k-symplectic affine Kie algebras

The notion of k-symplectic structures was introduced by A. Awane in his dissertation in 1984. Here we are interested by the classification of Lie algebras provided with such a structure. We introduce also the notion of affine structure associated to a K-symplectic structure on a Lie algebr

Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

On Some Geometric Structures Associated to a k-Symplectic Manifold

A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular we prove that, under some natural assumption, any ksymplectic manifold admits an Ehresmann connection, discussing some corollaries of this result, and we find vanishing theorems for characteristic classes on a k-symplectic manifold.Comment: To appear on J. Phys. A: Math. Theo

On some aspects of the geometry of differential equations in physics

In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular differential equations, and partial differential equations in field theories. The geometric structures underlying these systems are presented and commented. The main results concerning these structures are stated and discussed, as well as their influence on the study of the differential equations with which they are related. Furthermore, research to be developed in these areas is also commented.Comment: 21 page

The Cherenkov Telescope Array Large Size Telescope

The two arrays of the Very High Energy gamma-ray observatory Cherenkov Telescope Array (CTA) will include four Large Size Telescopes (LSTs) each with a 23 m diameter dish and 28 m focal distance. These telescopes will enable CTA to achieve a low-energy threshold of 20 GeV, which is critical for important studies in astrophysics, astroparticle physics and cosmology. This work presents the key specifications and performance of the current LST design in the light of the CTA scientific objectives.Comment: 4 pages, 5 figures, In Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), Rio de Janeiro (Brazil). All CTA contributions at arXiv:1307.223

Identification and application of a different glucose uptake system that functions as an alternative to the phosphotransferase system in Corynebacterium glutamicum

Corynebacterium glutamicum uses the phosphoenolpyruvate-dependent sugar phosphotransferase system (PTS) to uptake and phosphorylate glucose; no other route has yet been identified. Disruption of the ptsH gene in wild-type C. glutamicum resulted, as expected, in a phenotype exhibiting little growth on any of the PTS sugars: glucose, fructose, and sucrose. However, a suppressor mutant that grew on glucose but not on the other two sugars was spontaneously isolated from the PTS-negative strain WT Delta ptsH. The suppressor strain SPH2, unlike the wild-type strain, exhibited a phenotype of resistance to 2-deoxyglucose which is known to be a toxic substrate for the glucose-PTS of this microbe, suggesting that strain SPH2 utilizes glucose via a different system involving a permease and native glucokinases. Analysis of the C. glutamicum genome sequence using Escherichia coli galactose permease, which can transport glucose, led to the identification of two candidate genes, iolT1 and iolT2, both of which have been reported as myo-inositol transporters. When cultured on glucose medium supplemented with myo-inositol, strain WT Delta ptsH was able to consume glucose, suggesting that glucose uptake was mediated by one or more myo-inositol-induced transporters. Overexpression of iolT1 alone and that of iolT2 alone under the gapA promoter in strain WT Delta ptsH rendered the strain capable of growing on glucose, proving that each transporter played a role in glucose uptake. Disruption of iolT1 in strain SPH2 abolished growth on glucose, whereas disruption of iolT2 did not, revealing that iolT1 was responsible for glucose uptake in strain SPH2. Sequence analysis of the iol gene cluster and its surrounding region identified a single-base deletion in the putative transcriptional regulator gene Cgl0157 of strain SPH2. Introduction of the frameshift mutation allowed strain WT Delta ptsH to grow on glucose, and further deletion of iolT1 abolished the growth again, indicating that inactivation of Cgl0157 under a PTS-negative background can be a means by which to express the iolT1-specified glucose uptake bypass instead of the native PTS. When this strategy was applied to a defined lysine producer, the engineered strain displayed increased lysine production from glucose.ArticleAPPLIED MICROBIOLOGY AND BIOTECHNOLOGY. 90(4):1443-1451 (2011)journal articl