Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type

Результаты лечения пациентов с экстравазальной компрессией чревного ствола и атеросклеротическим его поражением

Introduction. Extravasal compression of celiac trunk is the cause of chronic abdominal ischemia syndrome (CAIS) along with atherosclerotic lesions of the visceral branches of the aorta. Patients with isolated compression and those in the older age group with compression combined with atherosclerotic lesion are distinguished. At present, the issues of indications for surgical treatment the pattern and technique of surgical intervention as well as the evaluation of decompression results in the early and distant postoperative period remain controversial and unsolved.Aim. The aim of our study was to determine indications and contraindications for surgical intervention, to improve the technique of the surgery, to evaluate and find ways to improve the closest and most distant results of laparoscopic decompression of the celiac trunk.Materials and methods. The article discusses the experience of performing 27 laparoscopic decompressions of the celiac trunk and the results of examination and treatment of 5 patients who underwent endovascular interventions due to a combined lesion -extravasal compression of the celiac trunk and atherosclerotic occlusion. Intraoperative laparoscopic ultrasound was performed in all cases of the celiac trunk decompression to determine the celiac trunk topography and assess the adequacy of its decompression.Results. The average duration of the surgery was 92 minutes. Intraoperative and early postoperative complications were not observed. Intraoperative blood loss didn't exceed 50 ml. Average duration of stay in the hospital was 5 days. According to the data of ultrasound examination, the average degree of celiac trunk compression before the operation was 76%, in the early postoperative period it decreased to 43%, and in the distant period it decreased to 32%.Discussion. Based on our experience, the key to successful management of patients with celiac trunk compression syndrome is a multidisciplinary approach to diagnosis and treatment. Patients need thorough differential diagnosis, including psychoneurologist consultation. Experience in treating patients with atherosclerotic lesions of the celiac trunk combined with extravasal compression has shown good immediate and distant decompression results and adverse results of the first stage of endovascular interventions.Conclusion. Laparoscopic decompression of the celiac trunk is an effective treatment method in patients without atherosclerotic lesions.Введение. Экстравазальная компрессия чревного ствола является причиной синдрома хронической абдоминальной ишемии (СхАИ) наряду с атеросклеротическим поражением висцеральных ветвей аорты. Выделяются пациенты, имеющие изолированную компрессию, и пациенты, относящиеся к старшей возрастной группе, имеющие компрессию в сочетании с атеросклеротическим поражением. В настоящее время спорными и нерешенными остаются вопросы показаний к хирургическому лечению, характера и техники оперативного вмешательства, а также оценки результатов декомпрессии в раннем и отдаленном послеоперационном периодах.Цель. Целью нашего исследования являлось определение показаний и противопоказаний к выполнению оперативного вмешательства, усовершенствование техники операции, оценка и поиски путей улучшения ближайших и отдаленных результатов лапароскопической декомпрессии чревного ствола.Материалы и методы. В статье рассматривается опыт выполнения 27 лапароскопических декомпрессий чревного ствола и результаты обследования и лечения 5 пациентов, перенесших эндоваскулярные вмешательства по поводу сочетанного поражения - экстравазальной компрессии чревного ствола и атеросклеротической окклюзии. Интраоперационное лапароскопическое УЗИ выполнялось во всех случаях декомпрессии чревного ствола для определения топографии чревного ствола и оценки адекватности его декомпрессии.Результаты. Средняя продолжительность операции составляла 92 мин. Интраоперационных осложнений и осложнений в раннем послеоперационном периоде не отмечено. Интраоперационная кровопотеря не превысила 50 мл. Средняя длительность пребывания в стационаре составила 5 дней. По данным ультразвукового исследования, средняя степень сужения чревного ствола до операции составляла 76%, в раннем послеоперационном периоде уменьшилась до 43%, а в отдаленном периоде снизилась до 32%.Обсуждение. Исходя из нашего опыта, ключом к успешному ведению пациентов с синдромом компрессии чревного ствола является мультидисциплинарный подход к диагностике и лечению. Пациенты нуждаются в тщательной дифференциальной диагностике, включая консультацию психоневролога. Опыт лечения пациентов, имеющих атеросклеротическое поражение чревного ствола в сочетании с экстравазальной компрессией, показал хорошие ближайшие и отдаленные результаты декомпрессии и неблагоприятные результаты выполненных первым этапом эндоваскулярных вмешательств.Заключение. Лапароскопическая декомпрессия чревного ствола является эффективным методом лечения у пациентов, не имеющих атеросклеротического поражения

Functions and graphs

The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple f

Effect of fermented non-starch polysaccharide complexes on sorption of heavy metal ions in biological systems

Hydrolytic action enzyme for modification of nonstarch polysaccharide complexes was developed and studied their influence on sorption activity in relation to heavy metals in biosystem

INVESTIGATION OF THE SORPTION OF METALS VEGETABLE SORBENTS

The paper presentsa study on thepatterns ofsorption of Cd2 +and Cu2 +complexes of plant polysaccharide from the seeds ofwild rose andthistle

SORPTION PROPERTIES OF PLANT POLYSACCHARIDE COMPLEXES

The article presents information on the laws of the sorption of water to grow-negative polysaccharide complexes of the pumpkin and briar, deter-mined the rate constant of swelling as a function of temperature and pH, the maximum degree of swelling and limit the time to achieve it

Formation of a model of strategic management of industrial tourism development in the region

Within the framework of this article it is proposed to form a model of strategic management of industrial tourism development in the region. Modern trends in the development of the tourism industry actively influence the development of the world economy as a whole, and the economy of the state and its regions. Tourism has become a huge separate part of economic activity, which can satisfy "special desires" of consumers. Satisfaction of these "basic desires" is carried out not only at the expense of the sphere of tourist services, but also organizations of other fields of activity – this explains the fact that tourism is one of the factors influencing the economic development of the country. The development of industrial tourism contributes to the emergence of new brands, improves the investment climate. Industrial tourism is a niche for the development of cooperation between the regional authorities, industrial and tourist companies. All of the above makes it necessary to improve the theoretical and scientific approaches to the development of strategic management of the development of industrial tourism in order to effectively use the industrial potential of the region, increase its investment attractiveness and the image of the region and the tourism industry, which will lead to the development of the region in both the tourism and industrial sectors. Towards the end of the 20th century, industrial tourism began to emerge in our country. Recently this trend is gaining momentum, and for its further development requires a competent system of strategic management. The relevance of this topic is due to the fact that in the conditions of modern market economy, it is necessary to search for new, non-traditional forms of tourism development of their management in order to attract tourists from a more diverse range of target groups, to stimulate the re-visit of industrial tourism in the region