Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions

The paper is a continuation of the study started in \cite{Yorzh1}. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of $\delta$ type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of $L_1$ and $C^M$ edge potentials) are obtained which link together two different quantum graphs under the assumption that their spectra coincide. Applications are given to the problem of recovering matching conditions for a quantum graph based on its spectrum.Comment: arXiv admin note: substantial text overlap with arXiv:1403.761

Trace formulae for graph Laplacians with applications to recovering matching conditions

Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an infinite series of trace formulae which link together two different graph Laplacians provided that their spectra coincide is derived. Applications are given to the problem of reconstructing matching conditions for a graph Laplacian based on its spectrum

Presentation potential using in pedagogical interaction process

The given article is aimed at considering multimedia presentation potential and its influence on strengthening classroom teacher-student interaction. In the article the importance of using this kind of activity in the study process is pointed in connection with educational state policy on the one hand. On the other hand, gained students’ skills as a final result of work with presentations met employers’ demand for both parent and world labour-markets and bring competitive benefit to the candidates. Scientific novelty and results. Multimedia presentation is considered as a specific complex of classroom activities. The students are oriented on the self analysis and presentation assessment. It is shown that well-organized process of peer students’ assessment allows to simultaneously helping in solving the didactic and methodical problems. To this purpose the system of assessment criteria should be developed. It has to be clear for students for making assessment feasible and time-saving. The example of a possible variant of criteria system is described; quality of the presentations prepared by students can be defined based on such system criteria. The author also analyzed software products of the three main platforms (Windows, Linux, MacOs) which have different tools and allow to follow users’ needs for creating presentations. In the article there is a comparative table of the two most popular software development: the program Microsoft PowerPoint and the web-service Prezi for realizing the relevance of their use in the study process. Practical significance of the present article concludes in author’s suggestions of some recommendations for presentation potential use as a tool of improving pedagogical interaction process with contemporary students. Целью данной статьи является рассмотрение потенциала мультимедийной презентации и его влияния на укрепление педагогического взаимодействия между преподавателем и обучающимися во время аудиторного занятия. В статье указывается на важность использования данного вида деятельности в учебном процессе в связи с требованиями государственной образовательной политики по отношению к современной ежедневной педагогической практике. Навыки, сформированные у обучающихся в результате работы с презентациями, высоко ценятся работодателями как на отечественном, так и на зарубежном рынках труда и дают их обладателям конкурентное преимущество. Научная новизна и результаты. Учебная мультимедийная презентация рассмотрена как особый комплексный вид деятельности, в который на занятии вовлечены все обучающиеся, наделенные соответствующим функционалом и ориентированные на самостоятельный разбор, анализ и оценивание предоставляемой информации. Показано что правильно организованный процесс оценивания студентами друг друга позволяет одновременно решить несколько задач дидактического и методического характера. Однако для этого необходимо разработать систему критериев оценки презентации, которая будет прозрачна и понятна обучающимся, а процесс оценивания будет посилен и не займет много времени. Описан пример возможного варианта системы критериев, на основе которых определяется качество подготовленных студентами презентаций. Автором проанализированы программные продукты на базе трех основных платформ (Windows, Linux, MacOs), обладающие разным инструментарием и позволяющие создавать презентации с учетом потребностей пользователей. Приводится сравнение двух наиболее популярных софтверных разработок: программы Microsoft PowerPoint и веб-сервиса Prezi с точки зрения актуальности и целесообразности их использования в учебном процессе. Практическая значимость статьи состоит в предложении и описании основных оценочных категорий работы с мультимедийными презентациями на аудиторном занятии. Даны рекомендации по использованию ее ресурсов для налаживания эффективного педагогического взаимодействия с учащимис

Mechanical alloys Mg-Me (Me: Ti, Fe, Ni, Al) & Mg-Me1-Me2(Ме1:Al, Me2: Ti, Fe, Ni) with low resistance and improved kinetics of hydrogenation/dehydrogenation for hydrogen storage applications

Changes in MgH2 decomposition kinetics were investigated in dependence on complex doping of MgH2 by Al, Ti, Ni,and Fe. Reactive mechanochemical alloying method (RMA) was applied in the temperature descending regime. It was found that addition of Al+Ni+Ti, Al+Ti, Fe+Ti (see below) and Al+Fe elements combinations led to a lower  thermal stability and, consequently, to a lowering of the temperature of hydrogen desorption onset. Whereas desorption began at temperature of 320 °C from the pure MgH2, the aditions of Al, Ni, Ti and Fe lowered the start of the desorption down to 250°C (at hydrogen pressure 0.1 MPa in the reactor). Very fast desorption kineticsprecize at 300 0C and PH 2= 0.1 MPa were observed for Mg+Me mixture in comparison with the pure Mg. Sorption capacity of investigated mechanically-alloyed composites varied from 5 to 6.5 wt. % H2. The tested materials showed a high potential as hydrogen storage alloys especially for stationary application

Fast diffusion of graphene flake on graphene layer

Diffusion of a graphene flake on a graphene layer is analyzed and a new diffusion mechanism is proposed for the system under consideration. According to this mechanism, rotational transition of the flake from commensurate to incommensurate states takes place with subsequent simultaneous rotation and translational motion until the commensurate state is reached again, and so on. The molecular dynamics simulations and analytic estimates based on ab initio and semi-empirical calculations demonstrate that the proposed diffusion mechanism is dominant at temperatures T ~ Tcom, where Tcom corresponds to the barrier for transitions of the flake between adjacent energy minima in the commensurate states. For example, for the flake consisting of ~ 40, 200 and 700 atoms the contribution of the proposed diffusion mechanism through rotation of the flake to the incommensurate states exceeds that for diffusion of the flake in the commensurate states by one-two orders of magnitude at temperatures 50 - 150 K, 200 - 600 K and 800 - 2400 K, respectively. The possibility to experimentally measure the barriers to relative motion of graphene layers based on the study of diffusion of a graphene flake is considered. The results obtained are also relevant for understanding of dynamic behavior of polycyclic aromatic molecules on graphene and should be qualitatively valid for a set of commensurate adsorbate-adsorbent systems.Comment: 33 pages, 6 figure