Star product algebras of test functions

We prove that the Gelfand-Shilov spaces S _α ^β are topological algebras under the Moyal *-product if and only if α ≥ β. These spaces of test functions can be used to construct a noncommutative field theory. The star product depends on the noncommutativity parameter continuously in their topology. We also prove that the series expansion of the Moyal product converges absolutely in S _α ^β if and only if β < 1/2. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 3–17, October, 2007.     

A relativistic quark model of mesons

We propose a relativistic quantum model to describe mesons comprising a quark and an antiquark with arbitrary masses. The Dirac equations describe the quarks, and the rigid string approximation accounts for the gluon field contribution. The model fits the meson spectra well and determines the masses of the s-, c-, and b-quarks and the relativistic wave functions of compound mesons. Translated from Teoreticheskaya i Mathematicheskaya Fizika, Vol. 116, No. 2, pp. 225–247, August, 1998.     

Single-spin asymmetry of inclusive π 0-meson production in 40-GeV pion interactions with a polarized target in the target-fragmentation region

Data on the single-spin asymmetry (A _N) of inclusive π ⁰ production in 40-GeV pion interactions with a polarized target, π^? + _↑→π⁰+X, are presented for the target-fragmentation region. The result is A _N=(?13.8±3.8)% for ?0.8<x _Fp _T<2 GeV/c and is compatible with zero for ?0.4<x _Fp _T<1.5 GeV/c. At a π ⁰ momentum of about 1.7 GeV/c in the c.m. frame, the asymmetry becomes nonzero both in the central and in the target-fragmentation region. The behavior of the asymmetry is similar to that observed in the beam-fragmentation region of the E-704 (FNAL, 200 GeV) and STAR (BNL, 20 TeV) experiments, which employed a polarized proton beam.     

Generation and Propagation of Fractional Fluxons in Josephson Media

Journal of Experimental and Theoretical Physics - We consider the problems related to the use of 0–π junctions with a nontrivial current–phase relation in Josephson transmission...     

Growing Regge trajectories in relativistic string models

A relativistic quantum model is suggested in which the Regge trajectories can grow faster than linearly. The model is a rigid string with a Lagrangian given by an exponential function of the string world-sheet curvature. Exactly solvable generalizations of the model are considered.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 209–217, February, 1996.     

On a spectral condition for infrared singular quantum fields

The problem of formulating the spectral condition for vacuum expectation values of quantum fields with singular infrared behavior is discussed. It is shown that this problem is closely connected with the problem of extending the Paley-Wiener-Schwartz theorem to wider distribution classes. Studying this connection leads to a generalized spectral condition applicable to fields of arbitrarily high singularity.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 405–411, December, 1995.     

Variations of trends of indicators describing complex systems: change of scaling precursory to extreme events

Socioeconomic and natural complex systems persistently generate extreme events also known as disasters, crises, or critical transitions. Here we analyze patterns of background activity preceding extreme events in four complex systems: economic recessions, surges in homicides in a megacity, magnetic storms, and strong earthquakes. We use as a starting point the indicators describing the system's behavior and identify changes in an indicator's trend. Those changes constitute our background events (BEs). We demonstrate a premonitory pattern common to all four systems considered: relatively large magnitude BEs become more frequent before extreme event. A premonitory change of scaling has been found in various models and observations. Here we demonstrate this change in scaling of uniformly defined BEs in four real complex systems, their enormous differences notwithstanding.     

Measurement of the single-spin asymmetry in the reaction π − d ↑ → π 0 X in the beam-fragmentation region at 40 GeV and p T of up to 2 GeV/c

The single-spin asymmetry A _N in the reaction π ^? + d _↑ → π ⁰ + X in the beam-fragmentation region at the energy of 40 GeV was investigated by using the PROZA setup installed at the U-70 accelerator of the Institute for High Energy Physics (IHEP, Protvino). It was measured to be A _N = (13.6 ± 2.6(stat.) ± 2.0(syst.))% in the intervals 0.7 < x _F < 1.0 and 1.0 < p _T < 1.8 GeV/c. The results agree with the asymmetry of π ⁰ mesons in the charge-exchange reaction π ^? + p _↑ → π ⁰ + n at the same values of the transverse momentum and beam energy. The asymmetry in the reaction K ^? + d _↑ → π ⁰ + X was simultaneously measured and found to be A _N = (11 ± 14)% for p _T > 1.2 GeV/c.     

Application of multiroot decision diagrams for integer functions

New data structures for representation of integer functions and matrices are proposed, namely, multiroot binary decision diagrams (MRBDD). Algorithms for performing standard operations on functions and matrices represented by MRBDDs are presented. Thanks to the more efficient reuse of structural elements, representation by multiroot binary decision diagrams is more efficient than the widely used multiterminal binary decision diagrams (MTBDD). Experimental results are given, which show that multiroot binary decision diagrams are a promising alternative to multiterminal binary decision diagrams, in particular, in probabilistic verification, manipulation of probability distributions, analysis of Petri nets, and other computational models.     

Bogolubov's methods in nuclear theory

Mathematical methods and physical ideas developed by Bogolubov are intensively used in the theory of the atomic nucleus. The variational Hartree-Fock-Bogolubov method and the self-consistent field method found wide application in calculating nuclear spectra and nucleus-nucleus interactions. The development of these methods led to the formulation of the quasiparticle-phonon nuclear model for calculating the properties of nuclear states at low, intermediate, and high excitation energies.