Published volumes
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 58, número 1 (2017)
June 2017
An interpolation theorem between CalderónHardy spaces.
Sheldy Ombrosi, Alejandra Perini, Ricardo Testoni
PDF
We obtain a complex interpolation theorem between weighted
CalderónHardy spaces for weights in a Sawyer class. The technique used is
based on the method obtained by J.O. Strömberg and A. Torchinsky; however, we
must overcome several technical difficulties associated with considering
onesided CalderónHardy spaces. Interpolation results of this type are
useful in the study of weighted weak type inequalities of strongly singular
integral operators.

119 
Quotient $p$Schatten metrics on spheres.
Esteban Andruchow, Andrea C. Antunez
PDF
Let $S(H)$ be the unit sphere of a Hilbert space $H$ and $U_p(H)$ the
group of unitary operators in $H$ such that $u1$ belongs to the
$p$Schatten ideal $B_p(H)$. This group acts smoothly and transitively
in $S(H)$ and endows it with a natural Finsler metric induced by the
$p$norm $\Vert z \Vert_p= \operatorname{tr}\left((z
z^*)^{p/2}\right)^{1/p}$.
This metric is given by \[ \Vert v \Vert_{x,p} = \min
\lbrace \Vert zy \Vert_p: y \in \mathfrak{g} _x \rbrace, \] where $z
\in \mathcal{B} _p(H)_ {ah}$ satisfies that $(d \pi_x)_1(z)=z \cdot x =
v$ and $ \mathfrak{g} _x$ denotes the Lie algebra of the subgroup of
unitaries which fix $x$. We call $z$ a lifting of $v$. A lifting $z_0$
is called a minimal lifting if additionally $ \Vert v \Vert_{x,p} =
\Vert z_0 \Vert_p$. In this paper we show properties of minimal
liftings and we treat the problem of finding short curves $ \alpha$
such that $ \alpha(0)=x $ and $ \dot{\alpha} (0)= v$ with $x \in S(H)$
and $v \in T_xS(H)$ given. Also we consider the problem of finding
short curves which join two given endpoints $x,y \in S(H)$.

2136 
Affine Szabó connections on smooth manifolds.
Abdoul Salam Diallo, Fortuné Massamba
PDF
We introduce a new structure, called affine Szabó connection. We prove
that, on $2$dimensional affine manifolds, the affine Szabó structure is
equivalent to one of the cyclic parallelisms of the Ricci tensor. A
characterization for locally homogeneous affine Szabó surfaces is obtained.
Examples of two and threedimensional affine Szabó manifolds are also given.

3752 
Connectedness of the algebraic set of vectors
generating planar normal sections of homogeneous isoparametric
hypersurfaces.
Cristián U. Sánchez
PDF
Let $M\subset \mathbb{S}^{n+1}\subset $ $\mathbb{R}^{n+2}$ be a homogeneous
isoparametric hypersurface and consider the algebraic set of unit tangent
vectors generating planar normal sections at a point $E\in M$ (denoted by
$\widehat{X}_{E}[M] \subset T_{E}(M)$). The present paper is devoted to prove
that $\widehat{X}_{E}[M]$ is connected by arcs. This in turn proves that
its projective image $X[M] \subset \mathbb{RP}(T_{E}(M))$ also has this
property.

5375 
Vanishing, Bass numbers, and cominimaxness of local
cohomology modules.
Jafar A'zami
PDF
Let $(R,m)$ be a commutative Noetherian regular local ring and $I$ be a proper
ideal of $R$. It is shown that $H^ {d1} _ \mathfrak{p} (R)=0$ for any
prime ideal $ \mathfrak{p} $ of $R$ with $ \dim(R/ \mathfrak{p})=2$,
whenever the set $ \{ n \in \mathbb{N} : R/ \mathfrak{p} ^ {(n)}$
is CohenMacaulay$\}$ is
infinite. Now, let $(R,m)$ be a commutative Noetherian unique factorization
local domain of dimension $d$, $I$ an ideal of $R$, and $M$ a finitely
generated $R$module. It is shown that the Bass numbers of the $R$module
$H^i_I(M)$ are finite, for all integers $i \geq 0$, whenever $
\operatorname{height} (I)=1$ or $d \leq 3$.

7783 
Soft ideals in ordered semigroups.
E. H. Hamouda
PDF
The notions of soft left and soft right ideals, soft quasiideal and soft
biideal in ordered semigroups are introduced. We show here that in ordered
groupoids the soft right and soft left ideals are soft quasiideals, and in
ordered semigroups the soft quasiideals are soft biideals. Moreover, we
prove that in regular ordered semigroups the soft quasiideals and the soft
biideals coincide. We finally show that in an ordered semigroup the soft
quasiideals are just intersections of soft right and soft left ideals.

8594 
On the Betti numbers of filiform Lie algebras over
fields of characteristic two.
Ioannis Tsartsaflis
PDF
An $n$dimensional Lie algebra $ \mathfrak{g} $ over a field $
\mathbb{F} $ of characteristic two is said to be of Vergne type
if there is a basis $e_1, \dots,e_n$ such that $ [e_1,e_i] =e_ {i+1} $
for all $2 \leq i \leq[e_i,e_j] n1$ and $ = c_ {i,j} e_ {i+j} $ for
some $c_ {i,j}
\in \mathbb{F} $ for all $i,j \ge 2$ with $i+j \le n$. We define the
algebra $ \mathfrak{m} _0$ by its nontrivial bracket relations: $
[e_1,e_i] =e_ {i+1} $, $2 \leq i \leq n1$, and the algebra $
\mathfrak{m} _2$: $ [e_1,e_i ] =e_ {i+1} $, $2 \le i \le[e_2, e_j ]
n1$, $ =e_ {j+2} $, $3 \le j \le n2$.
We show that, in contrast to
the corresponding real and complex cases, $ \mathfrak{m} _0(n)$ and $
\mathfrak{m} _2(n)$ have the same Betti numbers. We also prove that for
any Lie algebra of Vergne type of dimension at least $5$, there exists
a nonisomorphic algebra of Vergne type with the same Betti numbers.

95106 
Certain curves on some classes of threedimensional
almost contact metric manifolds.
Avijit Sarkar, Ashis Mondal
PDF
The object of the present paper is to characterize threedimensional
transSasakian generalized Sasakian space forms admitting biharmonic almost
contact curves with respect to generalized Tanaka Webster Okumura (gTWO)
connections and to give illustrative examples. The mean curvature vector of almost
contact curves has been analyzed on transSasakian manifolds with gTWO
connections. Some properties of slant curves on the same manifolds have been
established. Finally curvature and torsion, with respect to gTWO connections,
of Cparallel and Cproper slant curves in threedimensional almost contact
metric manifolds have been deduced.

107125 
Generalizations of Cline's formula for three generalized inverses.
Yong Jiang, Yongxian Wen, Qingping Zeng
PDF
It is shown that an element $a$ in a ring is Drazin invertible if and only if
so is $a^ {n} $; the Drazin inverse of $a$ is given by that of $a^ {n}
$, and vice versa. Using this result, we prove that, in the presence of
$aba=aca$, for any natural numbers $n$ and $m$, $(ac)^ {n} $ is Drazin
invertible in a ring if and only if so is $(ba)^ {m} $; the Drazin
inverse of $(ac)^ {n} $ is expressed by that of $(ba)^ {m} $, and vice
versa. Also, analogous results for the pseudo Drazin inverse and the
generalized Drazin inverse are established on Banach algebras.

127134 
Harmonic analysis associated with the modified
Cherednik type operator on the real line and PaleyWiener theorems
for its Hartley transform.
Hatem Mejjaoli
PDF
We consider a new differentialdifference operator $\Lambda$ on the
real line. We study the harmonic analysis associated with this
operator. Next, we establish the PaleyWiener theorems for its Hartley
transform on $\mathbb{R}$.

135162 
Elementary proof of the continuity of the topological
entropy at $\theta=\underline{1001}$ in the MilnorThurston
world.
Andrés Jablonski, Rafael Labarca
PDF
In 1965, Adler, Konheim and McAndrew introduced the topological entropy
of a given dynamical system, which consists of a real number that
explains part of the complexity of the dynamics of the system. In this
context, a good question could be if the topological entropy $H_{\mathrm{top}}
(f)$ changes continuously with $f$. For continuous maps this problem
was studied by Misisurewicz, Slenk and Urbański. Recently, and
related with the lexicographic and the MilnorThurston worlds, this
problem was studied by Labarca and others. In this paper we will
prove, by elementary methods, the continuity of the topological entropy
in a maximal periodic orbit ($ \theta= \underline{1001} $) in the
MilnorThurston world. Moreover, by using dynamical methods, we
obtain interesting relations and results concerning the largest
eigenvalue of a sequence of square matrices whose lengths grow up to
infinity.

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