Birational automorphisms of a three-dimensional double quadric with an elementary singularity

It is proved that the group of birational automorphisms of a three-dimensional double quadric with a singular point arising from a double point on the branch divisor is a semidirect product of the free group generated by birational involutions of a special form and the group of regular automorphisms. The proof is based on the method of `untwisting' maximal singularities of linear systems.Comment: 18 page

Curie law, entropy excess, and superconductivity in heavy fermion metals and other strongly interacting Fermi liquids

Low-temperature thermodynamic properties of strongly interacting Fermi liquids with fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump Delta C and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy fermion metal CeCoIn5, as well as He-3 films.Comment: 4 pages, 2 figures. V.2: a reference added; minor changes as in the published versio

Nucleon Form Factors from Generalized Parton Distributions

We discuss the links between Generalized Parton Distributions (GPDs) and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for GPDs at small momentum transfer, is extended to the large momentum transfer region and it is found to describe the basic features of proton and neutron electromagnetic form factor data. This parametrization is used to estimate the quark contribution to the nucleon spin.Comment: 18 pages, 5 figures, replaced with published versio

Probing confinement by direct photons and dileptons

The intensive synchrotron radiation resulting from quarks interacting with the collective confining color field in relativistic heavy ion collisions is discussed. The spectrum of photons with large transverse momentum is calculated and compared with the experimental data to demonstrate the feasibility of this type of radiation. A study of the earlier predicted azimuthal anisotropy in the angular distribution of dileptons with respect to the three-momentum of the pair is performed as well. This boundary-induced mechanism of lepton pair production is shown to possess the features that are distinctly different from the standard mechanisms and can potentially provide an efficient probe of quark-gluon plasma formation.Comment: 7 pages, 3 figures, Fig., Refs. and explanations added, typos corrected, text revise

Ultraslow Wave Nuclear Burning of Uranium-Plutonium Fissile Medium on Epithermal Neutrons

For a fissile medium, originally consisting of uranium-238, the investigation of fulfillment of the wave burning criterion in a wide range of neutron energies is conducted for the first time, and a possibility of wave nuclear burning not only in the region of fast neutrons, but also for cold, epithermal and resonance ones is discovered for the first time. For the first time the results of the investigation of the Feoktistov criterion fulfillment for a fissile medium, originally consisting of uranium-238 dioxide with enrichments 4.38%, 2.00%, 1.00%, 0.71% and 0.50% with respect to uranium-235, in the region of neutron energies 0.015-10.0eV are presented. These results indicate a possibility of ultraslow wave neutron-nuclear burning mode realization in the uranium-plutonium media, originally (before the wave initiation by external neutron source) having enrichments with respect to uranium-235, corresponding to the subcritical state, in the regions of cold, thermal, epithermal and resonance neutrons. In order to validate the conclusions, based on the slow wave neutron-nuclear burning criterion fulfillment depending on the neutron energy, the numerical modeling of ultraslow wave neutron-nuclear burning of a natural uranium in the epithermal region of neutron energies (0.1-7.0eV) was conducted for the first time. The presented simulated results indicate the realization of the ultraslow wave neutron-nuclear burning of the natural uranium for the epithermal neutrons.Comment: 35 pages, 19 figures (v2: Fig12 and some misprints in the text are fixed

Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails

We consider the Boltzmann equations for mixtures ofMaxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that power like tails can appear not just for granular particles (Maxwell models are far from reality in this case), but also in the system of particles interacting in accordance with laws of classical mechanics. In addition, non-existence of positive self-similar solutions with finite moments of any order is proven for a wide class of Maxwell models.Comment: 20 page