Right triangles with algebraic sides and elliptic curves over number fields

Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem. The proof allows the explicit construction of these triangles; for this purpose we find for any positive integer n an explicit cubic number field Q(\lambda) (depending on n) and an explicit point P_\lambda of infinite order in the Mordell-Weil group of the elliptic curve Y^2=X^3-n^2*X over Q(\lambda).Comment: To appear in Math. Slovac

Copper(I)-Phosphinite Complexes in Click Cycloadditions: Three-Component Reactions and Preparation of 5-Iodotriazoles

© 2016 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.The remarkable activity displayed by copper(I)–phosphinite complexes of general formula [CuBr(L)] in two challenging cycloadditions is reported: a) the one-pot azidonation/cycloaddition of boronic acids, NaN3, and terminal alkynes; b) the cycloaddition of azides and iodoalkynes. These air-stable catalysts led to very good results in both cases and the expected triazoles could be isolated in pure form under ‘Click-suitable’ conditions

The Full Automorphism Group of a Cyclic pp-gonal Surface

If $p$ is prime, a compact Riemann surface $X$ of genus $g\geq 2$ is called cyclic $p$-gonal if it admits a cyclic group of automorphisms $C_{p}$ of order $p$ such that the quotient space $X/C_{p}$ has genus 0. If in addition $C_{p}$ is not normal in the full automorphism $G$, then we call $G$ a non-normal cyclic $p$-gonal group. In the following we classify all non-normal $p$-gonal groups.Comment: 18 pages, 5 figure

Taming Brønsted acid reactivity: nucleophilic substitutions of propargylic alcohols with n-nucleophiles mediated by phosphorus-based Brønsted acid catalysts

The activity of diethyl phosphite and diphenyl phosphate in propargylation reactions with N-nucleophiles of varying basicity is presented. Careful choice of the reaction conditions minimised undesired rearrangements and arylation processes, typical side reactions with Brønsted acid catalysis. These systems are compatible with technical solvents and presence of air and they are also applicable to C-, O- and S-nucleophile