Non-linear water waves generated by impulsive motion of submerged obstacles

A fully non-linear problem on unsteady water waves generated by an impulsively moving obstacle is studied analytically. Our method involves reduction of the Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at a free surface. Exact model equations are derived in explicit form in a case where an isolated obstacle is presented by a totally submerged elliptic cylinder. A small-time asymptotic solution is constructed for a cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle; the generation of diverging waves is also observed

ВИЗНАЧЕННЯ ОСНОВНИХ ДЕТЕРМІНАНТ ПОПИТУ НА МІЖНАРОДНІ РЕЗЕРВИ В УКРАЇНІ: КОІНТЕГРАЦІЙНИЙ АНАЛІЗ

In this paper we searched for the most important determinants of reserve holdings inUkraineusing quarterly data from 2000 to 2013 years. We evaluated their importance using two econometric techniques: autoregressive distributed lag (ARDL) approach and Vector Error Correction model (VECM) approach. We find that the ratio of imports to GDP, the ratio of broad money to GDP, ratio of net foreign direct investment to GDP, the ratio of short term debt to GDP and GDP determine Ukraine’s long-run reserves demand function. Our empirical results show that shocks associated with the financial account is more dangerous for the Ukrainian economy than current account shocks. The low speed of adjustment coefficient of error correction model suggests that National Bank ofUkrainehas to carry out more active reserve management policy. Results denied the precautionary motive of reserves accumulation over the long term.В статье с помощью двух эконометрических техник (построение векторной модели коррекции ошибок и построение авторегрессионной модели с распределенным лагом) выявлено наличие долгосрочной и краткосрочной связи и их направление между международными резервами и факторами, определяющими их динамику. К основным факторам, которые уменьшают резервы в долгосрочном периоде относятся рост склонности к импорту, рост спроса на деньги и размера краткосрочного долга по остаточному сроку погашения, тогда как рост объемов ВВП и чистого притока прямых иностранных инвестиций увеличивают резервы. Доказано, что шоки, связанные с финансовым счетом платежного баланса, являются более опасными для украинской экономики, чем шоки текущего счета платежного баланса.У даній статті за допомогою двох економетричних технік (побудова векторної моделі коригування помилки та побудова авторегресійної моделі з розподіленим лагом) виявлено наявність довгострокового та короткострокового зв’язку та його напрямок між міжнародними резервами та факторами, що визначають їх динаміку. Основними факторами, що зменшують резерви у довгостроковому періоді визначено зростання схильності до імпорту, зростання попиту на гроші та розміру короткострокового боргу за залишковим терміном погашення, тоді як збільшують резерви зростання обсягів ВВП та чистого припливу прямих іноземних інвестицій. Доведено, що шоки, пов’язані з фінансовим рахунком платіжного балансу, є більш загрозливими для української економіки, ніж шоки поточного рахунку

Frobenius groups of automorphisms and their fixed points

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial: $C_G(F)=1$. In this situation various properties of $G$ are shown to be close to the corresponding properties of $C_G(H)$. By using Clifford's theorem it is proved that the order $|G|$ is bounded in terms of $|H|$ and $|C_G(H)|$, the rank of $G$ is bounded in terms of $|H|$ and the rank of $C_G(H)$, and that $G$ is nilpotent if $C_G(H)$ is nilpotent. Lie ring methods are used for bounding the exponent and the nilpotency class of $G$ in the case of metacyclic $FH$. The exponent of $G$ is bounded in terms of $|FH|$ and the exponent of $C_G(H)$ by using Lazard's Lie algebra associated with the Jennings--Zassenhaus filtration and its connection with powerful subgroups. The nilpotency class of $G$ is bounded in terms of $|H|$ and the nilpotency class of $C_G(H)$ by considering Lie rings with a finite cyclic grading satisfying a certain `selective nilpotency' condition. The latter technique also yields similar results bounding the nilpotency class of Lie rings and algebras with a metacyclic Frobenius group of automorphisms, with corollaries for connected Lie groups and torsion-free locally nilpotent groups with such groups of automorphisms. Examples show that such nilpotency results are no longer true for non-metacyclic Frobenius groups of automorphisms.Comment: 31 page

Development and implementation of special seminar “Innovative pedagogical technologies”

Taking into account modern requirements to teacher’s personality in primary education, his knowledge of innovative pedagogical technologies’ essence as well as knowledge of methodology,  relevance of the search for ways to improve the content and forms of future primary school teachers’ training has been revealed. One of the solutions to this problem can be introduction of a special seminar aimed at improving the level of innovative and technological competence of future teachers in primary education into the system of vocational training. The purpose of this article is to substantiate the conceptual and methodological significance of a special seminar "Innovative pedagogical technologies" as well as to describe process of diagnosing effectiveness of the developed special seminar. The aim of the research is achieved through the application of such theoretical and empirical methods of scientific knowledge as method of pedagogical diagnostics, methodical system modeling, method of pedagogical forecasting, analysis of results, synthesis of the results of experimental research. Based on the use of these methods, the main theoretical aspects of a special seminar development are presented, the components of its content and structure are reflected and the stages of testing effectiveness of the developed special seminar are described. The scientific novelty of the research is justified by the development of the conceptual foundations and content of the special seminar "Innovative pedagogical technologies", intended for use in the training of future primary school teachers, indicating methodological aspects of its implementation, as well as the development of a diagnostic system to test its effectiveness in the educational process of the University

ПОРУШЕННЯ ПРОДУКЦІЇЧИННИКІВ РОСТУ ПРИ ПЛАЦЕНТАРНІЙ ДИСФУНКЦІЇ.

Research is conducted 225 pregnant with placenta dysfunction (PD) with the purpose of determination of violations of products of factors of height (FH) in the different terms of pregnancy. It is shown that violation of products of FH in the system to mother- placenta- fetus is one of pathogenetic factors of development of PD. With the purpose of timely diagnostics of development of PD it is necessary to control the indexes of FH in the group of risk of pregnant, since the early terms of pregnancy.Проведено исследование 225 беременных с плацентарной дисфункцией (ПД) с целью определения нарушений продукции факторов роста (ФР) в разные сроки беременности. Показано, что нарушение продукции ФР в системе мать- плацента- плод является одним из патогенетических факторов развития ПД. С целью своевременной диагностики развития ПД необходимо контролировать показатели ФР в группе риска беременных, начиная с ранних сроков беременности.Проведено дослідження 225 вагітнихз плацентарною дисфункцією (ПД) з метою визначения порушень продукції чинників росту (ЧР) у різні строки вагітності. Показано, що порушення продукції ЧР в системі мати- плацента- плід є одним з патогенетичних факторів розвитку ПД. З метою своєчасної діагностики розвитку ПД необхідно контролювати показники ЧР у групі ризику вагітних, починаючи з ранніх термінів вагітності

Features of high-strength composite material structure creation

The basis of technology proposed is use of a sol-gel method for preventing polycrystalline corundum fiber from crystallization during heating to high temperature and for low-temperature synthesis of prescribed phases in a corundum matrix with the aim of improving the operating properties of composite materials based on corundum. As a result of firing a charge based on corundum powder modified with tetraethoxysilane and polycrystalline corundum fiber modified with ethylsilicate-32 at 1360°C materials are created with very good strength properties. The materials exhibit electrical insulation properties and are stable in ionized gas streams at the level of known analogs as a result of creating self-reinforced mullite and β-SiC corundum matrix, reinforced with polycrystalline fiber and rapidly sintered due to presence of silicon oxynitride