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

The paper contains definitions of normal, perfectly normal, collectionwise normal, hereditarily normal, paranormal mappings, and theorems on preservation of these properties under closed map-morphisms.

In this paper we consider the Sturm-Liouville problem in general form with Dirichlet boundary conditions under the minimal smoothness assumptions for the coefficients. We obtain the asymptotics formulas for eigenvalues and eigenfunctions of this problem. Under the assumption that the Lp-norm of eigenfunctions is equal to 1, we get uniform estimates of the Chebyshev norm.

The problem of realization of Boolean functions by initial Boolean automata with constant states and n inputs is considered. Initial Boolean automaton with constant states and n inputs is an initial automaton with output such that in all states the output functions are n-ary constant Boolean functions 0 or 1. An example of an initial Boolean automaton with the minimum number of constant states and

The connections between the set of geometric medians for a four-element set and the set of Steiner points for its three-element subsets in L1-predual spaces are studied. A Lipschitz selection for the mapping from quadruples of continuous functions on a Hausdorff compact space to the set of their geometric medians is presented.

A stationary AR(p) model is considered. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parametric estimates, an analog of the empirical distribution function is defined and tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. The asymptotic power of these tests under local

One-dimensional systems of Carleman and Godunov-Sultangazin are studied for two and three groups of particles, respectively. These systems are a special case of the discrete Boltzmann kinetic equation. Theorems on existence of global solution to these systems for perturbations in the weighted Sobolev space are presented. Thus, an exponential stabilization to the equilibrium state is obtained.

The issues related to applications of functional integrals to evolution equations are studied. In particular, this is the problem of representation of solutions to the Cauchy problem for the heat equation in the three-parameter Heisenberg group H3(ℝ) in terms of Wiener integral in the space of trajectories from C[0, t] × C[0, t].

The cascade search principle for zeros of (α, β)-search functionals and consequent fixed point and coincidence theorems are proved for collections of single-valued and set-valued mappings of (b1, b2)-quasimetric spaces. These results are extensions of previous author’s results for metric spaces. In particular, a generalization is obtained for the recent result on coincidences of a covering mapping

Au algorithm of labeling a directed graph so that the obtained transition graph represents a definite automaton is described.

Series with respect to a system of characters of a zero-dimensional compact Abelian group are considered. A generalization of an analogue of Dini test and its corollary obtained earlier for systems determined by bounded sequences {pk} are proved.

It is proved that all strong oscillation indicators considered as functionals on the set of solu¬tions to linear homogeneous two-dimensional differential systems with continuous coefficients bounded on the semi-axis are not residual (i.e. can be changed under changing the solution on a finite interval). An example of two-dimensional system with a solution whose all strong oscillation indicators differ

A machine predicts the next character in the input sequence if it outputs that character at the previous moment of time. In this paper we study the upper bound of prediction degree for some general regular superevents. The paper presents an upper bound for superevents predicted by the machine representing the superevents. In addition, the class of superevents is presented which this bound is attained

It is shown that central exponents of a local diffeomorpliism of a Riemannian manifold treated as functions on the direct product of the manifold and the space of its local diffeomorphisms with C1-compact-open topology belong to the fourth Baire class.

Asymptotic properties of the coefficients of orthorecursive expansion over a system of indicators of dyadic intervals associated with local properties of the expanded function are studied. Asymptotic formulas are obtained in the cases of differentiable functions and functions having a discontinuity of the first kind at the point under study.

Let X be an affine toric variety over an algebraically closed field of characteristic zero. Orbits of connected component of identity of automorphism group in terms of dimensions of tangent spaces of the variety X are described. A formula to calculate these dimensions is presented.

The method for finding asymptotics of the integral of a boundary-layer type function is proposed. The algorithm of application of the proposed method is described. Examples of application of the algorithm are considered.

It is proved that a given real number N > N0(∈) can be approached by a sum of squares of two primes to the distance not exceeding H = N31/64-1/300+∈, where ∈ is an arbitrary positive number.

The following theorem is proved: the union of countably many closed Ur-sets (r > 2) for the Vilenkin-Dzhafarli system is again a Ur-set for this system.

It is proved that the set of closed classes containing some minimal classes in the partially ordered set \({\cal L}_2^3\) of closed classes in the three-valued logic that can be homomorphically mapped onto the two-valued logic has the cardinality of continuum.

for each Boolean function we calculate the exact value of the minimal possible length of a complete fault detection test for logic networks implementing this function in the basis “conjunction, disjunction, negation” under one-type stuck-at faults at outputs of gates.