ЗАДАЧА З ІМПУЛЬСНОЮ ДІЄЮ ДЛЯ ОДНОГО РІВНЯННЯ КОЛИВАНЬ СТРУНИ

The development of modern science and technology requires thestudy of problems for differential equations describing processes withshort-term changes, or which are influenced by external forces, theduration of which can be neglected when compiling relevantmathematical models. Such tasks are found in thermophysics,mechanics, chemical technologies, biology, management theory and other branches of science and technology, where they studyprocesses under the influence of short-term forces and calledsystems with impulse action. Such systems contain differentialequations, an equation describing gaps in the first kind at moments ofimpulse action and impulse conditions. The presence of impulseaction substantially changes and complicates the behavior of thetrajectories of such problems, even for relatively simple differentialequations. The study of differential equations with impulse actionbegan with the development of nonlinear mechanics and attracted theattention of many researchers to the possibility to really describe theprocesses in nonlinear systems. In spite of the large number of worksdevoted to various questions of the theory of differential equationswith impulse action, a large number of problems of the qualitativetheory of such equations remain open for many cases. There is theinfluence of impulse action in fixed and non-fixed moments of time. Inthis paper we consider the process of oscillation of a string withinstantaneous increase of energy at moments when the full energy ofa string reaches this critical level. That is, the moments of impulseaction are not predetermined, but regulated by the process itself. Forsuch a task there are conditions for the existence of solutions forwhich the impulse action is carried out an infinite number of times andconstructed such solutions.Исследуется процесс колебаний струны с импульсным воздействием в моменты времени, когда полная энергия колебаний струныдостигает заданного критического значения. Определены условиясуществования решений, для которых импульсное воздействиепроисходит бесконечное количество раз и записано вид решений.Досліджено процес коливання струни з імпульсною дією при досягненні енергії коливання струни заданого критичного рівня. Визначено умови існування розв’язків, для яких імпульсна дія відбувається нескінчену кількість разів та записано вигляд розв’язків

Pyrene, a Test Case for Deep-Ultraviolet Molecular Photophysics

We determined the complete relaxation dynamics of pyrene in ethanol from the second bright state, employing experimental and theoretical broadband heterodyne detected transient grating and two-dimensional photon echo (2DPE) spectroscopy, using pulses with duration of 6 fs and covering a spectral range spanning from 250 to 300 nm. Multiple lifetimes are assigned to conical intersections through a cascade of electronic states, eventually leading to a rapid population of the lowest long-living excited state and subsequent slow vibrational cooling. The lineshapes in the 2DPE spectra indicate that the efficiency of the population transfer depends on the kinetic energy deposited into modes required to reach a sloped conical intersection, which mediates the decay to the lowest electronic state. The presented experimental–theoretical protocol paves the way for studies on deep-ultraviolet-absorbing biochromophores ubiquitous in genomic and proteic systems

Reduction of longitudinal axial residual stresses in near-root region of circumferential joint of steam pipeline in technological way

The paper proposes a variant for solving the problem of reduction of longitudinal residual stresses in near-root region of a circumferential welded joint of section of steam pipeline by FEM simulation of the stress-strain state of repaired section of a circumferential weld in the zone of lack of root penetration on a thin-wall shell of 89 mm diameter and 6 mm wall thickness from steel 20. The result of solving the problem is total distribution of stresses and residual plastic deformations in the repaired zone

Surgical treatment of intra-articular fractures of the proximal humerus

Background. The most severe category of fractures of the proximal humerus are  intra-articular injuries which are accompanied with humeral head ischemia caused by an injury and aggravated by surgical intervention. Due to frequent disruption of vascularization with subsequent necrosis of the humeral head, there is a need to stimulate reparative osteogenesis in intra-articular injuries to prevent ischemic changes in the humeral head. The aim of the study. To improve the results of surgical treatment of intra-articular fractures ofthe proximal humerus based on the development of a new osteosynthesis technique using non-free osteomuscular graft. Material and methods. We analyzed the results of treatment of 48patients with 11- C1 and 11-C2 intra-articular fractures of the proximal humerus, who had hospital treatment at the emergency department of traumatology of the Novosibirsk City Clinical Hospital No.  1 and were subsequently observed on an outpatient basis. An  analysis of literature data using search words was carried out in the PubMed and eLibrary databases. Results. According to the data obtained during the study, the functional and radiological results of the patients who were treated using the method of reparative stimulation with a non-free osteomuscular graft from the coracoid process are statistically significantly higher than the results of the control group. Conclusion. Using autoplasty with a non-free osteomuscular graft from the coracoid process improves the results and reduces the risk of developing post-traumatic aseptic necrosis of the humeral head

INFLUENCE OF CHANGE OF POSITION OF FEMUR PROXIMAL SEGMENT ELEMENTS ON DIAGNOSTICS AND TREATMENT TACTICS OF HIP JOINT PATHOLOGY

The aim. of the research was to create diagnostic method for determination of attitude position of elements of femur proximal segment for understanding of development of hip joint pathology and determination of surgical tactics of treatment. The method of precise determination of angle interrelations between the elements of hip joint with use of multispiral computed tomograms. Offered method of diagnostics of estimation of position of elements of femur proximal segment is a necessary way of research of understanding for development of degenerative changes in hip joint and. also for determination of tactics and. method of treatment

TREATMENT OF EARLY PERIPROSTHETIC INFECTION AT HIP REPLACEMENT

We carried out the analysis of results of treatment of patients with early periprosthetic infection after total hip replacement with use of tactics aimed at the preservation of an implant and function of the operated joint, based on a multi-stage surgical rehabilitation, clinical and. laboratory monitoring of the wound healing process. The efficiency of chosen tactics in 83 % of cases was shown. Based on these results an algorithm for treatment of early periprosthetic infection at the hip replacement that can be recommended for widespread use in clinical practice was offered

Features of revision hip arthroplasty: prolapse of the acetabular component into the pelvis cavity

The article is devoted to some features of revision hip arthroplasty, especially to the prolapse of the acetabular component into the pelvis cavity. International literature review is presented, in which the authors warn surgeons about some possible complications during the removal of the components using retroperitoneal and external approach. In case of contact of acetabular component with neurovascular bundle in pelvis, foreign authors recommend retroperitoneal approach

Расчет вероятности выполнения требований к диаметру пор в сварных швах

Виведено математичну залежність, яка враховує змінюваність в утворенні пор при зварюванні і дає можливість розрахувати ймовірність виконання вимог до діаметра пор по експериментально знайдених характеристиках статистичного розподілу кількості та діаметра пор на одиничній ділянці зварного шва. При виведенні математичної залежності використані статичні закони розподілу Вейбулла і Пуассона та правило множення ймовірностей. Розрахунком для граничних умов перевірена адекватність теоретично виведеної залежності. Отримана математична залежність дає змогу за обмеженою кількістю експериментальних даних визначати придатність процесів зварювання задовольняти вимоги при випробуваннях на стійкість до утворення пор у процесі розробки зварювальних матеріалів та призначенні параметрів режиму зварювання, при аналізуванні даних про дефектність у зварювальному виробництві, при аналізуванні можливих відмов процесу зварювання і наслідків таких відмов при оцінці технологічних ризиків у зварювальному виробництві.Mathematical dependence accounting changeability in formation of pores at welding and allows expecting probability of implementation of requirements to the diameter of pores from the experimentally found descriptions of the statistical distributing of amount and diameter of pores on the single area of the weld-fabricated guy-sutures is in-process shown out. For the development of mathematical dependence the static laws of distributing of Veybull and Puasson and rule of probabilities increasing were used. Adequacy of the theoretical dependence was tested by calculation of boundary conditions. Obtained mathematical dependence allows on the determination of the fitness of welding processes by the limited amount of experimental information, meeting the requirements at tests on firmness to formation of pores during development of welding materials, at setting of parameters of the welding mode, at the analysis of data about imperfectness in a welding production, at the analysis of possible refuses of process of welding and consequences of such refuses, at the estimation of technological risks in a welding production.Выведена математическая зависимость, которая учитывает изменчивость в образовании пор при сварке и позволяет рассчитать вероятность выполнения требований к диаметру пор по экспериментально найденным характеристикам статистического распределения количества и диаметра пор на единичном участке сварного шва. При выводе математической зависимости использованы статические законы распределения Вейбулла и Пуассона и правило умножения вероятностей. Расчетом для краевых условий проверена адекватность теоретически выведенной зависимости. Полученная математическая зависимость позволяет по ограниченному количеству экспериментальных данных определять пригодность процессов сварки, соответствие требованиям при испытаниях на стойкость к образованию пор в ходе разработки сварочных материалов, при назначении параметров режима сварки, при анализе данных о дефектности в сварочном производстве, при анализе возможных отказов процесса сварки и последствий таких отказов, при оценке технологических рисков в сварочном производстве

Comorbidities in patients with revision hip arthroplasty

Background. According to the existing concept of risk factors, the outcome of hip arthroplasty (HA) is affected not only by the quality of the prosthetic work, but also by the presence of one or more concomitant diseases. Purpose of the study - to perform a frequency analysis of co-morbidities in patients who underwent revidion HA, depending on the timing of its conduct. Materials and methods. On the basis of the endoprosthesis clinic at the Novosibirsk Research Institute of Traumatology and Orthopedics, a continuous sample of data was performed from medical records of patients (n = 667), who underwent revision HA in the period of 2013-2015. Primary HA was performed in various medical institutions in Russia and abroad in the period of 1992-2015. The cases of revision Ha were divided according to the terms of their implementation: postoperative (up to 2 months, n = 11), early remote (more than 2 months but less than 5years after HA, n = 371) and late remote (more than 5 years, n = 285). Variable coding and matrix creation, frequency analysis, average and relative risk (RR) calculation were performed. Results. The RR of postoperative and early revision intervention after HA is calculated depending on the presence of concomitant diseases. As a reference group, cases of late revision HA are taken. Calculation of the RR showed that the presence of concomitant diseases increases the risk of failure of the endoprosthesis in the postoperative period (in diabetes mellitus type 2 - 4.3 times, with excessive body weight and obesity - 2.0, with diseases of the nervous system - 3.9, liver - 2.8, veins of the lower extremities - in 2.9 and with chronic anemia - 3.7 times). The risk of undergoing revision HA in the early remote period is 1.7 times higher in the presence of concomitant malignant neoplasm than in the late remote period (p < 0.1). RR decreases with ischemic heart disease, chronic pyelonephritis, cholelithiasis and other pathology of the musculoskeletal system, i.e., revision interventions are performed in these patients much later. Conclusions. When analyzing the concomitant pathology, significant differences in the incidence of chronic diseases were found depending on the timing of the revision HA. Chronic diseases, which are risk factors for early failure of the endoprosthesis, have been identified. In cases when the risk of complications is high due to comorbidity it is more appropriate to refuse from the operation altogether

Reconstruction of bone segment of the glenoid at chronic recurrent anterior shoulder instability using porous titanium nickelide

A method of the surgical treatment of posttraumatic recurrent shoulder instability with bony defects using porous NiTiis presented. We operated 5 patients using this method. Recurrences of dislocation after surgical treatment have not been recorded. The method is an alternative to Latarjet procedure and iliac crest bone grafting. We use computerized tomography data in the preoperative making of NiTi graft. The graft is sawed from billet having a cylindrical shape about 1 cm thick. Than by using the drill we form two screw holes. A prepared graft is subsequently installed in the area of the glenoid bone defect. The advantages of this method are accurate reconstruction of the bony defect, minimal risk of recurrences, absence of resorption, reduction of procedure time