Physical applications of second-order linear differential equations that admit polynomial solutions

Conditions are given for the second-order linear differential equation P3 y" + P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of degree n. Several application of these results to Schroedinger's equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation yield polynomial solutions are explicitly given. Some new classes of exactly solvable differential equation are also discussed. The results of this work are expressed in such way as to allow direct use, without preliminary analysis.Comment: 13 pages, no figure

Observations of Lensed Relativistic Jets as a Tool of Constraining Lens Galaxy Parameters

The possibility of using lensed relativistic jets on very small angular scales to construct proper models of spiral lens galaxies and to independently determine the Hubble constant is considered. The system B0218+357 is used as an example to illustrate that there exists a great choice of model parameters adequately reproducing its observed large-scale properties but leading to a significant spread in the Hubble constant. The jet image position angle is suggested as an additional parameter that allows the range of models under consideration to be limited. It is shown that the models for which the jet image position angles differ by at least $40^o$ can be distinguished between themselves during observations on very small angular scales. The possibility of observing the geometric properties of lensed relativistic jets and measuring the superluminal velocities of knot images on time scales of several months with very long baseline space interferometers is discussed.Comment: 11 pages, 3 figures, Will be published in the Astronomy Letters, V.37, PP.483-490, 201

A new class of x-ray tails of early-type galaxies and subclusters in galaxy clusters: Slingshot tails versus ram pressure stripped tails

© 2019. The American Astronomical Society. All rights reserved.. We show that there is a new class of gas tails - slingshot tails - that form as a subhalo (i.e., a subcluster or early-type cluster galaxy) moves away from the cluster center toward the apocenter of its orbit. These tails can point perpendicular or even opposite to the subhalo direction of motion, not tracing the recent orbital path. Thus, the observed tail direction can be misleading, and we caution against naive conclusions regarding the subhalo's direction of motion based on the tail direction. A head-tail morphology of a galaxy's or subcluster's gaseous atmosphere is usually attributed to ram pressure stripping, and the widely applied conclusion is that gas stripped tail traces the most recent orbit. However, during the slingshot tail stage, the subhalo is not being ram pressure stripped (RPS) and the tail is shaped by tidal forces more than just the ram pressure. Thus, applying a classic RPS scenario to a slingshot tail leads not only to an incorrect conclusion regarding the direction of motion but also to incorrect conclusions regarding the subhalo velocity, expected locations of shear flows, instabilities, and mixing. We describe the genesis and morphology of slingshot tails using data from binary cluster merger simulations and discuss their observable features and how to distinguish them from classic RPS tails. We identify three examples from the literature that are not RPS tails but slingshot tails and discuss other potential candidates

Modeling the Images of Relativistic Jets Lensed by Galaxies with Different Mass Surface Density Distributions

The images of relativistic jets from extragalactic sources produced by gravitational lensing by galaxies with different mass surface density distributions are modeled. In particular, the following models of the gravitational lens mass distribution are considered: a singular isothermal ellipsoid, an isothermal ellipsoid with a core, two- and three-component models with a galactic disk, halo, and bulge. The modeled images are compared both between themselves and with available observations. Different sets of parameters are shown to exist for the gravitationally lensed system B0218+357 in multicomponent models. These sets allow the observed geometry of the system and the intensity ratio of the compact core images to be obtained, but they lead to a significant variety in the Hubble constant determined from the modeling results.Comment: 26 pages, 9 figures, will be published in the Astronomy Letters, 2011, v.37, N4, pp. 233-24

КТ-диагностика последствий COVID-19 поражения легких

Introduction. The possible formation of persistent residual changes in the lung after a COVID-19 began to be reported after the first wave of the pandemic, but their extent and prevalence have not been fully assessed.Purpose of the study. Evaluate CT patterns of residual changes in COVID-19 lung lesions. Materials and methods. We analyzed the clinical and radiation data of 868 patients (f/m — 441/427) who underwent COVID-19 and were observed in the clinics of First St.-Petersburg State Medical University n.a. academician I.  P. Pavlov since 2020 until 2021. The average age of the patients was 33,4±17,2 years. All patients underwent high-resolution computed tomography in dynamics — after 6 months or more. Statistical data processing was performed using the Statistika 16.0 software/statistical package.Results. Analysis of the results of CT examination revealed the following patterns of residual changes after a new coronavirus infection: ILAs (interstitial lung abnormalities) in 0,7%, the formation of fibrotic changes (NsIP, OIP) in 0,2% of patients, CT signs of constrictive bronchiolitis in 0,3% of patients, CT signs of persistence in 0,1% of patients, CT signs of the formation of pulmonary hypertension, identified in 0.3% of patients.Conclusions. CT allows to identify a variety of residual changes in COVID-19 lung lesions, which is important for assessing the prognosis of the disease and the tactics of its treatment. Введение. О возможном формировании стойких остаточных изменений в легочной ткани после перенесенного COVID-19 поражения начали сообщать уже после первой волны пандемии, однако их степень и распространенность оценены не полностью.Цель исследования: оценить особенности КТ-картины после перенесенного COVID-19 поражения легких.Материалы и методы. Проанализированы клинико-лучевые данные 868 больных (441 женщины и 427 мужчин), перенесших COVID-19 и наблюдавшихся в клиниках ПСПбГМУ им. акад. И. П. Павлова с 2020 по 2021 г. Средний возраст больных составлял 33,4±17,2 года. Всем пациентам была выполнена высокоразрешающая компьютерная томография в динамике — через 6 месяцев и более. При статистической обработке данных использовали программу/статистический пакет Statistiсa 16.0.Результаты. Анализ результатов КТ-обследования выявил следующие паттерны остаточных изменений после перенесенной новой коронавирусной инфекции: минимальные интерстициальные изменения — у 0,7% больных, формирование фиброзных изменений (неспецифической интерстициальной пневмонии, обычной интерстициальной пневмонии) — у 0,2% пациентов, КТпризнаки констриктивного бронхиолита  — у  0,3% пациентов, КТ-признаки персистенции COVID-19 поражения легких  — у 0,1% пациентов, КТ-признаки формирования легочной гипертензии — у 0,3% пациентов.Заключение. КТ позволяет выявить разнообразные последствия перенесенного COVID-19 поражения легких, что важно для оценки прогноза заболевания и тактики его лечения.

Однофотонная эмиссионная компьютерная томография легких у пациентов, перенесших новую коронавирусную инфекцию

Introduction. The most striking manifestations of the disease caused by the SARS-CoV-2 virus are manifested in the microvasculature of the lungs. The study of the residual manifestations of the disease seems to be relevant, since it can affect the development of complications and its outcome.Purpose of the work. To assess changes in the microvasculature of the lungs of patients who have undergone COVID infection at different times from the onset of the disease, and who have not previously had respiratory diseases.Material and methods. SPECT data were analyzed in 96 patients with proven coronavirus infection from May 2020 to April 2021 of varying severity. The results of SPECT, MSCT, FVD and coagulation hemostasis (D-dimer, fibrinogen, prothrombin index) were compared.Results. All patients were found to have changes in microcirculation in the lungs in the postcoid period. The severity of microcirculation disorders had a significant dependence (p<0,05, r=0,71) on the degree of damage to the pulmonary parenchyma and an average correlation dependence (r=0,48) on the timing of the postcoid period. Signs of PE/microthrombosis/post-thromboembolic changes were significantly more frequent (p<0,05, r=0.8) in patients with a more severe course of the disease.Conclusion. Disorders of microcirculation in the lungs are detected in patients, regardless of the severity of the pathological process. The method of automatic processing of the results of radiological studies of the lungs in comparison with the norm made it possible to quantitatively assess the degree of changes in microcirculation after pneumonia caused by the SARS-CoV-2 virus.Введение. Изучение остаточных проявлений заболевания, вызванного вирусом SARS-CoV-2, представляется актуальным, так как имеет прогностическое значение.Цель работы: оценить изменения в микроциркуляторном русле легких пациентов, ранее не имевших заболеваний легких и перенесших COVID-инфекцию.Материалы и методы. Проанализированы результаты ОФЭКТ-исследований, выполненных 96 пациентам с доказанной перенесенной инфекцией разной тяжести течения.Результаты. Выраженность нарушений микроциркуляции в легких пациентов в постковидном периоде зависела (p<0,05, r=0,71) от уровня поражения легочной паренхимы и от сроков постковидного периода (r=0,48). Признаки тромбоэмболии легочной артерии (ТЭЛА)/микротромбозов достоверно чаще (p<0,05, r=0,8) встречались у больных с более тяжелым течением заболевания.Заключение. Нарушения микроциркуляции в  легких сохраняются длительное время. В  зонах легких, где выявлялась ТЭЛА, кровоток не восстанавливается и формируются зоны локального пневмосклероза. Компьютерная программа Lung Scint Analyser позволила количественно оценить степень изменений микроциркуляции.