We define Hilbert–Siegel modular forms and Hecke “operators” acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert–Siegel forms (i.e. with arbitrary Siegel d...

In this note we announce a result which gives a complete determination of the differentiably simple algebras (in terms of the simple algebras), together with some related results and applications. At the present stage of the theory the algebras considered are for the most part assumed to be finite-dimensional, but otherwise are completely arbitrary (unless expressly stated), i.e. not necessaril...

We study birational transformations of certain fibtations of degree 4 del Pezzo surfaces over P, into other Mori fibre spaces, using Cox rings. We show that these Mori fibre spaces have a (relatively) big pliability although they are not rational. Our methods can be applied to study birational geometry of Mori dream spaces with low rank Cox ring.

Let V be an m-dimensional vector space over the complex numbers C. Fix a basis X, ,..., x, for V, and identify the polynomial ring R = C[x, ,..., x,] with the symmetric algebra of V in the obvious way. If A E GL( V) (the group of invertible linear transformations V + V), then A extends to a @-automorphism of R by (Aj)(x, ,..., xnz) =f(Ax, ,..., Ax,), where f E R. Suppose G is any subgroup of GL...

A series of 6,6-dihalo-2-azabicyclo[3.1.0]hexane and 7,7-dihalo-2-azabicyclo[4.1.0]heptane compounds were prepared by the reaction of dihalocarbene species with N-Boc-2,3-dihydro-1H-pyrroles or -1,2,3,4-tetrahydropyridines. Monochloro substrates were synthesised as well, using a chlorine-to-lithium exchange reaction. The behaviour of several aldehydes and ketones under reductive amination condi...

We examine epidemic thresholds for disease spread using susceptible-infected-susceptible models on scale-free networks with variable infectivity. Infectivity between nodes is modeled as a piecewise linear function of the node degree (rather than the less realistic linear transformation considered previously). With this nonlinear infectivity, we derive conditions for the epidemic threshold to be...

The efficient asymmetric synthesis of new chiral γ-chloro-α,β-diamino acid derivatives via highly diastereoselective Mannich-type reactions of N-(diphenylmethylene) glycine esters across a chiral α-chloro-N-p-toluenesulfinylimine was developed. The influence of the base, LDA or LiHMDS, used for the formation of the glycine enolates, was of great importance for the anti-/syn-diastereoselectivity...

A synthetic strategy for the modeling construction of the highly bridged azatetracyclic ABEF ring system of numerous lycoctonine-type C19-diterpenoid alkaloids bearing a characteristic oxygenated quaternary center at C-7 has been successfully developed. The tetracyclic core was constructed rapidly from a readily prepared 6,7-bicyclic AB ring precursor through a 13-step sequence via an advanced ...

The title compound, C(32)H(49)ClO(4), was obtained along with nitrile and lactam products in the POCl(3)-catalysed Beckmann rearrangement from 3β-acet-oxy-12-hydroxyiminoolean-28-olic acid methyl ester. The mechanism of the transformation leading to the title compound remains unclear and requires further investigation. Rings A, B and E are in chair conformations, ring C has a twisted-boat confo...

The title compound, C 11H12N4O2,was prepared via the transformation of sodium 4-acetyl-1-phenyl-1H-[1.2.3]triazolate under the action of meth-oxy-amine hydro-chloride. The dihedral angle between the triazole and phenyl rings is 25.12 (16)° and the C atom of the meth-oxy group deviates from the triazole plane by 0.894 (4)Å. The conformation of the CONHR-group is consolodated by an intra-molecula...