The regularizing properties of anisotropic radial basis functions

In the present work we consider the problem of interpolating scattered data using radial basis functions (RBF). In general, it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution. The work focuses on a metric-regularization approach, based on a new class of RBF, called anisotropic RBF. The work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric, supporting it by numerical examples.     

A differential-geometric criterion of the kinematic integrability of nonlinear differential equations

A theorem on the existence of a G-representation and a differential-geometric criterion of the kinematic integrability for nonlinear differential equations from the Λ²-G-classes is proved. Examples of zero-curvature representations and metrics for some equations of mathematical physics are presented. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

Inverse problems for a mathematical model of redox sorption

We consider a mathematical model of sorption that allows for external diffusion kinetics and a redox reaction. Two inverse problems are considered for this model, uniqueness is proved, and numerical solution methods are proposed. The efficiency of the numerical methods is investigated by computer experiments. __________ Translated from Prikladnaya Matematika i Informatika, No. 23, pp. 15–23, 2006.     

Circular dichroism spectra in mordant azo dyes

The photogyrotropic properties of several mordant yellow azo dyes in gelatin and polymer matrices that are in the normal state or exposed to circularly polarized light are investigated. A model explanation for the experimental data is given.     

Production and properties of metal-carbon composite coatings with a nanocrystalline structure

It is suggested to produce metal-carbon composite coatings by magnetron sputtering of mosaic cathodes, which are Group IV, V, and VI metals. The mosaic structure of the cathode elements are computer-optimized for each of the metals. Reflection electron diffraction studies show that the coatings have the amorphous or nanocrystalline structures, which are thermally stable. The coatings offer specific physical properties, in particular, low friction factor and high hardness.     

Revisiting Gouy phase

The aim of this paper is to highlight the added value of the generalized Gouy phase shift introduced by Siegman. Although suited for optical systems study, including those more complex than free space, we note that it did not meet the use that it deserves so far. The analysis of the whole of the ideas and analytical approaches associated to the important concept of the Gouy phase proves its effectiveness.

Usually, the resonance condition is systematically built on the basis of the equivalent empty cavity. Unfortunately, this approach does not cover some of the useful parameters of the real resonator. By means of the generalized Gouy phase and the self-consistent complex parameter q, we derive here a new approach for the calculation of the resonance condition for the real cavity. Moreover, the use of the generalized Gouy phase clearly simplifies the study of resonators, while making it possible to avoid the use of the Huygens’ Fresnel integral.     

Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Arene sulfenylation by arenesulfenamides and arenesulfenylacetates

Two systems for arene sulfenylation were investigated: arenesulfenamides in the presence of SO₃ and sulfenylacetate complexes with AlBr₃. A preference for the second reagent was demonstrated for sulfenylation of substrates bearing donor substituitents.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 324–326, February, 1995.