**I.**** Balakin S.V.** **Runs characteristics in a ternary Marcov Chain**

A ternary Markov chain is considered. There are functionals concerned with a number of events and a number of runs. Probability generating functions for joint distributions of this functionals are obtained. Precise formulas for expectations, variances and covariations are founded.

**II.**** Vechtomov E.M., Chuprakov D.V.** **Congruences on semirings of continious functions and F-spaces**

The congruences of semirings of non-negative continuous functions on topological space are investigated. In terms such congruences new algebraic characterizations of F-spaces and P-spaces are received.

**III.**** Mekler A.A.** **On positive integer characteriyation of regular variyng quasi-concave modulars**

The initiated in [1] study of the correspondence between quasi-concave modulars and sequences of positive integers is continued. In the presented paper are examenated especially regularly variying quasi-concave modulars. It is stated in Theorems 9, that a sequence of positive integers corresponds to a fast variyng quasi-concave modular (that means the case of regularity index α=0) iff it is equivalent to a integer sequence which tends to +∞. In Theorem 8 is proved that the sequence of positive integers corresponds to a slow variyng modular (the case of regularity index α=1) iff it is equivalent to a sequence of the form 211•••1211•••121••• •••••• where the lengths of blocks of units tends to +∞. In Theorem 5 the case of intermediate value of regularity index α: 0<α<1 is investigated.

**IV.**** Savelev L.J.** **Extension of a measure up to integral**

In this paper the task about a bend of cylindrical panel under effect of normal load is considiered. The normal load are distributed on field, simular to middle surface of a panel. The bend of panel on register of transversal shears by S.P.Timoshenko’s model is described. The mechanism of dependence of a moments for transversal shears is confirmed – the graphics of moments for change of curvature of middle surface and for change of transversal shears are be in anti-phases in fields of a maximal absolute values.

**V.**** Belyaeva N.A.** **The structural models of deformation processes**

Mathematical models of flow and deformation processes of materials with evolutionarizating structure are presented. The problems spread to wide sphere of structure-sensitive objects – from powder systems to polymer materials and composites. This models allow to define change of deformation, temperature and structure characteristics of varried systems in the various processing-hardening, non-Newtonian flow, solid-state extrusion.

**VI.**** Nikitenkov V.L.** **Basic property of the optimal integer-valued solving of the linear cutting problem**

It was proved that basic solution of the some modification linear cutting problem is optimal integer-valued solving of the integer cutting problem.

**VII.**** Sakovnich D.Y.** **Singularity in the format cutting problem**

In scope of format cutting problem the problem of minimization winder adjustments is considered. It was offered the method for getting the most singular solution if the problem.

**VIII.**** Kluchnikov E.A.** **SOA data store and search system**

The author consider SOA data store and search system written in Java. SOA approach makes such systems scalable and easy to integrate as basis of enterprise infrastructure. Java technology makes it easier to use the full power of modern servers.

**IX.**** Simakov A.V.**** ****Parallel compression of huge images**

In this paper we describe an efficient algorithm for parallel compression of huge images. The algorithm is based on wavelet transform. The article is focused on practical implementation and evaluation of this compression method. As a result, all described features are implemented in software library written in C language. This library and compression program is freely available through the Internet and distributed with full source code under the terms of Open Source GNU GPL license.

**X.**** Poroshkin A.G., Popova L.A.** **Remark about the outer measures geneated by measures**

It is proved that outer measures generated by measures in sense of Halmos, Vuklikh, Poroshkin are lower continuous, however the outer measure of Lebesque in R is not continuous from above and not exhaustive.

**XI.**** Tarasov V.N., Andryukova V.Yu.** **On stability and supercritical behavior of a spherical shell**

The problem of the spherical shell experiencing external normal pressure is considered. A precise formula is used for the calculation of the work of external forces. In the work a variational approach is applied. Cubic splines are used for the finite-dimensional approximation of displacements. The influence of nonlinear terms on the amount of the critical force is investigated.

**XII.**** Tulubenskaya E.V., Kargin R.V.** **The stability of the longitudinally compressed shank with unconstant rigidity at the border of two Winkler’s ambiences**

The stability of the longitudinally compressed shank with unconstant rigidity at the border of two Winkler’s ambiences is investigated. The algorithm is based on the local search variants.

**XIII.**** Jakovlev V.D.** **On one way of introducing integrals in the high school mathematics**