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Title: Matematychni Studii, Vol.44, No.2
ISSN: 1027-4634
Price: 50.00 USD
Year: 2015

B. Zabavsky, A. Gatalevych. New characterizations of commutative clean rings. P.115-118.
A ring is called clean if every its element is the sum of a unit and an idempotent. We introduce the notion of an avoidable element and describe class of the commutative clean rings as the rings in which zero is an avoidable element.
SubjClass 06F20, 13F99

V.V. Lyubashenko. Homotopy cooperads. P.119-160.
The theory of 2-monads is used as a ground to study non-symmetric cooperads. We give a new definition of homotopy cooperads. Ordinary and homotopy cooperads are placed in lax $Cat$- operads which are lax algebras over the free-operad strict 2 -monad. We give an~example of a homotopy cooperad cofree with respect to ordinary cooperads.
SubjClass 18D50

O.M. Mulyava, M.M. Sheremeta. On a new condition of finite Lipschitz of Orlicz-Sobolev class. P.161 -170.
For a~function $P$ continuos on $(-|, +|)$ increaing to $+|$ the lower and upper estimates for $frac{a(P(qs))}{a^p(P(s))}$ are found, where $p>1, q>1$ and $a$ is positive function continuous on $[x_0,+|)$, increasing to $+|$. The above results applied to Dirichlet series with positive exponents.
SubjClass 30B50

E.A. Sevost`yanov, D.S. Dolya. On removable singularities of a class of mappings. P.171-184.
A paper is devoted to study of local behavior of so-called $Q$-mappings including quasiconformal mappings and mappings with bounded distortion. It is showed that, such mappings have removable isolated singularities whenever the growth of the mappings is not more than some function of a~radius of a~ball.
SubjClass 30С65, 31A15, 32U20

S.V. Litynskyy, A.O. Muzychuk. Solving of initial-boundary value problems for the wave equation using retarded surface potential and Laguerre transform. P.185-203.
Approach for solving of initial-boundary value problems for the homogeneous wave equation is described and proved. It is based on the Laguerre transform in the time domain and the boundary integral equations. Retarded potentials are used for representation of generalized solutions of such problems. The densities of retarded potentials are expanded in Fourier-Laguerre series which coefficients have special convolution form. As a~result, initial-boundary value problems are reduced to a~sequence of boundary integral equations.
SubjClass 31B10, 35D30, 35J50, 35J57, 45B05

M.A. Belozerova, G.A. Gerzhanovskaya. Asymptotic representations of solutions of second order differential equations with nonlinearities close to regularly varying. P.204-214.
The asymptotic representation, necessary and sufficient conditions of the existence of sufficient broad classes of the solutions are found for differential equations of the second order that are in some sense similar to equations with nonlinearities, that are regularly varying at the singular points.
SubjClass 34C41, 34Е10

H.P. Lopushanska, A.O. Lopushansky, O.M. Myaus. Classical solution of the inverse problem for fractional diffusion equation under time-integrated over-determination condition. P.215-220.
We prove the correctness of the inverse problem on determination of a~pare of functions: a~classical solution $u$ of the first boundary value problem for linear diffusion equation $ D^alpha_t u-u_{xx} =F_0(x), (x,t)in (0,l) imes (0,T]$ with regularized fractional derivative of order $alphain (0,1)$ with respect to time and function $F_0(x)$ under integral by time over-determination condition.
SubjClass 35S15

INDEX, 2015. P.221-224.

Additional information:
Matematychni Studii
Proceedings of the Lviv Mathematical Society

Journal is devoted to research in all fields of mathematics. Original papers of moderate length are accepted; exception is possible for survey articles. Languages accepted are: English, French, German, Russian, and Ukrainian. Published quarterly.

Published for the Lviv Mathematical Society by VNTL Publishers with finansial and organizing support of the Lviv National University.

M.M.Sheremeta (Lviv), O.B.Skaskiv (Lviv), M.M.Zarichnyi (Lviv)

Editorial Board:
O.D.Artemovych (Ivano-Frankivs'k; Krakow, Poland), T.O.Banakh (Lviv), M.M.Bokalo (Lviv), R.Cauty (Paris, France), I.E.Chyzhykov (Lviv), A.A.Dorogovtsev (Kyiv), Yu.A.Drozd (Kyiv), S.Yu.Favorov (Kharkiv), Yu.D.Golovaty (Lviv), R.I.Grigorchuk (Moscow, Russia), I.Yo.Guran (Lviv), R.O.Hryniv (Lviv), S.D.Ivasyshen (Kyiv), B.N.Khabibullin (Ufa, Russia), V.V.Kirichenko (Kyiv), M.Ya.Komarnytskyi (Lviv), B.I.Kopytko (Lviv), A.A.Korenovskii (Odessa), O.V.Lopushanskyi (Lviv; Rzeszow, Poland), Ya.V.Mykytyuk (Lviv), I.V.Ostrovskii (Kharkiv; Ankara, Turkey), O.A.Pankov (Baltimore, USA), M.M.Popov (Chernivtsi), I.V.Protasov (Kyiv), B.Yo.Ptashnyk (Lviv), D.Repovs (Ljubljana, Slovenia), V.G.Samoilenko (Kyiv), A.M.Sedletskii (Moscow, Russia), O.G.Storozh (Lviv), V.I.Sushchansky (Glivice, Poland)

Technical editor:

Matematychni Studii
Dept. of Mechanics and Mathematics,
Lviv National University,
1 Universytetska St.,
79000, Lviv, Ukraine

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