**I.**** Antonova N.A.** **Dynamics in pulse-frequency-modulated control systems**

Conditions are obtained for existence of mT-periodic modes (m = 1, 2, 3) in one dimensional control systems employing pulse-frequency modulation of the first and second kinds.

**II.**** Bazhenov I.I.** **The property of nonatomicity for set families and vector measures**

We introduce the new concept of atom for family of subsets of some set. This notion coincides with the notion of atom of vector measure if the family in question contains only sets of zero measure. Sufficient conditions of nonatomicity of family of sets are given for one special case. We also establish sufficient conditions of nonatomicity of the vector measure n(E) = φ(m(E)) constructed by means of linear and continuous operator φ and vector measure m with values in topological vector space.

**III.**** Veksler A.I., Koldunov A.V.** **On the normed lattice and its normed completion**

Here (negative) answers on two problems conserning the relations between properties of a normed lattice and its normed completion are presented.

**IV.**** Vorobyova E.V.** **Some ergodic properties of the homogeneous Markov chain with the continuous parameter**

We prove for any Markov chain with finite space of states that the final probabilities vector is orthogonal to the columns of generator. And in the case of any discrete space of states we find an explicit formula for final probabilities in terms of the generator’s resolvent.

**V.**** Zvonilov V.I.** **Rigid Isotopies of Trinomial Curves with the Maximal Number of Ovals**

Let l be the number of ovals of nonsingular real trinomial curve у^{n} + b(x)у + w(x) = 0. In this paper the sharp upper bound for l is found for any n. The rigid isotopy is understood as a path in the space of nonsingular real trinomial curves with n fixed. The rigid isotopy classification of such curves with the maximal l is given. In particular case n=3 the rigid isotopy classification of trigonal M-curves is obtained.

**VI.**** Golovach P.A.** **Distance constrained labelings of trees**

An assignment of nonnegative integers to the vertices of a graph G is L(p_{1}, p_{2}, … , p_{k}) – labeling (or coloring) if for every two vertices at distance at most i <= k, the difference of the integers (labels) assigned to them is at least p_{i}. An interest to such labelings is motivated by their usage in models of telecommunication networks. We prove that the existence problem of L(p, 1, 1) – labeling with labels, that are at most λ, is NP-complete for trees.

**VII.**** Yermolenko A.V.** **The calculation of round plates with refined theories**

The Karman-Timoshenko-Naghdi type equations are used for the calculation of round plates with rigid boundary. The problem is solved not using additional condition about transversal shears on boudary.

**VIII.**** Zheludev V.A., Pevnyi А.В.** **Discrete periodic frames**

We construct the filter bank of perfect reconstruction for the discrete N-periodic signals. This bank generates the wavelet tight frames in the spaces C^{N} and R^{N}.

**IX.**** Malozemov V.N., Pevnyi А.В., Selyaninova N.A.** **Primal lifting scheme**

We present the analysis of the primal lifting scheme for the constructing of the wavelet decomposition of the discrete periodic signals. A description of the set of all control functions β_{ν}(k) is given.

**X.**** Mironov V.V.** **The account of transversal shears in a problem about a bend of the cylindrical panel**

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 momemts 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.

**XI.**** Mikhailovskii E.I.** **The classical linear theory of shells**

The equations and the boundary values of the modern classical linear theory are consecutively obtained. On equations’ deduction the Novozhilov-Finkel’shtein criterion was used to estimate the Kirchhoff-Love hypotheses. The final variant of shells’ theory includes the deformation boundary values, which were obtained by K.F. Chernykh for one-related middle surface and were generalized by the author of article for multirelated middle surface. It is shown that the compatibility conditions can be obtained directly from the equilibrium equations of shells’ theory; initially condition was obtained by A.L. Gol’denweiser from the Gauss-Petersson-Kodacci equations for deformed middle surface. The author’s operation form is used for recording the general equations of the linear shells’ theory.

**XII.**** Nikitenkov V.L.** **On the integer-valued solving of the linear cutting problem**

It was proved that optimal value of the target function for the integer-valued problem of linear cutting just slightly differs from the corresponding value for the linear cutting problem. On this basis it was offered the effective complex algorithm of integer-valued problem solution.

**XIII.**** Ezovskih V.E.** **Color sampling algorithms**

Three algorithms of color sampling suitable for color conversion are considered. Some practical features of realization are briefly discussed.

**XIV.**** Kotyrlo E.S.** **Methods of labor market demand prediction in professional skills structure**

The problem of labor demand prediction in professional skills structure is one of the main problems that impact on the labor market equilibrium and human capital efficiency. In this article prediction methods and their efficiency to using in labor market are analyzed; an analytic model of labor demand prediction in professional skills structure is constructed; a version of statistical survey execution is suggested.

**XV.**** Mironov V.V., Kuznetsova N.V.** **The task about axis-symmetrical eigen-oscillations of round rigidly fixed plates**

In this paper the task about axis-symmetrical eigen-oscillation of round rigidly fixed plates is considiered. The analytical solution is given.

**XVI.**** Nikitenkov V.L., Sakovnich D.J.** **Realization of complex algorithm for integer-valued problem of linear cutting**

Complex method for solving of integer-valued problem of linear cutting are considered. The results of testing on enterprize are describe.

**XVII.**** Nikitenkov V.L., Yasinsky V.I.** **Web-services of complex algorithm for integer-valued problem of linear cutting**

The problems of working over a network and the Internet, the superiority of Web-services over the other server-applications, a short description of the applied Web-service and the examples of Web-service query are discussed.

**XVIII.**** Pevnyi А.В., Istomina M.N.** **Mercedes-Benz frame in n-dimensional space**

We construct an equal-norm tight frame in Rn consisting of n+1 vectors. The angles between any different vectors are equal π/2 + arcsin(1/n).

**XIX.**** Poroshkin A.G., Gabova M.N., Grelya E.N.** **On the Arzela – Borel theorem.**

Let X be a topological space, (Y, V) — uniform space and (f_{α}) be a sequence or directedness of functions f_{α} : X —> Y. In this paper autors prove the generalization of Arzela — Borel theorem: when f_{α} ϵ C(X) ∀α and f_{α}(x) —> f(x) ∀x ϵ X, then f ϵ C(X) if and only if f_{α} converges to f on X quasi-uniformly.

**XX.**** Tarasov V.N., Pavlova L.A.** **The proof of geometric theorems by means of computer algebra**

Some geometric theorems can be stated in coordinate form as polynomials in algebra and can be proved by algorithmic methods. In article the theorems of Pascal and Pappe Alexandrinian are prooved by means of computer algebra. Also some properties of Torricellian point for arbitrary tetrahedron are stated.