Strong solutions of the thin film equation in spherical geometry

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile

English Reformer John Frith on Catholic Theology of Purgatory

The Catholic theology of purgatory and its refutation in the works of the ideologists of Protestantism in the first third of the XVI century is analyzed in the article. The works of the little-known in the domestic historiography of the English reformer John Frith (1503-1533) are investigated. Frith’s commitment to Protestant dogmas on justification by faith and the exceptional authority of Holy Scripture is shown. It is noted that Frith, following them, denied the existence of purgatory, since it cannot be confirmed by the Holy Scriptures, and he interpreted the “cleansing fire” mentioned in the New Testament texts symbolically as torment of conscience and repentance. It is claimed that the theologian considered faith to be the atoning sacrifice of Christ the only means of salvation. It is concluded that the denial of purgatory naturally led Frith to a refutation of the Catholic practice of papal acts of grace and their theological justification, for which he was arrested and sentenced to be burned. It is emphasized that J. Frith called purgatory "creation" of the Roman pontiff and saw purely material reasons for the emergence and existence of faith in purgatory. It is noted that criticism by the English reformer of the Catholic faith in purgatory was subsequently reflected in the Anglican creed

Polarons as stable solitary wave solutions to the Dirac-Coulomb system

We consider solitary wave solutions to the Dirac--Coulomb system both from physical and mathematical points of view. Fermions interacting with gravity in the Newtonian limit are described by the model of Dirac fermions with the Coulomb attraction. This model also appears in certain condensed matter systems with emergent Dirac fermions interacting via optical phonons. In this model, the classical soliton solutions of equations of motion describe the physical objects that may be called polarons, in analogy to the solutions of the Choquard equation. We develop analytical methods for the Dirac--Coulomb system, showing that the no-node gap solitons for sufficiently small values of charge are linearly (spectrally) stable.Comment: Latex, 26 page

Periodic Travelling Waves in Dimer Granular Chains

We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist

Markers of oxidative damage lipids and DNA in men with type 1 diabetes mellitus and different levels of albuminuria

BACKGROUND: Diabetic nephropathy is a specific kidney damage that affects up to 40% of type 1 diabetes mellitus patients. There is still insufficient knowledge about oxidative stress at the different levels of albuminuria.AIM: To assess the indicators of oxidative damage to lipids, DNA and antioxidant defense in men with type 1 diabetes mellitus and albuminuria different levels.MATERIALS AND METHODS: The study was conducted during 2018–2019. The main group included 56 men of reproductive age with type 1 diabetes mellitus (T1DM) divided into 2 groups: 24 patients with albuminuria level A1 (group A1) and 32 patients with albuminuria level A2 (group A2). The control group consisted of 28 healthy men. The oxidative stress indicators content, as well as the activity of antioxidant defense system various links was evaluated. Spectrophotometric, fluorimetric and enzyme immunoassay methods were used.RESULTS: In patients of the A1 group there were higher values of the median of primary — conjugated dienes, secondary — ketodienes and conjugated trienes, final — Schiff bases products and 8-hydroxy-2’-deoxyguanosine in comparison with the control. Similar changes in patients of the A2 group were found. Intergroup differences related to increased median values of TBARs and 8-hydroxy-2’-deoxyguanosine in patients of the A2 group compared with A1 group. The activity of the antioxidant defense system in A1 group relative to the control by increased values of the glutathione peroxidase, reduced glutathione, oxidized glutathione median, and retinol was characterized. A2 group had higher values of glutathione peroxidase, reduced glutathione and oxidized glutathione medians in comparison with controls. Correlation analysis in A1 group showed the relationships between the duration of the disease and the products of lipid peroxidation, glycated hemoglobin with 8-hydroxy-2’-deoxyguanosine. In A2 group, there was a relationship between the albumin/creatinine ratio and the duration of the disease, glomerular filtration rate and creatinine level.CONCLUSION: In men with T1DM, regardless of the albuminuria level, there are higher values of the oxidative damage lipids and DNA parameters, as well as the presence of close relationships between these parameters and the duration of the disease, which can be used to develop potential strategies for the prevention and early therapy of diabetic nephropathy

Paradox: Does liver insuffi ciency protect the patient? A hypothesis

Despite the fact that the key role of the liver in the formation of the immune response to injury is not in doubt, the mechanisms of weakening the immune response to infectious and noninfectious lesions in patients with hepatic failure remain unclear. We propose an original hypothesis of forming the ways to limit the amplitude of the systemic inflammatory response in patients with the end-stage liver disease. The basis of the hypothesis is the idea that as a result of reducing the intensity of the natural stimulation of membrane mCD14 receptors by the ligands of infectious nature, the basic mechanism of the systemic immune response induction by liver macrophages (Kupffer cells) is interrupted. According to the proposed hypothesis, in condition of liver failure, the synthesis of lipopolysaccharide-binding protein by hepatocytes is reduced. This leads to a decreased amplitude and intensity of the protective immune responses. This fact explains a number of clinical phenomena observed in patients with liver failure/dysfunction that consist in a reduced reactivity of the organism to the damage inflicted by infectious and noninfectious agents. The authors consider it possible to use this hypothesis in the search for new trends to prevent the immune system hyper-reactivity in sepsis, and to improve the therapeutic strategies for the management of patients at high risk of infectious complications after liver transplantation

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Маркеры почечного повреждения, липидного обмена и карбонильного стресса у пациентов с сахарным диабетом I типа и разным уровнем альбуминурии

The aim of this work was to study the levels of podocalyxin and β-2-microglobulin and parameters of lipid metabolism and carbonyl stress in type 1 diabetes mellitus (T1DM) patients with different levels of albuminuria.Materials and methods. 56 men of reproductive age with T1DM were divided into two groups: 24 patients with stage A1 albuminuria (group A1) and 32 patients with stage A2 albuminuria (group A2). The control group consisted of 28 healthy men. The levels of renal function markers, lipid metabolism parameters, and methylglyoxal were assessed using enzyme immunoassay and spectrophotometric and fluorometric methods.Results. Higher values for total cholesterol, triacylglycerol, and very-low-density lipoprotein medians in both groups A1 and A2 were found. In these groups, increased podocalyxin and methylglyoxal medians were revealed. Correlation analysis in the group A1 showed the presence of a relationship between the glomerular filtration rate (GFR) and creatinine. In the group A2, correlations between the generally accepted parameters of kidney injury (the albumin / creatinine ratio and GFR) and the duration of the disease and between GFR and the creatinine and methylglyoxal levels in the blood were identified. The podocalyxin level in this group correlated with the β2- microglobulin and methylglyoxal levels and lipid metabolism parameters. The level of β2-microglobulin correlated with the lipid metabolism parameters.Conclusion. Regardless of the level of albuminuria, men with T1DM had significantly increased levels of podocalyxin, lipid metabolism parameters, and methylglyoxal, as well as strong relationships between these parameters. The data of this study can be used for development of potential strategies for prevention and early treatment of diabetic nephropathy.Цель – изучение уровня подокаликсина, β-2-микроглобулина, показателей липидного обмена и карбонильного стресса у пациентов с сахарным диабетом (СД) I типа и разным уровнем альбуминурии.Материалы и методы. Проведено обследование 56 мужчин репродуктивного возраста с СД I типа, разделенных на две группы: 24 пациента с альбуминурией стадии А1 (группа А1) и 32 – с альбуминурией стадии А2 (группа А2). Контрольную группу составили 28 здоровых мужчин. Оценивался уровень почечных маркеров, компонентов липидного обмена и метилглиоксаля (МГ) с использованием иммуноферментных, спектрофотометрических и флюорометрических методов.Результаты. Установлены более высокие значения медиан общего холестерина, триацилглицеридов и липопротеидов очень низкой плотности в обеих группах с СД I типа. В данных группах отмечались также повышенные значения медианы подокаликсина и основного показателя карбонильного стресса – МГ. Проведенный корреляционный анализ в группе А1 показал наличие зависимости уровня скорости клубочковой фильтрации (СКФ) и креатинина. В группе А2 отмечались связи общепринятых показателей почечного повреждения (соотношения альбумин/креатинин и СКФ) с длительностью заболевания, показателя СКФ с уровнем креатинина и МГ. Уровень подокаликсина в данной группе коррелировал с уровнем β2-микроглобулина, МГ, показателей липидного обмена; β2-микроглобулин имел взаимосвязи с параметрами липидного обмена.Заключение. У мужчин с СД I типа вне зависимости от уровня альбуминурии отмечаются значительно более высокий уровень подокаликсина, увеличенные показатели липидного обмена и МГ, а также наличие тесных взаимосвязей между этими параметрами, что может быть использовано для разработки потенциальных стратегий профилактики и ранней терапии диабетической нефропатии

СРАВНИТЕЛЬНАЯ ОЦЕНКА СИМПАТИЧЕСКОЙ БЛОКАДЫ ПРИ ГРУДНОЙ ЭПИДУРАЛЬНОЙ И БИЛАТЕРАЛЬНОЙ ПАРАВЕРТЕБРАЛЬНОЙ АНЕСТЕЗИЯХ ПРИ ОПЕРАЦИЯХ ВЫСОКОЙ ТРАВМАТИЧНОСТИ НА ОРГАНАХ ВЕРХНЕГО ЭТАЖА БРЮШНОЙ ПОЛОСТИ

Objective: to compare the degree of sympathetic blockade caused by thoracic epidural or bilateral paravertebral anesthesia. Superior mesenteric artery blood flow was measured calculating the coefficient of flow resistance (resistance index) as an indicator of the degree of sympathetic block in patients undergoing high-traumaticity operations on the upper abdominal organs under thoracic epidural or bilateral paravertebral anesthesia. The patients of both groups were noted to develop sympathetic blockade with a statistically significant reduction in vascular resistance (resistance index) of the superior mesenteric artery and with an increase in blood flow in the visceral bed. The degree of sympathetic blockade was statistically significantly higher in patients under epidural anesthesia. Conclusion. Bilateral thoracic paravertebral blockade decreases sympathetic nervous system activation and may be used during high-traumaticity surgery if there are existing or predictable contraindications to epidural anesthesia. Цель исследования - сравнение выраженности симпатической блокады, обусловленной грудной эпидуральной или билатеральной паравертебральной анестезией. Проведены измерения кровотока по верхней брыжеечной артерии с расчётом коэффициента сопротивления потоку (индекса резис­тентности) как показателя выраженности симпатического блока у пациентов, которым выполняли высокотравматичные операции на органах верхнего этажа брюшной полости в условиях грудной эпидуральной или билатеральной паравертебральной анестезии. У пациентов обеих групп отмечались развитие симпатической блокады со статистически значимым снижением сосудистого сопротивления (индекса резистентности) верхней брыжеечной артерии и увеличение кровотока в висцеральном бассейне. Выраженность симпатической блокады была статистически значимо выше у пациентов с эпидуральной анестезией. Заключение. Билатеральная грудная паравертебральная блокада снижает активацию симпатичес­кой нервной системы и может быть применена при выполнении оперативных вмешательств высокой травматичности при имеющихся или прогнозируемых противопоказаниях к проведению эпидуральной анестезии