Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admit an action of the structure group by automorphisms. This paper proves the existence of suitably equivariant transition functions for such groupoids, generalising consequently the classification of principal bundles by means of their transition functions, to extensions of principal bundles by an equivariant form of \v{C}ech cohomology.Comment: 23 page

Cohomology of skew-holomorphic Lie algebroids

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.Comment: 16 pages. v2: Final version to be published in Theor. Math. Phys. (incorporates only very minor changes

Coupling Poisson and Jacobi structures on foliated manifolds

Let M be a differentiable manifold endowed with a foliation F. A Poisson structure P on M is F-coupling if the image of the annihilator of TF by the sharp-morphism defined by P is a normal bundle of the foliation F. This notion extends Sternberg's coupling symplectic form of a particle in a Yang-Mills field. In the present paper we extend Vorobiev's theory of coupling Poisson structures from fiber bundles to foliations and give simpler proofs of Vorobiev's existence and equivalence theorems of coupling Poisson structures on duals of kernels of transitive Lie algebroids over symplectic manifolds. Then we discuss the extension of the coupling condition to Jacobi structures on foliated manifolds.Comment: LateX, 38 page

Literature searches and reviews related to the prevalence of food allergy in Europe

In 2011, the European Food Safety Authority (EFSA) received a mandate from the Food Safety Authority of Ireland (FSAI) to review the available scientific data on the prevalence of each food allergy in Europe, to derive threshold concentrations for each allergen in foods when possible, and to review the analytical methods available for the detection/quantification of food allergens. This report presents the findings of a series of systematic reviews of the literature related to these aims. Systematic searches of relevant bibliographic databases and the grey literature were conducted, studies were selected for inclusion according to pre-specified criteria, relevant data was extracted from all included studies, and the quality of included studies assessed. The first systematic review examined the literature on the prevalence of food allergy (IgE-mediated and non-IgE mediated) in different regions of the World and in individual European countries for different age groups in relation to each of the following food allergens: milk/dairy, eggs, cereals, peanuts, nuts, celery, crustaceans, fish, molluscs, soy, lupin, mustard and sesame. For each of these allergens changes in prevalence trends over time were also examined. Additionally, emerging food allergens in different European countries were identified. Of the 7333 articles identified by the searches, data from 92 studies was included, 52 of which reported on studies conducted within Europe. The second systematic review examined the effects of food processing on the allergenicity of foods in relation to each of the following food allergens: milk/dairy, eggs, cereals, peanuts, nuts, celery, crustaceans, fish, molluscs, soy, lupin, mustard and sesame. From 1040 articles identified by the searches, 25 studies were included in this review. The final systematic review examined the evidence regarding the new analytical methods available to analyse/detect the food allergens considered in the previous systematic reviews in processed foods. From 1475 articles identified by the searches, 84 studies were included

Preparation of heteronuclear bridging methylene complexes

The reactions of the titanacyclobutane complexes (η^5-C_5H_5)_2TiCH_2CRR'CH_2 (la, R = R' = Me; lb, R = Me, R' = Pr) with M-X compounds (M =Ti, Zr, Rh, Ir, Pd, Pt; X = Cl, OMe) have been investigated. The titanacyclobutanes have been found to react as sources of (η^5-C_5H_5)_2TiCH_2, giving (η^5-C_5H_5)_2Ti(μ –CH_2)(μ-X)ML_n (L_n = ancillary ligands) products. Several such complexes have been isolated as crystalline solids; however, only (η^5-C_5H_5_2Ti(μ-CH_2)(μ-X)Rh(η^4-l,5-cyclooctadiene) is stable in solution at 25°C. The complex η^5-C_5H_5)_2iTi(μ-CH_2)(μ-Cl)Ti(η^5-C_5Me_5)Cl was found to react with CO to form the bridging ketene complex (η^5-C_5H_5)_2Ti-μ, η^2(C,O)-(OCCH_2)Ti(η^5-C_5Me_5)Cl_2

Constrained Curve Fitting

We survey techniques for constrained curve fitting, based upon Bayesian statistics, that offer significant advantages over conventional techniques used by lattice field theorists.Comment: Lattice2001(plenary); plenary talk given by G.P. Lepage at Lattice 2001 (Berlin); 9 pages, 5 figures (postscript specials