Centred TVD schemes for hyperbolic conservation laws

New first- and high-order centred methods for conservation lawsare presented. Convenient TVD conditions for constructing centredTVD schemes are then formulated and some useful results areproved. Two families of centred TVD schemes are constructedand extended to nonlinear systems. Some numerical results arealso presented.     

Interaction of laser radiation with an axially symmetric polarization with condensed media

The interaction of laser radiation with an axially symmetric polarization with condensed media is studied theoretically. The interaction results in the formation of ordered micro- and nanoscale structures that can be described in terms of the universal polariton model of laser-induced media damage. It is shown that the radially polarized radiation induces a periodic ring resonance grating that focuses the excited surface plasmon-polaritons, thus increasing the total light intensity in the center of the irradiated zone.     

Organolead chemistry : III. 207Pb chemical shifts in some organolead compounds

²⁰⁷Pb chemical shifts are reported for the compounds (CH₃)_4?nPb X_n, where n = 1 · 4, X = 4-FC₆H₄; n = 1, 2, 4, X = CH₃ CC; n = 1, 4, X = CH₂CH; n = 1, X = Cl, CH₃O, CH₃CO₂. A correlation between δ(²⁰⁷Pb) and δ(¹⁹F) for the 4-fluorophenyl derivatives is discussed, and solvent effects on δ(²⁰⁷Pb) for the propynyl derivatives are interpreted in terms of complex formation.     

Formation of Kerr waveguide and microgratings on a germanium surface under the action of femtosecond radiation of the mid-IR range

A new nonlinear physical model of the formation of ordered structures of a surface topography of a semiconductor by ultrashort pulses of linearly polarized laser radiation has been proposed. The model is based on the formation of the dynamic near-surface waveguide due to the optical Kerr effect, interference with the part of waveguide modes, and the formation of microgratings on the surface, which are oriented by polarization of radiation. The model is confirmed by experimental data.     

Irregular boundary value problem for the Sturm–Liouville operator

We consider an eigenvalue problem for the Sturm–Liouville operator with nonclassical asymptotics of the spectrum. We prove that this problem, which has a complete system of root functions, is not almost regular (Stone-regular) but its Green function has a polynomial order of growth in the spectral parameter.