Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet

Integrable systems associated with separation of the variables in real Riemannian spaces of constant curvature are considered. An isomorphism between all such systems and the hyperbolic Gaudin magnet is established. This isomorphism is used in a classification of all coordinate systems that admit separation of the variables, the basis of which is the classification of the correspondingL operators of the Gaudin magnet.Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 83–111, April, 1992.     

Gibbs random fields invariant under infinite-particle Hamiltonian dinamics

The Liouville operator for an infinite-particle Hamiltonian dynamics corresponding to interaction potentialU is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interactionU.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 3, pp. 424–459, March, 1992.     

Solar probe: a rendezvous with the Sun

Summary A study has been promoted by NASA to evaluate the scientific return and the technological problems of a close-to-the-Sun mission (Solar Probe). It has come out that using current technology it is possible to deliver at 4 solar radii from the Sun's centre a scientific payload with such performances to allow a great improvement of our understanding of the coronal phenomena. The mission concept currently under study uses planetary encounters to reach the required orbit. The final orbit period is 2.5 years, the estimated mission duration about 9 years. The orbit inclination is such as to give the maximum coverage in terms of heliographic latitude. During the perihelion phases a conical structure shields the spacecraft from the intense solar radiation. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

On the optimum set of polarization measurements for the scattering of two indentical fermions to determine the helicity amplitudes

The polarization asymmetries related to usual polarizations combine at least 4 different helicity amplitudes. The introduction of ±45° inclined transverse polarizations allows us to obtain the complete set of new polarization asymmetries combining only up to 3 helicity amplitudes. There are no further polarization asymmetries depending on a smaller number of helicity amplitudes. These expressions are most economical to determine the helicity amplitudes from observed data. Some of them are suitable to study especially the spin-flip effects. We give a complete Table of all such polarization asymmetries.     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

Universality in some classical Coulomb systems of restricted dimension

Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond–1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.Laboratoire associé au Centre National de la Recherche Scientifique-URA D0063.     

Reaction of D2 with palladium fulleride C60Pd4.9

Fullerene deuteride was obtained by the reaction of deuterium with solid palladium fulleride C₆₀Pd_4.9 under fairly mild conditions. The compound was identified by FD-MS, UV-Vis and IR spectroscopies, and TLC.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 483–484, February, 1996