No abstract

Known mathematical packages, MATLAB, Maple, Mathematica, MathCAD and others may get wrong, often plausible, the result of numerical solution of ODE systems with low, given by default, the requirements for mathematical accuracy of the results of the numerical solution of ODE systems. Since ODE system parameters obtained usually experimental, with a low mathematical precision, so the requirements for the precision of the results of mathematical solutions of ODE systems is low (for example, in MATLAB package required precision is 0.001). The article offers a basic set of tests to assess the range of applicability of the relevant solvers. The basic set of test problems for ODE solvers systems include linear ODE systems with the known analytic solution and nonlinear systems with known graphics solution. Presented comparative results of solutions for proposed problems using MATLAB solvers and manzhuk program from a library of standard mathematical programs SADEL (Sets of Algebraic and Differential Equations solvers Library), which has been designed for reliable and accurate solving of systems of linear algebraic equations (LAE) and ODE systems. The results can be used in mathematical modeling of dynamic systems described by ODE systems.

Aim – to study the functional state of the microvessels of the forearm skin in the acute phase of COVID-19 using the LDF method. Materials and methods. The study included 53 patients of moderate COVID-19. During the first day of hospitalization, all patients underwent LDF with amplitude-frequency Fourier analysis of tissue perfusion fluctuations using a portable LDF device with remote data transmission via Bluetooth protocol. The comparison group (CG) consisted of 28 healthy subjects matched in age and gender. Results. Patients in the acute phase of COVID-19, relative to CG, are noticed a decrease in the amplitude of endothelial vasomotions (Ae) – 0.0149 and 0.0198 PU (p<0.00005), an increase in the amplitude of myogenic vasomotions (Am) – 0.078 and 0.061 PU (p<0.01), an increase in the amplitude of blood flow pulse oscillations – 1.38 and 1.18 PU (p<0.01) and an increase in respiratory related blood flow oscillations – 0.48 and 0.29 PU (p<0.000001) respectively. Conclusion. The systemic inflammatory process in the acute phase of COVID-19 at the level of the skin microvasculature is characterized by: 1) vasomotor dysfunction of the endothelium; 2) a decrease of the perfusion efficiency of the endothelial regulation mechanism; 3) a decrease of the basal tone of smooth muscle cells of precapillary arterioles and capillary sphincters; 4) an increase of arterial blood flow to the capillary bed; 5) violation of the blood outflow from the microvasculature with the development of venular plethora.

, МГТУ им. Н.Э.Баумана, г. Москва Аннотация-В статье рассмотрены проблемы достоверного и точного решения систем ОДУ для среды моделирования разнородных динамических систем-ПA10 (PA10), которая будет превосходить по достоверности и точности моделирования подобные зарубежные программные продукты при не высокой, заданной по умолчанию, точности решения систем ОДУ. Основное назначение ПA10это достоверное и точное моделирование и оперативный инженерный анализ во временной области разнородных (multiphysics) систем и объектов, в первую очередь, изделий мехатроники. Рассматривается опыт создания математического ядра программы ПA10программы решателя систем ОДУ manzhuk, которая по достоверности и точности расчетов при невысоких требованиях к точности интегрирования превосходит соответствующие решатели пакета математических программ MATLAB, а тем более превосходит решатели систем ОДУ программы моделирования электронных схем общего назначения SPICE (Gear и Trapezoid методы). Ключевые словаавтоматизированное проектирование электронных схем, численное моделирование, системы инженерного анализа, динамические системы, обыкновенные дифференциальные уравнения (ОДУ), дифференциально-алгебраические уравнения (ДАУ).