Enhanced RFB method

The residual-free bubble method (RFB) is a parameter-free stable finite element method that has been successfully applied to a wide range of boundary-value problems exhibiting multiple-scale behaviour. If some local features of the solution are known a priori, the approximation properties of the RFB finite element space can be improved by enriching it on selected edges of the partition by edge-bubbles that are supported on pairs of neighbouring elements. Motivated by this idea, we define and analyse an enhanced residual-free bubble method for the solution of convection-dominated convection-diffusion problems in 2-D. Our a priori analysis highlights the limitations of the RFB method and the improved global approximation properties of the new method. The theoretical results are supported by detailed numerical experiments.     

On the Pósa-Seymour conjecture

Paul Seymour conjectured that any graph G of order n and minimum degree at least contains the k^th power of a Hamilton cycle. We prove the following approximate version. For any ϵ ≥ 0 and positive integer k, there is an n₀ such that, if G has order n ≥ n₀ and minimum degree at least $(\frac{k}{k+1} + \epsilon )n$, then G contains the k^th power of a Hamilton cycle. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 167–176, 1998     

On the number of flats spanned by a set of points in PG(d, q)

It is shown that for fixed 1 r s < d and > 0, if X PG(d, q) contains (1 + )q^s points, then the number of r-flats spanned by X is at least c()q^{(r+1)(s+1−r)}, i.e. a positive fraction of the number of r-flats in PG(s + 1,q).     

Oxygen separation induced by Xe ion beam upon electrodeposited oxygen-nickel and oxygen-chromium systems on iron substrate studied by conversion electron Mössbauer spectroscopy

Nickel was electrodeposited on one side and chromium on the other side of a sheet of α-iron enriched (∼85%) with⁵⁷Fe. The electrodeposited Ni and Cr contained oxygen and it could be separated by 500 keV xenon implantation. The separated oxygen formed an amorphous metal-oxide interphase at the interface of iron substrate and electrodeposited Ni or Cr.     

On triazoles. XXVII . The acylation,carbamoylation and thiocarbamoylation of tetrahydropyrido[4,3-d][1,2,4]triazolo[1,5-a]pyrimidinones

Isomeric 6,7,8,9-tetrahydropyrido[4,3-d][1,2,4]triazolo[1,5-a]pyrimidine-5(10H)-ones 3 , and -6(10H)-ones 4 were synthesised. Isomers 3 were converted to their 7-acyl 7 , 7-carbamoyl 8 and 7-thiocarbamoyl 9 derivatives.     

Ichthyosan in fish eye

Ichthyosan A and V are two highly elastoviscous glycan complexes present in the aqueus and vitreus [here aqueus and vitreus are used as nouns as was suggested by Balazs and Denlinger in The eye, vol 1A. Vegetative physiology and biochemistry, 3rd edn. Academic Press, New York, pp 533–589, 1984] of the fish eye. Ichthyosan A, with its high elastic properties, surrounds and stabilizes the lens of the eye. Ichthyosan V, within the collagen fibers, serves as a structure stabilizer of the gel vitreus. These two molecular complexes are non-covalent aggregates composed of hyaluronan, a chondroitin-proteoglycan (sulfate free), and a keratan-like molecule. The ratio of hyaluronan to chondroitin–proteoglycan varies in the two ichthyosans. Electrophoretic separation methods (both free and gel electrophoresis) demonstrate that the hyaluronan–proteoglycan aggregates move as one molecular entity. The average molecular weight of the ichthyosan varies from 5.2 to 13.0 million in various species. Aquatic mammals do not have ichthyosan in their eyes.     

Generalized pattern functions

Presented by I. Rosenberg.     

Preserving some numerical correspondencesbetween Hilbert space effects

In this paper we introduce some natural numerical quantities which measure differentkinds of correspondences between Hilbert space effects. We show that every objective map of the space ?(H) of all effects on the Hilbert space H which preserves any of these quantities is implemented by a unitary or antiunitary operator on H.     

Noncommutative version of Nikodym boundedness theorem for uniform space-valued functions

A Nikodym boundedness-type theorem with necessary and sufficient conditions for a family of functions defined on a ()-difference-poset and with values in a uniform space is proved. For a special important case — orthomodular lattice-the conditions are relaxed.     

Protein Alpha Shape Similarity Analysis (PASSA): a new method for mapping protein binding sites. Application in the design of a selective inhibitor of tyrosine kinase 2

We have developed a method that we have called Protein Alpha Shape Similarity Analysis (PASSA), that identifies interaction sites that can be utilised to achieve selectivity towards a protein. We have shown that this method is able to identify residues of tyrosine kinases that interact with known selective inhibitors using the following test cases: Abelson (Abl) kinase in complex with STI-571 and Janus kinase 2 (Jak2) in complex with AG-490. The 3D structures of the tyrosine kinase domains of Tyrosine kinase 2 (Tyk2) and Jak2 have been predicted by homology modelling. Computational docking of AG-490 and a set of tyrphostins known not to inhibit Jak2 indicated that our homology models are able to separate inhibitors from non-inhibitors. PASSA has also been used to identify unique properties of Tyk2. According to our results, interactions with hydrogen acceptors and donors on the following residues can be utilised to achieve selectivity towards Tyk2: Y955, E1053, D1062 and S1063. These residues are placed close to non-conserved hydrophobic pockets. The PASSA results, together with results from Multiple Copy Simultaneous Search (MCSS) were used to suggest functional groups of a selective Tyk2 inhibitor.