Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data

Siberian Mathematical Journal - We consider a problem for a first-order differential equation in a Hilbert space. We replace the initial data with some condition that...     

The dynamics of a two-component fluid in the presence of capillary forces

In the present paper we study the qualitative behavior ast→∞ of the solution of the Cauchy problem for a system of equations describing a dynamics of a two-component viscous fluid. The model under consideration takes into account the mutual diffusion of the fluid components as well as their capillary interaction. We describe the ω-limit set of trajectories of the dynamical system generated by the problem. It is proved that the stationary solution of the problem, is a homogeneous stationary distribution of one of the components, is asymptotically stable. Any other stationary solution is not asymptotically stable and is even unstable if there are no close stationary solutions corresponding to a smaller energy level. Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 293–305, August, 1997. Translated by A. M. Chebotarev     

Miniaturized resonant photoacoustic cell of inclined geometry for trace-gas detection

A photoacoustic cell intended for laser detection of trace gases is represented. The cell is adapted so as to enhance the gas-detection performance and, simultaneously, to reduce the cell size. The cell design provides an efficient cancellation of the window background (a parasite response due to absorption of laser beam in the cell windows) and acoustic isolation from the environment for an acoustic resonance of the cell. The useful photoacoustic response from a detected gas, window background and noise are analyzed in demonstration experiments as functions of the modulation frequency for a prototype photoacoustic cell with the internal volume ∼0.6 cm³. The minimal detectable absorption for the prototype is estimated to be ∼1.2×10⁻⁸ cm⁻¹ W Hz^−1/2.     

On the Problem of Describing Sequences of Best Trigonometric Rational Approximations

For a strictly decreasing sequence a_{n n=0} of nonnegative real numbers converging to zero, we construct a continuous 2-periodic function f such that R^T _n(f) = a_n, n=0,1,2,..., where R^T _n(f) are best approximations of the function f in uniform norm by trigonometric rational functions of degree at most n.     

Asymptotics of diagonal Hermite–Padé polynomials for the collection of exponential functions

Mathematical Notes - In the paper, the semigroup of weak limits of the powers of an infinite transformation of rank one of Chacon type is completely described.     

Deformation of a three-layer elastoplastic beam on an elastic foundation

We study the thermal force bending of an elastoplastic three-layer beam with a rigid filler; the beam is connected with an elastic foundation. The broken normal hypothesis is adopted to describe the kinematics of a packet nonsymmetric with respect to the thickness. The foundation reaction is described by Winkler’s model. The system of equilibrium equations and its exact solution in displacements are obtained and numerical results for a three-layer metal-polymeric beam are presented.