Abstracts
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Інститут прикладної математики і механіки НАН України
2017
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irk-123456789-1693812020-06-12T01:26:22Z Abstracts 2017 Article Abstracts // Український математичний вісник. — 2017. — Т. 14, № 4. — С. 605-608. — англ. 1810-3200 http://dspace.nbuv.gov.ua/handle/123456789/169381 en Український математичний вісник Інститут прикладної математики і механіки НАН України |
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Abstracts |
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Інститут прикладної математики і механіки НАН України |
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Abstracts // Український математичний вісник. — 2017. — Т. 14, № 4. — С. 605-608. — англ. |
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Український математичний вісник |
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2025-07-15T04:07:27Z |
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Український математичний вiсник
Том 14 (2017), № 4, 605 – 608
Abstracts
2010 MSC. 30C75
A. K. Bakhtin. Separating transformation and extremal problems on
nonoverlapping simply connected domains // Ukrainian Mathematical
Bulletin, 14 (2017), No. 4, 456–471.
In the paper we consider one well known problem of maximum of the func-
tional
In(γ) = rγ (B0, 0)
n∏
k=1
r (Bk, ak) ,
where B0,...,Bn are pairwise disjoint domains in C, a0 = 0, |ak| = 1, k = 1, n
are different points of the circle, γ ∈ (0, n], r(B, a) is the inner radius of the
domain B ⊂ C relative to the point a. In the case of simply connected domains
and n = 2, 3, 4 the solution of this problem for the maximum interval of values
of the parameter γ is obtained.
References. 23
2000 MSC. 30C75
I. V. Denega, B. A. Klischuk To the problem of extremal partition of
the complex plane // Ukrainian Mathematical Bulletin, 14 (2017), No. 4,
472–480.
In this paper we consider one classic problem of geometric function theory
of a complex variable on maximum of the functional
[r (B0, 0) r (B∞,∞)]
γ
n∏
k=1
r (Bk, ak) ,
where n ∈ N, n > 2, γ ∈ R+, An = {ak}nk=1 is a system of points such that
|ak| = 1, a0 = 0, B0, B∞, {Bk}nk=1 is a system of pairwise non-overlapping
domains, ak ∈ Bk ⊂ C, k = 0, n, ∞ ∈ B∞ ⊂ C, r(B, a) is the inner radius of
the domain B ⊂ C with respect to the point a ∈ B. In this paper we consider
the problem under some weaker restrictions on non-overlapping domains.
References. 12
ISSN 1810 – 3200. c⃝ Iнститут прикладної математики i механiки НАН України
606 Abstracts
2010 MSC. 35K59, 35B44, 35K58, 35K65
Ye. A. Yevgenieva. Limiting profile of solutions of quasilinear parabolic
equations with flat peaking // Ukrainian Mathematical Bulletin, 14 (2017),
No. 4, 481–495.
The paper deals with energy (weak) solutions u(t, x) of the class of equations
with the model representative
(|u|p−1u)t −∆p(u) = 0, (t, x) ∈ (0, T )× Ω, Ω ∈ Rn, n > 1, p > 0
with the following blow-up condition for energy:
E(t) :=
∫
Ω
|u(t, x)|p+1dx+
∫ t
0
∫
Ω
|∇xu(τ, x)|p+1dxdτ → ∞ as t→ T,
where Ω is a smooth bounded domain. In the case of flat peaking, namely, under
the following condition
E(t) 6 Fα(t) := ω0(T − t)−α ∀ t < T, ω0 > 0, α >
1
p+ 1
,
a precise estimate of solution profile has been obtained in a neighborhood of
blow-up time t = T .
References. 13
2010 MSC. 18B40, 37L05, 22A15, 20D45, 20M15, 20B25
V. M. Gavrylkiv. Automorphisms of semigroups of k-linked upfami-
lies // Ukrainian Mathematical Bulletin, 14 (2017), No. 4, 496–514.
A family A of non-empty subsets of a set X is called an upfamily if for
each set A ∈ A any set B ⊃ A belongs to A. An upfamily L is called k-linked
if
∩
F ≠ ∅ for any subfamily F ⊂ L of cardinality |F| ≤ k. The extension
Nk(X) consists of all k-linked upfamilies onX. Any associative binary operation
∗ : X×X → X can be extended to an associative binary operation ∗ : Nk(X)×
Nk(X) → Nk(X). In the paper, we study automorphisms of the extensions of
groups, finite monogenic semigroups and describe the automorphism groups of
extensions of null semigroups, almost null semigroups, right zero semigroups
and left zero semigroups.
References. 25
2010 MSC. 30A10, 30C10, 41A17
M. Imashkyzy, G. A. Abdullayev, F. G. Abdullayev. Bernstein–Walsh
type inequalities in unbounded regions with piecewise asymptoti-
cally conformal curve in the weighted Lebesgue space // Ukrainian
Mathematical Bulletin, 14 (2017), No. 4, 515–531.
In this work, we obtain pointwise Bernstein–Walsh-type estimation for al-
gebraic polynomials in the unbounded regions with piecewise asymptotically
conformal boundary, having exterior and interior zero angles, in the weighted
Lebesgue space.
References. 28
Abstracts 607
2010 MSC. 20A05, 20F99, 22A15, 06E15, 06E25
I. V. Protasov, K. D. Protasova. Recent progress in subset combi-
natorics of groups // Ukrainian Mathematical Bulletin, 14 (2017), No. 4,
532–547.
We systematize and analyze some results obtained in Subset Combinatorics
of G groups after publications the previous surveys [1–4]. The main topics: the
dynamical and descriptive characterizations of subsets of a group relatively their
combinatorial size, Ramsey-product subsets in connection with some general
concept of recurrence in G-spaces, new ideals in the Boolean algebra PG of
all subsets of a group G and in the Stone-Čech compactification βG of G, the
combinatorial derivation.
References. 28
2010 MSC. 30С62, 31A05, 31A20, 31A25, 31B25, 35Q15
V. I. Ryazanov. The Cauchy–Stieltjes integrals in the theory of
analytic functions // Ukrainian Mathematical Bulletin, 14 (2017), No. 4,
548–563.
We study various Stieltjes integrals as Poisson–Stieltjes, conjugate Poisson–
Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes and prove theorems on the
existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes
integral. These results hold for arbitrary bounded integrands that are differenti-
able a.e. and, in particular, for integrands of the class CBV (countably bounded
variation).
References. 29
D. Simsek, F. G. Abdullayev. On the recursive sequence xn+1 =
=
xn−(k+1)
1+xnxn−1...xn−k
// Ukrainian Mathematical Bulletin, 14 (2017), No. 4, 564–
574.
In this paper a solution of the following difference equation was investigated
xn+1 =
xn−(k+1)
1 + xnxn−1...xn−k
, n = 0, 1, 2, ...
where x−(k+1), x−k, ..., x−1, x0 ∈ (0,∞) and k = 0, 1, 2, . . . .
References. 13
O. Sukhorukova. Factorization of generalized γ-generating matri-
ces // Ukrainian Mathematical Bulletin, 14 (2017), No. 4, 575–594.
The class of γ–generating matrices and its subclasses of regular and singular
γ–generating matrices were introduced by D. Z. Arov in [8], where it was shown
that every γ-generating matrix admits an essentially unique regular–singular
factorization. The class of generalized γ-generating matrices was introduced
in [14,20]. In the present paper subclasses of singular and regular generalized γ-
generating matrices are introduced and studied. As the main result of the paper
608 Abstracts
a theorem of existence of regular–singular factorization for rational generalized
γ-generating matrix is found.
References. 20
2010 MSC. 41A30, 41A50, 41A63
S. Ya. Yanchenko. Order estimates of approximation characteristics
of functions from the anisotropic Nikol’skii–Besov classes // Ukrainian
Mathematical Bulletin, 14 (2017), No. 4, 595–604.
We obtained exact order estimates of the deviation of functions from ani-
sotropic Nikol’skii–Besov classes Br
p,θ(Rd) from their sections of the Fourier
integral. The error of the approximation is estimated in the metric of Lebesgue
space L∞(Rd).
References. 17
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