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We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The first-level thin disks have variable thickness vanishing at their edges. Hence some coefficients of the corresponding homogenized problem degenerate and its solution has a singular behavior near the boundary. We extract three qualitatively different cases of the asymptotic behavior of the solution as ε → 0. Bibliography: 26 titles. Illustrations: 2 figures. [ABSTRACT FROM AUTHOR]

The article focuses on the analysis of the new cases of vibrations which occur in thick cascade junctions having concentrated masses. It states that new transmission condition was found at the interface which was determined by the behavior of the short rods. It says that transmission conditions were affected by the concentration masses found in the short rods. It mentions experimental studies concerning vibrations which show that the eagerfrequencies of the body can be changed by the concentrated mass found on a small set of diameter. However, an accurate study of concentrated masses on object's behavior can be obtained through homogenization theory and asymptotic analysis.

We consider quasilinear and linear parabolic problems with rapidly oscillating coefficients in a domain Ω that is ε-periodically perforated by small holes of order [MediaObject not available: see fulltext.]. The holes are divided into three ε-periodical sets depending on boundary conditions. The homogeneous Dirichlet boundary conditions are imposed for holes of one set, whereas, for holes in the remaining sets, different inhomogeneous Neumann and nonlinear Robin boundary conditions involving additional perturbation parameters are imposed. For a solution to the quasilinear problem we find the leading terms of the asymptotic expansion and prove asymptotic estimates that show the influence of perturbation parameters. In the linear case, we construct and justify a complete asymptotic expansion of the solution by using the two-scale asymptotic expansion method. Bibliography: 25 titles. Illustrations: 1 figure. [ABSTRACT FROM AUTHOR]

We consider a parabolic semilinear problem with rapidly oscillating coefficients in a domain Ωε that is ε-periodically perforated by small holes of size $\mathcal {O}$(ε). The holes are divided into two ε-periodical sets depending on the boundary interaction at their surfaces, and two different nonlinear Robin boundary conditions σε( uε) + εκ m( uε) = ε g( m) ε, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as ε → 0 and establish a convergence theorem without using extension operators. An asymptotic approximation of the solution and the corresponding error estimate are also obtained. Bibliography: 60 titles. Illustrations: 1 figure. [ABSTRACT FROM AUTHOR]

We consider initial boundary value problems for parabolic differential equations with rapidly oscillating coefficients in thin perforated domains of rapidly varying thickness. Under certain symmetry conditions on the domain and coefficients, we construct an asymptotic expansion of a solution to the problem with homogeneous third kind conditions on the exterior boundary and the boundary of cavities. In the case of inhomogeneous Neumann conditions, we construct an asymptotic solution without symmetry assumptions and prove an asymptotic estimate in the corresponding Sobolev space. Bibliography: 27 titles. Illustrations: 1 figure. [ABSTRACT FROM AUTHOR]

Boundary value problems for the Poisson equation are considered in a multilevel thick junction consisting of a junction body and a lot of alternating thin rectangles of two levels depending on their lengths. Rectangles of the first level have a finite length, whereas rectangles of the second level have a length ε α, 0 < α < 1, where ε is the alternation period. On the boundary of thin rectangles, an inhomogeneous Neumann boundary condition involving additional perturbation parameters is imposed. We prove convergence theorems for solutions and energy integrals. Regarding the convergence of solutions of the original problem to solutions of the homogenized problem, we establish some (auxiliary) estimates necessary for obtaining the convergence rate. Bibliography: 48 titles. Illustrations: 3 figures. [ABSTRACT FROM AUTHOR]

Asymptotic behavior of one class of optimal control problems in thick junctions is investigated and a scheme of their homogenization is proposed. [ABSTRACT FROM AUTHOR]

Published data on both flora and phytocoenosis genesis and plant population dynamics are reviewed. Urbanized environment is rated as a stress factor for single plants and their communities. The change of plant population structure in cities and towns is analysed as the important indicator of the environment quality. The problems of phytoindication of environment quality in cities and towns for its optimization are considered.

The obtained results of the analysis of the peripherical blood granulocytes morphofunctional condition in those persons who took part in the elimination of aftermaths of the Chernobyl accident, presenting with persistent leucopenia, suggest to us the presence of significant changes in morphological, cytochemical, and functional indices in the remote period.

By calorimetric study of the collagen-water systems with 10-100% content of protein in the temperature range 20 + 90 degrees C we have measured the proper heat capacity of protein in native and denatured state. It is shown that S-like dependence of heat capacity on the water content for both native and denatured samples is caused by glass transition. At temperatures above the glass transition in moist collagen or above the denaturation of native collagen the translational mobility of segments in protein molecules appears. This mobility is most probably the cause of the increments in the temperature dependence of heat capacity. According to our results, for the denatured collagen the value of heat capacity in solution exceeds that for dry samples at least by the magnitude of heat capacity increment at glass transition.