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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

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 
Volume 63, number 2 (2022)
December 2022
Front matter

Blowup of positiveinitialenergy solutions for nonlinearly damped semilinear wave equations.
Mohamed Amine Kerker
We consider a class of semilinear wave equations with both strongly and
nonlinear weakly damped terms,
\[
u_{tt}\Delta u\omega\Delta u_t+\mu\vert u_t\vert^{m2}u_t=\vert u\vert^{p2}u,
\]
associated with initial and Dirichlet boundary conditions. Under certain
conditions, we show that any solution with arbitrarily high positive initial
energy blows up in finite time if $m < p$. Furthermore, we obtain a lower bound
for the blowup time.

293–303 
Binomial edge ideals of cographs.
Thomas Kahle and Jonas Krüsemann
We determine the Castelnuovo–Mumford regularity of binomial edge ideals of
complementreducible graphs (cographs). For cographs with $n$ vertices the
maximum regularity grows as $2n/3$. We also bound the regularity by
graphtheoretic invariants and construct a family of counterexamples to
a conjecture of Hibi and Matsuda.

305–316 
A compact
manifold with infinitedimensional coinvariant cohomology.
Mehdi Nabil
Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on $M$ by
diffeomorphisms, one can define the $\Gamma$coinvariant cohomology of $M$
to be the cohomology of the complex
$\Omega_c(M)_\Gamma=\operatorname{span}\{\omega\gamma^*\omega :
\omega\in\Omega_c(M),\,\gamma\in\Gamma\}$. For a Lie algebra $\mathcal{G}$
acting on the manifold $M$, one defines the cohomology of
$\mathcal{G}$divergence forms to be the cohomology of the complex
$\mathcal{C}_{\mathcal{G}}(M)=\operatorname{span}\{L_X\omega :
\omega\in\Omega_c(M),\,X\in\mathcal{G}\}$. In this short paper we present
a situation where these two cohomologies are infinite dimensional on a
compact manifold.

317–325 
Conformal vector fields on statistical manifolds.
Leila Samereh and Esmaeil Peyghan
Introducing the conformal vector fields on a statistical manifold, we present
necessary and sufficient conditions for a vector field on a statistical
manifold to be conformal. After presenting some examples, we classify the
conformal vector fields on two famous statistical manifolds. Considering
three statistical structures on the tangent bundle of a statistical
manifold, we study the conditions under which the complete and
horizontal lifts of a vector field can be conformal on these structures.

327–351 
The isometry
groups of Lorentzian threedimensional unimodular simply connected Lie groups.
Mohamed Boucetta and Abdelmounaim Chakkar
We determine the isometry groups of all threedimensional, connected, simply
connected and unimodular Lie groups endowed with a leftinvariant
Lorentzian metric.

353–378 
On the
differential and Volterratype integral operators on Focktype spaces.
Tesfa Mengestie
The differential operator fails to admit some basic structures including
continuity when it acts on the classical Fock spaces or weighted Fock
spaces, where the weight functions grow faster than the classical Gaussian
weight function. The same conclusion also holds in some weighted Fock
spaces including the Fock–Sobolev spaces, where the weight functions grow
more slowly than the Gaussian function. We consider modulating the classical
weight function and identify Focktype spaces where the operator admits the
basic structures. We also describe some properties of Volterratype
integral operators on these spaces using the notions of order and type of
entire functions. The modulation operation supplies richer structures for
both the differential and integral operators in contrast to the classical
setting.

379–395 
A note on the
density of the partial regularity result in the class of
viscosity solutions.
Disson dos Prazeres, Edgard A. Pimentel, and Giane C. Rampasso
We establish the density of the partial regularity result in the class of
continuous viscosity solutions. Given a fully nonlinear equation, we prove
the existence of a sequence entitled to the partial regularity result,
approximating its solutions. Distinct conditions on the operator driving
the equation lead to density in different topologies. Our findings include
applications to nonhomogeneous problems, with variablecoefficient models.

397–411 
Monster graphs
are determined by their Laplacian spectra.
Ali Zeydi Abdian, Ali Reza Ashrafi, Lowell W.
Beineke, Mohammad Reza Oboudi, and Gholam Hossein FathTabar
A graph $G$ is determined by its Laplacian spectrum (DLS) if every graph with
the same Laplacian spectrum is isomorphic to $G$. A multifan graph is a
graph of the form $(P_{n_1}\cup P_{n_2}\cup \cdots \cup
P_{n_k})\bigtriangledown K_1$, where $K_1$ denotes the complete graph of
size 1, $P_{n_1}\cup P_{n_2}\cup \cdots \cup P_{n_k}$ is the disjoint union
of paths $P_{n_i}$, $n_i\geq 1$ and $1 \leq i \leq k$; and a starlike tree
is a tree with exactly one vertex of degree greater than 2. If a
multifan graph and a starlike tree are joined by identifying their
vertices of degree more than 2, then the resulting graph is called a
monster graph. In some earlier works, it was shown that all multifan and
pathfriendship graphs are DLS. The aim of this paper is to generalize
these facts by proving that all monster graphs are DLS.

413–424 
Sharp bounds for
fractional type operators with $L^{\alpha,s}$Hörmander conditions.
Gonzalo H. IbañezFirnkorn, María Silvina Riveros,
and Raúl E. Vidal
We provide the sharp bound for a fractional type operator given by a kernel
satisfying the $L^{\alpha,s}$Hörmander condition and certain fractional
size condition, $0 < \alpha < n$ and $1 < s\leq \infty$. In order to prove
this result we use a new appropriate sparse domination. Examples of these
operators include the fractional rough operators. For the case $s=\infty$
we recover the sharp bound of the fractional integral, $I_{\alpha}$, proved
by Lacey et al.
[J. Functional Anal. 259 (2010), no. 5, 1073–1097].

425–442 
The isolation of
the first eigenvalue for a Dirichlet eigenvalue problem involving
the Finsler $p$Laplacian and a nonlocal term.
Andrei Grecu
We analyse the isolation of the first eigenvalue for an eigenvalue problem
involving the Finsler $p$Laplace operator and a nonlocal term on a bounded
domain subject to the homogeneous Dirichlet boundary condition.

443–453 
The algebraic
sets of vectors generating planar normal sections of
isoparametric hypersurfaces of FKM type.
Cristián U. Sánchez
We present a proof of the connectedness of the algebraic
set of vectors generating planar normal sections for all isoparametric
hypersurfaces, with positive multiplicities $m_{1}$ and $m_{2}$ of
FKM type.

455–473 
Orlicz version of mixed moment tensors.
ChangJian Zhao
Our main aim is to generalize the moment tensors $\mathbf{\Psi}_{r}(K)$ to
the Orlicz space. Under the framework of the Orlicz–Brunn–Minkowski theory, we
introduce a new affine geometric quantity $\mathbf{\Psi}_{\psi,r}(K,L)$, and call it
Orlicz mixed moment tensors of convex bodies $K$ and $L$. The fundamental
notions and properties of the moment tensors as well as related Minkowski
and Brunn–Minkowski inequalities are then extended to the Orlicz setting.
Diverse inequalities for certain new $L_p$mixed moment tensors
$\mathbf{\Psi}_{p,r}(K,L)$ are also derived. The new Orlicz inequalities in special
cases yield the Orlicz–Minkowski and the
Orlicz–Brunn–Minkowski inequalities, respectively.

475–488 
Affinity kernels on measure spaces and maximal operators.
Hugo Aimar, Ivana Gómez, and Luis Nowak
In this note we consider maximal operators defined in terms of families of
kernels and families of their level sets. We prove a general estimate that
extends some classical Euclidean cases and, under some mild transitivity
property, we show their basic boundedness properties on Lebesgue spaces.
The motivation of these problems has its roots in the analysis
associated to affinity kernels on large data sets.

489–503 
Bilinear differential operators and $\mathfrak{osp}(12)$relative cohomology on $\mathbb{R}^{11}$.
Abderraouf Ghallabi and Meher Abdaoui
We consider the $11$dimensional real superspace $\mathbb{R}^{11}$
endowed with its standard contact structure defined by the
1form $\alpha$. The conformal Lie superalgebra $\mathcal{K}(1)$
acts on $\mathbb{R}^{11}$ as the Lie superalgebra of contact vector
fields; it contains the Möbius superalgebra
$\mathfrak{osp}(12)$. We classify $\mathfrak{osp}(12)$invariant
superskewsymmetric binary differential operators from
$\mathcal{K}(1)\wedge\mathcal{K}(1)$ to $\mathfrak{D}_{\lambda,\mu;\nu}$
vanishing on $\mathfrak{osp}(12)$, where
$\mathfrak{D}_{\lambda,\mu;\nu}$ is the superspace of bilinear
differential operators between the superspaces of weighted
densities. This result allows us to compute the second differential
$\mathfrak{osp}(12)$relative cohomology of $\mathcal{K}(1)$ with
coefficients in $\mathfrak{D}_{\lambda,\mu;\nu}$.

505–522 
On the common
fixed points of double sequences of twoparameter nonexpansive
semigroups in strictly convex Banach spaces.
Rasoul Abazari and Asadollah Niknam
We obtain some results about common fixed points of strongly
continuous twoparameter semigroups of nonexpansive mappings in strictly
convex Banach spaces. Also, by using them we characterize common fixed
points of double sequences of such semigroups.

523–530 
