Abstracts
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2018
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| Назва видання: | Український математичний вісник |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/169404 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Abstracts // Український математичний вісник. — 2018. — Т. 15, № 2. — С. 295-297. — англ. |
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irk-123456789-1694042020-06-13T01:27:15Z Abstracts 2018 Article Abstracts // Український математичний вісник. — 2018. — Т. 15, № 2. — С. 295-297. — англ. 1810-3200 http://dspace.nbuv.gov.ua/handle/123456789/169404 en Український математичний вісник Інститут прикладної математики і механіки НАН України |
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Abstracts |
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Abstracts Український математичний вісник |
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Abstracts |
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Abstracts |
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Abstracts |
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Abstracts |
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abstracts |
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Інститут прикладної математики і механіки НАН України |
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2018 |
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Abstracts // Український математичний вісник. — 2018. — Т. 15, № 2. — С. 295-297. — англ. |
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Український математичний вісник |
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2025-07-15T04:08:45Z |
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2025-07-15T04:08:45Z |
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1837684517329960960 |
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Український математичний вiсник
Том 15 (2018), № 2, 295 – 297
Abstracts
2010 MSC. Primary 30C62, 31A05, 31A20, 31A25, 31B25, 35Q15;
Secondary 30E25, 31C05, 34M50, 35F45
E. S. Afanas’eva, V. I. Ryazanov, R. R. Salimov. To the theory of mappi-
ngs of the Sobolev class with the critical index // Ukrainian Mathemati-
cal Bulletin, 15 (2018), No. 2, 154–176.
It is established that any homeomorphism f of the Sobolev class W 1,1
loc with
outer dilatation KO(x, f) ∈ Ln−1
loc is the so-called lower Q-homeomorphism with
Q(x) = KO(x, f) and also a ring Q-homeomorphism with Q(x) = Kn−1
O (x, f).
This allows us to apply the theory of boundary behavior of ring and lower
Q-homeomorphisms. In particular, we have found the conditions imposed on
the outer dilatation KO(x, f) and the boundaries of domains under which any
homeomorphism of the Sobolev class W 1,1
loc admits continuous or homeomorphic
extensions to the boundary.
References. 49
2010 MSC. 32A10, 32A40, 32A60
A. I. Bandura, O. B. Skaskiv. Partial logarithmic derivatives and di-
stribution of zeros of analytic functions in the unit ball of bounded
L-index in joint variables // Ukrainian Mathematical Bulletin, 15 (2018),
No. 2, 177–193.
We obtain the sufficient conditions of boundedness of L-index in joint vari-
ables for analytic functions in the unit ball, where L : Cn → Rn
+ is a continuous
positive vector-function. They give an estimate of the maximum modulus of an
analytic function by its minimum modulus on a skeleton in a polydisc and descri-
be the behavior of all partial logarithmic derivatives outside some exceptional
set and the distribution of zeros. The deduced results are also new for analytic
functions in the unit disc of bounded index and l-index. They generalize known
results by G. H. Fricke, M. M. Sheremeta, A. D. Kuzyk, and V. O. Kushnir.
References. 37
2010 MSC. 42B99
S. O. Chaichenko, A. L. Shydlich. Approximative characteristics of
modular Orlicz spaces // Ukrainian Mathematical Bulletin, 15 (2018),
No. 2, 194–209.
ISSN 1810 – 3200. c⃝ Iнститут прикладної математики i механiки НАН України
296 Abstracts
We obtain the exact values of the best approximations, basic widths and
Kolmogorov widths for some sets of images of multipliers in the modular Orlicz
spaces lM. We give a description of the space SM,N of all multipliers from the
space lM to lN.
References. 30
2000 MSC. Primary 35C99; Secondary 32W50
T. Kolomiiets, A. Pogorui, R. M. Rodŕıguez-Dagnino. Solution of systems
of partial differential equations by using properties of monogenic
functions on commutative algebras // Ukrainian Mathematical Bulletin,
15 (2018), No. 2, 210–219.
Some systems of differential equations with partial derivatives are studi-
ed by using the properties of Gâteaux differentiable functions on commutati-
ve algebras. The connection between solutions of systems of partial differenti-
al equations and components of monogenic functions on the corresponding
commutative algebras is shown. We also give some examples of systems of partial
differential equations and find their solutions.
References. 8
2010 MSC. 35G15
Z. M. Nytrebych, V. S. Il’kiv, P. Ya. Pukach, O. M. Malanchuk.
Differential-symbol method of constructing the quasipolynomial
solutions of a two-point problem for a partial differential equation //
Ukrainian Mathematical Bulletin, 15 (2018), No. 2, 220–236.
We studied the solvability of a problem with local inhomogeneous conditions
two-point in time for a homogeneous differential equation which is second-order
in time and has generally the infinite order in spatial variables in the case where
the set of zeros of the characteristic determinant of the problem is not empty
and does not coincide with Cs. The existence of a solution of the problem under
the condition that the right-hand sides of the two-point conditions are quasi-
polynomials is proved. A differential-symbol method of constructing a solution
of the problem is proposed.
References. 26
2010 MSC. 2GA33, 46E30, 35A31
A. M. Najafov, A. M. Gasimova. On properties of functions
from Lizorkin–Triebel–Morrey type spaces // Ukrainian Mathematical
Bulletin, 15 (2018), No. 2, 237–250.
We have introduced new functional spaces of the Lizorkin–Triebel–Morrey
type, and a Sobolev-type inequality is proved. We have also shown that the
generalized derivatives of functions from this spaces satisfy the generalized
Hölder condition.
References. 17
Abstracts 297
2010 MSC. Primary 35R30; Secondary 35M33, 46E35
L. Pestov, D. Strelnikov. Approximate controllability of the wave
equation with mixed boundary conditions // Ukrainian Mathematical
Bulletin, 15 (2018), No. 2, 251–263.
We consider initial boundary-value problem for acoustic equation in the
time space cylinder Ω× (0, 2T ) with unknown variable speed of sound, zero ini-
tial data, and mixed boundary conditions. We assume that (Neumann) controls
are located at some part Σ × [0, T ], Σ ⊂ ∂Ω of the lateral surface of the cyli-
nder Ω × (0, T ). The domain of observation is Σ × [0, 2T ], and the pressure
on another part (∂Ω\Σ) × [0, 2T ]) is assumed to be zero for any control. We
prove the approximate boundary controllability for functions from the subspace
V ⊂ H1(Ω) whose traces have vanished on Σ provided that the observation
time is 2T more than two acoustic radii of the domain Ω. We give an explicit
procedure for solving Boundary Control Problem (BCP) for smooth harmonic
functions from V (i.e., we are looking for a boundary control f which generates
a wave uf such that uf (., T ) approximates any prescribed harmonic function
from V ). Moreover, using the Friedrichs–Poincaré inequality, we obtain a condi-
tional estimate for this BCP. Note that, for solving BCP for these harmonic
functions, we do not need the knowledge of the speed of sound.
References. 13
2010 MSC. 53A05, 53B21, 53B30, 53B35, 53C22
L. Rýparová, J. Mikeš, A. Sabykanov. On geodesic bifurcations of
product spaces // Ukrainian Mathematical Bulletin, 15 (2018), No. 2, 264–
271.
The bifurcation is described as a situation where there exist at least two
different geodesics going through the given point in the given direction. In the
previous works, the examples of local and closed bifurcations are constructed.
This paper is devoted to the further study of these bifurcations. We construct
an example of n-dimensional (pseudo-) Riemannian and Kählerian spaces which
are product ones that admit a local bifurcation of geodesics and also a closed
geodesic.
References. 6
2010 MSC. 30G35, 57R35
V. S. Shpakivskyi. On monogenic functions defined in different
commutative algebras // Ukrainian Mathematical Bulletin, 15 (2018),
No. 2, 272–294.
The correspondence between a monogenic function in an arbitrary
finite-dimensional commutative associative algebra and a finite collection of
monogenic functions in a special commutative associative algebra is established.
References. 21
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