We use the Dandelin–Gallucci theorem to give a proof of Wedderburn’s little theorem that every finite division ring is commutative, and the proof is geometric in the sense that the non-geometric concepts employed are of an elementary nature. As a consequence, we obtain a geometric proof that a finite Desarguesian projective space is Pappian.

Noise shapes the efficacy and evolution of biological communication systems. Although examined in auditory and visual communication, the effects of noise on olfactory communication remains poorly known. We propose using information theory as a tool for analyzing noise in one type of olfactory signaling: between plants and insects. Plants and insects are cornerstones of terrestrial ecosystems, a…

Let G be a connected reductive group with connected center defined over Fq, with Frobenius morphism F. We parameterize all of the real-valued irreducible complex characters of GF using the Jordan decomposition of characters.

For q an odd prime power with q > 169, we prove that there are always three consecutive primitive elements in the finite field Fq. Indeed, there are precisely eleven values of q <= 169 for which this is false. For 4 <= n <= 8, we present conjectures on the size of q0(n) such that q > q0(n) guarantees the existence of n consecutive primitive elements in Fq, provided that Fq has characteristic …

Genetically engineered fish containing growth hormone (GH) transgenes have been synthesized for more than 25 years, now with modifications made in multiple aquacultured species. Despite significant improvements in production characteristics being realized, these fish have not yet entered commercial production. The very strong enhancement of growth rates that can arise from GH transgenesis in fi…

To achieve a global brain circulation, many Latin American countries have incentivized training abroad and publishing in high impact factor journals. Such internationalization strategies are valuable, but we argue that a knowledge dialogue is a better model for global science to overcome North–South disparities and to achieve both excellence and relevance. Circulation implies transmitting int…

We explicitly give the relations between the hypergeometric solutions of the general hypergeometric equation and their duals, as well as similar relations for q-hypergeometric equations. They form a family of very general identities for hypergeometric series. Although they were foreseen already by Bailey in the 1930s on analytic grounds, we give a purely algebraic treatment based on general pr…

For the polynomial differential system x˙ = −y, y˙ = x + Qn(x, y), where Qn(x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n >= 2 has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochrono…

In this paper, we generalize the W2,p interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli [‘Interior a priori estimates for solutions of fully nonlinear equations’, Ann. of Math. 130 (1989) 189–213]. The generalizations are carried out in two directions. One is that we relax the regularity requirement on the ‘constant coefficients’ equations and …

In recent years, exciting scientific evidence has emerged highlighting the ecological importance of dead animals (i.e., carrion) and their consumption (i.e., scavenging), to the point that we could consider this the golden age of scavenging research. We now have a considerable body of theoretical and empirical work that indicates that scavenging is fundamental to properly understanding not only…