In [8], Swinnerton-Dyer considered the proportion of twists of an elliptic curve with full 2-torsion that have 2-Selmer group of a particular dimension. Swinnerton-Dyer obtained asymptotic results on the number of such twists using an unusual notion of asymptotic density. We build on this work to obtain similar results on the density of twists with particular rank of 2-Selmer group using the na...

Analysis of sequence data from the internal transcribed spacers (ITS) and 5.8S region of nuclear ribosomal DNA show that Canarian and Madeiran brooms (Genisteae) of the genera Teline, Adenocarpus, and Genista are related to Mediterranean species and not to species from adjacent parts of Morocco. Each separate colonization of the islands has resulted in contrasting patterns of adaptation and rad...

Genista species are sources of antioxidant phenolic compounds such as O- and C-glycosylflavonoids and isoflavonoids. A combination of a DPPH scavenging assay with HPTLC-MS, a fast and efficient method for identification of bioactive compounds, has been applied for evaluation of the radical scavenging activity of metabolites from Genista saharae Coss. & Dur. Different organs collected at vari...

The title mol-ecular salt, C15H21N2O(+)·ClO4 (-), crystallizes with four cations (A, B, C and D) and four anions in the chiral unit cell (space group P21). The alkaloid was isolated from the aerial parts of Genista Hispanica collected in the Samarkand region of Uzbekistan. Each cation is protonated at the N atom that bridges the alkaloid rings C and D. In each cation, ring A is almost planar an...

The anti-hyperglycemic flavonoid extract obtained from Genista tenera was first studied by liquid chromatography (LC)-diode array detection (DAD) which showed the presence of two major compounds. One of them was identified as genistein-7-O-glucoside. Luteolin-7-O-glucoside was detected as a minor constituent, while luteolin-7,3'-di-O-glucoside and rutin were found in trace amounts. LC-DAD-ESI-M...

Let E be an elliptic curve over Q, with L-function LE(s). For any primitive Dirichlet character χ, let LE(s, χ) be the L-function of E twisted by χ. In this paper, we use random matrix theory to study vanishing of the twisted L-functions LE(s, χ) at the central value s = 1. In particular, random matrix theory predicts that there are infinitely many characters of order 3 and 5 such that LE(1, χ)...

We study zeros of the L-functions L(f, s) of primitive weight two forms of level q. Our main result is that, on average over forms f of level q prime, the order of the L-functions at the central critical point s = 1 2 is absolutely bounded. On the Birch and Swinnerton-Dyer conjecture, this provides an upper bound for the rank of the Jacobian J0(q) of the modular curve X0(q), which is of the sam...

We provide a construction, refined from an inverse limit, that produces the mod 2 Steenrod and Dyer-Lashof algebras from each other. In fact, the construction relates various subalgebras and quotients of the universal Steenrod algebra of operations for H∞-ring spectra. We also describe how the construction transforms the axiomatic properties of homogeneous pre-Koszul algebras and Poincaré-Birkh...