CUBO, A Mathematical Journal <p align="justify">CUBO, A Mathematical Journal is a scientific journal founded in 1985 by the Universidad de La Frontera, Temuco - Chile. The journal publishes original papers containing substantial results in areas of pure and applied mathematics. CUBO appears in three issues per year and is indexed in DOAJ, zbMATH Open, MathSciNet, Latindex, Miar, Redib, SciELO-Chile and Scopus.</p> Universidad de La Frontera. Temuco, Chile. en-US CUBO, A Mathematical Journal 0716-7776 Quasi bi-slant submersions in contact geometry <p class="p1">The aim of the paper is to introduce the concept of quasi bi-slant submersions from almost contact metric manifolds onto Riemannian manifolds as a generalization of<span class="Apple-converted-space">&nbsp; </span>semi-slant and hemi-slant submersions. We mainly focus on quasi bi-slant submersions from cosymplectic manifolds. We give some non-trivial examples and study the geometry of leaves of distributions which are involved in the definition of the submersion. Moreover, we find some conditions for such submersions to be integrable and totally geodesic.</p> Rajendra Prasad Mehmet Akif Akyol Sushil Kumar Punit Kumar Singh Copyright (c) 2022 R. Prasad et al. 2022-04-04 2022-04-04 24 1 01–20 01–20 10.4067/S0719-06462022000100001 Infinitely many positive solutions for an iterative system of singular BVP on time scales <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>In this paper, we consider an iterative system of singular two-point boundary value problems on time scales. By applying Hölder’s inequality and Krasnoselskii’s cone fixed point theorem in a Banach space, we derive sufficient conditions for the existence of infinitely many positive solutions. Finally, we provide an example to check the validity of our obtained results.</p> </div> </div> </div> </div> K. Rajendra Prasad Mahammad Khuddush K. V. Vidyasagar Copyright (c) 2022 K. R. Prasad et al. 2022-04-04 2022-04-04 24 1 21–35 21–35 10.4067/S0719-06462022000100021 Smooth quotients of abelian surfaces by finite groups that fix the origin <p class="p1">Let \(A\) be an abelian surface and let \(G\) be a finite group of automorphisms of \(A\) fixing the origin. Assume that the analytic representation of \(G\) is irreducible. We give a classification of the pairs \((A,G)\) such that the quotient \(A/G\) is smooth. In particular, we prove that \(A=E^2\) with \(E\) an elliptic curve and that \(A/G\simeq\mathbb P^2\) in all cases. Moreover, for fixed \(E\), there are only finitely many pairs \((E^2,G)\) up to isomorphism. This fills a small gap in the literature and completes the classification of smooth quotients of abelian varieties by finite groups fixing the origin started by the first two authors.</p> Robert Auffarth Giancarlo Lucchini Arteche Pablo Quezada Copyright (c) 2022 R. Auffarth et al. 2022-04-04 2022-04-04 24 1 37–51 37–51 10.4067/S0719-06462022000100037 On graphs that have a unique least common multiple <p class="p1">A graph \(G\) without isolated vertices<span class="Apple-converted-space">&nbsp; </span>is a least common multiple of two graphs \(H_1\) and \(H_2\) if \(G\) is a<span class="Apple-converted-space">&nbsp; </span>smallest<span class="Apple-converted-space">&nbsp; </span>graph, in terms of number of edges, such that there exists<span class="Apple-converted-space">&nbsp;</span>a decomposition of \(G\) into edge disjoint copies of \(H_1\) and there exists a decomposition of \(G\) into edge disjoint copies of \(H_2\). The concept was introduced by G. Chartrand <em>et al.</em> and they proved that every two nonempty graphs have a least common multiple. Least common multiple of two graphs need not be unique. In fact two graphs can have an arbitrary large number of least common multiples. In this paper graphs that have a unique least common multiple with \( P_3 \cup K_2 \) are characterized.<span class="Apple-converted-space">&nbsp;</span></p> Reji T. Jinitha Varughese Ruby R. Copyright (c) 2022 Reji T. et al. 2022-04-04 2022-04-04 24 1 53–62 53–62 10.4067/S0719-06462022000100053 The topological degree methods for the fractional \(p(\cdot)\)-Laplacian problems with discontinuous nonlinearities <p class="p1">In this article, we<span class="Apple-converted-space">&nbsp; </span>use the topological degree based on the abstract Hammerstein equation to investigate the existence of weak solutions for a class of elliptic Dirichlet boundary value problems involving the fractional \(p(x)\)-Laplacian operator with discontinuous nonlinearities. The appropriate functional framework for this problems is the fractional Sobolev space with variable exponent.</p> Hasnae El Hammar Chakir Allalou Adil Abbassi Abderrazak Kassidi Copyright (c) 2022 H. El Hammar et al. 2022-04-04 2022-04-04 24 1 63–82 63–82 10.4067/S0719-06462022000100063 Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation <p class="p1">In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results.</p> Abderrahim Guerfi Abdelouaheb Ardjouni Copyright (c) 2022 A. Guerfi et al. 2022-04-04 2022-04-04 24 1 83–94 83–94 10.4067/S0719-06462022000100083 A characterization of \(\mathbb F_q\)-linear subsets of affine spaces \(\mathbb F_{q^2}^n\) <p class="p1">Let \(q\) be an odd prime power. We discuss possible definitions over \(\mathbb F_{q^2}\) (using the Hermitian form) of circles, unit segments and half-lines. If we use our unit segments to define the convex hulls of a set \(S\subset \mathbb F_{q^2}^n\) for \(q\notin \{3,5,9\}\) we just get the<span class="Apple-converted-space"> \(</span>\mathbb F_q\)-affine span of \(S\).</p> Edoardo Ballico Copyright (c) 2022 E. Ballico 2022-04-04 2022-04-04 24 1 95–103 95–103 10.4067/S0719-06462022000100095 Some results on the geometry of warped product CR-submanifolds in quasi-Sasakian manifold <p class="p1">The present paper deals with a study of warped product submanifolds of quasi-Sasakian manifolds and warped product CR-submanifolds of quasi-Sasakian manifolds. We have shown that the warped product of the type \( M = D_{\perp}{\times}{_{y}}{D}_{T}\) does not exist, where \( D_{\perp}\) and \( D_{T}\) are invariant and anti-invariant submanifolds of a quasi-Sasakian manifold \(\bar{M}\), respectively. Moreover we have obtained characterization results for CR-submanifolds to be locally CR-warped products.</p> Shamsur Rahman Copyright (c) 2022 S. Rahman 2022-04-04 2022-04-04 24 1 105–114 105–114 10.4067/S0719-06462022000100105 Optimality of constants in power-weighted Birman–Hardy–Rellich-Type inequalities with logarithmic refinements <p class="p1">The principal aim of this paper is to establish the optimality (<em>i.e.</em>, sharpness) of the constants \(A(m, \alpha)\) and \(B(m, \alpha)\), \(m \in \mathbb N\), \(\alpha \in \mathbb R\), of the form<span class="Apple-converted-space"> &nbsp;</span>\begin{align*} &amp;A(m, \alpha) = 4^{-m} \prod_{j=1}^{m} (2j - 1 -\alpha)^2, \\ &amp;B(m, \alpha) = 4^{-m} \sum_{k=1}^{m} \ \prod_{\substack{j = 1\\ j \ne k}}^{m} ( 2j - 1 - \alpha )^{2}, \end{align*} in the power-weighted Birman--Hardy--Rellich-type integral inequalities with logarithmic refinement terms recently proved in [41], namely,<span class="Apple-converted-space">&nbsp;</span>\begin{align*} &amp;\int_0^{\rho} dx \, x^{\alpha} \big| f^{(m )}(x) \big|^{2} \geq A(m, \alpha) \int_0^{\rho} dx \,<span class="Apple-converted-space">&nbsp; </span>x^{\alpha - 2m} \big|f(x)\big|^{2} &nbsp;\\ &amp;\quad+ B(m, \alpha) \sum_{k=1}^{N} \int_0^{\rho} dx \, x^{\alpha - 2m}\prod_{p=1}^{k}<span class="Apple-converted-space">&nbsp;</span>[\ln_{p}(\gamma/x)]^{-2} \big|f(x)\big|^{2}, <span class="Apple-converted-space">&nbsp;</span> \\ &amp; \, f \in C_{0}^{\infty}((0, \rho)), \; m, {N} \in \mathbb N, \; \alpha \in \mathbb R, \; \rho, \gamma \in (0,\infty),<span class="Apple-converted-space">&nbsp;</span>\; \gamma \geq e_{N} \rho. \end{align*} Here the iterated logarithms are given by \[ \ln_{1}( \, \cdot \,) = \ln(\, \cdot \,), \quad \ln_{j+1}( \, \cdot \,) = \ln( \ln_{j}(\, \cdot \,)), \quad j \in \mathbb N, \] and the iterated exponentials are defined via \[e_{0} = 0, \quad e_{j+1} = e^{e_{j}}, \quad j \in \mathbb N_{0} = \mathbb N \cup \{0\}. \] Moreover, we prove the analogous sequence of inequalities on the exterior interval \((r,\infty)\) for \(f \in C_{0}^{\infty}((r,\infty))\), \(r \in (0,\infty)\), and once again prove optimality of the constants involved.</p> Fritz Gesztesy Isaac Michael Michael M. H. Pang Copyright (c) 2022 F. Gesztesy et al. 2022-04-12 2022-04-12 24 1 115–165 115–165 10.4067/S0719-06462022000100115 Uniqueness of entire functions whose difference polynomials share a polynomial with finite weight <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>In this paper, we use the concept of weighted sharing of values to investigate the uniqueness results when two difference polynomials of entire functions share a nonzero polynomial with finite weight. Our result improves and extends some recent results due to Sahoo-Karmakar [J. Cont. Math. Anal. 52(2) (2017), 102–110] and that of Li <em>et al.</em> [Bull. Malays. Math. Sci. Soc., 39 (2016), 499–515]. Some examples have been exhibited which are relevant to the content of the paper.</p> </div> </div> </div> </div> Goutam Haldar Copyright (c) 2022 G. Haldar 2022-04-12 2022-04-12 24 1 167–186 167–186 10.4067/S0719-06462022000100167