Evidence for a Supernova in the Ic Band Light Curve of the Optical Transient of GRB 970508

Unique data on $BVRI$ brightness curves of the OT of GRB 970508 obtained with the 6-m telescope have been interpreted in the framework of the GRB-SN (supernovae) connection. The effect must be maximal in the I_c band as OT GRB 970228. The peak absolute (M_B) magnitude of the suggested SN must be around -19.5 for the OT of GRB 970508. If all or the main part of long GRBs are associated with SNe, the GRB host galaxies (for ground-based observations, at least) must be dimmer than the peak magnitude of the SN.Comment: 3 pages, 2 figures, oral presentation on 2nd Rome Workshop on Gamma-Ray Bursts in the Afterglow Er

The gamma-ray bursts and core-collapse supernovae - global star forming rate peaks at large redshifts

This is a brief review on the first Gamma-Ray Bursts (GRB) optical identifications - GRB host galaxies and Star Forming Rate (SFR) at relatively small redshifts (z), on the metallicities of GRB hosts, the similarities and differences between GRB hosts and galaxies at larger z, and on the SFR and GRB rate (GRBR) at high z. Evidences of a direct connection between long-duration GRBs and massive stars explosions (like Core-Collapse Super-Novae - CCSNe) are presented. Is there a fast decrease in SFR up to z ~10? Some unsolved problems related to GRBs are discussed: about the high-z GRB host galaxies, the high-z CCSN-GRB connection, and possible new crucial cosmological tests at high z.Comment: 9 pages, 4 figures, to be published by "World Scientific" in Proceedings of the XXIX International Workshop on High Energy Physics: New Results and Actual Problems in Particle & Astroparticle Physics and Cosmology (HEPFT2013), 26-28 June 2013, Protvino, Moscow region, Russi

A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum

Simple states, such as isobaric analog states or giant resonances, embedded into continuum are typical for mesoscopic many-body quantum systems. Due to the coupling to compound states in the same energy range, a simple mode acquires a damping width ("internal" dynamics). When studied experimentally with the aid of various reactions, such states reveal enhanced cross sections in specific channels at corresponding resonance energies ("external" dynamics which include direct decay of a simple mode and decays of intrinsic compound states through their own channels). We consider the interplay between internal and external dynamics using a general formalism of the effective nonhermitian hamiltonian and looking at the situation both from "inside" (strength functions and spreading widths) and from "outside" (S-matrix, cross sections and delay times). The restoration of isospin purity and disappearance of the collective strength of giant resonances at high excitation energy are discussed as important particular manifestations of this complex interplay.Comment: 23 pages, LaTeX, 5 ps-figures included, to appear in PRC (Jule 1997

On Construction of Recursion Operators From Lax Representation

In this work we develop a general procedure for constructing the recursion operators fro non-linear integrable equations admitting Lax representation. Svereal new examples are given. In particular we find the recursion operators for some KdV-type of integrable equations.Comment: Latex File (AMS format), 23 pages, to be published in Journal of Mathematical Physic

Integrable ODEs on Associative Algebras

In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our componentless approach we have solved a number of classification problems for integrable equations on free associative algebras. Also, in the simplest case, we have listed all possible Hamiltonian operators of low order.Comment: 19 pages, LaTe