Abstract Properties of the Henstock–Kurzweil integral are considered under restrictions imposed on a gauge function. A proof of the assertion on relationships between the classes of integrable functions and the classes of gauge functions is presented for several particular cases.

Abstract Various Perron stability properties of a two-dimensional differential system are studied. It is proved that, generally speaking, the complete Perron instability does not imply the global Perron instability, which may seem at first glance. It turns out that it is possible to construct a counterexample even with an infinitely differentiable right-hand side and a zero matrix of the first approximation

Abstract Plane sets each of which is Chebyshev in some norm are described in the paper.

Abstract The paper studies one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient. The solvability of the problem under consideration is proved. In addition, it is established that the solution to the mixed problem under study is stable with respect to an additive perturbation of the coefficient, as well as with respect to the boundary conditions and the right-hand

Abstract Expansions in a finite frame are considered as a continuous linear redundant coding. It is shown that coding of an element from an \(N\)-dimensional space with a frame consisting of \((N+M)\) elements allows detecting up to \(M\) errors and correcting up to \(\left\lfloor\dfrac{M}{2}\right\rfloor\) errors. It is also pointed out that these results are sharp. The results are direct continuous

Abstract A two-dimensional diagonal system of ordinary differential equations is constructed. The system possesses the following properties: the solution of the Cauchy problem with computable initial condition is a computable function, the lower Lyapunov exponent is noncomputable, and the upper central exponent of the system does not coincide with the higher Lyapunov exponent and is noncomputable.

Abstract The paper is a review of the results of the eponymous cycle of author’s works marked by the I.I. Shuvalov I degree prize 2018 for scientific research and more recent studies. The families of three-dimensional simple polytopes defined by the condition of cyclic \(k\)-edge-connectivity are investigated. They include, for instance, flag polytopes and Pogorelov polytopes as well as related families

Abstract The local case of A. Fomenko conjecture on the possibility of modeling Liouville foliations by integrable billiards is discussed. An extended version of its statements on numerical invariants on the edge of the Fomenko–Zieschang invariant of the Liouville foliation is proved. We show the realization of the Liouville foliation with some combinations of numerical mark values on a fixed edge

Abstract The paper is focused on studying self-similar random processes with a parameter \(H\) with additional property of stationarity of first-order increments. A general characterization of such processes is described in terms of the correlation theory. The spectral density of increments of such processes is calculated. Based on different approaches to defining the fractional Brownian motion, one

Abstract We consider weighted directed acyclic graphs to whose edges nonnegative integers as weights are assigned. The complexity of a linear ordering of vertices is examined for these graphs in the order of topological sorting. An accurate estimate for the Shannon function of the complexity of the linear ordering problem for weighted directed acyclic graphs is obtained.

Abstract The canonical mapping of cohomology with compact supports via linear functionals on homology, generally speaking, is not surjective. The image of the mapping is described by linear functionals with compact supports. In this paper we prove the formula \(H_{c}^{k}(X;\mathbb{R})={\textrm{Hom}}_{c}(H_{k}^{c}(X;\mathbb{R}),\mathbb{R})\), where \(X\) is a countable simplicial complex with an additional

Abstract Recently, the authors introduced a concept of a pair of Zamfirescu-type multi-valued mappings between metric spaces and proved a theorem on the existence of coincidence points for such pairs of mappings. It was shown that this theorem is a generalization of the fixed point theorem for a multi-valued Zamfirescu mapping by Neammanee and Kaewkhao (2010). In this paper, the main result is the

Abstract The limiting case of the system of equations of two-dimensional gas dynamics in the presence of the Coriolis force, which can be obtained under the assumption of small pressure, is considered. With this approach, the equation for the velocity vector (transport equation) is decoupled from the system and can be solved separately. An explicit asymptotic representation of a smooth solution to

Abstract The paper deals with a system consisting of \(n\) identical elements and one repairing device. While one element is working, others stay in reserve. The distribution of working and repairing times of elements are supposed to be exponential. The asymptotic distribution of the system lifetime under the conditions of its high reliability is investigated.

Abstract Sufficient conditions for the asymptotic stability of solutions to a fourth-order linear homogeneous Volterra integro-differential equation are established in the case where any nonzero solution to the corresponding linear homogeneous differential equation of the fourth order is not asymptotically stable. An illustrative example is given.

Abstract The well-known problem of the absence of independent events in some discrete probability spaces (finite or countable) is considered. It is proposed to study such spaces using the minimum absolute value of the correlation coefficient of event indicators (in the case of a countable space, the infimum is taken). Examples of probability space with a prime number of equally possible outcomes, a

Abstract The paper describes equivalent conditions under which an arbitrary unary algebra has no proper subalgebras. An algorithm for checking the absence of subalgebras or for finding proper subalgebras and their generators in a given unary algebra whose carrier and signature are finite is proposed.

Abstract Neural automata being finite automata represented by a composition of threshold Boolean functions with time delay are considered in the paper. A simple criterion to test whether a given automaton with time delay can be represented by a neural automaton is proved.

Abstract A concept of a Zamfirescu type pair of multi-valued mappings between metric spaces is introduced. A coincidence existence theorem is proved for such pairs of mappings. It is shown that the result is a generalization of the main result of the recent joint work by K. Neammanee and A. Kaevkhao, in which the concept of a multi-valued Zamfirescu mapping was introduced and the fixed point existence

Abstract For a family of non-autonomous dynamical systems continuously depending on a parameter, the set of lower semicontinuous points and the set of upper semicontinuous points of the \(\varepsilon\)-capacity of its systems considered a function of the parameter are described. For the set of upper semicontinuous points, this description is complete if the parameter belongs to a complete metric separable

Abstract Estimates of multiple trigonometric sums similar to the modern estimate of the zeta-sum are obtained. This allows estimating trigonometric sums twisted with the multivariate divisor function and corresponding sums with primes.

Abstract Some algorithms for computing transitive closure of a graph and matrix multiplication in the Boolean semiring and in the rings of residues are compared. The bounds for the size and depth of the corresponding Boolean circuits are given.

Abstract It is shown that Liouville foliations of the family of non-Euclidean analogs of Kovalevskaya integrable system on a pencil of Lie algebras have both compact and noncompact fibers. There exists a bifurcation of their compact common level surface into a noncompact one that has a noncompact singular fiber. In particular, this is true for the non-Euclidean \(e(2,1)\)-analog of the Kovalevskaya

Abstract We obtain a new formulation of a criterion for the minimal logarithmic growth rate for an arbitrary finite set with a given set of operations. It turns out that a finite set with operations has the minimal logarithmic growth rate if and only if the set of operations is not entirely contained in any of the precomplete (maximal) classes other than the classes preserving subsets and the classes

Abstract Let \(R\) be a linearly ordered noncommutative ring with \(1/2\) and let \(G_{n}(R)\) be the subsemigroup of \(\mathrm{GL}_{n}(R)\) consisting of all matrices with nonnegative coefficients. In the paper, endomorphisms of this semigroup are described for \(n\geqslant 3\).

Abstract A geometric characterization of Chebyshev sets and suns in three-dimensional polyhedral spaces with cylindrical norm is presented. A number of new properties of Chebyshev sets, suns, sets with continuous metric projection in three-dimensional spaces is put forward. The new recent fact established by A. R. Alimov and E. V. Shchepin that suns and Chebyshev sets are convex in tangent directions

Abstract The relations ‘‘between’’, ‘‘cycle’’, and ‘‘separation’’ were defined through the relation of linear order in the classical paper of Edward V. Huntington. In the current paper, the criteria for preserving these relations under injective mappings are obtained.

Abstract An approximate method for solving the Cauchy problem for nonlinear first-order ordinary differential equations is considered. The method is based on using the shifted Chebyshev series and a Markov quadrature formula. Some approaches are given to estimate the error of an approximate solution expressed by a partial sum of a certain order series. The error is estimated using the second approximation

Abstract Sums of double sine and cosine series with multiply monotone coefficients are studied. Sufficient conditions for such sums to belong to Orlich’s weighted classes are obtained.

Abstract The paper provides a criterion for substitutivity of symmetric Sturmian words infinite on both sides and its proof, and a theorem on the substitutivity of factor dynamics of circle rotations.

Abstract The paper is focused on decomposition of Boolean functions in the form \(f_{1}\circ\ldots\circ f_{m}\), where \(\circ\) is a commutative associative operation and \(f_{1},\ldots,f_{m}\) are Boolean functions with fewer arguments. For each commutative associative operation, we determine the necessary and sufficient conditions of the absence of such a decomposition and find the related complexity

Abstract The ruin probability of an insurance company is studied under two different risk models with stochastic premiums. We obtain upper bounds for the probability of ruin provided that either the aggregate claims process or the aggregate premium process is constructed using the renewal process.

Abstract The article considers the spectrum of one-dimensional natural vibrations of a layered medium with a periodic structure consisting of an isotropic elastic material and a viscous incompressible fluid. It is established that the spectrum points are the roots of transcendental equations. In order to solve these equations numerically for multi-layered media, the roots of quadratic equations are

Abstract We consider a class of integrable Hamiltonian systems with two degrees of freedom, i.e., billiard books, which are a generalization of billiard in domains bounded by arcs of confocal quadrics. When studying billiard, first of all, the question arises about the topology of the phase space and the isoenergetic manifold. We prove that the phase space and the isoenergetic manifold in the case

Abstract The mean field games equations, consisting of the coupled Kolmogorov–Fokker–Planck and Hamilton–Jacobi–Bellman equations, are studied. The equations are supplemented with initial and terminal conditions. It is shown that for a certain specific choice of data this problem can be reduced to solving a quadratically nonlinear ODE system. This situation occurs naturally in economic applications

Abstract A local version of the Fomenko conjecture on the possibility of the realization of the Liouville foliation with the Fomenko–Zieschang arbitrary topological invariant, which is a graph with numerical labels, by integrable billiards is discussed. It is proved that Liouville foliation with an arbitrary value of the integer mark which defines the Euler class of the Seifert manifold is algorithmically

Abstract Orthonormal bases of consecutive shifts of one polynomial are constructed in some spaces of multidimensional trigonometric polynomials. The methods for constructing Parseval frames of consecutive translations of a polynomial in wider classes of multidimensional trigonometric polynomials are proposed.

Abstract The problem of rolling the balanced dynamically nonsymmetric ball with a rotor on a rough horizontal plane is considered. Topological types of isoenergy surfaces of this integrable Hamiltonian system are found. Curves are constructed on the plane of the parameters \(\mathbb{R}^{2}(h,c)\) separating it into regions so that all points of the same region correspond to isoenergy surfaces with

Abstract A sequence of recursively constructed matrices which are dyadic analogues of Hilbert matrices is considered. The operator norm of these matrices in a Euclidean space is studied. Estimates of norms of matrices optimal in order and their lower triangular parts are obtained.

Abstract Planar billiards in nonconvex areas bounded by segments of confocal quadrics are studied. The topology of 2-dimensional fibers of Fomenko’s atoms is studied and a constructing algorithm is presented.

Abstract A new simpler proof of the asymptotic \(C(n)\sim\sqrt{2}\cdot 2^{n/2}\) of the Shannon function of the circuit complexity over the basis of multi-input generalized conjunctions is obtained.

Abstract The concept of a strongly homogeneous \(G\)-space is introduced. The conditions of equivalence between continuous homogeneity and strong homogeneity are obtained. The topological structure of an acting group of strongly homogeneous \(G\)-space is established.

Abstract In this paper three criteria for the height of an atom in terms of its \(f\)-graph are established. The obstacles to the oriented embeddability of the \(f\)-graph into the plane are found. The combinatorial properties of labeled oriented cycles, which are a generalization of chord diagrams, are investigated.

The problem of existence of periodic solutions to a quasilinear equation of forced oscillations of an I-beam whose one end is fixed and the second one is pivotally supported is studied. Properties of the differential operator are given and the theorem on the existence of a countable number of solutions is proved in the case the nonlinear term has a power growth.

Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. A generalization of an analogue of Hardy-Littlewood test and its consequences, which were earlier obtained in the case of bounded sequence {pk} defining the system, are proved.

Equivariant analogues of the Morse lemma with parameters and the theorem on the normal form of a semi-quasi-homogeneous function are proved.

An infinitely generated functional system of automata with a superposition operation contains both pre-complete classes and classes not embeddable in any pre-complete one. The paper describes a continual set of classes expanding to a pre-complete one.

A criterion and a sufficient condition of connectedness of Stone-Cech remainder of a locally compact space are obtained. Some examples of locally compact spaces with connected Stone-Cech remainder are given.

A method of searching for zeros of cone functionals is proposed and issues of its stability are considered.

The paper is focused on the study of the spectrum of the symbol of the equation describing the motion of a viscoelastic plate in a flow of fluid or gas. The lower bound of critical flow rate at which the motion becomes unstable is obtained using methods of operator analysis.

The problem of forming multi-colour images by a screen consisting of cellular automata is considered. The process of image formation is carried out using control inputs located on the edges of the screen. An elementary cellular automaton is called universal if it can be used to form an arbitrary image. The minimal number of states of an elementary cellular automaton of a universal screen is found.

Various variants of the concept of the V-realizability for predicate formulas are defined where indices of functions in the set V are used for interpreting the implication and the universal quantifier. It is proved that Markov’s principle is weakly V-realizable, not uniformly V-realizable, and uniformly V-realizable in any V-enumerable domain M ⊆ ℕ.

The Fomenko-Zieschang invariant of an interesting case of an integrable billiard book is calculated and it is shown that such a book models dynamics of the Goryachev-Chaplygin integrable case on a constant-energy surface.

The sharpness property of justification models is essential for formal analysis of epistemic scenarios like Russell’s prime minister example. The problem to axiomatize this property in the prepositional justification language was left open. We propose a solution and provide complete axiomatizations for the class of all sharp basic justification models and also for the class of all sharp justification

We prove that the partially ordered set Lk + 1k of all closed classes of (k + 1)-valued logic that can be homomorphically mapped onto k-valued logic has the cardinality of continuum.

Relations between the best m-term and best approximations in the spaces lp are studied for complex-valued sequences whose absolute values satisfy monotonicity-type conditions.

The ℝ-factorizability of an equivariant image of an ℝ-factorizable G-space with a d-open action of an ω-narrow P-group is proved. It is shown that the ℝ-factorizability, m-factorizability, and M-factorizability of G-spaces are preserved by d-open equivariant mappings. It is also proved that the ℝ-factorizability of topological groups is preserved under d-open homomorphisms.

Interrelation between partial moduli of smoothness of positive order considered in metrics and Lp1∞, L∞p2, and Lp1p2 is studied.

Bivariate maxima of particle scores in immortal branching processes with continuous time are studied. The limit distribution for a maximum of two scores at two points in time is found. The limit intensities of jumps up and down for the maximum of both scores or at least one score are obtained. In the case of independent scores, mean number of joint jumps up and down for all time are calculated. Results

Asymptotic formulas are obtained in the paper for x → +∞ for the fundamental system of solutions to the equation$$l(y): = {i^{2n + 1}}\{ {(q{y^{(n + 1)}})^{(n)}} + {(q{y^{(n)}})^{(n + 1)}}\} + py = \lambda y,\;\;\;\;\;\;x \in I: = [1, + \infty ),$$where λ is a complex parameter. It is assumed that q is a positive continuously differentiable function, p has the form p = σ(k), 0 ≤ k ≤ n, where σ( is