Abstract

In this paper, we consider a pseudo parabolic equation with weak-viscoelastic term, where the exponent in the source term is variable. Using a differential inequality technique, we prove that the solution with positive initial energy become unbounded at a finite time, and find an upper bound for this time. A lower grow-up rate of solution is also obtained.

Keywords: Blow-up; grow-up,weak-viscoelastic term; variable exponent source.

MSC: 35B44, 35K70

Abstract

In this paper, we begin by introducing the exponential change of $m$-th root Finsler metrics, referred to as exponentially transformed $m$-th root Finsler metric. For this metric, we derive the fundamental metric tensors along with their inverses. Additionally, we determine the spray coefficients and establish the conditions under which the transformed metric is projectively related to an $m$-th root metric. Furthermore, we investigate the conditions for the transformed Finsler space to exhibit locally duality flatness and projective flatness. We also identify the conditions under which the transformed metrics to be the Berwald metric, weakly Berwald metric, Landsberg metric, and weakly Landsberg metric. Lastly, we show that every exponential change of $m$-th root Finsler metrics with almost vanishing $H$-curvature has vanishing $H$-curvature.

Keywords: Finsler space; Exponential transformation; $m$-th root metric; projectively related metrics; locally dually flat metric; $H$-curvature.

MSC: 53B40, 53C60

Abstract

A central issue of the present paper is to consider the Korovkin-type approximation properties of the Lupaş-Jain operators using $A$-statistical convergence and Abel convergence, which are well-known summability methods. We provide an instance of a sequence of positive linear operators to which the weighted Korovkin-type theorem does not apply, but the $A$-statistical approximation theorem does. Our results are one-way more substantial than some approximation results given in [Başcanbaz-Tunca et al., On Lupaş-Jain Operators, Stud. Univ. Babeş-Bolyai Math., 63(4) (2018), 525--537].

Keywords: Lupaş-Jain operators; $A$-statistical convergence; Abel convergence; weighted spaces.

MSC: 41A25, 40A35, 41A36, 40G10, 40G15

Abstract

The primary objective of this paper is to investigate the commutativity of $\sigma$-prime rings with the second kind involution, involving pairs of derivations that satisfy specific differential identities. Finally, we present examples to illustrate that the conditions assumed in our results are essential and cannot be omitted.

Keywords: $\sigma$-prime ring; derivation; involution.

MSC: 16N60, 16W25

Abstract

Notions of $\mathcal{I}^\mathcal{K}$-limit points and $\mathcal{I}^\mathcal{K}$-cluster points of functions are studied in topological spaces. In the first countable space, all $\mathcal{I}^\mathcal{K}$-cluster points of a function $f:S\to X$ belong to the closure of each member of the filter base $\mathcal{B}_f(\mathcal{I}^\mathcal{K})$. Fréchet compactness is studied in the light of ideals $\mathcal{I}$ and $\mathcal{K}$ of subsets of $S$ and showed that in an $\mathcal{I}$-sequential Hausdorff space, Fréchet compactness and $\mathcal{I}$-Fréchet compactness are equivalent. Using the FDS-property introduced by D. Shakmatov, M. Tkachenko, R. Wilson in Houston J. Math., it is seen that $\mathcal{I}^\mathcal{K}$-Fréchet compactness, Fréchet compactness and $\mathcal{I}$-Fréchet compactness are equivalent for a particular class of ideals on $S$.

Keywords: Ideal; $\mathcal{I}$-nonthin; $\mathcal{I}$-Fréchet compactness; $\mathcal{I}^\mathcal{K}$-Fréchet compactness.

MSC: 54D30, 54A05

Abstract

In this paper, we introduce SCR-warped product lightlike submanifold of golden semi-Riemannian manifold. We obtain characterization theorem of SCR-warped product lightlike submanifold of the type $M_T \times_{\lambda} M_\bot$ of golden semi-Riemannian manifold. Further, we show that for a proper SCR-warped product lightlike submanifold of golden semi-Riemannian manifold, induced connection $\nabla$ is not a metric connection. Finally, we find necessary and sufficient conditions for SCR lightlike submanifold of golden semi-Riemannian manifold to be a SCR-warped product lightlike submanifold in terms of the canonical structures $P$ and $F$. Moreover, we give two non-trivial examples of SCR-warped product lightlike submanifold of golden semi-Riemannian manifold.

Keywords: Golden structure; golden semi-Riemannian manifolds; SCR warped product lightlike submanifold; lightlike submanifolds.

MSC: 53C15, 53C40, 53C50

Abstract

In this paper, we have proposed a new extension of the Chris-Jerry distribution called as Weighted Chris-Jerry Distribution which depends on two parameters. The statistical properties of this distribution such as moments, survival functions and hazard rate, reverse hazard rate, order statistics, entropies and likelihood ratio test are derived. The two parameters are estimated using maximum likelihood estimator. To illustrate this distribution, real life data set is considered. This data set is analyzed through this distribution, to show how the proposed model worked in it.

Keywords: Weighted distribution; Chris-Jerry distribution; reliability analysis; maximum likelihood estimator; order statistics; likelihood ratio test.

MSC: 53C15, 53C40, 53C50