifolds in a real space form with a
semisymmetric metric connection, obtained by Lee et al. [J. Inequal. Appl.
2014, 2014:327].

5362 
Monadic Wajsberg hoops.
Cecilia Rossana Cimadamore and José Patricio Díaz Varela
PDF
$\def\implica{\mathbin{\rightarrow}}
\def\cur{\mathcal}$Wajsberg hoops are the $\{\odot,\implica,
1\}$subreducts (hoopsubreducts) of
Wajsberg algebras, which are term equivalent to MValgebras and are the
algebraic models of Łukasiewicz infinitevalued logic. Monadic MValgebras
were introduced by Rutledge [Ph.D. thesis, Cornell University, 1959]
as an algebraic model for the monadic
predicate calculus of Łukasiewicz infinitevalued logic, in which only a
single individual variable occurs. In this paper we study the class of
$\{\odot, \implica, \forall, 1\}$subreducts (monadic hoopsubreducts) of
monadic MValgebras. We prove that this class, denoted by $\cur{MWH}$, is an
equational class and we give the identities that define it. An algebra in
$\cur{MWH}$ is called a monadic Wajsberg hoop. We characterize the subdirectly
irreducible members in $\cur{MWH}$ and the congruences by monadic filters. We
prove that $\cur{MWH}$ is generated by its finite members. Then, we introduce
the notion of width of a monadic Wajsberg hoop and study some of the
subvarieties of monadic Wajsberg hoops of finite width $k$. Finally, we
describe a monadic Wajsberg hoop as a monadic maximal filter within a certain
monadic MValgebra such that the quotient is the two element chain.

6383 
An extension of some properties for the Fourier transform operator on
$L^p(\mathbb{R})$ spaces.
M. Guadalupe Morales, Juan H. Arredondo, and Francisco J. Mendoza
PDF
In this paper the Fourier transform is studied using the Henstock–Kurzweil
integral on $\mathbb{R}$. We obtain that the classical Fourier transform
$\mathcal{F}_{p}: L^{p}(\mathbb{R})\rightarrow L^{q}(\mathbb{R})$,
$1/p+1/q=1$ and $1 < p\leq 2$, is represented by the integral on a subspace of
$L^{p}(\mathbb{R})$, which strictly contains $L^{1}(\mathbb{R})\cap
L^{p}(\mathbb{R})$. Moreover, for any function $f$ in that subspace,
$\mathcal{F}_{p} (f)$ obeys a generalized Riemann–Lebesgue lemma.

8594 
Khovanov homology of braid links.
Abdul Rauf Nizami, Mobeen Munir, and Ammara Usman
PDF
Although computing the Khovanov homology of links is common in literature, no
general formulae have been given for all families of knots and links. We give
the general formulae of the Khovanov homology of the family of $2$strand braid
links $\widehat{x_{1}^{n}}$ and the family of $3$strand braid links
$\widehat{\Delta^{2k}}$, where $\Delta=x_{1}x_{2}x_{1}$.

95118 
Classification of real solvable Lie algebras whose
simply connected Lie groups have only zero or maximal dimensional
coadjoint orbits.
Anh Vu Le, Van Hieu Ha, Anh Tuan Nguyen, Tran Tu Hai
Cao, and Thi Mong Tuyen Nguyen
PDF
We study a special subclass of real solvable Lie algebras
having small dimensional or small codimensional derived ideals. It is
wellknown that the derived ideal of any Heisenberg Lie algebra is
1dimensional and the derived ideal of the 4dimensional real Diamond
algebra is 1codimensional. Moreover, all the coadjoint orbits of any
Heisenberg Lie group as well as 4dimensional real Diamond group are orbits
of dimension zero or maximal dimension. In general, a (finite dimensional)
real solvable Lie group is called an MDgroup if its coadjoint orbits are
zerodimensional or maximal dimensional. The Lie algebra of an MDgroup
is called an MDalgebra and the class of all MDalgebras is called
MDclass. Simulating the mentioned above characteristic of Heisenberg Lie
algebras and 4dimensional real Diamond algebra, we give a complete
classification of MDalgebras having 1dimensional or 1codimensional
derived ideals.

119143 
