Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Size and Shape Effects in Optical Spectra of Silver and Gold Nanoparticles

Journal of Russian Laser Research - We report some theoretical results on the extinction, absorption, and scattering of light by individual silver and gold nanoparticles of different sizes and...     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Chaotic motion of a cylindrical body during contactless transportation from MEO to LEO by ion beam

Nonlinear Dynamics - The attitude dynamics of a cylindrical body under the action of an ion beam generated by the low-thrust engine of an active spacecraft is studied. The aim of the work is the...     

Thermodynamic parameters for the complexation of water‐insoluble betulin derivatives with (2‐hydroxypropyl)‐γ‐cyclodextrin determined by phase‐solubility technique combined with capillary zone electrophoresis

The complexation of betulinic and betulonic acids (BIA and BOA) (pentacyclic lupane triterpenoids) with (2‐hydroxypropyl)‐γ‐cyclodextrin (HP‐γ‐CD) was studied at different temperatures using the method combining phase‐solubility technique and CZE. In contrast to mobility shift ACE utilizing the electrophoretic mobility, in this approach, the peak areas are used. The apparent binding (stability, formation) constants are obtained by the Higuchi and Connors method from the linear segment of compound solubility diagrams in CD solutions. It was found that the apparent binding constants of the HP‐γ‐CD complexes of BIA and BOA decrease with increasing temperature. The binding constants of BOA complexes are slightly higher than those of BIA complexes; this can be explained by difference in the hydration degrees of carbonyl and hydroxyl groups. On the basis of the binding constants obtained and their temperature dependences (van't Hoff plot), the enthalpy as well as entropy changes and Gibbs free energies were calculated. It was found that the complexation was characterized by negative changes of enthalpy and entropy, that is, it was controlled by enthalpy changes. The results obtained can be used for the optimization of microcapsulation processes of BOA and BIA with the HP‐γ‐CD application in order to increase solubility and bioavailability of these compounds.