New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

Nonlinear vibrations of a charged drop due to the initial excitation of neighboring modes

The asymptotic analysis of the nonlinear vibrations of a charged drop that are induced by a multi-mode initial deformation of its equilibrium shape is performed. It is shown that when two, three, or several neighboring modes are present in the initial deformation spectrum, the mode with the number one (translational mode) appears in the second-order mode spectrum. The excitation of the translational mode follows from the requirement of center-of-mass immobility and causes the dipole components (which are absent in the linear analysis) to appear in the spectra of the acoustic and electromagnetic radiation of the charged drop.     

Vertical variability of sound fields in a coastal wedge

The results of measuring the vertical variability of sound fields are presented for a coastal wedge off the Pacific shelf of the Kamchatka peninsula. It is shown that the vertical radius of sound field correlation can reach ～30 m for frequencies within 600–800 Hz. The scatter of the specific parameters of the variability is in rather wide limits depending on the location of a vertical chain of receiving hydrophones, the hydrological conditions, the azimuth angle of the sound source, and the relief and bottom structure of the coastal wedge.     

Violation of isotopic invariance in strong interactions and mass spectrum of the 1/2+ baryon octet

The ideas developed by Gell-Mann and Okubo in studying violation of unitary symmetry are used to describe violation of isototic invariance in strong interactions. The present consideration is performed for the example of the mass spectrum of the octet formed by baryons of spin-parity 1/2⁺: only for this family are the widths of its particles much less than the scale of the effects being investigated, their masses being known from experiments to a fairly high precision. The Gell-Mann-Okubo formula is generalized in such a way that relations both for the splitting between the isomultiplets of the octet and for the mass splitting within these isomultiplets follow from the new formula. Moreover, a relation between masses that describes their electromagnetic splitting and which coincides in form with the Coleman-Glashow relation also follows from this formula. The relations obtained for the masses of the baryons belonging to the octet in question are satisfied to a precision not poorer than 3%.     

Investigation of the Photoluminescence of Individual Emission Bands of Mn2+ Ions in ZnS Plastically Strained Single Crystals

The photoluminescence spectra of ZnS : Mn plastically deformed single crystals are investigated. It is established that the plastic strain causes the relative concentrations of individual manganese emission centers to change together with conditions of excitation of the centers whose nearest environment has been rearranged upon plastic strain.     

Low-Frequency Parasitic Space-Charge Oscillations in the Helical Electron Beam of a Gyrotron

We developed a medium-power pulsed gyrotron equipped with diagnostic systems for studying low-frequency parasitic space-charge oscillations in the helical electron beam and the energy spectrum of electrons in the collector region. Methods for suppressing parasitic oscillations are proposed and tested. An explanation of the mechanism of suppression of these oscillations is given.     

Compatible Dubrovin–Novikov Hamiltonian Operators,Lie Derivative,and Integrable Systems of Hydrodynamic Type [Erratum]

Correction to the paper published in Vol. 133, No. 2, November, 2002.