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The mathematical model of the mechanical system, which is a section of the pipeline with built-in motor pump system and damper for vibration damping, has been developed. The mathematical model is represented by a system of partial differential equations of hydrodynamics for moving fluid in the pipeline and a system of two ordinary differential equations for the damping device. Solution the system of equations is performed using analytical and numerical methods. The numerical solution of the equations of hydrodynamics carried out using the finite element method, implemented in the programming environment of mathematical package freeFEM ++.

A nonlinear mathematical model of the system of drilling rig, consisting of the rig, the control cabin, the working platform and platforms with engines has been developed. The mathematical model of the rig with six degrees of freedom is represented by a system of nonlinear ordinary differential equations. The methodology for calculation the basic characteristics of oscillation using the method of polynomial transformations was developed. The formulas for the calculation by the method of polynomial transformations were obtained.

The article is devoted to numerical study of convergence of calculation results obtained on the basis of two nonlinear models of the theory of shells with thickness decrease. As models are considered nonlinear theory of thin shells, based on the hypotheses of the Kirchhoff-Chernykh and hypotheses type Tymoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. As an example, we consider the problem of axisymmetric conical compression and spherical shell by axial force. The convergence of results with decreasing thickness is disturbed in areas stability loss(buckling). Also happens when in the deformation process is violated the basic assumption of the theory of shells -the thickness is much smaller than radius of curvature (h < < R).

The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.

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The study describes the effectiveness of digital technological solutions in education. Students, postgraduates, teachers, and medical business representatives have tested a comprehensive educational product based on the capabilities of learning management system (LMS) platforms. The online course was implemented on the e-learning platforms such as Moodle, Schoology, TalentLMS, Canvas LMS, Docebo, iSpringLearn's, Brightspace, Absorb LMS. The implementation of advanced e-learning models ensured the effectiveness of the educational process. The focus on the development of the personal potential of each educational process participant made it possible to create a personalized learning environment and evoke a sense of personal significance and importance. The focus on feedback has created a creative communication environment for the exchange of knowledge, thoughts and ideas satisfying participants' educational needs for self-expression and creativity. The collective creativity of the educational process participants made it possible to develop a high-quality corporate culture of the students involved, which became the basis for establishing business partnerships in the system of education, science, and business. Based on the observations, a universal model of an effective educational process in the digital age has been developed.

IntroductionThe aim of this study was to perform a comparative and economic analysis of the degree of development of anxiety-depressive disorder in patients with different types of extrasystolic arrhythmia using different assessment scales.Material and methodsThe study was conducted in 2018–2019 at the premises of clinic No. 4, involving 450 patients (Moscow, Russia). Patients were divided into three groups: with coronary heart disease (CHD) (147 patients), with myocardiodystrophy (MCD) (113) and with cardiopsychoneurosis (CPN) (190). Everyone underwent round-the-clock electrocardiography (ECG) and echocardiography. If symptoms of depressive disorder are detected in a timely manner, the risk of adverse cardiovascular diseases may be reduced.ResultsDepression and anxiety indicators on all three scales differed significantly (p ≤ 0.05) in patients with supraventricular extrasystole (more than 40 points on the Zung scale, 14 points on the Montgomery-Asberg depression scale, more than 38 points on Zung and 3 points on Covi anxiety scales). For patients with ventricular extrasystole, a significant difference was established between groups 1 and 2 only in terms of the level of depression on the Zung scale. Factors of psychogenic origin determine the development of cardiac rhythm disturbances.ConclusionsThe study showed that for supraventricular extrasystoles, these factors determine the overall health of the patient. The differences between the three groups are significant on all scales of depression and anxiety (p ≤ 0.05). The most susceptible to depression and anxiety are patients with extrasystolic arrhythmias diagnosed with CHD, as well as MCD.