Estimates for functionals by deviations of the Riesz sums in seminormed spaces

Suppose that (X, p) is a sermonized space, is a linearly independent system of elements in X, is a sequence of linear bounded functionals such that c _k (x _l ) = δ _kl ,

On approximation of periodic functions by Fourier sums

Let L _p , 1 ≤ p< ∞, be the space of 2π-periodic functions f with the norm || f ||_p = ( ò _{- p}^p | f |^p )^{1 \mathord}

Spatial eigenmodes of a boundary layer with a triple-deck velocity field

The beforehand unclear relation between the viscous-inviscid interaction and the instability of viscous gas flows is illustrated using three-dimensional boundary-layer perturbations in the case of sub- and supersonic outer flows. The assumptions are considered under which asymptotic boundary layer equations with self-induced pressure are derived and the excitation mechanisms of eigenmodes (i.e., Tollmien-Schlichting waves) are described. The resulting dispersion relations are analyzed. The boundary layer in a supersonic flow is found to be stable with respect to two-dimensional perturbations, whereas, in the three-dimensional case, the modes become unstable. The increment of growth is investigated as a function of the Mach number and the orientation of the front of a three-dimensional Tollmien-Schlichting wave.     

Expansion of a Rarefied Gas Cloud in a Vacuum: Asymptotic Treatment

The unsteady expansion of a rarefied gas of finite mass in an unlimited space is studied. The long-time asymptotic behavior of the solution is examined at Knudsen numbers tending to zero. An asymptotic analysis shows that, in the limit of small Knudsen numbers, the behavior of the macroscopic parameters of the expanding gas cloud at long times (i.e., for small density values) has nothing to do with the free-molecular or continuum flow regimes. This conclusion is unexpected and not obvious, but follows from a uniformly suitable solution constructed by applying the method of outer and inner asymptotic expansions. In particular, the unusual temperature behavior is of interest as applied to remote sensing of rocket exhaust plumes.     

Sharp Estimates for Deviations of Linear Approximation Methods for Periodic Functions by Linear Combinations of Moduli of Continuity of Different Order

Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that is odd, . Then

Human hair instrumental neutron activation analysis and medicine

Periodically increasing and decreasing enthusiasm has accompanied the studies of medical significance of human hair elemental composition for at least two decades. In this field, nuclear analytical methods play an extremely important role, especially the instrumental neutron activation analysis (INAA). This paper tries to add some new knowledge to this problem. Two approaches are used — comparison of individual hair composition with certain diagnoses in clinic groups and comparison of population data with medical statistics. Rather large samples and multielement mathematical procedures helped reveal strong correlations valuable for diagnostic and health screening.     

Chemical force spectroscopy in heterogeneous systems: intermolecular interactions involving epoxy polymer,mixed monolayers,and polar solvents

We used chemical force microscopy (CFM) to study adhesive forces between surfaces of epoxy resin and self-assembled monolayers (SAMs) capable of hydrogen bonding to different extents. The influence of the liquid medium in which the experiments were carried out was also examined systematically. The molecular character of the tip, polymer, and liquid all influenced the adhesion. Complementary macroscopic contact angle measurements were used to assist in the quantitative interpretation of the CFM data. A direct correlation between surface free energy and adhesion forces was observed in mixed alcohol-water solvents. An increase in surface energy from 2 to 50 mJ/m(2) resulted in an increase in adhesion from 4-8 nN to 150-300 nN for tips with radii of 50-150 nm. The interfacial surface energy for identical nonpolar surface groups of SAMs was found not to exceed 2 mJ/m(2). An analysis of adhesion data suggests that the solvent was fully excluded from the zone of contact between functional groups on the tip and sample. With a nonpolar SAM, the force of adhesion increased monotonically in mixed solvents of higher water content; whereas, with a polar SAM (one having a hydrogen bonding component), higher water content led to decreased adhesion. The intermolecular force components theory was used for the interpretation of adhesion force measurements in polar solvents. Competition between hydrogen bonding within the solvent and hydrogen bonding of surface groups and the solvent was shown to provide the main contribution to adhesion forces. We demonstrate how the trends in the magnitude of the adhesion forces for chemically heterogeneous systems (solvents and surfaces) measured with CFM can be quantitatively rationalized using the surface tension components approach. For epoxy polymer, inelastic deformations also contributed heavily to measured adhesion forces.     

Iteration scheme for solution of inverse problem of probing for a radially inhomogeneous cylinder

An algorithm is constructed for solution of the inverse problem of probing for a radially stratified cylinder that employs the Newton-Kantorovich iteration procedure and Tikhonov's regularization method. A considerable portion of the calculations within the proposed solution can be performed analytically, which makes computer implementation highly effective. Illustrative results of numerical experiments are presented.Kharkov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 10, pp. 901–911, October, 1993.     

Finite-difference solution of a nonlinear initial-boundary-value problem for a nonlinear parabolic equation of second order

An implicit finite-difference scheme is constructed for solving a nonlinear initial-boundary-value problem for a nonlinear homogeneous parabolic equation of second order with a nonlinear boundary condition that contains the time derivative of the sought function. The results are used for numerical solution of the mathematical model of internal-diffusion kinetics of adsorption from a constant bounded volume.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 65, pp. 34–46, 1988.     

State of Chromium in Solid Solutions of Complex Bismuth Niobates Bi2BaCrxNb2-xO9(0.01 < x < 0.3)

Magnetic susceptibility and electric properties of complex bismuth niobates with the layered perovskite structure, containing chromium(III) atoms in niobium(V) sites, were studied. Clusters of chromium(III) atoms with a high antiferromagnetic exchange parameter (−45 cm⁻¹) were found, whose formation along the c axis of the structure is associated with the presence of vacancies in the oxygen sublattice.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 1, 2005, pp. 24–28.Original Russian Text Copyright © 2005 by Chezhina, Piir, Zhuk.