**I.**** Mikhailovskii E.I.** **Word about Valentin Valentinovich Novozhilov**

**II.**** Mikhailovskii E.I., Tarasov V.N.** **The constructive – nonlinear mechanics of plates and shells**

The review of the basic results obtained by authors and their disciples for last 20 years in the field of constructive-nonlinear mechanics of plates and shells is given. The general course of the proof proposed by authors of a method of the generalized reaction for the solving of contact problems with free boundary and a method of local search of eigenvalues of positively homogeneous operators for the solving of essentially nonlinear spectral problems is explained. Algorithms of local search of variants in a combination to their full search on a rare grid and with movement on parameter of rigidity of one of elastic environments are illustrated. Effect of accounting transversal deformations in the equations of mechanics of plates and shells is investigated.

**III.**** Belyaeva N.A.** **Deformation of viscoelastic materials with changing structure**

Deformation processes of materials with changeable structure is presentated. Worked out mathematical models are including wide field of objects beginning with systems-powder to polymer and composite materials. This models give a chance to define deformation, temperature and structure characteristicses during hardening, solid state extrusion and non-Newtonian flow.

**IV.**** Tarasov V.N., Andryukova V.Yu.** **Of nonlinear fluctuations of rectangular plates**

Linear and nonlinear fluctuations of rectangular plates are researched. The difference scheme for solving the dynamic equations of Karman is considered. The results of numerical experiments are analyzed, solutions obtained on the basis of a linear equations of vibrations of plates and the solutions obtained by numerical analysis of nonlinear Karman equations are compared.

**V.**** Belyaev Y.N.** **Characteristic matrix of laered-periodic structure**

The method of recurrent calculation of the matrix characterising distribution of elastic waves in periodic layered structure is offered. The estimation of efficiency of this method is made.

**VI.**** Sergey G. Bobkov.** **The growth of L**^{p}**-norms in presence of logarithmic sobolev inequalities**

The growth of L^{p}-norms is considered under various hypotheses, including LS_{q} (logarithmic Sobolev) inequalities.

**VII.**** Vechtomov E.M., Sidorov V.V.** **On difinability of semirings of continuous functions by their subalgebra lattice**

It is solved the problem of semirings of continuous functions difinability by their subalgebra lattice. Namely, it is proved that an isomorphism of lattices of all subalgebras of semirings of continuous nonnegative functions over arbitrary topological spaces implies an isomorphism of semirings of continuous functions.

**VIII.**** Petr A. Golovach, Pinar Heggernes.** **Choosability of P**_{5}**-free graphs**

A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k > 3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we prove that the problem is fixed parameter tractable on P_{5}-free graphs when parameterized by k. This graph class contains the well known and widely studied class of cographs. Our result is surprising since the parameterized complexity of k-coloring is still open on P_{5}-free graphs. To give a complete picture, we show that the problem remains NP-hard on P_{5}-free graphs when k is a part of the input.

**IX.**** Kostyakov I.V., Kuratov V.V.** **Limit transitions in gauge theories**

We show how to obtain Lagrangians with nonsemisimple gauge symmetry, using contractions. The limit transitions of SO(2) and SU(2) gauge theories are considered