An almost forgotten gem of Gauss tells us how to compute the area of a pentagon by just going around it and measuring areas of each vertex triangles (i.e. triangles whose vertices are three consecutive vertices of the pentagon). We give several proofs and extensions of this beautiful formula to hexagon etc. and consider special cases of affine–regular polygons. The Gauss pentagon formula is, in...

A bstract We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set uniformly transcendental master integrals. provide up O ( ε 2 ) dimensional regulator first time which are relevant at NNLO. Four independent pentagon integral topologies appear complete description colour structure we numerical solutions using canonical form dif...

We show how the data of a finite dimensional weak C∗-Hopf algebra can be encoded into a pair (H, V ) where H is a finite dimensional Hilbert space and V :H⊗H → H⊗H is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudomultiplicative unitary approac...

We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association jet at hadron colliders. construct system differential equations for all master integrals canonical form where analytic is reconstructed from numerical evaluations over finite fields. find can be represented as sum d-...

The experimental creation and annihilation of defects on single-walled carbon nanotubes (SWCNT) with the tip of a scanning tunneling microscopeare reported. The technique used to manipulate the wall structure of a nanotube at the atomic scale consists of a voltage ramp applied atconstant tunneling current between the tip and the nanotube adsorbed on a gold substrate. While topographic i...

To overcome the time and space constraints in disease diagnosis via the biosensing approach, we developed a new signal-transducing strategy that can be applied to colorimetric optical biosensors. Our study is focused on implementation of a signal transduction technology that can directly translate the color intensity signals-that require complicated optical equipment for the analysis-into signa...

An Ansatz is proposed for the heptagon relation, that is, an algebraic imitation of five-dimensional Pachner move 4–3. The formula in question realized terms matrices acting a direct sum one-dimensional linear spaces corresponding to 4-faces.

Edge structure and stability are crucial in determining both the morphology and the growth behaviours of hexagonal boron nitride (h-BN) domains in chemical vapour deposition (CVD) growth under near thermal equilibrium conditions. In this study, various edges of h-BN on three typical transition metal surfaces used for h-BN's CVD growth, Cu(111), Ni(111) and Rh(111), are explored with density fun...

Defect states in nitrogen-containing float-zone silicon are investigated both n- and p-type materials using deep-level transient spectroscopy (DLTS) minority-carrier (MCTS). This enables a mapping of the defect landscape entire electronic bandgap an investigation whether properties defects depend on semiconductor type. Two defects, E1/E2 pair E4/E6 pair, investigated, no evidence is found for to