Revista de la Unión Matemática Argentina
https://revistas.uns.edu.ar/revuma
<p>Revista de la Unión Matemática Argentina is an open access journal that publishes original research articles in all areas of pure and applied mathematics.</p> <p> </p> <p>We are currently using Open Journal Systems (OJS) to handle submissions. Please refer to <a title="Revista de la UMA" href="http://inmabb.criba.edu.ar/revuma/revuma.php" target="_self">our main website</a> for all other business with the journal.</p>Unión Matemática Argentinaen-USRevista de la Unión Matemática Argentina0041-6932<p><span style="color: #111111; font-size: 11px; line-height: 15px;"><span style="color: #111111; font-size: 11px; line-height: 15px;">Authors who publish with this journal agree to the following terms:<br></span></span><br>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a style="text-decoration: underline; color: #337755;" href="http://creativecommons.org/licenses/by/4.0/" target="_new">Creative Commons Attribution License</a> that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. <span style="font-weight: 400;">The Journal may retract the paper after publication if clear evidence is found that the findings are unreliable as a result of misconduct or honest error.</span></p>Three-dimensional $C_{12}$-manifolds
https://revistas.uns.edu.ar/revuma/article/view/3088
<p>The present paper is devoted to three-dimensional $C_{12}$-manifolds (defined by D. Chinea and C. Gonzalez), which are never normal. We study their fundamental properties and give concrete examples. As an application, we study such structures on three-dimensional Lie groups.</p>Gherici Beldjilali
Copyright (c) 2024 Gherici Beldjilali
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2024-02-142024-02-146711–141–1410.33044/revuma.3088On an extension of the Newton polygon test for polynomial reducibility
https://revistas.uns.edu.ar/revuma/article/view/2842
<pre>Let $R$ be a commutative local principal ideal ring which is not integral, $f$ a polynomial in $R[x]$ such that $f(0) \neq 0$ and $N(f)$ its Newton polygon. If $N(f)$ contains $r$ sides of different slopes, we show that $f$ has at least $r$ different pure factors in $R[x]$. This generalizes the Newton polygon method over a ring which is not integral.</pre>Brahim Boudine
Copyright (c) 2024 Brahim Boudine
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2024-02-212024-02-2167115–2515–2510.33044/revuma.2842Summing the largest prime factor over integer sequences
https://revistas.uns.edu.ar/revuma/article/view/3154
<p>Given an integer $n\ge 2$, let $P(n)$ stand for its largest prime factor. We examine the behaviour of $\displaystyle{\sum_{n\le x \atop n\in A} P(n)}$ in the case of two sets $A$, namely the set of $r$-free numbers and the set of $h$-full numbers.</p>Jean-Marie De KoninckRafael Jakimczuk
Copyright (c) 2024 Jean-Marie De Koninck, Rafael Jakimczuk
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2024-02-212024-02-2167127–3527–3510.33044/revuma.3154New classes of statistical manifolds with a complex structure
https://revistas.uns.edu.ar/revuma/article/view/2989
<p>We define new classes of statistical manifolds with a complex structure. Motivation for our work is the classification of almost Hermitian manifolds with respect to the covariant derivative of the almost complex structure, obtained by Gray and Hervella in 1980. Instead of the Levi-Civita connection, we use a statistical one and obtain eight classes of Kähler manifolds with the statistical connection. Besides, we give some properties of tensors constructed from covariant derivative of the almost complex structure with respect to the statistical connection. From the obtained properties, further investigation of statistical manifolds is possible.</p>Mirjana Milijević
Copyright (c) 2024 Mirjana Milijević
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2024-03-062024-03-0667137–4537–4510.33044/revuma.2989Coordinate rings of some $\mathrm{SL}_2$-character varieties
https://revistas.uns.edu.ar/revuma/article/view/3192
<p>We determine generators of the coordinate ring of $\mathrm{SL}_2$-character varieties. In the case of the free group $F_3$ we obtain an explicit equation of the $\mathrm{SL}_2$-character variety. For free groups $F_k$, we find transcendental generators. Finally, for the case of the $2$-torus, we get an explicit equation of the $\mathrm{SL}_2$-character variety and use the description to compute their $E$-polynomials.</p>Vicente MuñozJesús Martín Ovejero
Copyright (c) 2024 Vicente Muñoz, Jesús Martín Ovejero
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2024-03-082024-03-0867147–6447–6410.33044/revuma.3192Spectrality of planar Moran–Sierpinski-type measures
https://revistas.uns.edu.ar/revuma/article/view/2932
<p>Let $\{M_n\}_{n=1}^{\infty}$ be a sequence of expanding positive integral matrices with $M_n= \begin{pmatrix} p_n & 0\\0 & q_n \end{pmatrix}$ for each $n\ge 1$, and let $D=\left\{\begin{pmatrix} 0\\ 0 \end{pmatrix}, \begin{pmatrix} 1\\ 0 \end{pmatrix}, \begin{pmatrix} 0\\ 1 \end{pmatrix} \right\}$ be a finite digit set in $\mathbb{Z}^2$. The associated Borel probability measure obtained by an infinite convolution of atomic measures \[ \mu_{\{M_n\},D}=\delta_{M_1^{-1}D}*\delta_{(M_2M_1)^{-1}D}*\cdots*\delta_{(M_n\cdots M_2M_1)^{-1}D}*\cdots \] is called a Moran–Sierpinski-type measure. We prove that, under certain conditions, $\mu_{\{M_n\}, D}$ is a spectral measure if and only if $3\mid p_n$ and $3\mid q_n$ for each $n\geq2$.</p>Qian LiMin-Min Zhang
Copyright (c) 2024 Qian Li, Min-Min Zhang
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2024-03-122024-03-1267165–8065–8010.33044/revuma.2932Using digraphs to compute determinant, permanent, and Drazin inverse of circulant matrices with two parameters
https://revistas.uns.edu.ar/revuma/article/view/2815
<p>This work presents closed formulas for the determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.</p>Andrés M. EncinasDaniel A. JaumeCristian PaneloDenis E. Videla
Copyright (c) 2024 Andrés M. Encinas, Daniel A. Jaume, Cristian Panelo, Denis E. Videla
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2024-03-122024-03-1267181–10681–10610.33044/revuma.2815Existence and multiplicity of solutions for $p$-Kirchhoff-type Neumann problems
https://revistas.uns.edu.ar/revuma/article/view/2646
<p>We establish, based on variational methods, existence theorems for a $p$-Kirchhoff-type Neumann problem under the Landesman–Lazer type condition and under the local coercive condition. In addition, multiple solutions for a $p$-Kirchhoff-type Neumann problem are established using a known three-critical-point theorem proposed by H. Brezis and L. Nirenberg.</p>Qin JiangSheng MaDaniel Paşca
Copyright (c) 2024 Qin Jiang, Sheng Ma, Daniel Paşca
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2024-03-202024-03-20671107–121107–12110.33044/revuma.2646Poincaré duality for Hopf algebroids
https://revistas.uns.edu.ar/revuma/article/view/2832
<p>We prove a twisted Poincaré duality for (full) Hopf algebroids with bijective antipode. As an application, we recover the Hochschild twisted Poincaré duality of van den Bergh. We also get a Poisson twisted Poincaré duality, which was already stated for oriented Poisson manifolds by Chen et al.</p>Sophie Chemla
Copyright (c) 2024 Sophie Chemla
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2024-04-052024-04-05671123–136123–13610.33044/revuma.2832Gorenstein properties of split-by-nilpotent extension algebras
https://revistas.uns.edu.ar/revuma/article/view/3303
<p>Let $A$ be a finite-dimensional $k$-algebra over an algebraically closed field $k$. In this note, we study the Gorenstein homological properties of a split-by-nilpotent extension algebra. Let $R$ be a split-by-nilpotent extension of $A$. We provide sufficient conditions to ensure when a Gorenstein-projective module over $A$ induces a similar structure over $R$. We also study when a Gorenstein-projective $R$-module induces a Gorenstein-projective $A$-module. Moreover, we study the relationship between the Gorensteinness of $A$ and $R$.</p>Pamela Suarez
Copyright (c) 2024 Pamela Suarez
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2024-04-102024-04-10671137–144137–14410.33044/revuma.3303Distance Laplacian eigenvalues of graphs, and chromatic and independence number
https://revistas.uns.edu.ar/revuma/article/view/3235
<p>Given an interval $I$, let $m_{D^{L} (G)} I$ (or simply $m_{D^{L}} I$) be the number of distance Laplacian eigenvalues of a graph $G$ which lie in $I$. For a prescribed interval $I$, we give the bounds for $m_{D^{L} }I$ in terms of the independence number $\alpha(G)$, the chromatic number $\chi$, the number of pendant vertices $p$, the number of components in the complement graph $C_{\overline{G}}$ and the diameter $d$ of $G$. In particular, we prove that $m_{D^{L}(G) }[n,n+2)\leq \chi-1$, $m_{D^{L}(G)}[n,n+\alpha(G))\leq n-\alpha(G)$, $m_{D^{L}(G) }[n,n+p)\leq n-p$ and discuss the cases where the bounds are best possible. In addition, we characterize graphs of diameter $d\leq 2$ which satisfy $m_{D^{L}(G) } (2n-1,2n )= \alpha(G)-1=\frac{n}{2}-1$. We also propose some problems of interest.</p>Shariefuddin PirzadaSaleem Khan
Copyright (c) 2024 Shariefuddin Pirzada, Saleem Khan
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2024-04-162024-04-16671145–159145–15910.33044/revuma.3235Limit behaviors for a $\beta$-mixing sequence in the St. Petersburg game
https://revistas.uns.edu.ar/revuma/article/view/3364
<p>We consider a sequence of non-negative $\beta$-mixing random variables $\{X,X_n : n\geq1\}$ from the classical St. Petersburg game. The accumulated gains $S_n=X_1+X_2+\cdots+X_n$ in the St. Petersburg game are studied, and the large deviations and the weak law of large numbers of $S_n$ are obtained.</p>Yu MiaoQing YinZhen Wang
Copyright (c) 2024 Yu Miao, Qing Yin, Zhen Wang
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2024-04-242024-04-24671161–171161–17110.33044/revuma.3364Trivial extensions of monomial algebras
https://revistas.uns.edu.ar/revuma/article/view/2070
<pre>We describe the ideal of relations for the trivial extension $T(\Lambda)$ of a finite-dimensional monomial algebra $\Lambda$. When $\Lambda$ is, moreover, a gentle algebra, we solve the converse problem: given an algebra $B$, determine whether $B$ is the trivial extension of a gentle algebra. We characterize such algebras $B$ through properties of the cycles of their quiver, and show how to obtain all gentle algebras $\Lambda$ such that $T(\Lambda) \cong B$. We prove that indecomposable trivial extensions of gentle algebras coincide with Brauer graph algebras with multiplicity one in all vertices in the associated Brauer graph, result proven by S. Schroll.</pre> <p> </p>María Andrea GaticaMaría Valeria HernándezMaría Inés Platzeck
Copyright (c) 2024 María Andrea Gatica, María Valeria Hernández, María Inés Platzeck
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2024-04-242024-04-24671173–196173–19610.33044/revuma.2070On the Eneström–Kakeya theorem and its various forms in the quaternionic setting
https://revistas.uns.edu.ar/revuma/article/view/3504
<p>We study the extensions of the classical Eneström–Kakeya theorem and its various generalizations regarding the distribution of zeros of polynomials from the complex to the quaternionic setting. We aim to build upon the previous work by various authors and derive zero-free regions of some special regular functions of a quaternionic variable with restricted coefficients, namely quaternionic coefficients whose real and imaginary components or moduli of the coefficients satisfy suitable inequalities. The obtained results for this subclass of polynomials and slice regular functions produce generalizations of a number of results known in the literature on this subject.</p>Abdullah Mir
Copyright (c) 2024 Abdullah Mir
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2024-04-242024-04-24671197–211197–21110.33044/revuma.3504