On antiperiodic boundary value problem for a semilinear differential inclusion of a fractional order q. The investigation of control systems with nonlinear units forms a complicated and very important part of contemporary mathematical control theory and harmonic analysis, which has numerous applications and attracts the attention of a number of researchers around the world.

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A linear parabolic equation with nonlocal boundary conditions of the BitsadzeSamarsky type is considered. The existence and uniqueness theorem of the periodic solution is proved.

**Keywords**: nonlocal problem, parabolic equation, monotone operator.

A model of motion of a dynamic system with the condition that the trajectory passes through

arbitrarily specified points at arbitrarily specified times is constructed. The simulated motion

occurs at the expense of the input vector-function, calculated for the first time by the method of

indefinite coefficients. The proposed method consists in the formation of the vector function of

the trajectory of the system and the input vector function in the form of linear combinations of

Abstract. The article consists of two parts. The first part is devoted to general questions that are related to uncertainty: causes and sources of uncertainties appearance, classification of uncertainties in economic systems and approach to their assessment. In the second part the concept of maximin, based on the principle of guaranteed result (Wald’s principle) is considered. In this case, maximin is interpreted from viewpoint of two-level hierarchical game.

Oligopoly is a basic concept in the theory of competition. This structure is the central object of research in the economics of markets. There are many mathematical models of the market that are formalized in the form of an oligopoly in economic theory.

Formalizing routing problems of many traveling salesman (\(mTSP\)) in complex networks leads to $ NP $-complete pseudobulous conditional optimization problems. The subclasses of polynomially solvable problems are distinguished, for which the elements of the distance matrix satisfy the triangle inequality and other special representations of the original data. The polynomially solvable assignment problem can be used to determine the required number of salesmen and to construct their routes.

The main aim of the work is to study the numerical solutions of the focusing nonlinear Schrodinger (NLS) equation.

The article is devoted to the current and actively developing direction of

development of the analysis of smooth measures on smooth infinite-dimensional manifolds. The

importance of this direction is dictated by the vast area of its applications, which include infinite-

dimensional analysis and a number of sections of mathematical physics of systems with an infinite

We consider algebraic bundles over a two-dimensional compact oriented

connected manifold. In 1961 J. Fell, J. Tomiyama, M. Takesaki showed that every n-homogeneous

C^{∗}-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic

bundle. By using this realization we prove in the work that every 3-homogeneous C^{∗}-algebra over

two-dimensional compact oriented connected manifold can be generated by three idempotents.

Such algebra can not be generated by two idempotents.

In the article we study properties of some sequences of numbers (so-called “hyper-

sums” and “hyper-products”) which one can construct on the basis of given numerical sequence.

We consider such sequences for arithmetic, geometric progressions and Fibonacci numbers. We

obtain explicit formulas for its calculation and study problems of asymptotic behavior. As a

main result, we prove new asymptotic formula for hyper-products of arithmetic progression that

generalized Stirling’s formula and asymptotic of super-factorial.

Previously, boundary value problems, spectral and initial boundary value problems were investigated based on the symmetric sesquilinear form $(\\eta, u)_{H^{1}(\\Omega)}=\\Phi_{0}(\\eta, u)$.

The common approach to construction of \\textsf{J}-selfadjoint dilation for linear

operator with nonempty regular point set is considered in this article.

This paper describes a method for constructing periodic solutions for special-type nonlinear equations with periodic coefficients.

The basis of this method is to represent the desired solution in a nonstandard trigonometric series as a power series in $\\sin{t}$.

The coefficients of such a series are calculated in a recursive way.

Such a representation is permissible not only for continuous periodic solutions, but also for solutions with singularities.

The article contains an overview of the results on the application of majority logic of combinational logic schemes.

In this first part, the theoretical foundations of majority algebra, its axiomatization and primitive functions, and the use of majority logic in solving practical problems of circuit synthesis are considered.

%Some physical implementations of majority elements are indicated.

%The first (2007--2015) majority logic immunization algorithms are considered and their results are compared.

The *Strong Coalitional Equilibrium* (SCE), is introduced for normal form games under uncertainty. This concept is based on the synthesis of the notions of individual rationality, collective rationality in normal form games without side payments, and a proposed coalitional rationality. For presentation simplicity, SCE is presented for 4-person games under uncertainty. Sufficient conditions for the existence of SCE in pure strategies are established via the saddle point of the Germeir's convolution function.

It is well known that for dimensions 4 and greater there are topological manifolds admitting no smooth structure. Therefore, dynamical systems as well as functions on such manifolds may only be considered as topological and continuous, respectively. Nevertheless, these systems and functions have the same properties as the smooth ones and they are closely related to the topology of the ambient manifold.

We investigate a problem on small motions of a body partially filled with an

ideal fluid under the action of an elastic and damping forces. The initial

boundary value problem is reduced to the Cauchy problem for a first-order

differential operator equation in a Hilbert space. Properties of the resulting

operator matrices, which are coefficients of the equation, are studied.

Theorems on strong solvability of the Cauchy problem and the initial boundary

value problem are proven.

The article contains an overview of the results on the application of the

majority logic of combinational logic circuits. In the first part, the

theoretical foundations of the questions of majority algebra and some

algorithms for solving practical problems of synthesis of circuits are

considered. This second part describes algorithms based on majority-inverter

graphs MIG and majority primitives combination MPC.

Memetics of social networks is a popular section of scientific research. The article deals with the problems of meme distribution, mathematical modeling of distribution processes, and tools for socio-political research. It is shown that the life cycle of a stream of Internet memes and a separate meme has its own specifics and ecology. The task of identifying the real stage of the life cycle (LC) is much more difficult than for the economic LC of the enterprise.

The current state of IT development allows us to talk about the formation of a new type of society, not only informational, but also digital. Virtual communications plays important role in its development. The network of these communications creates a new space of being -- virtual. When we talk about virtual space, we primarily mean Internet. Internet memes are one of the important phenomena that embody the features of information and virtual processes of the XXI century.

In article coefficient criteria of the stability of coalitional structure in\ndifferential linear-quadratic positional game of 4 persons are established.

Following the approach adopted in the article, it is possible to obtain\ncoefficient criteria of the stability of coalitional structures both in games\nwith a large number of players and for other coalitional structures.

A method of constructing a transport network using a satellite image and a set of paths as input data is considered. Software has been developed for building a transport network model based on the specified input data. Examples of the program's operation on various sections of transport networks are considered. The advantages and disadvantages of the developed method are described.

This survey focuses on the following problem: it is necessary, observing the behaviour of the object, automatically figure out how to improve (optimize) the quality of his functioning and to identify constraints to the improvement of this quality. In other words, build the objective function (or set of objective functions in multiobjective case) and constraints - i.e. the mathematical model of optimization - by mean machine learning.

In this paper, some properties of basis invariants of the unitary group $W (J_3(4))$ of order 336 generated by reflections in 3-dimensional unitary space are studied. There is developed a new method of finding in explicit form the basic invariants of group $W(J_3(4))$. This method is based on the following property of group $W(J_3(4))$ – group $W(J_3(4))$ contains group $B_3$ of symmetries of the cube, and Pogorelov polynomials of the form $$

J_{m_i}(G) = \sum\limits_{\sigma \in G}(\overrightarrow{x}, \sigma\ \overrightarrow{s})^{m_i},