We use the subgraph replacement method to prove a simple product formula for the tilings of an octagonal counterpart of Propp’s quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi-octagon.

The effect of aperture shape on an image, known in photography as ‘bokeh’, is an important characteristic of depth of field in real-world cameras. However, most real-time depth of field techniques produce Gaussian bokeh rather than the circular or polygonal bokeh that is almost universal in real-world cameras. ‘Scattering’ (i.e. point-splatting) techniques provide a flexible way to model any ap...

We derived explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square-octagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N-->∞.

In this study, an antenna is proposed that operates at THz spectrum for sixth generation (6G) short-range future wireless communications. A modified photonic band gap (MPBG) substrate employed to design octagonal ring shaped microstrip patch with wideband and high gain properties. Unlike the conventional (PBG) form, MPBG structure created by variable sized cylindrical air holes. The radii of ea...

Cyclosporin synthetase, a multifunctional polypeptide, catalyses the biosynthesis of the set of natural cyclosporins. We report that this enzyme is also capable of introducing a beta-alanine into position 7 or 8 of the ring instead of the alpha-alanines present at these positions in cyclosporin A. This leads to 34-membered rings in contrast to the 33-membered ring of the cyclo-undecapeptide cyc...

We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of nite approximants, we nd that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble, and thus diiers from the critical level-spacing distribution observed at the metal...

Place memory is relevant for exploration and forage behaviour. When food supply is dispersed, a win-shift has advantage over a win-stay strategy. In the Olton Octagonal Maze, the rat follows a win-shift strategy using working memory. However, in the Olton 4x4 version, the rat follows a win-stay strategy, using both working and long-term memories. It has been suggested that the neocortex is requ...

The well-known forking lemma by Pointcheval and Stern has been used to prove the security of the so-called generic signature schemes. These signature schemes are obtained via the Fiat-Shamir transform from three-pass identification schemes. A number of five-pass identification protocols have been proposed in the last few years. Extending the forking lemma and the Fiat-Shamir transform would all...

In this note an ‘extended Burnside ring’ is defined, generated by classes of semisimple module categories over Rep(G) with quasifibre functors. Here G is a finite group and representations are taken over an algebraically closed field of characteristic 0. It is shown that this is equivalent to a ring generated by centrally extended G-sets and hence the name. Ring homomorphisms into the multiplic...

Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.