Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Regio- and stereoselective microwave-assisted synthesis of 5-alkyl-4-alkenyl-4-phenyl-1,3-oxazolidin-2-ones

Chiral symmetrical alk-2-yne-1,4-diols have been stereoselectively transformed into 5-alkyl-4-alkenyl-4-phenyl-1,3-oxazolidin- 2-ones, which are precursors of quaternary α-amino β-hydroxy acids. The key step was the cyclization of the bis(tosylcarbamates) of 2- phenylalk-2-yne-1,4-diols, easily obtained from the starting chiral diols. These cyclizations were accomplished with complete regioselectivity and up to 92:8 dr in the presence of catalytic amounts of Ni(0) or Pd (II) derivatives under microwave heating.

Web content accessibility guidelines: from 1.0 to 2.0

This poster explains the changes introduced in the Web Content Accessibility Guidelines (WCAG) 2.0 from WCAG 1.0 and proposes a checklist for adapting existing websites. Finally, it describes the most common criticisms of the WCAG and places them in the context of its origin and initial aims.

The t-SNAREs syntaxin 1 and SNAP-25 are present on organelles that participate in synaptic vesicle recycling

Syntaxin 1 and synaptosome-associated protein of 25 kD (SNAP-25) are neuronal plasmalemma proteins that appear to be essential for exocytosis of synaptic vesicles (SVs). Both proteins form a complex with synaptobrevin, an intrinsic membrane protein of SVs. This binding is thought to be responsible for vesicle docking and apparently precedes membrane fusion. According to the current concept, syntaxin 1 and SNAP-25 are members of larger protein families, collectively designated as target-SNAP receptors (t-SNAREs), whose specific localization to subcellular membranes define where transport vesicles bind and fuse. Here we demonstrate that major pools of syntaxin 1 and SNAP-25 recycle with SVs. Both proteins cofractionate with SVs and clathrin-coated vesicles upon subcellular fractionation. Using recombinant proteins as standards for quantitation, we found that syntaxin 1 and SNAP-25 each comprise approximately 3% of the total protein in highly purified SVs. Thus, both proteins are significant components of SVs although less abundant than synaptobrevin (8.7% of the total protein). Immunoisolation of vesicles using synaptophysin and syntaxin specific antibodies revealed that most SVs contain syntaxin 1. The widespread distribution of both syntaxin 1 and SNAP-25 on SVs was further confirmed by immunogold electron microscopy. Botulinum neurotoxin C1, a toxin that blocks exocytosis by proteolyzing syntaxin 1, preferentially cleaves vesicular syntaxin 1. We conclude that t-SNAREs participate in SV recycling in what may be functionally distinct forms.

Neuronal activity controls the antagonistic between PGC-1α and SMRT in regulating antioxidant defences

Transcriptional coactivators and corepressors often have multiple targets and can have opposing actions on transcription and downstream physiological events. The coactivator peroxisome proliferator-activated receptor-γ coactivator (PGC)-1α is under-expressed in Huntington's disease and is a regulator of antioxidant defenses and mitochondrial biogenesis. We show that in primary cortical neurons, expression of PGC-1α strongly promotes resistance to excitotoxic and oxidative stress in a cell autonomous manner, whereas knockdown increases sensitivity. In contrast, the transcriptional corepressor silencing mediator of retinoic acid and thyroid hormone receptors (SMRT) specifically antagonizes PGC-1α-mediated antioxidant effects. The antagonistic balance between PGC-1α and SMRT is upset in favor of PGC-1α by synaptic activity. Synaptic activity triggers nuclear export of SMRT reliant on multiple regions of the protein. Concommitantly, synaptic activity post-translationally enhances the transactivating potential of PGC-1α in a p38-dependent manner, as well as upregulating cyclic-AMP response element binding protein-dependent PGC-1α transcription. Activity-dependent targeting of PGC-1α results in enhanced gene expression mediated by the thyroid hormone receptor, a prototypical transcription factor coactivated by PGC-1α and repressed by SMRT. As a consequence of these events, SMRT is unable to antagonize PGC-1α-mediated resistance to oxidative stress in synaptically active neurons. Thus, PGC-1α and SMRT are antagonistic regulators of neuronal vulnerability to oxidative stress. Further, this coactivatorcorepressor antagonism is regulated by the activity status of the cell, with implications for neuronal viability.