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> en-US (Mauricio Godoy Molina) (Ignacio Castillo B.) Mon, 22 Aug 2022 00:00:00 -0400 OJS 60 Numerical analysis of nonlinear parabolic problems with variable exponent and \(L^1\) data <p class="p1">In this paper, we make the numerical analysis of the mild solution which is also an entropy solution of parabolic problem involving the \(p(x)-\)Laplacian operator with \(L^1-\) data.</p> Stanislas Ouaro, Noufou Rabo, Urbain Traoré Copyright (c) 2022 S. Ouaro et al. Mon, 22 Aug 2022 00:00:00 -0400 Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\) <p class="p1">In this paper, we are concerned about the well-posedness of Vlasov-Poisson equation near vaccum in weighted Sobolev space \(W^{m, p}(w)\). The most difficult part comes from estimates of the electronic term \(\nabla_{x}\phi\). To overcome this difficulty, we establish the \(L^p\)-\(L^q\) estimates of the electronic term \(\nabla_{x}\phi\); some weight is introduced as well<span class="Apple-converted-space">&nbsp; </span>to obtain the off-diagonal estimate. The weight is also useful when it comes to control the higher-order derivative term.</p> Cong He, Jingchun Chen Copyright (c) 2022 C. He et al. Mon, 22 Aug 2022 00:00:00 -0400 Variational methods to second-order Dirichlet boundary value problems with impulses on the half-line <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>In this paper, the existence of solutions for a second-order impulsive differential equation with a parameter on the half-line is investigated. Applying Lax-Milgram theorem, we deal with a linear Dirichlet impulsive problem, while the non-linear case is established by using standard results of critical point theory.</p> </div> </div> </div> </div> Meriem Djibaoui, Toufik Moussaoui Copyright (c) 2022 M. Djibaoui et al. Mon, 22 Aug 2022 00:00:00 -0400 On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds <p class="p1">We investigate Monge-Ampère type equations on almost Hermitian manifolds and show an \(a\) \(priori\) \(L^\infty\) estimate for a smooth solution of these equations.</p> Masaya Kawamura Copyright (c) 2022 M. Kawamura Mon, 22 Aug 2022 00:00:00 -0400 Perfect matchings in inhomogeneous random bipartite graphs in random environment <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erdős-Rényi random bipartite graphs in a random environment. We show that the expected number of perfect matchings obeys a precise asymptotic.</p> </div> </div> </div> </div> Jairo Bochi, Godofredo Iommi, Mario Ponce Copyright (c) 2022 J. Bochi et al. Mon, 22 Aug 2022 00:00:00 -0400 On existence results for hybrid \(\psi-\)Caputo multi-fractional differential equations with hybrid conditions <p class="p1">In this paper, we study the existence and uniqueness results of a fractional hybrid boundary value problem with multiple fractional derivatives of \(\psi-\)Caputo with different orders. Using a useful generalization of Krasnoselskii’s fixed point theorem, we have established results of at least one solution, while the uniqueness of solution is derived by Banach's fixed point. The last section is devoted<span class="Apple-converted-space">&nbsp; </span>to an example that illustrates the applicability of our results.</p> Fouad Fredj, Hadda Hammouche Copyright (c) 2022 F. Fredj et al. Mon, 22 Aug 2022 00:00:00 -0400 Graded weakly 1-absorbing prime ideals <p class="p1">In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let \(G\) be a group and \(R\) be a \(G\)-graded commutative ring with a nonzero identity \(1\neq0\). A proper graded ideal \(P\) of \(R\) is called a graded weakly 1-absorbing prime ideal if for each nonunits \(x,y,z\in h(R)\) with \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.</p> Ünsal Tekir, Suat Koç, Rashid Abu-Dawwas, Eda Yıldız Copyright (c) 2022 Ü. Tekir et al. Mon, 22 Aug 2022 00:00:00 -0400 On Severi varieties as intersections of a minimum number of quadrics <p class="p1">Let \({\mathscr{V}}\) be a variety related to the second row of the Freudenthal-Tits Magic square in \(N\)-dimensional projective space over an arbitrary field. We show that there exist \(M\leq N\) quadrics intersecting precisely in \({\mathscr{V}}\) if and only if there exists a subspace of projective dimension \(N-M\) in the secant variety disjoint from the Severi variety. We present some examples of such subspaces of relatively large dimension. In particular, over the real numbers we show that the Cartan variety (related to the exceptional group \({E_6}\)\((\mathbb R)\)) is the set-theoretic intersection of 15 quadrics.</p> Hendrik Van Maldeghem, Magali Victoor Copyright (c) 2022 H. Van Maldeghem et al. Mon, 22 Aug 2022 00:00:00 -0400 Ideal based graph structures for commutative rings <p class="p1">We introduce a graph structure \(\Gamma^{\ast}_2(R)\) for commutative rings with unity. We study some of the properties of the graph \(\Gamma^{\ast}_2(R)\). Also we study some parameters of \(\Gamma^{\ast}_2(R)\) and find rings for which \(\Gamma^{\ast}_2(R)\) is split.</p> M. I. Jinnah, Shine C. Mathew Copyright (c) 2022 M. I. Jinnah et al. Mon, 22 Aug 2022 00:00:00 -0400 Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces <p class="p1">The purpose of this paper is to prove some results on fixed point, coincidence point, coupled coincidence point and coupled common fixed point for the mappings satisfying<span class="Apple-converted-space">&nbsp; </span>generalized \((\phi, \psi)\)-contraction conditions in complete partially ordered<span class="Apple-converted-space"> \(</span>b\)-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. A few examples are illustrated to support our findings.</p> N. Seshagiri Rao, K. Kalyani Copyright (c) 2022 N. Seshagiri Rao et al. Mon, 22 Aug 2022 00:00:00 -0400