2018
Том 70
№ 9

# Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal)

Editor-in-Chief: A. M. Samoilenko
ISSN: 0041-6053, 1027-3190

Ukrains'kyi Matematychnyi Zhurnal (UMZh) was founded in May 1949. Journal is issued by Institute of Mathematics NAS of Ukraine. English version is reprinted in the Springer publishing house and called Ukrainian Mathematical Journal.

Ukrains'kyi Matematychnyi Zhurnal focuses on research papers in the principal fields of pure and applied mathematics. The journal is published monthly, each annual volume consists of 12 issues. Articles in Ukrainian, Russian and English are accepted for review.

UMZh indexed in: MathSciNet, zbMATH, Scopus, Web of Science, Google Scholar.

Impact Factor*: 0.189
*2015 Journal Citation Reports, Thomson Reuters

SCImago Journal Rank (SJR) 2015: 0.31; H-index: 13
Source Normalized Impact per Paper (SNIP) 2014: 0.605
Impact per Publication (IPP) 2014: 0.216

Mathematical Citation Quotient (MCQ) 2014: 0.22

## Latest Articles (September 2018)

Brief Communications (English)

### Coefficient estimates for two subclasses of analytic and bi-univalent functions

Ukr. Mat. Zh. - 2018. - 70, № 9. - pp. 1289-1296

We introduce two new subclasses of the class $\sigma$ of analytic and bi-univalent functions in the open unit disk $U$. Furthermore, we obtain the estimates for the first two Taylor – Maclaurin coefficients $|a_2|$ and $|a_3|$ for the functions from these new subclasses.

Article (English)

### Some results on the global solvability for structurally damped models with a special nonlinearity

Ukr. Mat. Zh. - 2018. - 70, № 9. - pp. 1211-1231

The main purpose of this paper is to prove the global (in time) existence of solution for the semilinear Cauchy problem $$u_{tt} + (-\Delta )^{\sigma} u + (-\Delta )^{\delta} u_t = |u_t|^p,\; u(0, x) = u_0(x),\; u_t(0, x) = u_1(x)$$. The parameter $\delta \in (0, \sigma]$ describes the structural damping in the model varying from the exterior damping $\delta = 0$ up to the visco-elastic type damping $\delta = \sigma$. We will obtain the admissible sets of the parameter p for the global solvability of this semilinear Cauchy problem with arbitrary small initial data u0, u1 in the hyperbolic-like case $\delta \in \Bigl(\cfrac{\sigma}{2} , \sigma \Bigr)$, and in the exceptional case $\delta = 0$.

Brief Communications (Russian)

### Inequalities for inner radii of symmetric disjoint domains

Ukr. Mat. Zh. - 2018. - 70, № 9. - pp. 1282-1288

We study the following problem: Let $a_0 = 0, | a_1| = ... = | a_n| = 1,\; a_k \in B_k {\subset C}$, where $B_0, ... ,B_n$ are disjoint domains, and $B_1, ... ,B_n$ are symmetric about the unit circle. It is necessary to find the exact upper bound for $r^{\gamma} (B_0, 0) \prod^n_{k=1} r(B_k, a_k)$, where $r(B_k, a_k)$ is the inner radius of Bk with respect to $a_k$. For $\gamma = 1$ and $n \geq 2$, the problem was solved by L. V. Kovalev. We solve this problem for $\gamma \in (0, \gamma_n], \gamma_n = 0,38 n^2$, and $n \geq 2$ under the additional assumption imposed on the angles between the neighboring line segments $[0, a_k]$.