Generalised sifting in black-box groups

We present a generalisation of the sifting procedure introduced originally by Sims for computation with finite permutation groups, and now used for many computational procedures for groups, such as membership testing and finding group orders. Our procedure is a Monte Carlo algorithm, and is presented and analysed in the context of black-box groups. It is based on a chain of subsets instead of a subgroup chain. Two general versions of the procedure are worked out in detail, and applications are given for membership tests for several of the sporadic simple groups. Our major objective was that the procedures could be proved to be Monte Carlo algorithms, and their costs computed. In addition we explicitly determined suitable subset chains for six of the sporadic groups, and we implemented the algorithms involving these chains in the {\sf GAP} computational algebra system. It turns out that sample implementations perform well in practice. The implementations will be made available publicly in the form of a {\sf GAP} package

Formulas for primitive Idempotents in Frobenius Algebras and an Application to Decomposition maps

In the first part of this paper we present explicit formulas for primitive idempotents in arbitrary Frobenius algebras using the entries of representing matrices coming from projective indecomposable modules with respect to a certain choice of basis. The proofs use a generalisation of the well known Frobenius-Schur relations for semisimple algebras. The second part of this paper considers \Oh-free \Oh-algebras of finite \Oh-rank over a discrete valuation ring \Oh and their decomposition maps under modular reduction modulo the maximal ideal of \Oh, thereby studying the modular representation theory of such algebras. Using the formulas from the first part we derive general criteria for such a decomposition map to be an isomorphism that preserves the classes of simple modules involving explicitly known matrix representations on projective indecomposable modules. Finally we show how this approach could eventually be used to attack a conjecture by Gordon James in the formulation of Meinolf Geck for Iwahori-Hecke-Algebras, provided the necessary matrix representations on projective indecomposable modules could be constructed explicitly.Comment: 16 page

N 3,N 6,2,5,7-Penta­phenyl-2,5,7-triaza­bicyclo­[2.2.1]heptane-3,6-diamine

In the title compound, C34H31N5, the observed molecular geometry suggests that anomeric effects are present in terms of short C—N bond lengths and reduced pyramidality of the N atoms

Polynomial-time proofs that groups are hyperbolic

Funding: UK EPSRC grant number EP/I03582X/1.It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings (1971), to define a new class of van Kampen diagrams, which represent groups as quotients of virtually free groups. We then present a polynomial-time procedure that analyses these diagrams, and either returns an explicit linear Dehn function for the presentation, or returns fail, together with its reasons for failure. Furthermore, if our procedure succeeds we are often able to produce in polynomial time a word problem solver for the presentation that runs in linear time. Our algorithms have been implemented, and when successful they are many orders of magnitude faster than KBMAG, the only comparable publicly available software.PostprintPeer reviewe

Ion-doped brushite cements for bone regeneration

Decades of research in orthopaedics has culminated in the quest for formidable yet resorbable biomaterials using bioactive materials. Brushite cements most salient features embrace high biocompatibility, bioresorbability, osteoconductivity, self-setting characteristics, handling, and injectability properties. Such type of materials is also effectively applied as drug delivery systems. However, brushite cements possess limited mechanical strength and fast setting times. By means of incorporating bioactive ions, which are incredibly promising in directing cell fate when incorporated within biomaterials, it can yield biomaterials with superior mechanical properties. Therefore, it is a key to develop fine-tuned regenerative medicine therapeutics. A comprehensive overview of the current accomplishments of ion-doped brushite cements for bone tissue repair and regeneration is provided herein. The role of ionic substitution on the cements physicochemical properties, such as structural, setting time, hydration products, injectability, mechanical behaviour and ion release is discussed. Cell-material interactions, osteogenesis, angiogenesis, and antibacterial activity of the ion-doped cements, as well as its potential use as drug delivery carriers are also presented.This study was funded by the Portuguese Foundation for Science and Technology (FCT) and the German Academic Exchange Service (Deutscher Akademischer Austauschdienst, DAAD) for the transnational cooperation FCT/DAAD 2018-2019. The authors also thank the funds provided under the distinctions attributed to JMO (IF/01285/2015) and SP (CEECIND/03673/2017). Furthermore, funding by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG), Grant Nr. HU 2498/1-1; GB 1/22-1, and the Emerging Talents Initiative of the FAU is acknowledged

Suspicion of respiratory tract infection with multidrug-resistant Enterobacteriaceae: epidemiology and risk factors from a Paediatric Intensive Care Unit

Enterobacteriaceae distribution. Distribution of Enterobacteriaceae isolates (n = 167) in lower respiratory tract material, MDR (n = 51) vs susceptible (n = 116) organisms during the study period. (XLSX 14 kb