Quadratic integrals of motion for the systems of identical particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.Comment: 6 pages, no figure

Effects of Ketogenic Diets on Cardiovascular Risk Factors: Evidence from Animal and Human Studies.

The treatment of obesity and cardiovascular diseases is one of the most difficult and important challenges nowadays. Weight loss is frequently offered as a therapy and is aimed at improving some of the components of the metabolic syndrome. Among various diets, ketogenic diets, which are very low in carbohydrates and usually high in fats and/or proteins, have gained in popularity. Results regarding the impact of such diets on cardiovascular risk factors are controversial, both in animals and humans, but some improvements notably in obesity and type 2 diabetes have been described. Unfortunately, these effects seem to be limited in time. Moreover, these diets are not totally safe and can be associated with some adverse events. Notably, in rodents, development of nonalcoholic fatty liver disease (NAFLD) and insulin resistance have been described. The aim of this review is to discuss the role of ketogenic diets on different cardiovascular risk factors in both animals and humans based on available evidence

Quadratic integrals of motions for the systems of identical particles-quantum case

The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed.Comment: 6 pages, no figure

Quantum double and κ\kappa-Poincar\'e symmetries in (2+1)-gravity and Chern-Simons theory

We review the role of Drinfeld doubles and kappa-Poincare symmetries in quantised (2+1)-gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and kappa-Poincare symmetries associated with the isometry groups of (2+1)-gravity. In particular, we explain that the usual kappa-Poincare symmetries with a timelike deformation are not directly associated with (2+1)-gravity. These kappa-Poincare symmetries are linked to Chern-Simons theory only in the de Sitter case, and the relevant Chern-Simons theory is physically inequivalent to (2+1)-gravity.Comment: 11 pages, no figures, expanded version of talk at the conference Theory Canada 4, references and explanations added, typos correcte

Note on clock synchronization and Edwards transformations

Edwards transformations relating inertial frames with arbitrary clock synchronization are reminded and put in more general setting. Their group theoretical context is described.Comment: 11 pages, no figures; final version, to appear in Foundations of Physics Letter

Projective representation of k-Galilei group

The projective representations of k-Galilei group G_k are found by contracting the relevant representations of k-Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective representations of G_k by vector representations of some its extension.Comment: 15 pages Latex fil