2019
Том 71
№ 10

All Issues

Volume 48, № 3, 1996

Article (Russian)

Optimization of quadratures on classes of functions given by differential operators with Real Spectra

Babenko V. V., Rudenko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 291-300

We study the problem of optimization of quadrature formulas for broad classes of periodic functions defined in terms of differential operators with real spectra. We analyze quadrature formulas containing values of functions and values of the images of functions under the action of some differential operators. The rectangular formula is proved to be optimal.

Article (Russian)

On exact values of quasiwidths of some classes of functions

Shabozov M. Sh., Vakarchuk S. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 301-308

In the Hilbert space L 22), Δ = [0, 2 π] we establish exact estimates of the Kolmogorov quasiwidths of some classes of periodic functions of two variables whose averaged modules of smoothness of mixed derivatives are majorizable by given functions.

Article (Russian)

Generalized moment representations and invariance properties of Padé approximants

Holub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 309-314

By the method of generalized moment representations, we generalize the well-known invariance properties of Padé approximants under linear-fractional transformations of approximated functions.

Article (Ukrainian)

Valiron-type and valiron-titchmarsh-type theorems for entire functions of order zero

Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 315-325

By using known asymptotics of the counting function of zeros of an entire function f of order zero, we determine the asymptotics of In f under the condition that all zeros off lie on the same ray. The inverse problem is also analyzed.

Article (Russian)

Copositive pointwise approximation

Dzyubenko H. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 326-334

We prove that if a functionfC (1) (I),I: = [−1, 1], changes its signs times (s ∈ ℕ) within the intervalI, then, for everyn > C, whereC is a constant which depends only on the set of points at which the function changes its sign, andk ∈ ℕ, there exists an algebraic polynomialP n =P n (x) of degree ≤n which locally inherits the sign off(x) and satisfies the inequality $$\left| {f\left( x \right) - P_n \left( x \right)} \right| \leqslant c\left( {s,k} \right)\left( {\frac{1}{{n^2 }} + \frac{{\sqrt {1 - x^2 } }}{n}} \right)\omega _k \left( {f'; \frac{1}{{n^2 }} + \frac{{\sqrt {1 - x^2 } }}{n}} \right), x \in I$$ , where ω k (f′;t) is thekth modulus of continuity of the functionf’. It is also shown that iffC (I) andf(x) ≥ 0,xI then, for anynk − 1, there exists a polynomialP n =P n (x) of degree ≤n such thatP n (x) ≥ 0,xI, and |f(x) −P n (x)| ≤c(k k (f;n −2 +n −1 √1 −x 2),xI.

Article (Ukrainian)

Operator methods in the problem of perturbed motion of a rotating body partially filled with liquid

Komarenko A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 335-348

We apply operator methods to the investigation of an initial boundary-value problem which describes the perturbed motion of a body with cavity partially filled with an ideal liquid relative to the uniform rotation of this system about a fixed axis. We prove the existence and uniqueness of generalized solutions with finite energy and establish a sufficient condition for the stability of motion and some properties of the spectrum of the problem under consideration.

Article (Ukrainian)

Nonperiodic locally solvableT(Ā)-groups

Kuzennyi N. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 349-361

We constructively describe nonperiodic locally solvableT(Ā) -groups and select three types of groups of this sort.

Article (Ukrainian)

Nonlocal parabolic boundary-value problem

Matychuk M. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 362-367

For a parabolic system with time-dependent coefficients, we construct its Green function and present the classical solution of a two-point problem with nonlocal boundary conditions given by differential polynomials.

Article (Ukrainian)

Tauberian and Abelian Theorems for random fields with strong dependence

Olenko A. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 368-382

We prove Tauberian and Abelian theorems for Hankel-type integral transformations.

Article (Russian)

Absolutely decomposable groups

Protasov I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 383-392

We establish numerous results concerning the construction of decomposable and absolutely decomposable groups.

Article (Russian)

Strong summability of orthogonal expansions of summable functions. II

Lasuriya R. A., Stepanets O. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 393-405

We study the problem of strong summability of Fourier series in orthonormal systems of polynomialtype functions and establish local characteristics of the points of strong summability of series of this sort for summable functions. It is shown that the set of these points is a set of full measure in the region of uniform boundedness of the systems under consideration.

Article (Ukrainian)

Generalized periodic solutions of quasilinear equations

Khoma L. G., Khoma N. H.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 406-411

We study a boundary-value periodic problem for the quasilinear equationu ff u xx =F[u,u f u x ],u(0,t) =u (π,t),u (x, t + π/q) =u(x, t), 0 ≤xπ,t ∈ ℝ,q ∈ ℕ. We establish conditions under which the theorem on the uniqueness of a smooth solution is true.

Article (Ukrainian)

Generalization of the fricke theorem on entire functions of finite index

Sheremeta M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 412-417

We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index.

Brief Communications (Russian)

Solvable groups of finite non-abelian sectional rank

Dashkova O. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 418-421

We study non-Abelian solvable groups of finite non-Abelian sectional rank and prove that their (special) rank is finite.

Brief Communications (Russian)

On the existence of an invariant manifold for weakly nonlinear matrix differential equations

Lipchan V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 422-424

For a system of nonlinear matrix differential equations with small parameter, we establish conditions of the existence of an invariant manifold in terms of the Green function.

Brief Communications (Russian)

Turnpike theorems for convex problems

Mamedov M. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 425-428

We prove turnpike theorems for systems described by differential inclusions with convex graphs.

Brief Communications (Russian)

On groups factorizable in commuting almost locally normal subgroups

Chernikov N. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 429-431

We prove that an RN-group (in particular, locally solvable) G =G 1 G 2 ...G n with G i and π(G i ) ∩ π(G j ) = ⊘,ij is a periodic hyper-Abelian group if the subgroupsG j are almost locally normal.