This study aims to explore how cross-border e-commerce (CBEC) enterprises achieve a desired balance state of supply chain resilience and vulnerability. proposes the concept vulnerability, which refers proximity current ideal one anti-ideal one. To evaluate state, model is constructed using integrating fuzzy Analytic Hierarchy Process (AHP) Technique for Order Preference by Similarity Ideal Solu...

Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce ...

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.

One of the common chronic inflammatory skin diseases is Acne Vulgaris that affects up to 80% of a teen-age population. The progress of acne lesions is due to colonization of Propionibacterium acnes (P .acnes) in hair follicles. Treatment of acne includes topical or systemic therapy or combination therapy, with a tendency to perform topical therapy in mild to moderate acne. Nanoemulsions, small ...