Degenerating the elliptic Schlesinger system

We study various ways of degenerating the Schlesinger system on the elliptic curve with R marked points. We construct a limit procedure based on an infinite shift of the elliptic curve parameter and on shifts of the marked points. We show that using this procedure allows obtaining a nonautonomous Hamiltonian system describing the Toda chain with additional spin sl(N, ?) degrees of freedom.     

Synthesis of D-Mannite Esters

Mono- and diesters of D-mannite with aromatic acids are synthesized. The structures of the resulting compounds are confirmed by IR spectroscopy, PMR, and ¹³ C NMR.     

Actions of Hopf Algebras on General Quantum Mal'tsev Power Series and Quantum Planes

A classification of automorphisms, derivations, and Hopf algebra actions of the quantum plane and its completions is presented. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 18, Algebra, 2004.     

On varieties of bounded lie algebras

Siberian Mathematical Journal -     

Λ(1520) → Λγ radiative-decay width

The radiative decay Λ(1520) → Λγ was recorded in the exclusive reaction p + N → Λ(1520)K ⁺ + N at the SPHINX facility. The branching ratio for this decay and the corresponding partial width were found to be, respectively, Br[Λ(1520) → Λγ] = (1.02 ± 0.21) × 10^?2 and Γ[Λ(1520) → Λγ] = 159 ± 35 keV (the quoted errors are purely statistical, the systematic errors being within 15%).     

Toward improving the accuracy of testing the equivalence of the inertial and the gravitational mass under terrestrial conditions

An experiment aimed at testing the equivalence of the inertial and the gravitational mass is considered in which use is made of a facility including a vacuum chamber with two coupled oscillators (a pendulum and dynamical damper that form a vibrational system featuring two degrees of freedom) and falling onto the Sun. The layout of the facility and its basic parameters are presented. The pendulum and the dynamical damper have the same natural frequency, which is equal to the frequency of their rotation about the Sun. This frequency is dependent on the date of the experiment and can be calculated on the basis of the time equation. In the proposed facility, the amplitude of oscillations of the damper is 1.2×10^?5 rad, which is much greater than the value of 10^?7 rad previously achieved in the experiment that tested the equivalence principle to the highest precision of about 10^?12. This precision can be considerably improved. The result is presented that was obtained from a measurement during the solar eclipse in Moscow on August 11, 1999.     

A Proton Beam Delivery System Variant for the Oncological Ophthalmological Center for Proton Radiation Therapy at the NRC “Kurchatov Institute”—PNPI

Physics of Atomic Nuclei - A variant of the proton beam delivery system with an energy of 60 MeV for the future oncological ophthalmological center for proton radiation therapy at the isochronous...     

Binary and multiparticle electron-electron interaction on the surface

It is shown for the first time that electron-electron scattering of slow electrons with an energy of 10–50 eV at the surface of some metals is mainly an event of binary scattering of particles with conserved total momentum and energy, while analogous scattering at the surface of a semiconductor (n-Si) and an insulator (MgO) is a multiparticle event. A model is proposed, in which the electron subsystem of a solid is characterized by short-range order. Each electron is at the center of a spherical cell and surrounded by nearest neighbors (electrons) with a coordination number of 12. The overlap of the fields of charges gives rise to a negative potential U _c (r) ≈ U _c , which is virtually constant along the coordinate and contains spherical cells with a central field U(r) of individual charges. The value of constant negative potential U _c depends on the extent of electron screening, which is high for metals and low for semiconductors and insulators. In metals, scattering governed by the binary mechanism may take place (i.e., scattering of a primary electron in the central field of an electron of the metal); this is ensured by a relatively small value of constant potential U _c . The electron subsystem of the metal behaves as a Fermi gas of weakly interacting quasiparticles. Electron screening in semiconductors and insulators is insignificant, and constant negative potential U _c is an order of magnitude higher than the analogous potential in metals. Slow primary electrons are scattered in the total field of many charges before they reach the central field of an individual electron. The electron subsystem of a semiconductor and an insulator in the excitation range studied here behaves as an ensemble of strongly interacting particles.