We discuss the construction of finite noncommutative geometries on Hopf algebras and finite groups in the ‘quantum groups approach’. We apply the author’s previous classification theorem, implying that calculi in the factorisable case correspond to blocks in the dual, to classify differential calculi on the quantum codouble C(G)◮<CG = D∗(G) of a finite group G. We give D∗(S3) as an example. We ...

A bstract Based on the Simplified Differential Equations approach, we present results for two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain boundary terms and establish one-dimensional integral representation integrals in Generalised Polylogarithms, when alphabet contains non-factorisable square roots. The are relevant study NNLO QCD corrections W,...

We compute the non-factorisable ${\cal O}(\alpha_s^2)$ corrections to $t$-channel single-top quark production at LHC. These peculiar arise because of interactions between heavy- and light-quark lines appear for very first time next-to-next-to-leading order in perturbative QCD. find that change cross section relevant kinematic distributions this process by about half a percent.

We compute the non-factorisable contribution to two-loop helicity amplitude for $t$-channel single-top production, last missing piece of virtual corrections this process. Our calculation employs analytic reduction master integrals and auxiliary mass flow method their fast numerical evaluation. study impact these on basic observables that are measured experimentally in production

The structure of the gaussian auxiliary field approximation in the theory of phase ordering kinetics is analysed with the aim of placing the method within the context of a systematic theory. While we are unable to do this for systems with a scalar order parameter, where the approximation remains uncontrolled, a systematic development about the gaussian approximation can be outlined for systems ...

a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

The regular embeddings of complete bipartite graphs Kn,n in orientable surfaces are classified 5 and enumerated, and their automorphism groups and combinatorial properties are determined. The method depends on earlier classifications in the cases where n is a prime power, obtained in collaboration with Du, Kwak, Nedela and Škoviera, together with results of Itô, Hall, Huppert and Wielandt on fa...

We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple, analogous to known results for the double. Among them, we prove that in the factorisable case the triple is isomorphic to a twisting of g ⊕ g ⊕ g by a certai...

In Drosophila, the eye primordium is specified as a subdomain of the larval eye disc. Here, we show that the Zn-finger transcription factor teashirt (tsh) marks the region of the early eye disc where the eye primordium will form. Moreover, tsh misexpression directs eye primordium formation in disc regions normally destined to form head capsule, something the eye selector genes eyeless (ey) and ...