47 research outputs found
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