Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure

The Poisson bracket compatible with the classical reflection equation algebra

We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes the $XXX$ Heisenberg magnet with boundary conditions, the generalized Toda lattices and the Kowalevski top.Comment: 13 pages, LaTeX with AmsFont

MMF linac high energy part LLRF system status

Accelerated beam quality and level of beam losses are strongly affected by accelerating field phase and amplitude stability and accuracy. Due to this a constant attention was paid to the Low Level RF systems of the MMF linac. During the last 4-5 years many components of LLRF system of high -energy part of MMF linac were significantly rebuilt and reconstructed, and as a result higher accuracy and longterm stability were achieved, along with the higher reliability and more simple maintenance. Besides, the time needed to carry out a procedure of linac accelerating cavities, longitudinal tuning (setting and adjusting of nominal values of amplitudes and phases in the accelerating cavities), was reasonably decreased. Also, a preamplifier feeding the input of the klystron amplifier was modified to get more reliable operation

Эндопротезирование таранной кости керамическим эндопротезом в сочетании с тибиальным компонентом эндопротеза голеностопного сустава: клинический случай

Background: Surgical treatment of patients with talus posttraumatic aseptic necrosis and its consequences usually includes tibiotalocalcaneal arthrodesis with various foot joints according to additional indications. This type of surgical treatment has number of significant disadvantages: traumatic surgical technique, permanent loss of movement in functionally significant joints, high risk of non-union, high frequency of residual deformities, the need for long periods of limb immobilization. The question arises: how to overcome the existing disadvantages and improve the results of talus posttraumatic aseptic necrosis treatment? A potential solution to this problem is the total talus endoprosthetics. Clinical case: A 64-year-old patient came to the clinic complaining of pain and deformity of the right foot and ankle area. After the examination, talus posttraumatic aseptic necrosis was diagnosed. The patient underwent ankle joint arthroplasty using total talus ceramic endoprosthesis in combination with the tibial component of the ankle joint endoprosthesis, a course of rehabilitation treatment was performed. Results: The VAS and AOFAS scales indicators showed a significant improvement both in the pain decrease (from 75 mm before surgery to 10 mm after), and in the functional state according to AOFAS by 2.2 times (from 36 to 80 points 20 months after surgery). By the last follow-up the patient could take more than 8000 steps a day. Conclusions^ Considering the good clinical result achieved, the ankle joint arthroplasty using total talus ceramic endoprosthesis in combination with the tibial component of the ankle joint endoprosthesis can be considered a promising method of treatment of this severe pathology.Актуальность. Для оперативного лечения пациентов с посттравматическим асептическим некрозом таранной кости и его последствиями обычно используют большеберцово-таранно-пяточный артродез, включающий различные суставы стопы по дополнительным показаниям. Такой вид хирургического лечения, несмотря на свои достоинства, обладает рядом существенных недостатков: высокая травматичность, необратимая потеря движений в функционально значимых суставах, высокий риск несращений и остаточных деформаций, необходимость длительных сроков иммобилизации конечности. Возникает вопрос: как преодолеть существующие недостатки и улучшить результаты лечения пациентов с посттравматическим асептическим некрозом таранной кости? Потенциальным решением данной проблемы является эндопротезирование таранной кости. Описание клинического случая. Пациентка 64 лет обратилась в клинику с жалобами на боль и деформацию правой стопы и области голеностопного сустава. После проведенного обследования был диагностирован посттравматический асептический некроз таранной кости. Пациентке было выполнено эндопротезирование таранной кости керамическим эндопротезом в сочетании с тибиальным компонентом эндопротеза голеностопного сустава, выполнен курс реабилитационного лечения. Результаты. Показатели шкал VAS и AOFAS продемонстрировали существенное улучшение как в виде снижения болевых ощущений в 7,5 раз: с 75 мм перед операцией до 10 мм, так и функционального состояния по AOFAS в 2,2 раза: с 36 до 80 баллов через 20 мес. после хирургического вмешательства. К последнему контрольному визиту пациентка могла делать более 8000 шагов в день. Заключение. Учитывая хороший клинический результат, эндопротезирование таранной кости керамическим эндопротезом в сочетании с тибиальным компонентом эндопротеза голеностопного сустава можно считать перспективным методом лечения посттравматического асептического некроза таранной кости

Посухостійкість гібридів яблуні з участю сорту Видубицька плакуча в умовах Лісостепу України

Objective – to determine the drought-resistance of hybrids of Vydubytska plakucha apple × Malus domestica Borkh cultivars in Forest-Steppe of Ukraine, waterlogging of tissues, water-retaining capacity, the general deficit of water in leaves and their turgorisation. Material and methods. The drought tolerance of 15 hybrids of the apple of the Vydubytska plakucha × cultivers M. domestica from the gene-pool M.M. Gryshko National Botanical Garden of the NAS of Ukraine. Hyb ri dization was carried out to obtain decorative forms, apple trees with a sign of «weeping», inherited from the сultivar Vydubytska plakucha. Results. The greatest amount of water was recorded in the leaves of hybrids of the V. p. × Khoroshovka (56.8 %), V. p. × 1–22 (54.3 %), the smallest – in the leaves of hybrids V. p. × Oranzheve (51.6 %), V. p. × Uralske nalyvne (50.0 %). Water deficiency in the leaves was 15–25 %, which does not lead to lethal damage to plants. A high percentage of the moisture content was characteristic of the V. p. × Khoroshovka, and the lowest was the hybrid of the V. p. × Renet Koksa Oranzhevyy. Conclusion. The most drought-resistant are the hybrids of V. p. × Khoroshovka and V. p. × Luyiza, less stable – V. p. × Renet Koksa Oranzhevyy, V. p. × Uralske nalyvne, V. p. × Antor, the intermediate place is occupied by hybrid V. p. × Uelsi.Мета – визначити посухостійкість гібридів яблуні ‘Видубицька плакуча’ × сорти Malus domestica Borkh. у Лісостепу України, обводненість тканин, водоутримувальну здатність, загальний дефіцит води у листках та їх тургорисцентність. Матеріал та методи. Оцінено посухостійкість 15 гібридів яблуні 'Видубицька плакуча' × сорти M. domestica з генофонду Національного ботанічного саду імені М.М. Гришка НАН України. Гібридизацію було проведено для одержання декоративних форм яблуні з ознакою “плакучість”, успадкованою від сорту ‘Видубицька плакуча’. Результати. Найбільшу кількість води відзначено в листках гібридів В. п. × Хорошовка (56,8 %), В. п. × 1-22 (54,3 %), найменшу – в листках гібридів В. п. × Оранжеве (51,6 %), В. п. × Уральське наливне (50,0 %). Водний дефіцит у листках становив 15—25 %, що не призводить до летального пошкодження рослин. Найвищим відсотком утримання вологи характеризувалися В. п. × Хорошовка, а найнижчим – гібрид В. п. × Ренет Кокса Оранжевий. Висновок. Найпосухостійкішими є гібриди В. п. × Хорошовка та В. п. × Луїза, менш стійкими – В. п. × Ренет Кокса Оранжевий, В. п. × Уральське наливне, В. п. × Антор, проміжне місце посідає гібрид В. п. × Уєлсі

Resonances and O-curves in Hamiltonian systems

We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.Comment: 12 page

Impact of Friction Stir Processing Parameters on Forming the Structure and Properties in AISI 420 Steel Surface Layer

Research has been done into the influence of friction thermomechanical treatment parameters on forming the structure and properties in a surface layer of 20X13 steel. The paper presents a theoretical approach towards controlling the process variables. A hardened layer with a thickness of 1,7 mm was obtained after 20X13 steel had been subjected to the process. The thickness of the layer that had a microhardness of ≥600HV0,05 turned out to be about 0,75mm while the microstructure of the hardened layer was martensitic, martensitic and perlitic with dispersed inclusions of carbides. It was established that the feed has the biggest influence on the thickness of the hardened layer.     Keywords: friction stir processing, rotation speed, tool feed, normal force, microhardness, microstructure

Coulomb Blockade in low mobility nanometer size Si:MOSFETs

We investigate coherent transport in Si:MOSFETs with nominal gate lengths 50 to 100nm and various widths at very low temperature. Independent of the geometry, localized states appear when G=e^{2}/h and transport is dominated by resonant tunnelling through a single quantum dot formed by an impurity potential. We find that the typical size of the relevant impurity quantum dot is comparable to the channel length and that the periodicity of the observed Coulomb blockade oscillations is roughly inversely proportional to the channel length. The spectrum of resonances and the nonlinear I-V curves allow to measure the charging energy and the mean level energy spacing for electrons in the localized state. Furthermore, we find that in the dielectric regime, the variance var(lng) of the logarithmic conductance lng is proportional to its average value consistent with one-electron scaling models.Comment: 4 pages, 4 figure

Graphical Analysis of the Growth Rate of National Economies by Considering the Supply Chain Strategy in 25 Countries over the Period From 2000 to 2016

The article presents the graphical analysis of economic indicators for 25 countries: GDP growth rate (%) and GDP per person employed (thousand US dollars) for the period from 1990 to 2016 by considering the supply chain strategy (SCS) and transparency. The authors carried out the decomposition of economic growth rates of selected countries according to the following factors: 1) extensive factors – the growth rate of the capital stock and the size of labor force; 2) intensive factors – RD expenditures; 3) the dynamics of foreign direct investment in the country 4) supply chain strategy. Over the past 16 years, only a few countries from the sample have shown growth of the national economy higher than the growth rates of the world economy. These are China, Turkmenistan, India, Malaysia, and Singapore (their economies grew at a rate of more than 5% per year). The most dynamic renewal of fixed assets can be observed in China, the United States and Japan. At the same time, over the past 10 years China has demonstrated an active investment policy, increasing the investment in fixed assets almost five times. China and India were countries that most actively used the size of labor force as a factor of extensive growth. Korea, Japan, Germany, USA, China and Singapore demonstrated the most dynamic growth in RD expenditures. Despite the non-monotonous dynamics of foreign direct investment in these countries, over the entire period of observation from 1990 to 2017, the United States has been the most attractive country for foreign direct investment. At the same time, the most significant growth in foreign direct investment was recorded in China and, recently, in the United Kingdom