We study sets of lines of AG(n, q) and PG(n, q) with the property that no three lines form a triangle. As a result the associated point-line incidence graph contains no 6-cycles and necessarily has girth at least 8. One can then use the associated incidence matrices to form binary linear codes which can be considered as LDPC codes. The relatively high girth allows for efficient implementation o...

Following analogy of the ‘db’ triangle in the quark mixing case, we have explored the construction of the ‘ν2.ν3’ leptonic unitarity triangle using the MNS matrix obtained by Bjorken et al. through generalization of the tribimaximal scenario. In particular, for the Ue3 range 0.05− 0.15, the existence of leptonic unitarity triangle indicates a fairly good possibility of having non zero CP violat...

In this work we introduce a new method for representing and evolving snakes that are constrained to lie on a prescribed surface (triangle mesh). The new representation allows to automatically adapt the snake resolution to the surface tesselation and does not need any (unstable) back-projection operations. Furthermore, it enables efficient and robust collision detection and gives us complete con...

In this paper we introduce a simple and efficient scheme for encoding the connectivity and the stripification of a triangle mesh. Since generating a good set of triangle strips is a hard problem, it is desirable to do this just once and store the computed strips with the triangle mesh. However, no previously reported mesh encoding scheme is designed to include triangle strip information into th...

The article presents an analysis of the dynamic response underground main pipeline under action a longitudinal wave, propagating in soil along pipe. It is assumed that elastic pipe has finite length. A linear viscoelastic model "pipe-soil" system interaction considered. influence pulse form triangle on deformed state investigated. comparative results obtained for some values coefficients and vi...

The binomial coefficients and Catalan triangle numbers appear as weight multiplicities of the finite-dimensional simple Lie algebras and affine Kac–Moody algebras. We prove that any binomial coefficient can be written as weighted sums along rows of the Catalan triangle. The coefficients in the sums form a triangular array, which we call the alternating Jacobsthal triangle. We study various subs...

This article highlights interactions of diverse areas: the Heron formula for the area of a triangle, the Descartes circle equation, and right triangles with integer or rational sides. New and old results are synthesized. We first exploit elementary observations about circles to characterize an arbitrary triangle using three circles. A fourth circle brings a certain symmetry – the four radii are...

In July 1951, Canada’s Department of External Affairs despatched a secret policy paper to the heads overseas Canadian posts, instructing diplomats abroad not refer ‘inner triangle’ with Britain and United States or encourage its development into formal alliance. The explicitly named ‘Anglo-Saxon was acknowledged affectionately as ‘cornerstone foreign policy’ but regarded damaging ultimate goal ...

PTA hosted in a copper metallo-supramolecular triangle undergoes post-assembly oxidation to form PTAO in aerated solutions. The oxidation is triggered by selected co-solvents that also govern the formation of the final crystalline product leading to a discrete host-guest triangle {PTAO@[Cu(o-L)]3} or to a 1D coordination polymer {(PTAO)2@[Cu8][Cu2]}∞ containing a {Cu8} ring with a double hostin...