Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod

We study waves in a rod of finite length with a viscoelastic constitutive equation of fractional distributed-order type for the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain case corresponding to stress relaxation. In solving system of differential and integro-differential equations we use the Laplace transformation in the time domain

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33In this paper, a comparative analysis of the models involving fractional derivatives of di®erent orders is given. Such models of viscoelastic materials are widely used in various problems of mechanics and rheology. Rabotnov's hereditarily elastic rheological model is considered in detail. It is shown that this model is equivalent to the rheological model involving fractional derivatives in the stress and strain with the orders proportional to a certain positive value less than unit. In the scienti¯c literature such a model is referred to as Koeller's model. Inversion of Rabotnov's model developed by himself based on algebra of operators results in similar rheological dependences. Inversion of Koeller's model carried out using Miller's theorem coincides inherently with Rabotnov's inversion procedure.∗ This paper has been partially supported by the Russian Foundation for Basic Research under Grant No. 05-08-17936

Soliton-Like Solutions in the Problems of Vibrations of Nonlinear Mechanical Systems: Survey

In the given chapter, free vibrations of different nonlinear mechanical systems with one-degree-of-freedom, two-degree-of-freedom, and multiple-degree-of-freedoms are reviewed with the emphasis on the vibratory regimes which could go over into the aperiodic motions under certain conditions. Such unfavorable and even dangerous regimes of vibrations resulting in the irreversible process of energy exchange from its one type to another type are discussed in detail. The solutions describing such processes are found analytically in terms of functions, which are in frequent use in the theory of solitons

Chiral String in a Curved Space: Gravitational Self-Action

We analyze the effective action describing the linearised gravitational self-action for a classical superconducting string in a curved spacetime. It is shown that the divergent part of the effective action is equal to zero for the both Nambu-Goto and chiral superconducting string.Comment: 5 pages, LaTe

Vacuum polarization near cosmic string in RS2 brane world

Gravitational field of cosmic strings in theories with extra spatial dimensions must differ significantly from that in the Einstein's theory. This means that all gravity induced properties of cosmic strings need to be revised too. Here we consider the effect of vacuum polarization outside a straight infinitely thin cosmic string embedded in a RS2 brane world. Perturbation technique combined with the method of dimensional regularization is used to calculate ${}_{vac}^{ren}$ for a massless scalar field.Comment: 8 pages, RevTeX

Demokratiseringsprocessen av postsovjetiska länder. En jämförande analys av den demokratiska utvecklingen i Ukraina och Vitryssland efter Sovjetunionens fall.

Syftet med denna studie är att ta reda på vad som gör att Ukraina lyckats bli en erkänd demokrati samtidigt som Vitryssland förblir en auktoritär diktatur. Vi ska i denna jämförande analys titta på de demokratiseringsprocesser som ägt rum i de båda länderna. Vi kommer lägga energi på staten, det civila samhället och globaliseringen. Vår analys visade att det efter självständighetsförklaringarna fanns auktoritära tendenser båda länderna. Trots att Kutjma så tidigt som 1998 tog avstånd från ett direkt auktoritärt styre liknande det i Vitryssland förblev Ukraina en semi-diktatur fram till den orangea revolutionen då landet fick en ny chans att bygga demokrati. Orangea revolutionen och företeelser som gjorde denna möjlig ligger till grund för den demokratiska framgången i Ukraina. Vitryssland saknar de nödvändiga förutsättningar som kan resulteras i någon liknande aktion som orangea revolutionen. Bland de förutsättningarna är det viktigt att nämna: någorlunda liberaliserad politik, politisk konkurrens, förekomsten av internationella NGOs samt oberoende medier

DIGITALIZATION OF EDUCATION AS A DRIVER OF DIGITAL TRANSFORMATION OF UKRAINE

The article analyzes the development of the education system of Ukraine, taking into account the potential of digitalization in the context of globalization. A specific object of research is the process of transformation of the education system through the introduction of digital services and technologies. In order to conduct a comprehensive assessment of the digitalization potential of the educational system of Ukraine, the disadvantages and advantages of digitalization of educational institutions are analyzed using the example of the implementation of distance learning. The process of digitalization of modern education under the influence of the process of universal computerization and the requirements of the modern information society is considered. Examples of modern computer technologies that are already used in the learning process, their impact on society are given. The scheme of the implementation of international experience in Ukrainian educational institutions is given, the norms and directives of the EU governments in the formation and development of the European Higher Education Area are analyzed. The description of international projects to be implemented by universities is presented. The elements of E-learning are introduced into the educational process based on the results of the projects, including measures aimed at improving the quality of educational services and the qualifications of the teaching staff: a series of trainings related to modern teaching methods of education, practical seminars for teachers and students, etc. Structural model of the functioning of the electronic knowledge platform is presented, elements of the platform for providing educational activities in the field of digitalization in Ukraine are described. Based on a review of publications, regulatory requirements and directives, the article discusses the trends in the process of digital transformation of Ukraine

LEGAL REGULATION ISSUES OF CRYPTOCURRENCY CIRCULATION IN UKRAINE

The aim of the article is a comparative legal study of laws and regulations that determine the legal principles for the regulation of cryptocurrency circulation in some foreign countries and in Ukraine and, on this basis, a definition of ways to improve domestic legislation in this sphere. The subject of the study is an interrogation of legal regulation issues of cryptocurrency circulation in Ukraine. Methodology. The study is based on a legal comparison of the regulation of cryptocurrency circulation in Ukraine and in foreign countries. Based on a comparative legal study of certain provisions of Ukrainian legislation, the possibilities and limits of implementation of positive foreign experience in this sphere are determined. The results of the study revealed that to implement foreign experience for the legal regulation of cryptocurrency circulation, it is necessary to postpone the final transition to a floating rate regime by reinforcing state interference. Moreover, it is necessary to strengthen currency control not only for currency transactions with cryptocurrency but also for the activities of entities that determine the state policy on cryptocurrency regulation, as well as operate respectively using instruments provided for by the regulations of the current legislation. Practical implications. The positive experience of the formation of the foreign exchange market in other countries demonstrates that the gradual transition to cryptocurrency circulation is the beginning of the natural market rate, the balance of payments and gradual liberation of the national economy from the pressure of administrative and corruption restrictions. Relevance/originality. The legal analysis of the regulation of cryptocurrency circulation in Ukraine and the definition of problems is the basis for developing the most promising directions for the development of domestic legislation in this sphere

Система уравнений теплообмена и изменения массы фазы в проточных аккумуляторах теплоты фазового перехода

The article proposes a system of differential equations describing the processes in the latent phase transition heat accumulators (PTHA) and formulates an appropriate boundary value problem.  Herewith a simplified mathematical model is used with the main assumptions such as one-dimensional flow, quasi-stationary temperature fields and one-dimensional change of phase boundary.In contrast to other publications associated with calculations of latent PTHA based on the similar simplifications, the article uses such a parameter as a specific mass of phase per unit of the accumulator length (per running meter of length), as the unknown function, thereby providing the universal writing of differential equations for all the latent PTHA where the simplifications used are appropriate in their deriving.The specific features of different accumulators are that the coefficients in the equations represent different functions that are proper for a specific design of these devices. There are two examples noted to calculate these coefficients (of the thermal resistances) for specific types of accumulators, calculated on the basis of one-dimensionality and quasi-stationarity as applied to the change of phase boundary.The proposed mathematical model owing to its generality allows to describe a wide class of latent heat accumulators which have the heat transfer fluids, and on this basis analyze the features of the charging and discharging processes as well as to have the opportunity to find the optimal parameters to optimize the unit as a whole.В статье предложена система дифференциальных уравнений, описывающих процессы в проточных аккумуляторах теплоты фазового перехода (АФП) и поставлена соответствующая краевая задача. При этом используется упрощенная математическая модель со следующими основными допущениями – предполагается одномерность течения теплоносителя, квазистационарность температурных полей, одномерность перемещения границы раздела фаз.В отличие от других работ, посвященных расчетам проточных АФП, основанных на аналогичных упрощениях, использование в данной статье такого параметра, как удельная масса фазы на единицу длины аккумулятора (на погонный метр длины) в качестве неизвестной (искомой) функции, приводит к записи дифференциальных уравнений универсальной для всех проточных АФП, в которых приемлемы используемые при их выводе упрощения. Конкретные отличия для различных аккумуляторов выражаются в том, что коэффициенты в уравнениях представляют собой разные функции, соответствующие конкретному конструктивному исполнению этих устройств. Отмечены два примера вычисления таких коэффициентов (термических сопротивлений) для конкретных типов аккумуляторов, вычисляемых на основе одномерности и квазистационаности применительно к границе раздела фаз.Представленная математическая модель в силу своей общности позволяет описать широкий класс проточных аккумуляторов теплоты и на этой основе проводить анализ особенностей процессов зарядки и разрядки, а также осуществлять выбор их оптимальных параметров с целью оптимизации работы энергетической установки в целом.