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)

Sharp Remez-type inequalities of various metrics for differentiable periodic functions, polynomials, and splines

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 173-188

We prove a sharp Remez-type inequality of various metrics $$\| x\| q \leq \| \varphi_r\| q \biggl\{\frac{\| x\|_{L_p([0,2\pi ]\setminus B)}}{\|\varphi r\|_{ L_p([0,2\pi ]\setminus B_1)}}\biggr\}^{\alpha } \| x(r)\|^{1 - \alpha}_{ \infty} ,\; q > p > 0, \;\alpha = (r + 1/q)/(r + 1/p),$$ for $2\pi$ -periodic functions $x \in L^r_{\infty}$ satisfying the condition $$L(x)p \leq 2^{-\frac 1p}\| x\|_p,\quad (\ast )$$ where $$L(x)p := \mathrm{s}\mathrm{u}\mathrm{p} \Bigl\{ \| x\| L_p[a,b] : [a, b] \subset [0, 2\pi ], | x(t)| > 0, t \in (a, b)\Bigr\},$$ $B \subset [0, 2\pi ], \mu B \leq \beta /\lambda$ ($\lambda$ is chosen so that $\| x\| p = \| \varphi \lambda ,r\| L_p[0,2\pi /\lambda ] ), \varphi_r$ is the ideal Euler’s spline of order r, and $$B_1 := \biggl[\frac{-\pi - \beta /2}{2} , \frac{-\pi + \beta /2}{2} \biggr] \bigcup \biggl[ \frac{\pi - \beta /2}{2}, \frac{\pi + \beta /2}{2} \biggr].$$ As a special case, we establish sharp Remez-type inequalities of various metrics for trigonometric polynomials and polynomial splines satisfying the condition $(\ast )$.

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 $EX^2(\mathrm{l}\mathrm{o}\mathrm{g} | X| )^{r-1}(\mathrm{l}\mathrm{o}\mathrm{g} \mathrm{l}\mathrm{o}\mathrm{g} | X| )^{-\frac 12} < \infty$.

Anniversaries (Ukrainian)

Oleksandr Mykolaiovych Sharkovs’kyi (on his 80th birthday)

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 257-260