Elasticity and inelasticity of biomorphic silicon carbide ceramics

The effect of the vibration strain amplitude on the Young modulus and ultrasonic absorption (internal friction) in biomorphic SiC ceramics is investigated in the temperature range 116–296 K. The biomorphic SiC ceramics is prepared through pyrolysis of eucalyptus with subsequent infiltration of silicon. It is demonstrated that the vibration loading of samples in air and under vacuum is accompanied by a number of unexpected effects. The behavior of the studied ceramics is governed by at least two mechanisms, which, to a large extent, are responsible for the elastic and inelastic properties of the material. One mechanism is associated with the adsorption-desorption of environmental molecules (hypothetically, owing to the presence of pores and residual carbon), and the other mechanism involves microplastic deformation due to the motion of dislocations or other (similar) structural units.     

Spectral stability of nonnegative self-adjoint operators

The survey is devoted to spectral stability problems for uniformly elliptic differential operators under the variation of the domain and to the accompanying estimates for the difference of the eigenvalues. Two approaches to the problem are discussed in detail. In the first one it is assumed that the domain is transformed by means of a transformation of a certain class, and the spectral stability with respect to this transformation is investigated. The second approach is based on the notion of a transition operator and allows direct comparison of the eigenvalues on domains which are close in that or another sense. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 15, Differential and Functional Differential Equations. Part 1, 2006.     

Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

The problem of the boundedness of the Riesz potential I _α , 0 < α < n, in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted L _p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, these sufficient conditions coincide with the necessary ones. V. Guliyev’s research was partially supported by the grant of the Azerbaijan-U. S. Bilateral Grants Program II (project ANSF Award / AZM1-3110-BA-08) and the Turkish Scientific and Technological Research Council (TUBITAK, programme 2221, no. 220.01-619-4889).     

Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations

The real interpolation method is considered and it is proved that for general local Morrey-type spaces, in the case in which they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters. This result is a particular case of the interpolation theorem for much more general spaces defined with the help of an operator acting from some function space to the cone of nonnegative nondecreasing functions on (0, ∞). It is also shown how the classical interpolation theorems due to Stein-Weiss, Peetre, Calderón, Gilbert, Lizorkin, Freitag and some of their new variants can be derived from this theorem.     

An analog of Young’s inequality for convolutions of functions for general Morrey-type spaces

An analog of the classical Young’s inequality for convolutions of functions is proved in the case of general global Morrey-type spaces. The form of this analog is different from Young’s inequality for convolutions in the case of Lebesgue spaces. A separate analysis is performed for the case of periodic functions.     

Interference effects in the theory of multiphoton laser-simulated bremsstrahlung for electron wave packets that are broad in their momentum representation

The interference peculiarities of absorption and emission of external laser field quanta by a spatially narrow electron wave packet during its scattering at a potential center are considered. The angular and energy distributions for an electron due to scattering in a laser field are obtained and analyzed within the framework of the perturbation theory based on interaction with the potential center. A new mechanism of effective heating of plasma produced in a cluster under the effect of intense external laser field is found. Drastic changes in angular distribution due to the interference of incident and scattered parts of an electron wave packet are revealed.     

Elasticity and inelasticity of ceramic samples of graphitelike boron nitride

This paper reports a study of the effect of temperature and strain amplitude on Young’s modulus and ultrasonic damping in ceramic samples of graphitelike boron nitride prepared in the RF and USA by different technologies and using various additions to improve the mechanical properties of the ceramic. It is shown that, in addition to the influence on the effective elasticity modulus, additions improve the sample microplasticity, which apparently increases the strength of the material.     

Spectral stability of the Robin Laplacian

We consider the Robin Laplacian in two bounded regions Ω₁ and Ω₂ of ℝ ^N with Lipschitz boundaries and such that Ω₂ ⊂ Ω₁, and we obtain two-sided estimates for the eigenvalues λ _n,2 of the Robin Laplacian in Ω₂ via the eigenvalues λ _{n, 1} of the Robin Laplacian in Ω₁. Our estimates depend on the measure of the set difference Ω\Ω₂ and on suitably defined characteristics of vicinity of the boundaries ∂Ω₁ and ∂Ω₂, and of the functions defined on ∂Ω₁ and on ∂Ω₂ that enter the Robin boundary conditions.     

Thermally stimulated acoustic splitting of an elastic wave in polycrystalline niobium subjected to electron-beam remelting

The effect of temperature on the Young’s modulus of electron-beam-remelted polycrystalline niobium is studied in the temperature range 20–1000°C. The impurity content in the material is Ta<0.5 wt% and O₂<0.1 wt%. The acoustic split of the resonant frequency is found in the temperature range 60–180°C, which makes the determination of the Young’s modulus uncertain. Mechanisms behind the thermally stimulated splitting of an elastic wave and the behavior of the Young’s modulus over a wide temperature interval are discussed.