**I****.**** ****Vechtomov**** ****E****.****M****., ****Lubiagina**** ****E****.****N****.** **Lattices**** ****continuous function with values in unit segment**

In this paper we prove that the lattice of ideals (lattice of congruences) in lattice C(X,[0,1]) dtermines any compactum X. We study the lattice of all continuous [0,1]-value functions on topological spaces X. We proved that any compactum X determined by the lattice of ideals (the lattice of congruences) of a lattice C(X, **I**). We described the closed ideals of topological lattices C_{p}(X, **I**) with the topology of pointwise convergence. We have that a Tikhonov space X defined by the lattice C_{p}(X, **I**) as a consequence.

**II.**** Vechtomov E.M., Petrov A.A.** **Semirings with idempotent multiplication**

In this paper we study the structural properties of multiplicatively idempotent semitings. This class of semirings contains all Boolean rings and all kinds of distributive lattices with zero. Particular attention is paid to the finite multiplicatively idempotent semirings and twice idempotent semirings.

**III.**** Mekler A.A.** **Remarks on the correspondence between the topological invariants of spaces, Marcinkiewicz and Orlicz, I**

In this paper is presented a parallel approach to treating of some invariants of two kinds of classical Banach Function Spaces namely Marcinkiewcz and Orlicz spaces which are denoted M_{ψ} and L^{*}_{φ}, respectively. The exposition has the goal to state that there is such a way of mutually associating into couples (M_{ψ}, L^{*}_{ψ-}) (as well as (M_{φ+}, L^{*}_{φ})) that isomorphic properties of one of counterpart transfer into they of another one. Moreover by the way the isomorphic properties at ∞ allow to be reduced to ones at 0.

**IV.**** Mekler A.A.** **Remarks on the correspondence between the topological invariants of spaces, Marcinkiewicz and Orlicz, II**

In terms of behavior of limit densities of positive integer sequences an unique interpretation of some topological invariants of Orlicz, respectively, Marcinkiewicz functional spaces (in particular their coincidence) is given.

**V. ****Nikitenkov V.L., Kholopov A.A.** **The exact formulae for the optimal parameters of ASM**

An additive-split method (ASM) is used for solving an equation x=b-Ax in a Banach space with linear operator A. The exact formulae for the optimal parameters of ASM which extend mostly the real spectral interval of convergence are given.

**VI. ****Belyaeva N.A., Stepanova A.S.** **Flow of viscous structure fluid among two cylinders**

Presents the second part of the article (the first part was published in the [1]) devoted to the impact assessment transient viscosity on flow map of incompressible structure fluid among two cylinders with swirl. The state [1] analyzestationary axial flow of incompressible fluid with constant viscosity, it present numerical solution and checking findings with theretical research was presented in [2-4], where vortex deduced analytically by method solution determination in view of polynoms.

**VII.**** Yermolenko A.V.** **A variant of the refined theory of flat plates for the solution of contact problems**

Using the method of generalized reaction it was obtained the solution of contact problem for an axisymmetric circular plate and an absolutely rigid base. In addition the solution was obtained with using the Karman-Timoshenko-Naghdi type equations, which were given to the lower surface of the plate.

**VIII.**** Belyaeva N.A., Kamburov D.M.** **Computing System “Solid-phase extrusion”**

Computing system combines algorithms and software modules for calculating the parameters of viscoelastic flow of a compressible structured composite material in the solid-phase extrusion, developed at the Department of Mathematical Modelling and Cybernetics of Syktyvkar State University.

**IX. ****Belyaeva N.A., Khudoyeva E.E.** **Computing complex “Thermoviscoelastic models of the formation of axisymmetric products”**

The computing complex integrates series of programs developed within the mathematical models of the formation of axisymmetric products (cylinder, sphere) in the process of their obtaining in the parallel reactions of polymerization and crystallization. The article gives a description and operating principles of the complex.

**X. ****Vasiliev A.A., Nikitenkov V.L., Kimask K.V., Malkov S.V.**** ****Internet-version course of mathematics for nonmathematical specialities (with chapters from elementary mathematics)**

The Internet-version (current) course of mathematics for nonmathematical specialities (with chapters from elementary mathematics) is described.

**XI. ****Nikitenkov V.L, Bayborodina O.V., Poberii A.A.** **Generalization algorithm packing sliced rolls**

In this article considered generalization problem packing sliced rolls, that is consider in article [10]. Now we shall look at situation not only one diameter, but several diameters and problem of overspending would solved not by adding new formats packing paper (PP), it would solved by changing current formats by others, which would give us lesser overspending.

**XII. ****Vasiliev A.N., Gintner A.N.** **Two approaches to the solution of one classical problem of computational geometry**

In this work consider problem of finding the largest empty circle and the smallest covering circle. The implementation of algorithms for solving these problems by using methods of computational geometry, in particular of Delaunay triangulation and its dual Voronoi diagram is discribed. In the work also performed numerical experiments and graphically presents results of problems.