https://revistas.uns.edu.ar/revuma/issue/feed Revista de la Unión Matemática Argentina 2024-12-19T12:04:26-03:00 Revista de la UMA revuma@criba.edu.ar Open Journal Systems <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>&nbsp;</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> https://revistas.uns.edu.ar/revuma/article/view/3335 Warped product lightlike submanifolds with a slant factor 2022-10-16T01:02:17-03:00 Megha Pruthi meghapruthi4194@gmail.com Sangeet Kumar sp7maths@gmail.com <p>In the present study, we investigate a new type of warped products on manifolds with indefinite metrics, namely, warped product lightlike submanifolds of indefinite Kaehler manifolds with a slant factor. First, we show that indefinite Kaehler manifolds do not admit any proper warped product semi-slant lightlike submanifolds of the type $N_{T}\times_{\lambda}N_{\theta}$, $N_{\theta}\times_{\lambda}N_{T}$, $N_{\perp}\times_{\lambda}N_{\theta}$ and $N_{\theta}\times_{\lambda}N_{\perp}$, where $N_{T}$ is a holomorphic submanifold, $N_{\perp}$ is a totally real submanifold and $N_{\theta}$ is a proper slant submanifold. Then, we study warped product semi-slant lightlike submanifolds of the type $B\times_{\lambda}N_{\theta}$, where $B = N_{T}\times N_{\perp}$, of an indefinite Kaehler manifold. Following this, we give one non-trivial example for this kind of warped products of indefinite Kaehler manifolds. Then, we establish a geometric estimate for the squared norm of the second fundamental form involving the Hessian of warping function $\lambda$ for this class of warped products. Finally, we present a sharp geometric inequality for the squared norm of second fundamental form of warped product semi-slant lightlike submanifolds of the type $B\times_{\lambda}N_{\theta}$.</p> 2024-12-18T00:00:00-03:00 Copyright (c) 2024 Megha Pruthi, Sangeet Kumar https://revistas.uns.edu.ar/revuma/article/view/3622 The Green ring of a family of copointed Hopf algebras 2023-03-02T10:15:41-03:00 Cristian Vay cristian.vay@unc.edu.ar <p>The copointed liftings of the Fomin–Kirillov algebra $\mathcal{FK}_3$ over the algebra of functions on the symmetric group $\mathbb{S}_3$ were classified by Andruskiewitsch and the author. We demonstrate here that those associated to a generic parameter are Morita equivalent to the regular blocks of well-known Hopf algebras: the Drinfeld doubles of the Taft algebras and the small quantum groups $u_{q}(\mathfrak{sl}_2)$. The indecomposable modules over these were classified independently by Chen, Chari–Premet and Suter. Consequently, we obtain the indecomposable modules over the generic liftings of $\mathcal{FK}_3$. We decompose the tensor products between them into the direct sum of indecomposable modules. We then deduce a presentation by generators and relations of the Green ring.</p> 2024-12-18T00:00:00-03:00 Copyright (c) 2024 Cristian Vay https://revistas.uns.edu.ar/revuma/article/view/3574 Haar wavelet characterization of dyadic Lipschitz regularity 2022-09-14T14:22:06-03:00 Hugo Aimar haimar@santafe-conicet.gov.ar Carlos Exequiel Arias carias@santafe-conicet.gov.ar Ivana Gómez ivanagomez@santafe-conicet.gov.ar <p>We obtain a necessary and sufficient condition on the Haar coefficients of a real function $f$ defined on $\mathbb{R}^+$ for the Lipschitz $\alpha$ regularity of $f$ with respect to the ultrametric $\delta(x,y)=\inf \{|I|: x, y\in I; \, I\in\mathcal{D}\}$, where $\mathcal{D}$ is the family of all dyadic intervals in $\mathbb{R}^+$ and $\alpha$ is positive. Precisely, $f\in \mathrm{Lip}_\delta(\alpha)$ if and only if ${\vert\langle{f}{h^j_k}\rangle\vert}\leq C 2^{-(\alpha + 1/2)j}$ for some constant $C$, every $j\in\mathbb{Z}$ and every $k=0,1,2,\ldots$ Here, as usual, $h^j_k(x)= 2^{j/2}h(2^jx-k)$ and $h(x)=\mathcal{X}_{[0,1/2)}(x)-\mathcal{X}_{[1/2,1)}(x)$.</p> 2024-12-26T00:00:00-03:00 Copyright (c) 2024 Hugo Aimar, Carlos Exequiel Arias, Ivana Gómez https://revistas.uns.edu.ar/revuma/article/view/3473 Cluster algebras of type $\mathbb{A}_{n-1}$ through the permutation groups $S_{n}$ 2022-07-20T18:49:57-03:00 Kodjo Essonana Magnani kodjo.essonana.magnani@usherbrooke.ca <p>Flips of triangulations appear in the definition of cluster algebras by Fomin and Zelevinsky. In this article we give an interpretation of mutation in the sense of permutation using triangulations of a convex polygon. We thus establish a link between cluster variables and permutation mutations in the case of cluster algebras of type $\mathbb{A}$.</p> 2025-02-28T00:00:00-03:00 Copyright (c) 2025 Kodjo Essonana Magnani https://revistas.uns.edu.ar/revuma/article/view/3670 Large-scale homogeneity and isotropy versus fine-scale condensation: A model based on Muckenhoupt-type densities 2022-10-27T17:17:23-03:00 Hugo Aimar haimar@santafe-conicet.gov.ar Federico Morana fmorana@santafe-conicet.gov.ar <p><!--StartFragment --></p> <div>In this brief note we aim to provide, through a well-known class of singular densities in harmonic analysis, a simple approach to the fact that the homogeneity of the universe on scales of the order of a hundred million light years is entirely compatible with the fine-scale condensation of matter and energy. We give precise and quantitative definitions of homogeneity and isotropy on large scales. Then we show that Muckenhoupt densities have the ingredients required for a model of the large-scale homogeneity and the fine-scale condensation of the universe. In particular, these densities can take locally infinitely large values (black holes) and, at the same time, they are independent of location at large scales. We also show some locally singular densities that satisfy the large-scale isotropy property.</div> <p><!--EndFragment --></p> 2025-03-29T00:00:00-03:00 Copyright (c) 2025 Hugo Aimar, Federico Morana https://revistas.uns.edu.ar/revuma/article/view/3511 Clique coloring EPT graphs on bounded degree trees 2023-02-15T21:43:50-03:00 Pablo De Caria pdecaria@mate.unlp.edu.ar María Pía Mazzoleni pia@mate.unlp.edu.ar María Guadalupe Payo Vidal gpayovidal@mate.unlp.edu.ar <p>The edge-intersection graph of a family of paths on a host tree is called an EPT graph. When the host tree has maximum degree $h$, we say that the graph is $[h,2,2]$. If the host tree also satisfies being a star, we have the corresponding classes of EPT-star and $[h,2,2]$-star graphs. In this paper, we prove that $[4,2,2]$-star graphs are $2$-clique colorable, we find other classes of EPT-star graphs that are also $2$-clique colorable, and we study the values of $h$ such that the class $[h,2,2]$-star is $3$-clique colorable. If a graph belongs to $[4,2,2]$ or $[5,2,2]$, we prove that it is $3$-clique colorable, even when the host tree is not a star. Moreover, we study some restrictions on the host trees to obtain subclasses that are $2$-clique colorable.</p> 2025-03-29T00:00:00-03:00 Copyright (c) 2025 Pablo De Caria, María Pía Mazzoleni, María Guadalupe Payo Vidal https://revistas.uns.edu.ar/revuma/article/view/3697 On the wellposedness of a fuel cell problem 2023-04-08T11:20:29-03:00 Luisa Consiglieri lconsiglieri@gmail.com <p>This paper investigates the existence of weak solutions to a fuel cell problem modeled by a boundary value problem (BVP) in the multiregion domain. The BVP consists of the coupled Stokes/Darcy-TEC (thermoelectrochemical) system of elliptic equations, with Beavers–Joseph–Saffman and regularized Butler–Volmer boundary conditions being prescribed on the interfaces, porous-fluid and membrane, respectively. The present model includes macrohomogeneous models for both hydrogen and methanol crossover. The novelty in the coupled Stokes/Darcy-TEC system lies in the presence of the Joule effect together with the quasilinear character given by (1) temperature dependence of the viscosities and the diffusion coefficients; (2) the concentration-temperature dependence of Dufour–Soret and Peltier–Seebeck cross-effect coefficients, and (3) the pressure dependence of the permeability. We derive quantitative estimates of the solutions to clarify smallness conditions on the data. We use fixed-point and compactness arguments based on the quantitative estimates of approximated solutions.</p> 2025-03-31T00:00:00-03:00 Copyright (c) 2025 Luisa Consiglieri