Non-degenerate maps and sets

Incidences with k-non-degenerate sets and their applications

We study point-sphere and point-plane incidences in three-dimensional space. In particular, for 1 < k < n, we say that a set of spheres (resp., planes) is k-non-degenerate if no circle is contained in k spheres of the set (resp., if no line is contained in k planes of the set). We prove that, for every ε > 0, the number of incidences between a set of m points and a k-non-degenerate set of n sph...

Semi-θ-Open Sets and New Classes of Maps

Quantum current modelling on tri-layer graphene nanoribbons in limit degenerate and non-degenerate

Graphene is determined by a wonderful carrier transport property and high sensitivityat the surface of a single molecule, making them great as resources used in Nano electronic use.TGN is modeled in form of three honeycomb lattices with pairs of in-equivalent sites as {A1, B1},{A2, B2}, and {A3, B3} which are located in the top, center and bottom layers, respectively. Trilayer...

Conductivity Coefficient Modeling in Degenerate and Non-Degenerate Modes on GNSs

Carbon nanoscrolls (CNSs) with tubular structure similar to the open multiwall carbonnanotube have been of hot debate during recent years. Due to its unique property, Graphene Nanoscroll (GNS) have attracted many research groups’ attention and have been used by them. They specially studied on energy storage devices such as batteries and super capacitors. These devices can be schematically...

Non - degenerate Hilbert cubes in random sets par

A slight modification of the proof of Szemerédi’s cube lemma gives that if a set S ⊂ [1, n] satisfies |S| ≥ n2 , then S must contain a non-degenerate Hilbert cube of dimension blog2 log2 n− 3c. In this paper we prove that in a random set S determined by Pr{s ∈ S} = 1 2 for 1 ≤ s ≤ n, the maximal dimension of nondegenerate Hilbert cubes is a.e. nearly log2 log2 n+log2 log2 log2 n and determine t...