let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

The incorporation of dilute concentrations bismuth into traditional III–V alloys produces significant reductions in bandgap energy presenting unique opportunities strain and engineering. However, the disparity between ideal growth conditions for host matrix those required substitutional has caused material quality these III–V–Bi to lag behind that conventional semiconductors. InSb1−xBix, while ...

The longitudinal optical conductivity is the most important property for graphene-baseddevices. So investigating this property for spatially separated few-layer graphene systems analytically and numerically is the main purpose of our study. Each layer can be mono- or bi-layer graphene. The density-density correlation function has been screened by the dielectric function using the random p...

Due to the increasing use of digital medical images, a need exists to develop an approach for automatic image annotation, which provides textual labels for images. Thus added labels can be used to access images using textual queries. Automatic image annotation can be separated into two individual tasks: feature extraction and image classification. In this paper, the authors present feature extr...

fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. the purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. to provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and can appear either at the group level or within certain groups. such cases, an ideal model should be able to encourage variable selection consistently. Bi-level has become even more challenging have heavy-tailed distribution outliers exist in random errors covariates. this paper, we st...