CUBO, A Mathematical Journal

Numerical analysis of nonlinear parabolic problems with variable exponent and \(L^1\) data

Stanislas Ouaro — 2022-08-22

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.

Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\)

Cong He — 2022-08-22

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 to obtain the off-diagonal estimate. The weight is also useful when it comes to control the higher-order derivative term.

Variational methods to second-order Dirichlet boundary value problems with impulses on the half-line

Meriem Djibaoui — 2022-08-22

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.

On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds

Masaya Kawamura — 2022-08-22

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.

Perfect matchings in inhomogeneous random bipartite graphs in random environment

Jairo Bochi — 2022-08-22

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.

On existence results for hybrid \(\psi-\)Caputo multi-fractional differential equations with hybrid conditions

Fouad Fredj — 2022-08-22

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 to an example that illustrates the applicability of our results.

Graded weakly 1-absorbing prime ideals

Ünsal Tekir — 2022-08-22

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.

On Severi varieties as intersections of a minimum number of quadrics

Hendrik Van Maldeghem — 2022-08-22

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.

Ideal based graph structures for commutative rings

M. I. Jinnah — 2022-08-22

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.

Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces

N. Seshagiri Rao — 2022-08-22

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 generalized \((\phi, \psi)\)-contraction conditions in complete partially ordered \(b\)-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.