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For a compact Riemannian m-manifold (M m , g) , m > 1 , endowed with a nontrivial conformal vector field ζ with a conformal factor σ , there is an associated skew-symmetric tensor φ called the associated tensor, and also, ζ admits the Hodge decomposition ζ = ζ ¯ + ∇ ρ , where ζ ¯ satisfies div ζ ¯ = 0 , which is called the Hodge vector, and ρ is the Hodge potential of ζ. The main purpose of this article is to initiate a study on the impact of the Hodge vector and its potential on M m . The first result of this article states that a compact Riemannian m-manifold M m is an m-sphere S m (c) if and only if (1) for a nonzero constant c, the function − σ / c is a solution of the Poisson equation Δ ρ = m σ , and (2) the Ricci curvature satisfies R i c ζ ¯ , ζ ¯ ≥ φ 2 . The second result states that if M m has constant scalar curvature τ = m (m − 1) c > 0 , then it is an S m (c) if and only if the Ricci curvature satisfies R i c ζ ¯ , ζ ¯ ≥ φ 2 and the Hodge potential ρ satisfies a certain static perfect fluid equation. The third result provides another new characterization of S m (c) using the affinity tensor of the Hodge vector ζ ¯ of a conformal vector field ζ on a compact Riemannian manifold M m with positive Ricci curvature. The last result states that a complete, connected Riemannian manifold M m , m > 2 , is a Euclidean m-space if and only if it admits a nontrivial conformal vector field ζ whose affinity tensor vanishes identically and ζ annihilates its associated tensor φ. [ABSTRACT FROM AUTHOR]

In this paper, we find three nontrivial characterizations of Euclidean spheres. In the first result, we show that the existence of a nonzero nontrivial concircular vector field ω on a compact and connected hypersurface N of the Euclidean space Rm+1 with a mean curvature α constant along the integral curves of ω and a shape operator T satisfying T(ω)=αω implies that α is a constant and N is isometric to a sphere, and the converse also holds. In the second result, we show that the presence of a unit Killing vector field v on a compact and connected hypersurface N of a Euclidean space Rm+1 gives a nonzero function σ=g(Tv,v) with shape operator T, and the integral of the function mασRic(v,v) has a certain lower bound, and is isometric to an odd-dimensional sphere, and the converse holds too. Finally, we show that for a compact and connected hypersurface N with support ρ and basic vector field u, the integral of the Ricci curvature Ric(u,u) has a specific lower bound and is necessarily isometric to a sphere, and the converse also holds. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by D Σ (δ , η , λ , t , r) . These functions are connected to the Bazilevič functions and the λ -pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in D Σ (δ , η , λ , t , r) and derive upper bounds for the initial Taylor–Maclaurin coefficients | a 2 | and | a 3 | . Additionally, we establish connections between our results and previous research papers on this topic. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of single-valued neutrosophic soft uniform spaces as a view point of the entourage approach. We investigate the relationship among singlevalued neutrosophic soft uniformities, single-valued neutrosophic soft topologies and single-valued neutrosophic soft interior operators. Also, we study several single-valued neutrosophic soft topologies induced by a single-valued neutrosophic soft uniform space. [ABSTRACT FROM AUTHOR]

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-II censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory. [ABSTRACT FROM AUTHOR]

A novel lifetime distribution has been defined and examined in this study. The odd Lindley–Pareto (OLiP) distribution is the name we give to the new distribution. The new density function can be written as an odd Lindley-G distribution with Pareto amplification. The moment-generating function and characteristic function, entropy and asymptotic behavior, order statistics and moments, mode, variance, skewness, and kurtosis are some of the aspects of the OLiP distribution that are discovered. Seven non-Bayesian estimation techniques and Bayesian estimation utilizing Markov chain Monte Carlo were compared for performance. Additionally, when the lifetime test is truncated after a predetermined period, single acceptance sampling plans (SASPs) are created for the newly suggested, OLiP distribution. The median lifetime of the OLiP distribution with pre-specified factors is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer's risk, the OLiP distribution's parameters, and the truncation time, numerical results are obtained. The new distribution is illustrated using mortality rates of COVID-19 patients in Canada and vinyl chloride data in (g/L) from ground-water monitoring wells that are located in clean-up-gradient areas. [ABSTRACT FROM AUTHOR]