Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.     

Grating coatings with gain

Using an integral theory of grating diffraction we calculate efficiencies greater than 100% if a coating with gain is taken into account. A connection with guided modes is conjectured. The application in optical computing seems to be possible.     

Electric generators of singlet delta oxygen for an oxygen-iodine laser

Experimental and theoretical research into electric generators of singlet delta oxygen (SDO) for an oxygen-iodine laser made at the Lebedev Physics Institute and TRINITI is discussed. Breakdown and current-voltage characteristics of self-sustained electric discharge in SDO were studied both experimentally and theoretically, indicating that SDO and pure oxygen have quite different electric features. The electric properties and spectroscopy of an e-beam sustained discharge (EBSD) in oxygen and oxygen gas mixtures were experimentally studied. A comprehensive numerical model describing SDO kinetics in different kinds of discharge was developed. The pulsed EBSD in pure oxygen and its mixtures with noble gases was shown to be very unstable and characterized by low input energy. When adding small amounts of carbon monoxide or hydrogen, the electric stability of the EBSD increases, the specific input energy (SIE) per molecular component being more than order of magnitude higher and coming to 6.5 kJ/(l atm(O₂ + CO)) for the gas mixture O₂: Ar: CO = 1: 1: 0.1. Theoretical calculations demonstrated that, for an SIE of 6.5 kJ/(l atm), the SDO yield may reach ∼20%, exceeding its threshold value needed for oxygen-iodine laser operation at room temperature. The calibration of the optical scheme for measuring the SDO absolute concentration and yield using the detection of luminescence of the SDO going from a chemical SDO generator was performed. The measurement of the SDO yield demonstrated that it was ∼10.5% for an SIE of ∼3.0 kJ/(l atm(O2 + CO)), which is about 1.5 times less than the results of theoretical calculations for such an SIE. SDO production in RF slab discharge ignited in oxygen gas mixtures was experimentally studied, experimental SDO yield being about 10%. The choice of electrode material was demonstrated to be very important. Original Text ? Astro, Ltd., 2006.     

On the distribution of the number of real zeros of a random polynomial

In this note, we find the distibution of the number of real zeros of a random polynomial. We also derive a formula for the expected number of complex zeros lying in a given domain of the complex plane. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 69–79.     

The matrix equation AX-YB=C and related problems

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23.     

Definition and properties of characteristic frequencies of a linear equation

The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of nonstability is given. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005.     

Electrochemical Recovery of Silver from Lead Alloys in Chloride Melts

Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry.