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

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

Presents the second part of the article (the first part was published in the previous issue this “Messenger”: 2010.- Vyp.11 – C.5-51) devoted to the stability and supercritical behavior of stractures and structures in unilateral restractions on the movement. The article, as stated in the preface, is a review. However, as set out in this part of the method of motion in the parameter stiffness of the elastic medium is published for the first time.

**III.**** Gryshchenko A.E., Kononov A.I., Mikhailova N.A.** **Study the scale effect by the birefringence method**

Studied by the birefrigency method are the properties of surface layers of some polymers of various molecular composition. It was shown that surface layers are characterized with orientational order of chain-like molecules in the films.the thicknesses of optically anisotropic surface layers are shown to be in the range of 10-400 micrometers. It was concluded that the odserved “scale” effect should be taken into account in the studies of thin films properties. Such the effect results from the fact that the surface layers properties differ significantly from those ones in bulk volume.

**IV.**** Yermolenko A.V.** **On the solution of inverse problems using the ****К****arman-Timoshenko-Naghdi type theory**

The aim of this paper is to prove the role of the Karman-Timoshenko-Naghdi type theory on the solution of inverse problems. Inverse problems are considered for cylindrical plates and round axis-symmetric paltes.

**V.**** Nikitenkov V.L., Kholopov A.A.** **The optimal parameters of an additive-split method (ASM)**

An equation x = b – Ax in a Banach space with continuous linear operator A is solving by so cold additive-split method when operator is split to some parts and an appropriate iteration procedure is used. The optimal parameters of splitting are those to extend mostly the spectral region of convergence for a self-conjugate operator.

**VI.**** Kluchnikov E.A.** **Web-application performance tuning**

The problems of performance of Web applications and solutions. Result of the research is to create a productive template library based on dynamic code generation.

**VII.**** Belyaeva N.A., Dovzhko E.S.** **Spherical product hardening with pressure in front of**

The stress state of a formed spherical product is considered from the view of the body continuously increases. The full stress tensor is given on the growing surface. The pressure from the liquid layer on the formed solid part is taken into account.

**VIII.**** Belyaeva N.A., Pryanishnikova E.A.** **Granularity in a nonisothermal extrusion composite material**

The structural mathematical model of non-isothermal extrusion of a composite material using a generalized model of Newton is presented. The novelty of the proposed model is the joint consideration of Reo-Dimamics, kinetics of structuring and temperature factor.

**IX.**** Mikhailovskii E.I., Holmogorov V.V., Gintner V.V.** **The longitudinal stability of a cylindrical shell at external and internal Winkler’s restrictions**

In this paper the problem of stability of a cylindrical shell, subjected to longitudinal compression, in the conditions of external and internal one–sided constraint restrictions Winkler’s type is considered. The local method of search of eigenvalues of positively homogeneous operator is applied. In the numerical study of the problem displacements are approximated by splines.

**X.**** Nikitenkov V.L., Tyufyakov A.V.** **Tetris-eliminator and the algorithm of successive refinement of backlash in the vector requirements**

To solve the integer problem of linear cutting proposed algorithms to obtain optimal solution either for the initial vector requirements, or if there is tighter tolerances. Discussed in the Ask the degeneracy of the obtained solutions and numerical results.

**XI.**** Pevnyi A.B., Duriagin A.M.** **The maximal redundancy of real harmonic frames**

The author uses idea from article of M. Püschel, J. Kovacevic and constructs real harmonic frames. They possess the maximal redundancy.

**XII.**** Pevnyi A.B., Istomina M.N., Maksimenko V.V.** **Construction of equiangular tight frames**

Investigate the question of the existence of equiangular tight frame. For the case m = 2n proposed algorithms equiangular tight frames.

**XIII.**** Pevnyi A.B., Kotelina N.O.** **Lower bound for cardinality of spherical design using linear programming**

The theorem of Delsarte for lower bound for cardinality of spherical design and its modification using only even polynomials are given. The corresponding grid problem of linear programming is considered and the results of calculations are given.