1. INTRODUCTION. The groups of invertible matrices over finite fields are among the first groups we meet in a beginning course in modern algebra. Eventually, we find out about simple groups and that the unique simple group of order 168 has two representations as a group of matrices. And this is where we learn that the group of 2 × 2 unimodular matrices over a seven-element field, with I and −I ...

In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the continuous Fano inequality established in [DW13, Corollary 1, Propositions 1 and 2], as well as the generalized Fano inequality in [HV94, Equation following (10)].

We present a numerical study of solitary waves in one dimensional (1D) granular lattices. Our system consists of an array of deformable spheres which we model using Hertzian interactions between neighbouring bodies. A general discussion of the origin of solitary waves is presented. We then provide an analysis of the Hertz force. For the case of a uniform chain of spheres, we derive an approxima...

A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety. Indee...

Let us first recall our setting. In the toric case, there is a correspondence between n-dimensional nonsingular Fano varieties and ndimensional Fano polytopes, where the Fano varieties are biregular isomorphic if and only if the corresponding Fano polytopes are unimodularly equivalent. Here, given a lattice N of rank n, a Fano polytope Q ⊆ NR := N ⊗Z R is given as a lattice polytope containing ...

A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety, indee...

We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all fourdimensional toric Fano manifolds, all four-dimensional products of lower-dimensional Fano manifolds, and certain complete intersections in projective bundles.

We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.