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

Volume 60, number 1 (2019)
June 2019
Primary decomposition and secondary representation of modules.
Masoumeh Hasanzad, Jafar A'zami
In this paper we study the notions of primary decomposition and
secondary representation of modules over a commutative ring with
identity. Also we review these concepts over injective and projective
modules.

1–8 
Lie $n$multiplicative mappings on triangular $n$matrix rings.
Bruno L. M. Ferreira, Henrique Guzzo Jr.
We extend to triangular $n$matrix rings and Lie $n$multiplicative maps a
result about Lie multiplicative maps on triangular algebras due to Xiaofei Qi
and Jinchuan Hou.

9–20 
Higher order mean curvatures of SAC halflightlike submanifolds of indefinite almost contact manifolds.
Fortuné Massamba, Samuel Ssekajja
We introduce higher order mean curvatures of screen almost conformal (SAC)
halflightlike submanifolds of indefinite almost contact manifolds, admitting a
semisymmetric nonmetric connection. We use them to generalize some known
results by Duggal and Sahin on totally umbilical halflightlike submanifolds
[Int. J. Math. Math. Sci. 2004, no. 68, 37373753].
Also, we derive a new integration formula via the divergence of some special
vector fields tangent to these submanifolds, which we later use to characterize
minimal and maximal submanifolds. Several examples, where possible, are also
included to illustrate the main concepts.

21–44 
Branching laws: some results and new examples.
Oscar Márquez, Sebastián Simondi, Jorge A. Vargas
For a connected, noncompact simple matrix Lie group $G$ so that a maximal
compact subgroup $K$ has a three dimensional simple ideal, in this note we
analyze the admissibility of the restriction of irreducible square integrable
representations for the ambient group when they are restricted to certain
subgroups that contain the three dimensional ideal. In this setting we provide
a formula for the multiplicity of the irreducible factors. Also, for general
$G$ such that $G/K$ is an Hermitian $G$manifold we give a necessary and
sufficient condition so that an arbitrary square integrable representation of
the ambient group is admissible over the semisimple factor of $K$.

45–59 
On the structure of split involutive HomLie color algebras.
Valiollah Khalili
In this paper we study the structure of arbitrary split involutive regular
HomLie color algebras. By developing techniques of connections of roots for
this kind of algebras, we show that such a split involutive regular HomLie
color algebra $\mathcal{L}$ is of the form
$\mathcal{L}=\mathcal{U}\oplus\sum_{[\alpha]\in\Pi/\sim} I_{[\alpha]}$, with
$\mathcal{U}$ a subspace of the involutive abelian subalgebra $\mathcal{H}$ and
any $I_{[\alpha]}$, a welldescribed involutive ideal of $\mathcal{L}$, satisfying
$[I_{[\alpha]}, I_{[\beta]}]=0$ if $[\alpha]\neq[\beta]$. Under certain conditions, in the
case of $\mathcal{L}$ being of maximal length, the simplicity of the algebra is
characterized and it is shown that $\mathcal{L}$ is the direct sum of the
family of its minimal involutive ideals, each one being a simple split
involutive regular HomLie color algebra. Finally, an example will be provided
to characterise the inner structure of split involutive HomLie color algebras.

61–77 
The multivariate bisection algorithm.
Manuel López Galván
The aim of this paper is to study the bisection method in $\mathbb{R}^n$.
We propose a multivariate bisection method supported by the
Poincaré–Miranda theorem in order to solve nonlinear systems of equations.
Given an initial cube satisfying the hypothesis of the Poincaré–Miranda theorem,
the algorithm performs congruent refinements through its center by
generating a root approximation. Through preconditioning we will prove the
local convergence of this new root finder methodology and moreover we will
perform a numerical implementation for the two dimensional case.

79–98 
Some new $Z$eigenvalue localization sets for tensors and their applications.
Zhengge Huang, Ligong Wang, Zhong Xu , Jingjing Cui
In this paper some new $Z$eigenvalue localization sets for general tensors are
established, which are proved to be tighter than those newly derived by Wang et
al. [Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 187–198].
Also, some relationships between the $Z$eigenvalue inclusion sets presented by
Wang et al. and the new $Z$eigenvalue localization sets for tensors are given.
Besides, we discuss the effects of orthonormal transformations for the proposed
sets. As applications of the proposed sets, some improved upper bounds for the
$Z$spectral radius of weakly symmetric nonnegative tensors are given. Numerical
examples are also given to verify the advantages of our proposed results over
some known ones.

99–119 
Direct theorems of trigonometric approximation for variable exponent Lebesgue spaces.
Ramazan Akgün
Jackson type direct theorems are considered in variable exponent Lebesgue
spaces $L^{p(x)}$ with exponent $p(x)$ satisfying $1\leq
\operatorname{ess\,inf}_{x\in [0,2\pi ]}p(x)$, $\operatorname{ess\,sup}_{x\in
[0,2\pi]}p(x) < \infty$, and the Dini–Lipschitz condition. Jackson
type direct inequalities of trigonometric approximation are obtained for the
modulus of smoothness based on one sided Steklov averages
\[
\mathfrak{Z}_{v}f(\cdot) := \frac{1}{v}\int\nolimits_{0}^{v}f
(\cdot+t) \,dt
\]
in these spaces. We give the main properties of the modulus of smoothness
\[
\Omega_{r}(f,v)_{p(\cdot)} := \left\Vert
(\mathbf{I}\mathfrak{Z}_{v})^{r}f\right\Vert_{p(\cdot)}\quad
(r\in \mathbb{N})
\]
in $L^{p(x)}$, where $\mathbf{I}$ is the identity operator. An
equivalence of the modulus of smoothness and Peetre's $K$functional is
established.

121–135 
Pricing American put options under stochastic volatility using the Malliavin derivative.
Mohamed Kharrat
The aim of this paper is to develop a methodology based on Malliavin
calculus, in order to price American options under stochastic volatility. This
leads to compute the conditional expectation $\mathbb{E}(P_{t}(X_{t},
V_{t})\mid(X_{l},V_{l}))$ for any $ 0\leq l < t$, where $V_{t}$ is generated by the
CoxIngersollRoss (CIR) process. Some simulations and comparisons are
given.

137–147 
Trajectorial market models: arbitrage and pricing intervals.
Sebastián E. Ferrando, Alfredo L. González, Iván L. Degano, Massoomeh Rahsepar
The paper develops general, nonprobabilistic market models based on trajectory
sets and minmax price bounds leading to price intervals for European options.
The approach provides the trajectory based analogue of a martingale process as
well as a generalization that allows a limited notion of arbitrage in the
market while still providing coherent option prices. An illustrative example is
described in detail. Several properties of the price bounds are obtained, in
particular a connection with risk neutral pricing is established for trajectory
markets associated to a continuoustime martingale model.

149–185 
Relative modular uniform approximation by means of the power series method with applications.
Kuldip Raj, Anu Choudhary
We introduce the notion of relative convergence by means of a four dimensional
matrix in the sense of the power series method, which includes Abel's as well as
Borel's methods, to prove a Korovkin type approximation theorem by using the
test functions $\{1,y,z,y^{2}+z^{2}\}$ and a double sequence of positive linear
operators defined on modular spaces. We also endeavor to examine some
applications related to this new type of approximation.

187–208 
Top local cohomology modules over local rings and the weak goingup property.
Asghar Farokhi, Alireza Nazari
Let $(R,\mathfrak{m})$ be a Noetherian local ring and let $\widehat{R}$ denote the
$\mathfrak{m}$adic completion of $R$. In this paper, we introduce the concept of the
weak goingup property for the extension $R\subseteq \widehat{R}$ and we give
some characterizations of this property. In particular, we show that this
property is equivalent to the strong form of the Lichtenbaum–Hartshorne
Vanishing Theorem. Also, when $R$ satisfies the weak goingup property, we show
that for a finitely generated $R$module $M$ of dimension $d$, and ideals $\mathfrak{a}$
and $\mathfrak{b}$ of $R$, we have $\operatorname{Att}_{R}(\operatorname{H}^{d}_{\mathfrak{a}}(M)) =
\operatorname{Att}_{R}(\operatorname{H}^{d}_{\mathfrak{b}}(M))$ if and only if $\operatorname{H}^{d}_{\mathfrak{a}}(M)\cong
\operatorname{H}^{d}_{\mathfrak{b}}(M)$, and we find a criterion for the cofiniteness of Artinian top
local cohomology modules.

209–215 
Formal torsors under reductive group schemes.
Benedictus Margaux
We consider the algebraization problem for torsors over a proper formal scheme
under a reductive group scheme. Our results apply to the case of semisimple
group schemes (which is addressed in detail).

217–224 
Hörmander conditions for vectorvalued kernels of singular integrals and their commutators.
Andrea L. Gallo, Gonzalo H. Ibañez Firnkorn, María Silvina Riveros
We study Coifman type estimates and weighted norm inequalities for singular
integral operators and their commutators, given by the convolution with a
vectorvalued kernel. We define a weaker Hörmander type condition
associated with Young functions for the vectorvalued kernels. With this
general framework we obtain as an example the result for the square operator
and its commutator given in [M. Lorente, M. S. Riveros, and A. de la Torre,
J. Math. Anal. Appl. 336 (2007), no. 1, 577–592].

225–245 
On the selfconjugateness of differential forms on bounded domains.
Ricardo Abreu Blaya, Juan Bory Reyes, Efrén Morales Amaya, José María Sigarreta Almira
Suppose $\Omega$ is a bounded domain in $\mathbb{R}^n$ with boundary $\Gamma$ and let
$\mathcal{W}$ be a nonhomogeneous differential form harmonic in $\Omega$ and
Höldercontinuous in $\Omega\cup\Gamma$. In this paper we study and obtain
some necessary and sufficient conditions for the selfconjugateness of $\mathcal{W}$ in
terms of its boundary value $\mathcal{W}_\Gamma=\omega$.

247–256 
A remark on transSasakian 3manifolds.
Yaning Wang, Wenjie Wang
Let $M$ be a transSasakian $3$manifold of type $(\alpha,\beta)$. In this
paper, we give a negative answer to the question proposed by S. Deshmukh
[Mediterr. J. Math. 13 (2016), no. 5, 2951–2958], namely we prove
that the differential equation $\nabla\beta=\xi(\beta)\xi$ on $M$ does not
necessarily imply that $M$ is homothetic to either a Sasakian or cosymplectic
manifold even when $M$ is compact. Many examples are constructed to illustrate
this result.

257–264 
Finite
dimensional Hopf algebras over the KacPaljutkin algebra $H_8$.
Yuxing Shi
Let $H_8$ be the Kac–Paljutkin algebra [Trudy Moskov. Mat.
Obšč. 15 (1966), 224–261], which is the neither
commutative nor cocommutative semisimple eight dimensional Hopf
algebra. All simple Yetter–Drinfel'd modules over $H_8$ are given,
and finitedimensional Nichols algebras over $H_8$ are determined
completely. It turns out that they are all of diagonal type. In
fact, they are of Cartan types $A_1$, $A_2$, $A_2\times A_2$,
$A_1\times \cdots \times A_1$, and $A_1\times \cdots \times
A_1\times A_2$, respectively. By the way, we calculate
Gelfand–Kirillov dimensions for some Nichols algebras. As an
application, we complete the classification of the
finitedimensional Hopf algebras over $H_8$ according to the
lifting method.

265–298 
