On nonformal simply connected symplectic manifolds

For any $N \geq 5$ nonformal simply connected symplectic manifolds of dimension $2N$ are constructed. This disproves the formality conjecture for simply connected symplectic manifolds which was introduced by Lupton and Oprea.Comment: 20 pages, LaTeX; the short announcement see in math.SG/9810065; a revised versio

Massey products in symplectic manifolds

The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are exposed. The construction uses the symplectic blow-up and is based on the author results, which describe conditions under which the blow-up of a symplectic manifold X along its submanifold Y inherits nontrivial Massey products from X ot Y. This gives a general construction of nonformal symplectic manifolds.Comment: LaTeX, 48 pages, 2 figure

Развитие юридического образования в Украине (Development of legal education in Ukraine)

В статье исследуется процесс реформирования и развития юридического образования в период с ХХ по ХХ века. Сформулированы предложения общих подходов к реформированию юридического образования в Украине. Предложены пути совершенствования качества юридического образования населения в Украине. (The article examines the process of reforming and legal education development in the period from the 20th to the 21st century. This article formulates proposals on common approaches to reforming legal education in Ukraine. It proposes ways to improve the quality of legal education in Ukraine’s population.

Sur la forme de la boule unit\'{e} de la norme stable unidimensionnelle

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then the realizable forms as stable ball of Riemannan manifolds of dimension larger than three. For a Riemannian manifold $(M, g)$ fixed, we show that a broad class of polytopes can appear as stable ball of metrics in the conformal class of $g$. We use for that a polyhedral technique.Comment: 13 pages, in Frenc

Scientific and theoretical justification of the essence of territories development

У статті здійснено науково-теоретичне обґрунтування сутності розвитку територій. З метою вивчення та детального аналізу поняття «розвиток» у роботі узагальнено існуючі підходи до розвитку в контексті визначення його цілей, серед яких виділено: функціонально-ресурсний, системний, поведінковий, кластерний, стратегічний, сценарний. Визначено, що за змістовним наповненням розвиток представляє собою комплекс змін, за допомогою яких соціальна система, яка орієнтована на задоволення основних потреб і запитів окремих людей і груп населення, рухається від стану загальної незадоволеності до нових більш сприятливих матеріальних і духовних умов життя. Обґрунтовано, що ефективність розвитку території характеризує стан регіону як соціально-економічної системи, яка відображатиме характерні особливості різного роду економічних, соціальних та інших явищ у процесі вдосконалення його функціонування й у контексті задоволення їм певних суспільних потреб. Доведено взаємозв’язок між забезпеченням розвитку території та вирішенням багатьох територіальних соціально-економічних проблем. Виявлено ключові ознаки розвитку території, а саме: стійкість та збалансованість. Досліджено теорії регіональної політики, які було класифіковано у три групи: теорії розміщення, теорії регіонального зростання і теорії державного регулювання економічного розвитку. Виявлено внутрішні чинники розвитку території, серед яких найбільший вплив мають: територіальні, адміністративні, економічні, інституційні, демографічні, організаційні. Доведено важливість побудови терміносистеми економічного розвитку території, яка сприятиме схематизації структури даного поняття та його більш ґрунтовній інтерпретації.The article presents the scientific and theoretical justification of the essence of territorial development. For the purpose of study and detailed analysis of the «development» concept, the work generalizes existing approaches to development in the context of its goals determining, among which are distinguished: functional-resource, systemic, behavioral, cluster, strategic, scenario. It has been determined that, by meaningful content, development is a complex of changes by which a social system, which oriented on satisfying the basic needs and needs of individuals and population groups moves from a state of general dissatisfaction to new more favorable material and spiritual living conditions. It is substantiated that the effectiveness of a territory development characterizes the region state as a socio-economic system, which will reflect the characteristic features of various economic, social and other phenomena in the process of improving its functioning and in the context of meeting certain social needs. The relationship between ensuring of the territory development and the solution of many territorial socio-economic problems is proved. The key features of the territory development were identified, namely: sustainability and balance. Theories of regional policy are investigated, which were classified into 3 groups: placement theories, regional growth theories and theories of state regulation of economic development. Internal factors of the territory development are identified, among which the most significant influence is: territorial, administrative, economic, institutional, demographic, organizational. An importance of term system building of the territory economic development, which will contribute to the schematization of this concept structure and its more thorough interpretation, is proved

Statistical Testing of Blockchain Hash Algorithms

Various methods are used for statistical testing of cryptographic algorithms, for example, NIST STS (A Statistical Test Suite for the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications) and DIEHARD (Diehard Battery of Tests of Randomness). Tests consists of verification the hypothesis of randomness for sequences generated at the output of a cryptographic algorithm (for example, a keys generator, encryption algorithms, a hash function, etc.). In this paper, we use the NIST STS technique and study the statistical properties of the most common hashing functions that are used or can be used in modern blockchain networks. In particular, hashing algorithms are considered which specified in national and international standards, as well as little-known hash functions that were developed for limited use in specific applications. Thus, in this paper, we consider the most common hash functions used in more than 90% of blockchain networks. The research results are given as average by testing data of 100 sequences of 108 bytes long, which means that is, the size of the statistical sample for each algorithm was 1010 bytes. Moreover, each test (for each of the 100 sequences) was considered as an independent observation. In addition, the article presents statistical portraits for each algorithm under study (diagrams of the numbers of passing each test)

Reflection of hydrogen and deuterium atoms from the beryllium, carbon, tungsten surfaces

Particle reflection coefficients for scattering of hydrogen and deuterium atoms from amorphous beryllium, carbon and tungsten were obtained, which are of interest for thermonuclear reactor physics. For the case of deuterium scattering from tungsten the data were also calculated for polycrystalline and crystalline target. The calculations were carried out by two methods: by modeling the trajectories of the incident particles and by using the binary collision approximation. Interaction potentials between hydrogen and helium atoms and the selected materials were calculated in the scope of the density function theory using program DMol for choosing wave functions. The dependence of the reflection coefficient RN on the potential well depth was found. The results demonstrate a good agreement with the available experimental values.Peer reviewe