Abstract: The problem of implicit expressibility in the three-valued logic P3 is considered. A set of implicitly maximal classes preserving two-element subsets is described. PubDate: 2018-11-01

Abstract: Properties of the Hausdorff mapping H taking each compact metric space to the space of its non-empty closed subsets endowed with the Hausdorff metric are studied. It is shown that this mapping is non-stretching (i.e., a Lipschitz mapping whose Lipschitz constant equals 1). Several examples of classes of metric spaces such that the distances between them are preserved by the mapping H are given. The distance between any connected metric space with a finite diameter and any simplex with a greater diameter is calculated. Some properties of the Hausdorff mapping are discussed, which may be useful to understand whether the mapping H is isometric or not. PubDate: 2018-11-01

Abstract: The space M of all nonempty compact metric spaces considered up to an isometry and endowed with the Gromov–Hausdorff distance is studied. It is shown that each ball in M centered at a single-point space is convex in the weak sense, i.e., any two points of the ball can be connected by a shortest curve lying inside the ball, but it is not convex in the strong sense, i.e., not every shortest curve connecting some points of the ball lies inside the ball. It is also shown that each ball of sufficiently small radius centered at a generic metric space is convex in the weak sense. PubDate: 2018-11-01

Abstract: Sufficient conditions for the uniqueness of solutions to first and third kind Volterra integral equations in the space of functions continuous on the semiaxis are established in the case when the kernels of these equations can be alternating on the diagonal. Illustrative examples are given. PubDate: 2018-11-01

Abstract: —We prove the criterion of existence of a Parseval frame of a priori given dimension in the space of trigonometric polynomials of the form TQ(x) = \({\sum\limits_{k \in Q} {cke} ^{ikx}}\) consisting of serial shifts of a polynomial (ck ∈ C, where Q is a finite set of integer numbers). The form of a frame of serial shifts of one function is also indicated. The result is applied to some particular cases. PubDate: 2018-11-01

Abstract: Ul’yanov’s inequality on the connection between moduli of continuity in different metrics is well known for functions of one variable. Functions of two variables are analyzed in this paper. The sharp Ul’yanov’s inequality for full moduli of smoothness of positive order in different mixed metrics is proved. PubDate: 2018-11-01

Abstract: We study a fourth-order differential operator with a sign-alternating weight function with separated boundary conditions. For large values of the spectral parameter the asymptotics of the solutions to the corresponding differential equations is derived. The study of boundary conditions makes it possible to obtain an equation for eigenvalues of the considered differential operator. The indicator diagram of this equation is studied. The asymptotics of eigenvalues in various sectors of the indicator diagram is obtained. PubDate: 2018-11-01

Abstract: In this paper we compare the speed and quality of CUDA implementation for a new edge detection algorithm based on geometrical coding with the CUDA implementation of Canny algorithm commonly used in OpenCV library. The comparison shows that the new approach can really compete with the Canny operator and in some cases even overcomes it in speed and quality. Examples of geometrical coding edge detection in different situations are presented. PubDate: 2018-11-01

Abstract: It is shown that a majority Boolean function of n variables can be computed by a depth–2 circuit consisting of majority gates with fan–in n–2 (for each оdd n greater than 5). PubDate: 2018-09-01

Abstract: The exponent of convergence of a singular series in the asymptotic formula for the number of solutions to a multidimensional problem is obtained. PubDate: 2018-09-01

Abstract: Non–empty compact subsets of the Euclidean space located optimally (i.e., the Hausdorff distance between them cannot be decreased) are studied. It is shown that if one of them is a single point, then it is located at the Chebyshev center of the other one. Many other particular cases are considered too. As an application, it is proved that each three–point metric space cari be isometrically embedded into the orbit space of the group of proper motions acting on the compact subsets of the Euclidean space. In addition, it is proved that for each pair of optimally located compact subsets all intermediate compact sets in the sense of Hausdorff metric are also intermediate in the sense of Euclidean Gromov–Hausdorff metric. PubDate: 2018-09-01

Abstract: A closure under composition operation and weak version of inversion operation is considered on the set of functions of k–valued logic. The cardinality of the set of all such closed classes is calculated. PubDate: 2018-09-01

Abstract: The paper considers the construction of formulas describing relations between entities from a Russian sentence. We describe rules which help constructing such formulas from a syntax graph. PubDate: 2018-09-01

Abstract: Singular points that cannot be removed by small deformations of 1–forms and invariant with respect to the action of a cyclic group of order 3 are classified. It is proved that for ℤ3–invariant 1–forms the equivariant index of a singular point, as an element of the representation ring of the group, coincides with the class of the representation on the space of germs of forms of highest order factored by the subspace of forms divisible by the given 1–form. PubDate: 2018-09-01

Abstract: It was proved that the complexity of square root computation in the Galois field GF(3s), s = 2kr, is equal to O(M(2k)M(r)k + M(r) log2r) + 2kkr1+o(1), where M (n) is the complexity of multiplication of polynomials of degree n over fields of characteristics 3. The complexity of multiplication and division in the field GF(3s) is equal to O(M(2k)M(r)) and O(M(2k)M(r)) + r1+o(1), respectively. If the basis in the field GF(3r) is determined by an irreducible binomial over GF(3) or is an optimal normal basis, then the summands 2kkr1+o(1) and r1+o(1) can be omitted. For M(n) one may take n log2nψ(n) where ψ(n) grows slower than any iteration of the logarithm. If k grow and r is fixed, than all the estimates presented here have the form Or (M (s) log 2s) = s (log 2s)2ψ(s). PubDate: 2018-09-01

Abstract: We prove that the lower topological entropy considered as a function on the space of sequences of continuous self–maps of a metric compact space belongs to the second Baire class and the upper one belongs to the fourth Baire class. PubDate: 2018-09-01

Abstract: The asymptotic behavior of stream intensity extreme values in ON/OFF models of teletraffic under permanent and periodic measurements is studied. It is assumed that the intensity of each source has a distribution with a heavy (regularly varying) tail. A joint limiting distribution for maxima with a common linear normalization, marginal distributions, and the distribution of the maxima ratio are obtained. The extremal index for a sequence of periodic measurements is calculated. PubDate: 2018-07-01

Abstract: An optimal control problem is constructed so that its control runs over an everywhere dense winding of a k-dimensional torus for arbitrary natural k ≤ 249 998 919 given in advance. The construction is based on Galois theory and the Wolstenholme primes distribution. PubDate: 2018-07-01

Abstract: A conservative difference scheme with linear dependence of the pressure on the density of gas is proposed for gas dynamics equations. The scheme allows us to simulate 1-D flows inside a cylindrical domain with time-variable cross-sections and guarantees the positive sign of the density function. PubDate: 2018-07-01