Abstract Expressions arising from the Bruggeman approach for the homogenization of dielectric–magnetic composite materials, without ignoring the sizes of the spherical particles, are presented. These expressions exhibit the proper limit behavior. The incorporation of size dependence is directly responsible for the emergence of dielectric–magnetic coupling in the estimated relative permittivity ...

The Hash function Skein is one of the 5 finalists of NIST SHA-3 competition. It is designed based on the threefish block cipher and it only uses three primitive operations: modular addition, rotation and bitwise XOR (ARX). In this paper, we combine two short differential paths to a long differential path using the modular differential technique. And we present the semi-free start near-collision...

This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Markov traces on Hecke algebras to the framework of HOMFLYPT Skein modules. Some o...

In this section we consider composite systems made up of several particles, each carrying orbital angular momentum decribed by spherical harmonics Y`m(θ, φ) as eigenfunctions and/or spin. Often the socalled total angular momentum, classically speaking the sum of all angular momenta and spins of the composite system, is the quantity of interest, since related operators, sums of orbital angular m...

Pulling back the weight systems associated with the exceptional Lie algebras and their standard representations by a modification of the universal VassilievKontsevich invariant yields link invariants; extending them to coloured 3-nets, we derive for each of them a skein relation.