Weighted order statistic filters (WOSF) generate linearly separable Boolean functions. In some cases, 2 different WOSF may generate the same Boolean function. We thus can collect all of the WOSF together, which generate the same Boolean function. In this paper, we construct equivalent classes of WOSF, the BF equivalent class and the global equivalent class. Besides, we use minimum weight vector...

In this paper, we introduce and study new concepts of order L-weakly M-weakly compact operators. As consequences, obtain some characterizations Banach lattices with continuous norms or whose topological duals have norms. It is proved that if $$T:E \longrightarrow F$$ an operator between two lattices, then T only its adjoint $$T'$$ compact. Also, show compact, Some related results are also obtai...

For a graph G let f(G) be the largest integer k so that there are two vertex-disjoint subgraphs of G, each with k vertices, and that induce the same number of edges. Clearly f(G) ≤ bn/2c but this is not always achievable. Our main result is that for any fixed α > 0, if G has n vertices and at most n2−α edges then f(G) = n/2 − o(n), which is asymptotically optimal. The proof also yields a polyno...