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.

Systems of Boolean functions inducing algebras of Bernoulli distributions whose universal set has a single limit point are considered. A criterion for an algebra generated by a given distributions set to have a single limit point is proved.

A single-channel queuing system with regenerative input flow is considered. It is assumed that the stability condition is fulfilled. A statistical estimator of the parameter of large deviations of waiting time is proposed. Its consistency and asymptotic normality are proved, the asymptotic confidence interval for the parameter of large deviations is constructed.

About four centuries ago, considering flat sections of cone x2 + y2 = z2 (along the axis of revolution on the plane Oxy), Robert Hooke wrote one fundamental differential equation \((x,y,z)^{\prime\prime} = - {{4{\pi ^2}k} \over {{{(\sqrt {{x^2} + {y^2} + {z^2}})}^3}}}\; \cdot \;(x,y,z)\), which thereafter set the foundation of the law of universal gravitation and explanation of movement of charged

The asymptotics of the Feynman integrals of the form \({\cal F}(t) = \int\limits_0^{+ \infty} {{{(P(x,t))}^{- \lambda}}dx}\) is studied for t → +0. The first term of the asymptotics is calculated in the general case and a method for obtaining a complete asymptotic expansion in the case of one essential face is presented.

Let L be an extension of the language of arithmetic, F be a class of number-theoretical functions. A notion of the V-realizability for L-formulas is defined in such a way that indexes of functions in V are used for interpreting the implication and the universal quantifier. It is proved that the semantics for L based on the V-realizability coincides with the classic semantics if and only if V contains

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.

Formulas calculating the number of degenerate atoms with one singular point are obtained.

Description of bifurcations and symmetries of integrable systems is an important branch of geometry that has many applications. Important results have been obtained recently in the descriptions of bifurcations of integrable billiards and in modelling of Hamiltonian systems of mechanics and dynamics by billiards. The paper contains interesting problems, as well as a research program for the near future

Ul’yanovs inequality connecting moduli of continuity in different metrics is well known for functions of one variable. In this paper functions of two variables are considered. Sharp Ul’yanov’s inequalities connecting partial moduli of smoothness of positive order are proved in different mixed metrics.

Lyapunov reducibility of any bounded and sometimes unbounded linear homogeneous differential system to some bounded linear homogeneous differential equation is established. The preservation of the additional property of periodicity of coefficients is guaranteed, and for two-dimensional or complex systems the constancy of their coefficients is preserved. The differences in feasibility of asymptotic

An approach to using Chebyshev series to solve canonical second-order ordinary differential equations is described. This approach is based on the approximation of the solution to the Cauchy problem and its first and second derivatives by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using the Markov quadrature formula. It is shown that

The description of the set of lower semi-continuity points and the set of upper semi-continuity points of the topological entropy of the systems considered as a function on some parameter is obtained for a family of dynamical systems continuously dependent on parameter.

An absolute L-realizability of predicate formulas is introduced for all countable extensions L of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.

It is proved that the cosine and sine Fourier transforms are permutable with the opposite sign on the positive real axis. This property implies that the cosine and sine Fourier transforms coincide in absolute value on the semiaxis for a wide class of functions.

On the one hand, we show that the upper-limit analogues of Vinograd-Millionshchikov central exponents determined on the space of regular linear differential systems are equal to lower-limit ones. A similar fact is also valid for analogues of Bohl-Persidsky general exponents on the space of almost reducible systems. On the other hand, we present an example of a two-dimensional regular differential system

The path connectedness of spheres in Gromov-Hausdorff space is studied. It is proved that (1) each sphere centered at the single point space is path connected; (2) for any compact metric space X there exists a number RX such that each sphere centered at X and whose radius is greater than RX is path connected.

The problem of the minimal number of multiplication operations sufficient for joint computing three monomials in three variables is considered. For this problem, we propose a simple proof of the upper bound that is asymptotically equal to the lower bound. The known proof of a similar bound contains more than 60 pages.

The asymptotics of the transfer matrix of Sturm-Liouville equation with piecewise-entire potential function on a curve in the complex plane is obtained and studied for large absolute values of the spectral parameter.

Explicit formulas for the initial data stabilization algorithm for the stationary solution are obtained by zero approximation method for the semi-implicit difference scheme approximating a system of equations for the dynamics of a one-dimensional viscous barotropic gas. The spectrum of the corresponding linearized system on the stationary solution is studied and theoretical convergence estimates are

Necessary and sufficient conditions to be Noetherian are obtained for two-dimensional singular integral operators on Lebesgue spaces with a weight coefficient. A formula for calculation of their index is given.

The full diagnostic test for contact circuits in the presence of one-type contact faults (breaking or closure) is considered. We constructively establish that any Boolean function can be realized by a contact circuit permitting a non-trivial full diagnostic test, i.e., a test containing not all input vectors.

The oscillation, rotatability, and wandering characteristic indicators of Lyapunov type are studied for two-dimensional linear homogeneous differential systems determining rotations of the phase plane. A complete set of order relations between them is obtained. For each of those indicators it is established whether it is continuous or discontinuous as a function of the coefficients of the system.

The way of communication coding using “multiplicative gammation” in algebras with strong filtration is proposed. This class of algebras was introduced earlier by the author for needs of Gröbner–Shirshov bases theory in a wide context. It includes semigroup algebras of ordered semigroups and universal enveloping algebras of Lie algebras, in particular, a polynomial algebra and a free associative algebra

Partial functions of the k-valued logic monotone with respect to an arbitrary partially ordered set with the least and largest elements and distinct from a lattice are considered. It is shown that the set of closed classes of partial monotone functions containing a precomplete in Pk class of everywhere determined monotone function is infinite.