2017
Том 69
№ 2

# 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 (February 2017)

Article (Russian)

### Estimates of the area of solutions of the pseudolinear differential equations with Hukuhara derivative in the space $\text{conv} (R^2)$

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 189-214

We obtain estimates for the areas of the solutions of differential equations with Hukuhara derivative of a special form in the space $\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v} (R^2)$. The main methods used for the investigation are the method of comparison, the methods of the Minkowski – Aleksandrov geometry of convex bodies, and the Chaplygin –Wa˙zewski method of approximate integration of differential equations. The obtained results enable us to reduce the estimates of the area of solutions to the investigation of differential equations of the first order.

Article (English)

### Еxact rates in the Davis – Gut law of iterated logarithm for the first moment convergence of independent identically distributed random variables

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 240-256

Let $\{X, X_n, n \geq 1\}$ be a sequence of independent identically distributed random variables and let $S_n = \sum^n_{i=1} X_i$, $M_n = \max_{1\leq k\leq n} |S_k|$. For $r > 0$, let $a_n(\varepsilon)$ be a function of $\varepsilon$ such that $a_n(\varepsilon ) \mathrm{l}\mathrm{o}\mathrm{g} \mathrm{l}\mathrm{o}\mathrm{g} n \rightarrow \tau$ as $n \rightarrow \infty$ and $\varepsilon \searrow \surd r$. If $EX^2I\{|X| \geq t\} = o(\text{log}\text{log}t)^{-1})$ as $t \rightarrow \infty$ , then, by using the strong approximation, we show that $$\lim_{\varepsilon \searrow \surd r} \frac 1{-\text{log}(\varepsilon^2 - r)} \sum ^{\infty}_{n=1}\frac{(\text{log} n)^{r-1}}{n^{3/2}}E \Bigl\{ M_n - (\varepsilon + a_n(\varepsilon ))\sigma \sqrt{2n \text{log log} n} \Bigr\}_{+} = \frac{2\sigma \varepsilon^{-2\tau \sqrt{r}}}{\sqrt{2\pi}r}$$ holds if and only if $EX = 0, EX^2 = \sigma^2$, and $EX = 0, EX^2 = \sigma^2$ та $EX^2(\mathrm{l}\mathrm{o}\mathrm{g} | X| )^{r-1}(\mathrm{l}\mathrm{o}\mathrm{g} \mathrm{l}\mathrm{o}\mathrm{g} | X| )^{-\frac 12} < \infty$.

Brief Communications (English)

### Reducing sequences

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 279-283

We introduce and examine two new classes of distinguished sequences in the unit disk for the space of bounded analytic functions. One of these sequences is intermediate between interpolating and zero sequences.