Further results on elementary Lie algebras and Lie A-algebras.

A finite-dimensional Lie algebra L over a field F of characteristic zero is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. This paper is a continuation of the study of these algebras initiated by the authors in a previous paper. If we denote by $\mathcal{A}$, $\mathcal{G}$, $\mathcal{E}$, $\mathcal{L}$, $\Phi$ the classes of A-algebras, almost algebraic algebras, E-algebras, elementary algebras and $\phi$-free algebras respectively, then it is shown that: \mathcal{L} \subset \Phi \subset \mathcal{G} \mathcal{L} \subset \mathcal{A} \subset \mathcal{E} \mathcal{G} \cap \mathcal{A} = \mathcal{L}. It is also shown that if L is a semisimple Lie algebra all of whose minimal parabolic subalgebras are $\phi$-free then L is an A-algebra, and hence elementary. This requires a number of quite delicate properties of parabolic subalgebras. Finally characterisations are given of $E$-algebras and of Lie algebras all of whose proper subalgebras are elementary

Effectiveness of influenza vaccination programme in preventing hospital admissions, Valencia, 2014/15 early results

Preliminary results for the 2014/15 season indicate low to null effect of vaccination against influenza A(H3N2)-related disease. As of week 5 2015, there have been 1,136 hospital admissions, 210 were due to influenza and 98% of subtype A strains were H3. Adjusted influenza vaccine effectiveness was 33% (range: 6–53%) overall and 40% (range: 13% to 59%) in those 65 years and older. Vaccination reduced by 44% (28–68%) the probability of admission with influenza.The study was funded by a contract between FISABIO and Sanofi-Pasteur

Conceptual design of the early implementation of the NEutron Detector Array (NEDA) with AGATA

The NEutron Detector Array (NEDA) project aims at the construction of a new high-efficiency compact neutron detector array to be coupled with large (Formula presented.) -ray arrays such as AGATA. The application of NEDA ranges from its use as selective neutron multiplicity filter for fusion-evaporation reaction to a large solid angle neutron tagging device. In the present work, possible configurations for the NEDA coupled with the Neutron Wall for the early implementation with AGATA has been simulated, using Monte Carlo techniques, in order to evaluate their performance figures. The goal of this early NEDA implementation is to improve, with respect to previous instruments, efficiency and capability to select multiplicity for fusion-evaporation reaction channels in which 1, 2 or 3 neutrons are emitted. Each NEDA detector unit has the shape of a regular hexagonal prism with a volume of about 3.23l and it is filled with the EJ301 liquid scintillator, that presents good neutron- (Formula presented.) discrimination properties. The simulations have been performed using a fusion-evaporation event generator that has been validated with a set of experimental data obtained in the 58Ni + 56Fe reaction measured with the Neutron Wall detector array

Influence of Milk-Feeding Type and Genetic Risk of Developing Coeliac Disease on Intestinal Microbiota of Infants: The PROFICEL Study

Interactions between environmental factors and predisposing genes could be involved in the development of coeliac disease (CD). This study has assessed whether milk-feeding type and HLA-genotype influence the intestinal microbiota composition of infants with a family history of CD. The study included 164 healthy newborns, with at least one first-degree relative with CD, classified according to their HLA-DQ genotype by PCR-SSP DQB1 and DQA1 typing. Faecal microbiota was analysed by quantitative PCR at 7 days, and at 1 and 4 months of age. Significant interactions between milk-feeding type and HLA-DQ genotype on bacterial numbers were not detected by applying a linear mixed-model analysis for repeated measures. In the whole population, breast-feeding promoted colonization of C. leptum group, B. longum and B. breve, while formula-feeding promoted that of Bacteroides fragilis group, C. coccoides-E. rectale group, E. coli and B. lactis. Moreover, increased numbers of B. fragilis group and Staphylococcus spp., and reduced numbers of Bifidobacterium spp. and B. longum were detected in infants with increased genetic risk of developing CD. Analyses within subgroups of either breast-fed or formula-fed infants indicated that in both cases increased risk of CD was associated with lower numbers of B. longum and/or Bifidobacterium spp. In addition, in breast-fed infants the increased genetic risk of developing CD was associated with increased C. leptum group numbers, while in formula-fed infants it was associated with increased Staphylococcus and B. fragilis group numbers. Overall, milk-feeding type in conjunction with HLA-DQ genotype play a role in establishing infants' gut microbiota; moreover, breast-feeding reduced the genotype-related differences in microbiota composition, which could partly explain the protective role attributed to breast milk in this disorder

Further results on elementary Lie algebras and Lie A-algebras.

A finite-dimensional Lie algebra L over a field F of characteristic zero is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. This paper is a continuation of the study of these algebras initiated by the authors in a previous paper. If we denote by $\mathcal{A}$, $\mathcal{G}$, $\mathcal{E}$, $\mathcal{L}$, $\Phi$ the classes of A-algebras, almost algebraic algebras, E-algebras, elementary algebras and $\phi$-free algebras respectively, then it is shown that: \mathcal{L} \subset \Phi \subset \mathcal{G} \mathcal{L} \subset \mathcal{A} \subset \mathcal{E} \mathcal{G} \cap \mathcal{A} = \mathcal{L}. It is also shown that if L is a semisimple Lie algebra all of whose minimal parabolic subalgebras are $\phi$-free then L is an A-algebra, and hence elementary. This requires a number of quite delicate properties of parabolic subalgebras. Finally characterisations are given of $E$-algebras and of Lie algebras all of whose proper subalgebras are elementary

On upper modular subalgebras of a Lie algebra.

This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. We give some necessary and some sufficient conditions for a subalgebra to be upper modular. For algebraically closed fields of any characteristic these enable us to determine the structure of Lie algebras having abelian upper modular subalgebras which are not ideals. We then study the structure of solvable Lie algebras having an abelian upper modular subalgebra which is not an ideal and which has trivial intersection with the derived algebra; in particular the structure is determined for algebras over the real field. Next we classify non-solvable Lie algebras over fields of characteristic zero having an upper modular atom which is not an ideal. Finally it is shown that every Lie algebra over a field of characteristic different from two and three in which every atom is upper modular is either quasi-abelian or a μ-algebra

Two Generator Subalgebras Of Lie Algebras.

In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al. [10] have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this paper is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability

On Lie algebras all of whose minimal subalgebras are lower modular.

The main purpose of this paper is to study Lie algebras L such that if a subalgebra U of L has a maximal subalgebra of dimension one then every maximal subalgebra of U has dimension one. Such an L is called lm(0)-algebra. This class of Lie algebras emerges when it is imposed on the lattice of subalgebras of a Lie algebra the condition that every atom is lower modular. We see that the effect of that condition is highly sensitive to the ground field F. If F is algebraically closed, then every Lie algebra is lm(0). By contrast, for every algebraically non-closed field there exist simple Lie algebras which are not lm(0). For the real field, the semisimple lm(0)-algebras are just the Lie algebras whose Killing form is negative-definite. Also, we study when the simple Lie algebras having a maximal subalgebra of codimension one are lm(0), provided that the characteristic of F is different from 2. Moreover, lm(0)-algebras lead us to consider certain other classes of Lie algebras and the largest ideal of an arbitrary Lie algebra L on which the action of every element of L is split, which might have some interest by themselves

On Flags And Maximal Chains Of Lower Modular Subalgebras Of Lie Algebras.

In this paper we study the class ${\cal F}$ of Lie algebras having a flag of subalgebras, and the class ${\cal Ch}_{lm}$ of Lie algebras having a maximal chain of lower modular subalgebras. We show that ${\cal F} \subseteq {\cal Ch}_{lm}$ and that both are extensible formations that are subalgebra closed. We derive a number of properties relating to these two classes, including a classification of the algebras in each class over a field of characteristic zero