By a 35-year-old theorem of Shelah, λ + ♦(λ+) does not imply ♦λ for regular uncountable cardinals λ. Here, it is proved that λ + ♦(λ+) is equivalent to ♦λ for every singular cardinal λ.

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 …

Tahun Terbit

2010

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…

Zagier’s well-known work on traces of singular moduli relates the coefficients of certain weakly holomorphic modular forms of weight 1 2 to traces of values of the modular j-function at imaginary quadratic points. A real quadratic analogue was recently studied by Duke, Imamo¯glu, and T´oth. They showed that the coefficients of certain weight 1/2 mock modular forms fD =d>0a(d,D)qd, D>0 ar…

The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalities for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal amount of smoothing, as well as a variant of that which describes quantitatively an improvement of the inequality as one gets away from certain characteristi…

Tahun Terbit

2010

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…