Vol 21, No 3 (2015)

In this paper, we study the initial-boundary problem with nonlinear dynam- ical boundary condition for the pseudohyperbolic equation. This problem repre- sents a mathematical model of longitudinal vibration in a thick short bar with dynamic nonlinear second-order boundary damping. The existence and unique- ness of a generalized solution are proved. The proof is based on a priori estimates and Galerkin procedure. This approach allows to construct approximation in the suitable for practical application form.

In the present work we study the solvability of spatial nonlocal boundary value problems for linear one-dimensional pseudoparabolic and pseudohyperbolic equations with constant coefficients, but with general nonlocal boundary conditions by A.A. Samarsky and integral conditions with variables coefficients. The proof of the theorems of existence and uniqueness of regular solutions is carried out by the method of Fourier. The study of solvability in the classes of regular solutions leads to the study of a system of integral equations of Volterra of the second kind. In particular cases nongeneracy conditions of the obtained systems of integral equations in explicit form are given.

In this article for the mixed type equation with a singular coefficient Keldysh problem of incomplete boundary conditions is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral prob- lem the criterion of uniqueness is established. The solution is constructed as the summary of Fourier-Bessel row. At the foundation of the uniform convergence of a row there is a problem of small denominators.Under some restrictions on these tasks evaluation of separation from zero of a small denominator with the corresponding asymptotics was found, which helped to prove the uniform con- vergence and its derivatives up to the second order inclusive, and the existence theorem in the class of regular solutions.

In the paper the detailed review and comparison of modern methods of digital object processing in present-day interference optical techniques (namely, photomechanics) are given. The methods of fringe thinnig, fringe clustering, fringe tracing are discussed. Applications of methods to digital photomechanics and fracture mechanics parameter determination are considered. The example of cracked semidisc for compression is analyzed.

The article provides a formulation to the problem of spherical drop motion into laminar boundary layer over a flat semi-infinite plate (Blasius problem). The paper presents the solution in the package Ansys Fluent without taking into account deformation and rotation of drops. The article describes building of geometric area, construction of the grid models, boundary and initial conditions statement, methods of solution, course of computation. The article describes the examples of problem solving for various initial conditions of a drop, compares the results obtained using different methods. There is good agreement between the results. A combination of different methods for solving similar problems is the guarantee of a successful solution.

In the article the stress-strain state near a Mode II crack tip under plane stress conditions in power-law materials is considered. It is noted that nowadays the whole eigenspectrum and orders of stress singularity at the crack tip for a power-law medium are of prevailing interest. Additional eigenvalues for the stress field at a static mode II crack under plane stress condition are numerically obtained for different values of the exponent n via the Runge-Kutta method in conjunction with the shooting method. However, in this case the shooting method is multi-parameter since it is necessary to select two parameters and, consequently, the results obtained require further verification and justification. For this purpose the technique developed in perturbation theory for study of nonlinear eigenvalue problems is offered and applied for eigenvalue problems arising from fracture mechanics analysis.

On the example of research of chromatographic spectra of retention of light components of headspace of medicinal herbs of lavender (Lavandula Spica), peppermint (Mentha piperita L.) and estragon (tarragon herb, Artemisia dracunculus L.), the possibility of express estimate of their authenticity per totality of retention index of light components in the mode of linear programming of temperature on capillary column with polydimethylsiloxane stationary phase with the use of present in the laboratories available gas chromatographic equipment with flame ionization detector is shown.

Systems with participation of nitrates and halogenides of alkaline metals find more and more broad practical application.The four-component mutual system Li, Na // F, Br, NO3 is for the first time described and studied. With the use of innovative methodology of research for the system Li, Na // F, Br, NO3 the model of a tree of phases confirmed experimentally with the DTA method is constructed. The power-intensive three- fold eutectic structure of LiF-LiNO3-NaBr with a temperature of melting of 220,8 ◦C for application as the medium temperature heataccumulator is revealed.

The article presents a characterization of mycobiota of the formed snow cover in Samara in 2013 and 2014. In the snow cover of suburb, uncontaminated areas of coastal parks Strukovsky and Zagorodnyi micromycetes were detected in the form of single colonies, or were not detected at all. Increase of microscopic fungi in the snow cover of the city (42 CFU/ml) was observed on the territories bordering highways, streams of people, that is due to the horizontal transfer of air masses. The composition of dominant micromycetes of the snow cover (a measure of occurrence was greater than 60 %) in 2013 and 2014 varied considerably and depended on the climatic conditions of the previous warm period of the year and the strength of the current winter frosts. Subdominant (incidence below 11 %), of the snow cover in winter periods studied were similar and were the fungi of the genus Alternaria, constantly prevailing in mycobiota air environment of the city in the summer-autumn period.