Ordered nanopatterns of triblock copolymer polystyrene-block-poly(2-vinylpyridine)-block- poly (ethylene oxide)(PS-b-P2VP-b-PEO) have been achieved by the addition of lithium chloride (LiCl). The morphological and structural evolution of PS-b-P2VP-b-PEO/LiCl thin films were systematically investigated by varying different experimental parameters, including the treatment for polymer solution aft...

Nanosphere lithography (NSL) masks were created by spin-coating of polystyrene particles onto silicon surfaces. Fluorinated hydrocarbon films were coated on the nanosphere lithography masks using plasma-enhanced chemical vapor deposition (PECVD) to obtain ordered arrays of fluorinated hydrocarbon. Atomic force microscope images show hexagonally ordered nanodots of dimension 225 ± 11 nm with a h...

We count the ordered sum-free triplets of subsets in group $\mathbb{Z}/p\mathbb{Z}$, i.e., $(A,B,C)$ sets $A,B,C \subset \mathbb{Z}/p\mathbb{Z}$ for which equation $a+b=c$ has no solution with $a\in A$, $b \in B$ and $c C$. Our main theorem improves on a recent result by Semchankau, Shabanov, Shkredov using different simpler method. proof relates previous results number independent regular grap...

and Applied Analysis 3 Lemma 3. Let (X; ≽) be a Banach lattice. Then the positive coneX is weakly closed. Proof. It is clear that the positive coneX of the Banach lattice X is convex. We have mentioned that the positive coneX of the Banach latticeX is norm closed. ApplyingMazur’s lemma (see [12] or [15]), we have in a Banach space, a convex set is norm closed if and only if it is weakly closed....

Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ord...