Global spectrum fluctuations for the β\beta-Hermite and β\beta-Laguerre ensembles via matrix models

We study the global spectrum fluctuations for $\beta$-Hermite and $\beta$-Laguerre ensembles via the tridiagonal matrix models introduced in \cite{dumitriu02}, and prove that the fluctuations describe a Gaussian process on monomials. We extend our results to slightly larger classes of random matrices.Comment: 43 pages, 2 figures; typos correcte

Regioisomeric and substituent effects upon the outcome of the reaction of 1-borodienes with nitrosoarene compounds

A study of the reactivity of 1-borodienes with nitrosoarene compounds has been carried out showing an outcome that differs according to the hybridization state of the boron moiety. Using an sp2 boron substituent, a one-pot hetero-Diels–Alder/ring contraction cascade occurred to afford N-arylpyrroles with low to good yields depending on the electronic properties of the substituents on the borodiene, whereas an sp3 boron substituent led to the formation of stable boro-oxazines with high regioselectivity in most of the cases, in moderate to good yields. 1H and 11B NMR studies on two boro-oxazine regioisomers showed that selective deprotection can be performed. Formation of either the pyrrole or the furan derivative is pH- and regioisomer-structure-dependent. The results obtained, together with previous B3LYP calculations, support mechanistic proposals which suggest that pyrrole, or furan, formation proceeds via oxazine formation, followed by a boryl rearrangement and an intramolecular addition–elimination sequence