Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

A Second-Order Theory for Electron Plasma Solitary Waves in a Cylindrical Waveguide

To describe the long time asymptotic behaviour of weakly nonlinear plasma waves propagating in a strongly magnetized plasmafilled cylindrical waveguide the usual KDV equation which is first order in wave amplitude is extended to second order including the effects of finite temperature, mobile ions and giving a proper treatment to the radial co-ordinate for all possible modes of propagation. The second-order effects on the first-order solitary wave profile, phase speed and first order correction to the wavelength are all determined and discussed.     

Galactic model of element formation

A cosmological model is presented that produces He, C, O, D, Li, Be, and B in their observed abundances without a Big Bang. The elements are produced during the 1.5-Gy formation period of a galaxy, with C, O, and other heavy elements produced by stars of M>12 M₃ , He by stars of 6 M_s<M<12 M_s, and D, Li, Be, and B by cosmic-ray reactions in a nearly pure H plasma halo. Thus, the model shows that the major elements used in astrophysical studies can be produced during galactic formation by exactly the same processes known to function today at much lower rates     

Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.     

Asymptotic integration of a problem of convection

Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 69–75, July–August, 1989.     

The effect of geoacoustic characteristics of the bottom on the long-range sound propagation in an inhomogeneous ocean

The long-range sound propagation from a deep ocean to a receiving system located on the shelf is modeled. The waveguide model is constructed on the basis of the data of an acoustic-oceanographic experiment carried out in the northwestern Pacific. The sensitivity and the frequency dependence of the difference in the sound field levels at the crossing of the frontal zone on the geoacoustic characteristics of the bottom of the shelf and the continental slope are investigated. It is shown that the level difference decreases by 8.2 dB as the velocity of longitudinal waves increases by 100 m/s in the range within 1490–1820 m/s.