The spectrum of an elliptic operator of second order

Under minimal requirements on the coefficients and the boundary of the domain it is proved that the spectrum of the first boundary-value problem for an elliptic operator of second order always lies in the half-plane Re , where is the leading eigenvalue to which there corresponds a nonnegative eigenfunction. On the line Re = , there are no other points of the spectrum.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 351–358, September, 1976.     

Chemistry of Dioxacyclanes: XI. Synthesis and Properties of Unsaturated Derivatives of 1,3-Dioxolanes

1'3-Dioxolanes were synthesized by reactions of 3-cyclohexenecarboxaldehyde, 5-norbornene-2-endo-carboxaldehyde with 1,2-ethanedithiol and 3-(2-propenyloxy)- and 3-propoxy-1,2-propanediols, aswell as of propionaldehyde, benzaldehyde, and trichloroacetaldehyde with the latter two thiols. Dichlorocarbene addition, bromination, and epoxidation of the ring C = C were accomplished, and activity of the resulting products as dienophiles in Dield-Alder reactions was assessed.     

Crystal structure of ternary Laves phases in Co—Mn—Nb,Co—Mn—Ta,Co—Re—Nb,and Co—Re—Ta systems

Ternary Laves phases in the three-component systems Co—Mn—Nb, Co—Mn—Ta, Co—Re—Nb, and Co—Re—Ta at 1200 K were established for the first time and crystallographic parameters of these phases were determined.     

Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions

Some recent works related to the Rayleigh function are analyzed that reestablish results that have been known in the literature for over one hundred years.     

Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities,Estimates, Expansions,etc., for Zeros of Bessel Functions

This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.     

Some remarks concerning the Fourier transform in the space L 2(ℝ n )

For the Fourier transform in the space L ₂(?²) of square integrable multivariable functions, two practically useful estimates are proved in certain classes of functions characterized by a generalized continuity modulus.     

On the Riesz basis property of the root functions in certain regular boundary value problems

The differential operatorly=y+q(x)y with periodic (antiperiodic) boundary conditions that are not strongly regular is studied. It is assumed thatq(x) is a complex-valued function of classC ⁽⁴⁾[0, 1] andq(0)q(1). We prove that the system of root functions of this operator forms a Riesz basis in the spaceL ₂(0, 1).Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 558–563, October, 1998.     

Investigation of electron-beam-excited molecular gas lasers

Physical processes are investigated in active media of high-pressure gas lasers operating on electronic transitions of molecules. Lasing was obtained in the VUV ( = 172 nm) region of the spectrum by exciting compressed xenon and an Ar:Xe mixture. The effect of the temperature and pressure on the kinetics of the processes in the active laser media Ar:N₂, Xe:0₂, and Ar:Kr:F₂ are investigated. A new class of excimers, consisting of one halide and two inert atoms, is observed for the first time ever, and the temperature dependence of the spontaneous and laser emissions of XrF* is investigated; this dependence is due to the redistribution of the energy drawn from the electron beam among the excimers KrF^* and Kr2^F*.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva, Vol. 142, pp. 172–202, 1983.     

Spin exchange in iodine-doped polydiacetylene

It is shown that the observed transformation of the ESR spectrum in polydiacetylene films upon doping with iodine agrees with an exchange interaction between the spin systems of localized paramagnetic centers (S) and polaron states (P) by means of which current-carrier transport occurs. The data obtained indicate carrier transport in the form of uncorrelated hops with probability determined by the lifetime of an exchange-coupled (S-P) pair. Fiz. Tverd. Tela (St. Petersburg) 41, 1879–1881 (October 1999)