in this paper, given a poset $(x,leq)$, we introduce some  drifts on a groupoid $(x,*)$ with respect to $(x,leq)$, and we obtain several properties of these drifts related to the notion of $bin(x)$. we discuss some connections between fuzzy subalgebras and upward drifts.

Abstract: We shall make an overview about fusion categories and some classes of examples related to finite groups. We shall discuss the notions of nilpotency and solvability of a fusion category introduced in the work of Etingof, Gelaki, Nikshych and Ostrik. Then we shall present some results on the solvability of braided fusion categories with Frobenius-Perron dimensions of simple objects $\le...

Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then$gf$ is finit...

Introduction: The improvement of technology has increased noise levels in hospital Wards to higher than international standard levels (35-45 dB). Higher noise levels than the maximum level result in patient’s instability and dissatisfaction. Moreover, it will have serious negative effects on the staff’s health and the quality of their services. The purpose of this survey is to analyze the leve...

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...