Наближення дробових iнтегралiв гельдерових функцiй

The paper is devoted to the rate of convergence of integral sums of two different types to fractional integrals. The first theorem proves the H¨older property of fractional integrals of functions from various integral spaces. Then we estimate the rate of convergence of the integral sums of two types corresponding to the H¨older functions, to the respective fractional integrals. We illustrate the obtained results by several figures. Pages of the article in the issue: 18 - 25 Language of the article: EnglishСтаттю присвячено дослiдженню швидкостi збiжностi iнтегральних сум двох типiв до дробового iнтегралу. В першiй теоремi доведено гельдерiвську властивiсть дробових iнтегралiв вiд функцiй з рiзних iнтегральних просторiв. Потiм ми оцiнюємо швидкiсть збiжностi iнтегральних сум, побудованих за гельдерiвськими функцiями, до вiдповiдних дробових iнтегралiв. Отриманi результати проiлюстровано декiлькома чисельними прикладами

ПЕРЕВАГИ І ПРОБЛЕМНІ ПИТАННЯ ФОРМУВАННЯ ТА РОЗВИТКУ ОБ’ЄДНАНИХ ТЕРИТОРІАЛЬНИХ ГРОМАД

The article analyzes the legislative, normative and institutional support for the implementation of the reform of the territorial organization of power on the basis of decentralization and analyzes the dynamics of the formation of the united territorial communities. The main directions and measures for improving the legislative support of the process of formation of capable territorial communities, strengthening of providing them with expertmethodical and resource support are determined.В статье исследовано законодательно-нормативное и институциональное обеспечение реализации реформы территориальной организации власти на основе децентрализации и проанализирована динамика формирования объединенных территориальных общин. Определены основные направления и мероприятия по совершенствованию законодательного обеспечения процесса формирования способных территориальных общин, усиление предоставления им экспертно-методической и ресурсной поддержки.У статті досліджено законодавчо-нормативне та інституційне забезпечення реалізації реформи територіальної організації влади на засадах децентралізації та проаналізовано динаміку формування об’єднаних територіальних громад. Визначено основні напрями та заходи щодо вдосконалення законодавчого забезпечення процесу формування спроможних територіальних громад, посилення надання їм експертно-методичної та ресурсної підтримки

Study of the dependence of Young's modulus of vertically aligned carbon nanotubes on their aspect ratio

The reported study was funded by RFBR according to the research projects No.16-29-14023 ofi_m, No.18-32-00652 and by grant of the Southern Federal University (project No. VnGr-07/2017-26)

Дружба поета-ветеринара О. О. Олеся з родиною М. Хороманського

Вперше подаються історичні відомості про вплив О. Олеся на творчість польського письменника М. Хороманського

Adhesive coatings based on aligned arrays of carbon nanostructures

This work was financially supported by Russian Foundation for Basic Research (projects 16-29-14023 and 18-32-00652) and Internal grant of the Southern Federal University (project VnGr-07/2017-26)

Дружба поета-ветеринара О. О. Олеся з родиною М. Хороманського

For the first time is given historical information about influence of О. Оles on creativity of the Polish writer М. Choromansky.Впервые подаются исторические сведения о влиянии О. Олеся на творчество польского писателя М. Хороманского.Вперше подаються історичні відомості про вплив О. Олеся на творчість польського письменника М. Хороманського

Linear and nonlinear optical properties of ZnO/PMMA nanocomposite films

The nanoscale crystals (NCs) of ZnO were embedded into polymethylmethacrylate (PMMA) polymeric matrix and nanocomposite films were prepared by modified spin coating method. The surface of the ZnO/PMMA nanocomposite films has been investigated using atomic force and scanning electron microscopy. The prepared films are highly transparent, the ultraviolet-visible spectra show their high optical quality. The second and third harmonic generation (SHG and THG) studies of ZnO/PMMA nanocomposite films with different concentrations of ZnO NCs were carried out at λ=1.064 μm and the effective values of the second and third order nonlinear susceptibilities were estimated to be higher than that of ZnO bulk for the films at low concentration of ZnO NCs. This could indicate that surface effects in ZnO/PMMA nanocomposite films have a dominant role over bulk effects for the SHG and THG processes

Redox-dependent dimerization of p38 alpha mitogen-activated protein kinase with mitogen-activated protein kinase kinase 3

The kinase p38α MAPK (p38α) plays a pivotal role in many biological processes. p38α is activated by canonical upstream kinases that phosphorylate the activation region. The purpose of our study was to determine whether such activation may depend on redox-sensing cysteines within p38α. p38α was activated and formed a disulfide-bound heterodimer with MAP2K3 (MKK3) in rat cardiomyocytes and isolated hearts exposed to H2O2 This disulfide heterodimer was sensitive to reduction by mercaptoethanol and was enhanced by the thioredoxin-reductase inhibitor auranofin. We predicted that Cys-119 or Cys-162 of p38α, close to the known MKK3 docking domain, were relevant for these redox characteristics. The C119S mutation decreased whereas the C162S mutation increased the dimer formation, suggesting that these two Cys residues act as vicinal thiols, consistent with C119S/C162S being incapable of sensing H2O2 Similarly, disulfide heterodimer formation was abolished in H9C2 cells expressing both MKK3 and p38α C119S/C162S and subjected to simulated ischemia and reperfusion. However, the p38α C119S/C162S mutants did not exhibit appreciable alteration in activating dual phosphorylation. In contrast, the anti-inflammatory agent 10-nitro-oleic acid (NO2-OA), a component of the Mediterranean diet, reduced p38α activation and covalently modified Cys-119/Cys-162, probably obstructing MKK3 access. Moreover, NO2-OA reduced the dephosphorylation of p38α by hematopoietic tyrosine phosphatase (HePTP). Furthermore, steric obstruction of Cys-119/Cys-162 by NO2-OA pretreatment in Langendorff-perfused murine hearts prevented the p38-MKK3 disulfide dimer formation and attenuated H2O2-induced contractile dysfunction. Our findings suggest that cysteine residues within p38α act as redox sensors that can dynamically regulate the association between p38 and MKK3.</p