A criterion for the HN N-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HN N-extension with arbitrary base group is proved. Then these results are applied to give for groups from two classes of one-relator groups the necessary and sufficient condition to be residually a finite p...

This letter provides a theoretical extension to the elastic properties of polycrystals in order to describe elastic wave scattering from grain boundaries. The extension allows the longitudinal and shear attenuation coefficients for scattering to be derived and is valid for polycrystals containing crystallites of any symmetry class. Attenuation curves are given for polycrystalline SiO2, ZrO2, an...

Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod extension involves evaluating the derivative of the integrand, a new extension is introduced using n + 2 points which requires only values of the integrand. However, this new rule does not exist for all n...

A cryptographic pairing evaluates as an element in an extension field, and the evaluation itself involves a considerable amount of extension field arithmetic. It is recognised that organising the extension field as a “tower” of subfield extensions has many advantages. Here we consider criteria that apply when choosing the best towering construction, and the associated choice of irreducible poly...

We present an extension of Astrée to concurrent C software. Astrée is a sound static analyzer for run-time errors previously limited to sequential C software. Our extension employs a scalable abstraction which covers all possible thread interleavings, and soundly reports all run-time errors and data races: when the analyzer does not report any alarm, the program is proven free from those classe...

We investigate the associativity property for varying-arity aggregation functions and introduce the more general property of preassociativity, a natural extension of associativity. We discuss this new property and describe certain classes of preassociative functions.

We present the ideas behind algorithmic proofs of identities involving sums and integrals of large classes of special functions. Recent results allowed a new extension of the class of holonomic functions.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.

The interpretation by Duskin and Glenn of abelian sheaf cohomology as connected components of a category of torsors is extended to homotopy classes. This is simultaneously an extension of Verdier’s version of Čech cohomology to homotopy.