57 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
Generalized Symmetries and Some new Solution of the Fokker-Planck Equation
In this paper, the third and fourth generalized symmetries of the Fokker-Planck equation are directly computed. We show how to get higher order generalized symmetries by using of the recursion operators, and we derive some exact solutions
Hamiltoniens classiques et géométrie k-symplectique
We put in obvIously hamilonian maps of classical mecanics in the context of thepolarized Poisson manifolds
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 Class-A GPCR Dopamine D2 Receptor Forms Transient Dimers Stabilized by Agonists: Detection by Single-Molecule Tracking
Whether class-A G-protein coupled receptors (GPCRs) exist and work as monomers or dimers has drawn extensive attention. A class-A GPCR dopamine D2 receptor (D2R) is involved in many physiological and pathological processes and diseases, indicating its critical role in proper functioning of neuronal circuits. In particular, D2R homodimers might play key roles in schizophrenia development and amphetamine-induced psychosis. Here, using single-molecule imaging, we directly tracked single D2R molecules in the plasma membrane at a physiological temperature of 37 degrees C, and unequivocally determined that D2R forms transient dimers with a lifetime of 68 ms in its resting state. Agonist addition prolonged the dimer lifetime by a factor of ~1.5, suggesting the possibility that transient dimers might be involved in signaling
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
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