Cycloaddition reaction between C30 and hula-I, 3-diene was studied within the Snimework of AM I (RHF)level. The reaction involving the double bond between two hexagons and a hexagon and a pentagon, as wellas the cycloaddition products followed by disrotatory ogs s electrocyclic ring openings were considered.Thermodynamics parameters and stability energy and innsation state are evaluated in thre...

We construct arbitrarily sparse locally-jammed packings of nonoverlapping congruent disks in various finite area regions — in particular, we give constructions for the square, hexagon, and for certain flat tori.

In this paper, we study deployment patterns to achieve full coverage and k-connectivity (k ≤ 6) under different ratios of the sensor communication range (denoted by Rc) to the sensing range (denoted by Rs) for homogeneous wireless sensor networks (WSNs). In particular, we propose new patterns for 3and 5-connectivity. We also discover that there exists a hexagon-based universally elemental patte...

Summary . In this article we prove, using Mizar [2], [1], the Pappus’s hexagon theorem in real projective plane: “Given one set of collinear points A, B, C , and another a, b, c then intersection X, Y, Z line pairs Ab aB, Ac aC, Bc bC are collinear” https://en.wikipedia.org/wiki/Pappus’s_hexagon_theorem More precisely, prove that structure ProjectiveSpace TOP-REAL3 [10] (where is a metric space...