Current volume
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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

Current issue
Articles are published here before the issue is completed.
Vol. 67, no. 2 (2024)
Decidable objects and molecular toposes.
Matías Menni
We study several sufficient conditions for the molecularity/localconnectedness of
geometric morphisms. In particular, we show that if $\mathcal{S}$ is a Boolean topos,
then, for every hyperconnected essential geometric morphism $p : \mathcal{E} \rightarrow
\mathcal{S}$ such that the leftmost adjoint $p_{!}$ preserves finite products, $p$ is
molecular and $p^* : \mathcal{S} \rightarrow \mathcal{E}$ coincides with the full
subcategory of decidable objects in $\mathcal{E}$. We also characterize the reflections
between categories with finite limits that induce molecular maps between the respective
presheaf toposes. As a corollary we establish the molecularity of certain geometric
morphisms between Gaeta toposes.

397–415 
Extinction time of an epidemic with infectionagedependent infectivity.
Anicet MougabePeurkor, Ibrahima Dramé, Modeste N'zi, and Étienne Pardoux
This paper studies the distribution function of the time of extinction of a subcritical
epidemic, when a large enough proportion of the population has been immunized and/or the
infectivity of the infectious individuals has been reduced, so that the effective
reproduction number is less than one. We do that for a SIR/SEIR model, where infectious
individuals have an infectionagedependent infectivity, as in the model introduced in
Kermack and McKendrick's seminal 1927 paper. Our main conclusion is that simplifying the
model as an ODE SIR model, as it is largely done in the epidemics literature, introduces a
bias toward shorter extinction time.

417–443 
On hyponormality and a commuting property of Toeplitz operators.
Houcine Sadraoui and Borhen Halouani
In this work we give sufficient conditions for
hyponormality of Toeplitz operators on a weighted Bergman
space when the analytic part of the symbol is a monomial
and the conjugate part is a polynomial. We also extend a
known commuting property of Toeplitz operators with a
harmonic symbol on the Bergman space to weighted Bergman
spaces.

445–453 
Genus and book thickness of reduced cozerodivisor graphs of commutative rings.
Edward Jesili, Krishnan Selvakumar, and Thirugnanam Tamizh Chelvam
For a commutative ring $R$ with identity, let $\langle a\rangle$ be the principal ideal
generated by $a\in R$. Let $\Omega(R)^*$ be the set of all nonzero proper principal ideals
of $R$. The reduced cozerodivisor graph $\Gamma_r(R)$ of $R$ is the simple undirected
graph whose vertex set is $\Omega(R)^*$ and such that two distinct vertices $\langle
a\rangle$ and $\langle b\rangle$ in $\Omega(R)^\ast$ are adjacent if and only if $\langle
a \rangle\nsubseteq\langle b\rangle$ and $\langle b\rangle\nsubseteq\langle a\rangle$. In
this article, we study certain properties of embeddings of the reduced cozerodivisor
graph of commutative rings. More specifically, we characterize all Artinian nonlocal rings
whose reduced cozerodivisor graph has genus two. Also we find the book thickness of the
reduced cozerodivisor graphs which have genus at most one.

455–473 
Boundedness of geometric invariants near a singularity which is a suspension of a singular curve.
Luciana F. Martins, Kentaro Saji, Samuel P. dos Santos, and Keisuke Teramoto
Near a singular point of a surface or a curve, geometric invariants diverge in general,
and the orders of this divergence, in particular the boundedness about these invariants,
represent the geometry of the surface and the curve. In this paper, we study the
boundedness and orders of several geometric invariants near a singular point of a surface
which is a suspension of a singular curve in the plane, and those of the curves passing
through the singular point. We evaluate the orders of the Gaussian and mean curvatures, as
well as those of the geodesic and normal curvatures, and the geodesic torsion for the
curve.

475–502 
Complete presentation and Hilbert series of the mixed braid monoid $MB_{1,3}$.
Zaffar Iqbal, Muhammad Mobeen Munir, Maleeha Ayub, and Abdul Rauf Nizami
The Hilbert series is the simplest way of finding dimension and degree of an algebraic
variety defined explicitly by polynomial equations. The mixed braid groups were introduced
by Sofia Lambropoulou in 2000. In this paper we compute the complete presentation and the
Hilbert series of the canonical words of the mixed braid monoid $MB_{1,3}$.

503–516 
Onesided EP elements in rings with involution.
Cang Wu, Jianlong Chen, and Yu Chen
This paper investigates the onesided EP property of elements in rings with involution.
Let $R$ be a ring with involution $\ast$. Then $a \in R$ is said to be left (resp. right)
EP if $a$ is Moore–Penrose invertible and $aR \subseteq a^{\ast}R$ (resp. $a^{\ast}R
\subseteq aR$). Many properties of EP elements are extended to onesided versions. Some
new characterizations of EP elements are presented in relation to the absorption law for
Moore–Penrose inverses.

517–528 
Evolution of first eigenvalues of some geometric operators under the rescaled List's extended Ricci flow.
Shahroud Azami and Abimbola Abolarinwa
Let $(M,g(t), e^{\phi}d\nu)$ be a compact weighted Riemannian manifold and let
$(g(t),\phi(t))$ evolve by the rescaled List's extended Ricci flow. In this paper, we
study the evolution equations for first eigenvalues of the geometric operators,
$\Delta_{\phi}+cS^{a}$, along the rescaled List's extended Ricci flow. Here
$\Delta_{\phi}=\Delta\nabla\phi.\nabla$ is a symmetric diffusion operator, $\phi\in
C^{\infty}(M)$, $S=R\alpha\nabla \phi^{2}$, $R$ is the scalar curvature with respect to
the metric $g(t)$ and $a, c$ are some constants. As an application, we obtain some
monotonicity results under the rescaled List's extended Ricci flow.

529–543 
The $w$core–EP inverse in rings with involution.
Dijana Mosić, Huihui Zhu, and Liyun Wu
The main goal of this paper is to present two new classes of generalized inverses in order
to extend the concepts of the (dual) core–EP inverse and the (dual) $w$core inverse.
Precisely, we introduce the $w$core–EP inverse and its dual for elements of a ring with
involution. We characterize the (dual) $w$core–EP invertible elements and develop several
representations of the $w$core–EP inverse and its dual in terms of different wellknown
generalized inverses. Using these results, we get new characterizations and expressions
for the core–EP inverse and its dual. We apply the dual $w$core–EP inverse to solve
certain operator equations and give their general solution forms.

545–565 
