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 63, number 1 (2022)
June 2022
Front matter

Spectral distances in some sets of graphs.
Irena M. Jovanović
Some of the spectral distance related parameters (cospectrality, spectral
eccentricity, and spectral diameter with respect to an arbitrary graph matrix)
are determined in one particular set of graphs. According to these results,
the spectral distances connected with the adjacency matrix and the
corresponding distance related parameters are computed in some sets of trees.
Examples are provided of graphs whose spectral distances related to the
adjacency matrix, the Laplacian and the signless Laplacian matrix are
mutually equal. The conjecture related to the spectral diameter of the set of
connected regular graphs with respect to the adjacency matrix is disproved
using graph energy.

1–20 
Approximation via
statistical $K_{a}^{2}$convergence on twodimensional weighted
spaces.
Sevda Yıldız
We give a nonregular statistical summability method named
statistical $K_{a}^{2}$convergence and prove a Korovkin type approximation
theorem for this new and interesting convergence method on twodimensional
weighted spaces. We also study the rate of statistical $K_{a}^{2}$convergence
by using the weighted modulus of continuity and afterwards we present a
nontrivial application.

21–39 
Some relations
between the skew spectrum of an oriented graph and the spectrum
of certain closely associated signed graphs.
Zoran Stanić
Let $R_{G'}$ be the vertexedge incidence matrix of an
oriented graph $G'$. Let $\Lambda(\dot{F})$ be the signed graph whose
vertices are identified as the edges of a signed graph $\dot{F}$, with a pair of
vertices being adjacent by a positive (resp. negative) edge if and only if the
corresponding edges of $\dot{G}$ are adjacent and have the same
(resp. different) sign. In this paper, we prove that $G'$ is bipartite if and
only if there exists a signed graph $\dot{F}$ such that $R_{G'}^\intercal
R_{G'}2I$ is the adjacency matrix of $\Lambda(\dot{F})$. It occurs that
$\dot{F}$ is fully determined by $G'$. As an application, in some particular
cases we express the skew eigenvalues of $G'$ in terms of the eigenvalues of
$\dot{F}$. We also establish some upper bounds for the skew spectral radius of
$G'$ in both the bipartite and the nonbipartite case.

41–50 
The convex and
weak convex domination number of convex polytopes.
Zoran Lj. Maksimović, Aleksandar Lj. Savić, and Milena S. Bogdanović
This paper is devoted to solving the weakly convex dominating set problem and
the convex dominating set problem for some classes of planar graphs—convex
polytopes. We consider all classes of convex polytopes known from
the literature and present exact values of weakly convex and convex
domination number for all classes, namely $A_n$, $B_n$, $C_n$, $D_n$,
$E_n$, $R_n$, $R''_n$, $Q_n$, $S_n$, $S''_n$, $T_n$, $T''_n$ and $U_n$. When
$n$ is up to 26, the values are confirmed by using the
exact method, while for greater values of $n$ theoretical proofs are
given.

51–68 
The
$\mathfrak{A}$principal real hypersurfaces in complex
quadrics.
TeeHow Loo
A real hypersurface in the complex quadric $Q^m=SO_{m+2}/SO_mSO_2$ is said to
be $\mathfrak{A}$principal if its unit normal vector field is singular of
type $\mathfrak{A}$principal everywhere. In this paper, we show that a
$\mathfrak{A}$principal Hopf hypersurface in $Q^m$, $m\geq3$, is an open
part of a tube around a totally geodesic $Q^{m+1}$ in $Q^m$. We also show
that such real hypersurfaces are the only contact real hypersurfaces in
$Q^m$. The classification for complete pseudoEinstein real hypersurfaces
in $Q^m$, $m\geq3$, is also obtained.

69–91 
On the module intersection graph of ideals of rings.
Thangaraj Asir, Arun Kumar, and Alveera Mehdi
Let $R$ be a commutative ring and $M$ an $R$module. The $M$intersection
graph of ideals of $R$ is an undirected simple graph, denoted by $G_{M}(R)$,
whose vertices are nonzero proper ideals of $R$ and two distinct vertices are
adjacent if and only if $IM\cap JM\neq 0$. In this article, we focus on how
certain graph theoretic parameters of $G_M(R)$ depend on the properties of
both $R$ and $M$. Specifically, we derive a necessary and sufficient condition
for $R$ and $M$ such that the $M$intersection graph $G_M(R)$ is either
connected or complete. Also, we classify all $R$modules according to
the diameter value of $G_M(R)$. Further, we characterize rings $R$ for
which $G_M(R)$ is perfect or Hamiltonian or pancyclic or planar.
Moreover, we show that the graph $G_{M}(R)$ is weakly perfect and cograph.

93–107 
On Baer modules.
Chillumuntala Jayaram, Ünsal Tekir, and Suat Koç
A commutative ring $R$ is said to be a Baer ring if for each $a\in R$,
$\operatorname{ann}(a)$ is generated by an idempotent element $b\in R$.
In this paper, we extend the notion of a Baer ring to modules in terms
of weak idempotent elements defined in a previous work by Jayaram and
Tekir. Let $R$ be a commutative ring with a nonzero identity and let
$M$ be a unital $R$module. $M$ is said to be a Baer module if for each
$m\in M$ there exists a weak idempotent element $e\in R$ such that
$\operatorname{ann}_{R}(m)M=eM$. Various examples and properties of
Baer modules are given. Also, we characterize a certain class of
modules/submodules such as von Neumann regular modules/prime submodules
in terms of Baer modules.

109–128 
A
characterization of Stone and linear Heyting algebras.
Alejandro Petrovich and Carlos Scirica
An important problem in the variety of Heyting algebras $\mathcal{H}$ is to
find new characterizations which allow us to determinate if
a given $H\in \mathcal{H}$ is linear or Stone. In this work we present
two Heyting algebras, $H^{ns}$ and $H^{snl}$, such that:
(a) a Heyting algebra $H$ is a Stone–Heyting algebra if and only if
$H^{ns}$ cannot be embedded in $H$, and (b) $H$ is a linear Heyting algebra if
and only if neither $H^{ns}$ nor $H^{snl}$ can be embedded in $H$.

129–136 
Positive periodic
solutions of a discrete ratiodependent predatorprey model with
impulsive effects.
Cosme Duque and José L. Herrera Diestra
Studies of the dynamics of predatorprey systems are abundant in the
literature. In an attempt to account for more realistic models, previous
studies have opted for the use of discrete predatorprey systems with
ratiodependent functional response. In the present research we go a step
further with the inclusion of impulsive effects in the dynamics. More
concretely, by assuming that the coefficients involved in the system and
the impulses are periodic, we obtain sufficient conditions for the
existence of periodic solutions. We present some numerical examples to
illustrate the effectiveness of our results.

137–151 
The total
coindependent domination number of some graph
operations.
Abel Cabrera Martínez, Suitberto Cabrera García,
Iztok Peterin, and Ismael G. Yero
A set $D$ of vertices of a graph $G$ is a total dominating set if every vertex
of $G$ is adjacent to at least one vertex of $D$. The total dominating set
$D$ is called a total coindependent dominating set if the subgraph induced
by $V(G)  D$ is edgeless. The minimum cardinality among all total
coindependent dominating sets of $G$ is the total coindependent
domination number of $G$. In this article we study the total coindependent
domination number of the join, strong, lexicographic, direct and rooted
products of graphs.

153–168 
On the image set
and reversibility of shift morphisms over discrete alphabets.
Jorge Campos, Neptalí Romero, and Ramón Vivas
We provide sufficient conditions in order to show that the image set of
a continuous and shiftcommuting map defined on a shift space over an
arbitrary discrete alphabet is also a shift space. Additionally, if
such a map is injective, then its inverse is also continuous and
shiftcommuting.

169–184 
$C$groups and
mixed $C$groups of bounded linear operators on nonarchimedean
Banach spaces.
Abdelkhalek El Amrani, Aziz Blali, and Jawad Ettayb
We introduce and study $C$groups and mixed $C$groups of
bounded linear operators on nonarchimedean Banach spaces. Our main result
extends some existing theorems on this topic. In contrast with the classical
setting, the parameter of a given $C$group (or mixed
$C$group) belongs to a clopen ball $\Omega_{r}$ of the ground
field $\mathbb{K}$. As an illustration, we discuss the solvability of
some homogeneous $p$adic differential equations for $C$groups and
inhomogeneous $p$adic differential equations for mixed $C$groups when
$\alpha=1$. Examples are given to support our work.

185–201 
Stability
conditions and maximal green sequences in abelian categories.
Thomas Brüstle, David Smith, and Hipolito Treffinger
We study the stability functions on abelian categories introduced by
Rudakov and their relation with torsion classes and maximal green
sequences. Moreover, we introduce the concept of red paths, a stability
condition in the sense of Rudakov that captures information of the wall
and chamber structure of the category.

203–221 
Trees with a
unique maximum independent set and their linear properties.
Daniel A. Jaume, Gonzalo Molina, and Rodrigo Sota
Trees with a unique maximum independent set encode the maximum matching
structure in every tree. In this work we study some of their linear
properties and give two graph operations, stellare and Scoalescence, which
allow building all trees with a unique maximum independent set. The null
space structure of any tree can be understood in terms of these graph
operations.

223–238 
New uncertainty
principles for the $(k,a)$generalized wavelet transform.
Hatem Mejjaoli
We present the basic $(k,a)$generalized wavelet theory and
prove several Heisenbergtype inequalities for this transform.
After reviewing Pitt's and Beckner's inequalities for
the $(k,a)$generalized Fourier transform, we connect both inequalities
to show a generalization of uncertainty principles for the
$(k,a)$generalized wavelet transform. We also present two concentration
uncertainty principles, namely the Benedicks–Amrein–Berthier's uncertainty
principle and local uncertainty principles. Finally, we connect these
inequalities to show a generalization of the uncertainty principle of
Heisenberg type and we prove the Faris–Price uncertainty principle for the
$(k,a)$generalized wavelet transform.

239–279 
A Clemens–Schmid
type exact sequence over a local basis.
Genaro HernandezMada
Let $k$ be a finite field of characteristic $p$ and let $X \rightarrow
\operatorname{Spec} k[[t]]$ be a
semistable family of varieties over $k$. We prove that there exists a
Clemens–Schmid type exact sequence for this family. We do this by
constructing a larger family defined over a smooth curve
and using a Clemens–Schmid exact sequence in characteristic $p$
for this new family.

281–292 
