The oscillatory properties of differential systems are investigated: oscillation, wandering, rotation, and nonoscillation, nonwandering, and nonrotation. Their radial and general radial analogues are defined and studied: ray, wide, and narrow. A number of statements about the presence or absence of some logical interrelations between the various listed properties are formulated and proven.
An efficient numerical algorithm for solving the external three-dimensional Stokes problem is proposed and implemented. This algorithm is based on calculating the density of surface forces in terms of the Green function and provided that the surface of a body is approximated by a set of elementary basic elements of rectangular or triangular shape. The density function is considered piecewise constant. The resulting system of boundary singular integral equations is reduced to a system of linear algebraic equations by an analytical or semianalytical method based on explicit integration of singularities and quadrature formulas of high order of accuracy. This approach also allows restoring a continuous velocity field up to the boundary of the body, which is verified using the problem of a wedge-shaped body in flow. Based on the obtained algorithm, the problem of increasing the efficiency of two configurations of Savonius rotor-type wind power plants by adding a reflective screen is numerically solved.
We examine the classical Poisson risk model. Numerical methods are studied for determining the probability of ruin in this model under specified conditions for the claim size distribution. The accuracy of the methods is investigated, and computational challenges that may arise in their application are discussed, along with numerical experiment results. Also, we derive the nonruin probability formula for uniform payments and initial capital in [0,1] .
Upper bound of switchable power of planar automata circuits implementation by some deterministic finite automaton (DFA) class is obtained in the paper. A circuit is presented that implements automata with 2^n states for positive integer n with switchable power no higher than O(2^n/2d(n)) , where d(n) depends on the DFA subclass.
We consider the weak oscillation exponents of hypermultiple roots (a simple zero is counted once, and a multiple zero is counted infinitely many times) of solutions as functions on the direct product of the space of linear differential systems with compact-open topology and the space of initial vectors. It is shown that the lower exponent belongs to the second Baire class, and upper one belongs to the third Baire class.
The aim of this paper is to prove the following statements for trigonometric cosine series with fractionally monotone coefficients. Our main result is the possibility of transition from the cosine series to the corresponding series with Fejer kernels. It is also proved that if the monotony of the coefficients a_n is greater than 2, then we get the estimate of the difference ratio for high orders of the function f(x)=a_02+∑_n=1^∞a_ncos(nx) .
As part of the author’s series of works, the phenomenon of stochastic nontransitivity for tuples of three random variables with a joint polynomial density of a special type on the unit cube is studied. It is shown when this density defines a copula and when there is nontransitivity. Maximization of the measure of nontransitivity is carried out.
An estimate with a precise constant is obtained for the Fourier transform of an integrable function of bounded variation on ℝ .
A scale of Sobolev-type spaces is constructed including classical Sobolev and Sobolev–Slobodetskii spaces, spaces consisting of Sobolev functions satisfying certain differential relations. This approach allows defining Sobolev spaces for functions defined on a topological space and to prove embedding theorems.
It is proved that a finally compact p -space is metrizable iff the space X^2∖Δ has a countable rectangular open cover. A similar theorem is valid for separable M -spaces.
New cases of seventh-order integrable dynamical systems homogeneous in terms of variables are presented, in which a system on a tangent bundle to a three-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which have a dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes the previously considered fields. Complete sets of both the first integrals and invariant differential forms are given.
In this paper, the method of constructing exceptional coverings of finite groups by investigating lattices in Euclidean spaces is demonstrated. Namely, the 4 -tuple cover of the sporadic Mathieu group M_22 is constructed.
A mathematical model of convergence to the equilibrium state of one of the main mechanisms of neurogenic regulation of blood pressure, arterial baroreceptor reflex, is proposed. The baroreceptor complex model consists of two interacting hybrid automata, one representing the sympathetic nervous system and the other the cardiovascular system. A theorem on the convergence of the baroreceptor complex to the equilibrium state is proved.
In this paper, we study the Baire property of the space K_1(X,M) , that is, the mappings of the first functional Lebesgue class, where M is a compact space. We study the class compact spaces for which the Baire property of the space K_1(X,{0,1}) is equivalent to the Baire property of the space K_1(X,M) for any M from this class. We prove that this class contains π -monolithic compacta. In particular, a necessary and sufficient condition is obtained for the space X under which the space K_1(X,G) is Baire for any compact topological group G .
In this paper, we consider the situation when some of the perturbed solutions (which could form an arbitrary but essential part of all the solutions) with the initial values close enough to the point of equilibrium do not remain close to that point but return back to it at arbitrarily late times instances. Such a situation can be described with the use of the special characteristics that is the measure of Perron stability, for which the possible range of values if found in the paper.
Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a binary action of a topological group G on a space X is obtained. The concept of transitive binary G -space is introduced, and a classification of transitive distributive binary G -spaces is given in the case of a compact group G .
Studying of a nonlinear problem for differential equations in smooth functional spaces often begins with the studying the problem in weaker integrable spaces. And then follows some bootstrap like procedure of smoothness raising. The aim of this short communication is to attract the attention of the reader to a way of a possible notable simplification for different bootstrap procedures via application of mixed interpolation between integrable and smooth spaces. As an example, we present an a priori estimate for the 3D stationary Navier–Stokes system in a smooth space.
The character of the regularity of the Poisson potential for a uniformly parabolic equation with Dini-continuous coefficients is studied. The potential density is continuous and bounded with all derivatives up to and including the second order. In particular, it follows from the results that the Dini condition for the principal coefficients of the equation is sharp for the existence of a regular solution to the Cauchy problem in the form of a Poisson potential.
A simple algorithm for finding the exponent and real logarithm of a real square matrix of the second order is presented, in which it is not required to reduce it to Jordan form. The method of such calculation of the exponent of a given matrix, proposed by A.F. Filippov, also applies to its algorithm, the set of which may be empty, single-element, and infinite — countable and even continuous.
