Given a graph Γ with vertex set X, the graph group of Γ, denoted by G(Γ), is the group generated by the elements of X subject to the relations xy = yx for each pair x and y of adjacent vertices in Γ. In the literature graph groups are also known as partially commutative or right angled Artin groups. It has been known for some time that certain surface groups are embeddable into graph groups [4,...

This study investigates the contributions of position versus orientation information in shape perception by putting the two in conflict. Sampling the orientation of, e.g., a rounded pentagon and positioning the samples on a circle creates a stimulus in which element positions are consistent with a circle but element orientations with a pentagon. Whether orientation or position dominates the per...

Abstract: We compute the one-loop scalar massless pentagon integral I6−2ǫ 5 in D = 6−2ǫ dimensions in the limit of multi-Regge kinematics. This integral first contributes to the parity-odd part of the one-loop N = 4 five-point MHV amplitude m 5 at O(ǫ). In the high energy limit defined by s ≫ s1, s2 ≫ −t1,−t2, the pentagon integral reduces to double sums or equivalently two-fold Mellin-Barnes i...

Instructional technology, and the cognitivist and systems paradigms that underpin it, grew out of the military-industrial complex during the Cold War. Much as the Pentagon and this military complex defined the architecture of the Internet, they also essentially created, ex nihilo, the fields of instructional technology and instructional design. The results of the ongoing dominance or influence ...

A Fullerene with pentagons, hexagons, and heptagons is considered. The number of carbons is 458. It contains 8 heptagonal rings, 21 pentagons, and 212 hexagons. Keywords-component; fullerene; heptagon; pentagon adjacency penalty rule; fullerene with many carbons

The constraints of a monoidal category are too strong for some applications in physics. Although the natural isomorphism property is founded on strong physical principles (see Joyce [2]) there are no conclusive grounds for requiring that the pentagon and triangle diagrams hold. For example in Joyce [4,5] recouplings embodying the Pauli exclusion principle are natural isomorphisms that do not sa...

A finite set of points in the plane is described as in convex position if it forms the set of vertices of a convex polygon. This work studies the ratio between the maximum area of convex heptagons with vertices in P and the area of the convex hull of P, where the planar point set P is in convex position.

A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star K1,3 and we present a structural result concerning the existence of a pair of adjacent ...