Применение метода дифференциальных неравенств для обоснования решения системы параболических уравнений в виде движущегося фронта

Investigations of initial boundary value problems for parabolic equations solutions are an important component of mathematical modeling. In this regard of special interest for mathematical modeling are the boundary value problem solutions that undergo sharp changes in any area of space. Such areas are called internal transitional layers. In case when the position of a transitional layer changes over time, the solution of a parabolic equation behaves as a moving front. For the purpose of proving the existence of such initial boundary value problem solutions, the method of differential inequalities is very effective. According to this method the so-called upper and lower solutions are to be constructed for the initial boundary value problem. The essence of an asymptotic method of differential inequalities is in receiving the upper and lower solutions as modifications of asymptotic submissions of the solutions of boundary value problems. The existence of the upper and lower solutions is a sufficient condition of existence of a solution of a boundary value problem. While proving the differential inequalities the so-called ”quasimonotony” condition is essential. In the present work it is considered how to construct the upper and lower solutions for the system of the parabolic equations under various conditions of quasimonotony.Исследование решений начально-краевых задач для параболических уравнений является важной составляющей математического моделирования. Особый интерес для математического моделирования представляют краевые задачи, решения которых претерпевают резкое изменение в какой-либо области пространства. Такие области называются внутренними переходными слоями. В том случае, если положение переходного слоя изменяется со временем, решение параболической задачи имеет вид движущегося фронта. При доказательстве существования у начально-краевых задач решений такого вида весьма эффективным оказывается метод дифференциальных неравенств, согласно которому для данной краевой задачи строятся так называемые верхнее и нижнее решения. Суть асимптотического метода дифференциальных неравенств заключается в том, чтобы получать верхнее и нижнее решения как модификации асимптотических представлений решений краевых задач. Существование верхнего и нижнего решений является достаточным условием существования решения краевой задачи. В ходе проверки выполнения дифференциальных неравенств существенным оказывается так называемое условие квазимонотонностии. В настоящей работе рассмотрено, каким образом можно построить верхнее и нижнее решения для системы параболических уравнений при различных условиях квазимонотонности

Асимптотический анализ в задаче моделирования процесса переноса газовой примеси в приповерхностном слое атмосферы

In the present work the model boundary value problem for a stationary singularly perturbed reaction-diffusion-advection equation arising at the description of gas impurity transfer processes in an ecosystem ”forest – swamp” is considered. Application of a boundary functions method and an asymptotic method of differential inequalities allow to construct an asymptotics of the boundary layer type solution, to prove the existence of the solution with such an asymptotics and its asymptotic stability by Lyapunov as the stationary solution of the corresponding parabolic problem with the definition of local area of boundary layer type solution formation. The latter has a certain importance for applications, since it allows to reveal the solution describing one of the most probable conditions of the ecosystem. In the final part of the work sufficient conditions for existence of solutions with interior transitional layers (contrast structures) are discussed.Рассматривается модельная краевая задача для стационарного сингулярно возмущенного уравнения реакция-диффузия-адвекция, возникающая при описании процессов переноса газовой примеси в экосистеме 컈лес–болотоо. Применение метода пограничных функций иасимптотического метода дифференциальных неравенств позволяет построить асимптотику решения погранслойного типа, доказать существование решения с такой асимптотикой и его асимптотическую устойчивость по Ляпунову, как стационарного решения соответствующей параболической задачи с определением локальной области формирования решения погранслойного типа. Последнее имеет определенное прикладное значение, т.к. позволяет выявить решение, описывающее одно из наиболее вероятных состояний экосистемы. В заключительной части работы обсуждаются достаточные условия существования решений с внутренними переходными слоями (контрастных структур)

Comparative Pharmacoepidemiological Assessment of Antihypertensive Drugs Administration Structure in Pregnant Women in Routine Medical Practice in Kursk and Chisinau

Aim. To study the structure of antihypertensive drugs prescription in pregnant women in routine practice in Kursk and Chisinau.Material and methods. The study design was observational descriptive cross-sectional. Authors conducted a survey of doctors in medical organizations in Kursk and Chisinau in 2017-2018.Results. Respondents from Kursk and Chisinau preferred methyldopa in prescriptions of central alpha-adrenergic receptor agonists. Doctors from Chisinau used clonidine in 14.3% of cases. The leading place in the group of calcium channel blockers belonged to short-acting nifedipine. Among beta-blockers in Kursk, doctors most often prescribed bisoprolol (43.3%), metoprolol (21.7%) and nebivolol (13.3%), while in Chisinau the preference was given to metoprolol (32.1%), atenolol (19.6%) and bisoprolol (16.1%). From the group of diuretics, Kursk doctors mainly prescribed hydrochlorothiazide (10%), indapamide (6.7%); in Chisinau, indapamide was the leader (19.6%), hydrochlorothiazide was used less frequently (7,1%). From the class of alpha-blockers, prazosin occupied the leading position among respondents in Kursk, and terazosin in Chisinau.Conclusion. The priority drug classes in both regions were calcium channel blockers, central alpha-adrenergic receptor agonists and beta-blockers. A small number of not recommended drugs prescriptions have been registered. In general, the prescribed treatment corresponded to the current guidelines and protocols for the management of patients with arterial hypertension during pregnancy

‘In vivo’ optical approaches to angiogenesis imaging

In recent years, molecular imaging gained significant importance in biomedical research. Optical imaging developed into a modality which enables the visualization and quantification of all kinds of cellular processes and cancerous cell growth in small animals. Novel gene reporter mice and cell lines and the development of targeted and cleavable fluorescent “smart” probes form a powerful imaging toolbox. The development of systems collecting tomographic bioluminescence and fluorescence data enabled even more spatial accuracy and more quantitative measurements. Here we describe various bioluminescent and fluorescent gene reporter models and probes that can be used to specifically image and quantify neovascularization or the angiogenic process itself

The Asymptotical Analysis for the Problem of Modeling the Gas Admixture in the Surface Layer of the Atmosphere

In the present work the model boundary value problem for a stationary singularly perturbed reaction-diffusion-advection equation arising at the description of gas impurity transfer processes in an ecosystem ”forest – swamp” is considered. Application of a boundary functions method and an asymptotic method of differential inequalities allow to construct an asymptotics of the boundary layer type solution, to prove the existence of the solution with such an asymptotics and its asymptotic stability by Lyapunov as the stationary solution of the corresponding parabolic problem with the definition of local area of boundary layer type solution formation. The latter has a certain importance for applications, since it allows to reveal the solution describing one of the most probable conditions of the ecosystem. In the final part of the work sufficient conditions for existence of solutions with interior transitional layers (contrast structures) are discussed

STUDIES ON THE ROLE OF CYTOKINES POLYMORPHISM IN PATHOGENESIS OF CHRONIC URTICARIA

Fifty patients with chronic autoimmune urticaria (CAU) and forty-eight patients with chronic idiopathic urticaria (CIU) have been examined. Blood serum contents of IL-4, IL-10 and IL-17A, spontaneous and induced cytokine production in blood cells, as well as polymorphism of IL-4 (C-589T), IL-10 (G-1082A), IL-17A (G-197A) cytokine genes has been studied. No differences have been detected when studying IL-4 levels, depending on genetic variants of IL-4 gene in patients with CAU and CIU. Increased IL-10 amounts in patients with CIU still did not show any correlations with IL-10 genotype (G-1082A). Increased IL-17A levels in patients with CAU were associated with homozygous genotype of AA in comparison to control group, and with heterozygous GA genotype, in comparison to CIU group. The revealed differences of cytokines` genes polymorphism in CAU and CIU provide a molecular-genetic evidence for different clinical forms of chronic urticaria

COMPARATIVE PHARMACOEPIDEMIOLOGICAL ASSESSMENT OF ANTIHYPERTENSIVE DRUGS PRESCRIPTION IN OUTPATIENT PRACTICE IN KURSK AND CHISINAU

Aim. To study the structure of medical prescriptions of antihypertensive agents for patients with arterial hypertension (HT) in the outpatient practice of Kursk (Russia) and Chisinau (Republic of Moldova).Material and methods. The questioning of doctors of medical organizations in Kursk and Chisinau was carried out as a one-stage descriptive study from October 2015 to February 2016. The questionnaires included questions on the pharmacoepidemiological aspects of prescribing antihypertensive drugs. Total number of respondents was 218, of them – 106 (26 cardiologists and 80 therapists) in Kursk and 112 (28 cardiologists and 84 therapists) in Chisinau.Results. In the real practice for HT treatment doctors in Kursk used more often beta-adrenoblockers (BAB), somewhat less often – angiotensinconverting enzyme (ACE) inhibitors, then diuretics. The shares of calcium channels blockers (CCB) and angiotensin II receptors blockers (ARB) were small – 8.8 and 5.2%, respectively. In Chisinau doctors gave preference to ACE inhibitors, then diuretics and BAB. Frequency of CCB prescriptions was almost identical to that of ARA – 13.7 and 13.6%, respectively. The additional antihypertensives, including central action drugs and alpha-adrenoblockers, were used rarely in both Chisinau and Kursk (1.3 and 1.6%, respectively). Doctors of Chisinau, when carrying out combined pharmacotherapy, gave priority to free combinations of antihypertensive drugs (64.4%), fixed combinations were used in 26.7% of cases. In Kursk, the ratio of these specified tactics of combined therapy was 53.5 and 34.1%, respectively. Among the pharmaceutical companies whose medicines were preferred by doctors in Kursk and in Chisinau, the leading positions were taken by KRKA (38.0 and 25.4%, respectively), Gideon Richter (13.5 and 28.7%, respectively) and Berlin-Chemie (26.7 and 15.6%, respectively).Conclusion. ACE inhibitors, diuretics, BAB were priority classes in the prescribing antihypertensive drugs according to survey of doctors in Kursk and Chisinau. In the conditions of the existing pharmaceutical market of Chisinau doctors used ARB and CCB more often than doctors from Kursk. The main share of doctor’s prescriptions in Kursk and Chisinau, considered both for group of antihypertensive drugs, and for certain representatives of each group of drugs, corresponds to the current recommendations on the pharmacotherapy of patients with HT