A double-sided shadow minimization problem in the Boolean cube layer is investigated in this paper. The problem is to minimize the size of the union of the lower and upper shadows of a k-uniform family of subsets of [n]. It is shown that if 3 ≤ k ≤ n− 3, there is no total order such that all its initial segments have minimal double-sided shadow. Denote by ([n] k ) the family of all subsets of t...

The goal of this paper is to introduce the notions of , -double fuzzy ideals and , -double fuzzy ideal bases where and are strictly two-sided, commutative quanta and also investigate the relationships between these two structures. Then, we construct a functor from the category of , -double fuzzy ideal spaces to the category of , -double fuzzy cotopological spaces. Furthermore, we show the exist...

Abstract Double-sided lapping is an precision machining method capable of obtaining high-precision surface. However, during the process thin pure copper substrate, workpiece will be warped due to influence residual stress, including stress and initial which deteriorate flatness ultimately affect performance components. In this study, finite element (FEM) was adopted study effect stress-related ...