Various versions of equations of two-fluid plasma called the equations of electromagnetic hydrodynamics are considered. They are a generalization of the classical magnetic hydrodynamics equations obtained by adding dispersive terms. Application of finite-difference methods for solving these equations is analyzed. The Riemann problem is solved numerically, and various types of discontinuity structures that expand with time are considered. These are fast and slow magnetosonic structures and Alfven structures. In the case of moderate amplitudes, fast and slow magnetosonic structures are typical in the theory of nondissipative structures. It is found that due to the disappearance of dispersion, short waves can overturn under certain initial conditions, which requires the analysis of discontinuous solutions or the inclusion of additional dissipative or dispersive terms into the equations. In the case when the fluid dynamic viscosity is added, a shock-type structure is discovered. The evolutionary nature of the discontinuity and the conditions on the discontinuity are studied.

Equations for a tube with elastic waves (tube with controlled pressure, fluid-filled tube, and gas-filled tube) are considered. A full membrane model and the nonlinear theory of hyperelastic materials are used for describing the tube walls. The Riemann problem is solved, and its solutions confirm the theory of reversible discontinuity structures. Dispersion of short waves for such equations vanishes; for this reason, dissipative discontinuity structures can be included. The equations under examination are complicated due to which general numerical methods are developed. Application of the centered three-layer cross-type scheme and schemes based on the approximation of time derivatives using the Runge–Kutta method of various orders is considered. A technology for correcting schemes based on the Runge–Kutta method by adding dissipative terms is developed. In the scalar case, the third- and fourth-order methods do not require correction. The possibility of using terms with high-order derivatives for computing solutions that simultaneously include dissipative and nondissipative discontinuities is analyzed.

Aim. To compare the cardio-ankle vascular index (CAVI) and the novel START vascular stiffness index and assess their values and correlations with clinical parameters.Material and methods. This multicenter study included 928 (403 men and 525 women) randomly selected patients, aged 18 to 89 years (mean age, 41±15,8 years). Inclusion criteria were age over 18 years. There were following exclusion criteria: mental disorder, severe somatic diseases and cancer, contraindications for volume sphygmography using the Fukuda Denshi VS-1500 VaSera system, no patient consent, ankle-brachial index 1,3. Further, according to the main parameters obtained using volum sphygmography, a novel START index was calculated. Comparison of index values and analysis of their correlation with clinical indicators, such as age, systolic blood pressure, diastolic blood pressure, pulse pressure (PP), body mass index and heart rate (HR), were carried out using simple and multiple linear regression, dispersion analysis, calculation of the Pearson coefficient (r), in the software environment R version 4.0.2.Results. Statistical analysis revealed a high correlation between START and CAVI indices (r=0,986, p0,05). According to multiple linear regression, the relationship between diastolic blood pressure at the age of 30-60 years and PP at the age of 18-40 years with the START index is more pronounced than with the CAVI index. However, further study of the mathematical model did not reveal a significant difference in the index values for groups with and without high blood pressure.Conclusion. The START vascular stiffness index significantly correlates with the CAVI index, showing no significant differences from CAVI in quantitative relationships with blood pressure, body mass index, heart rate, and sex in various subgroups of the subjects.

Stability of solitary waves that are solutions to one of the variants of the Boussinesq equation is investigated. This equation describes elastic waves in the presence of an electromagnetic field. The Evans function method and direct numerical solution of the equation are used to identify the instability of solitary waves. The results obtained by both methods coincided. A method for identifying instability and a method for calculating an eigenfunction that grows with time by analyzing numerical solutions of a partial differential equation are developed.

Aim. To compare the novel arterial stiffness index START and the cardio-ankle vascular index (CAVI) in hypertensive (HTN) patients. Material and methods. A total of 709 people with HTN aged 24 to 64 years were examined by volume sphygmography using VaSera VS-1000 (Fukuda Denshi, Japan). CAVI and START values obtained retrospectively from pulse wave velocity and blood pressure were studied using an online calculator.Results. The median CAVI score was within the normal range (0,05). In the older age group (61-70 years), the median START index was 7,27, for the CAVI index — 8,4 (p>0,05). The growth pattern of the START score with age was higher by 38,5% than the CAVI index by 25,6% (p=0,034). A high degree of correlation between CAVI and START was noted (r=0,823, p<0,001). Parameters were associated with age (r=0,412 for CAVI and r=0,355 for START; p<0,001), smoking duration (r=0,390 and r=0,361; p<0,001), glomerular filtration rate (r=-0,317 and r= -0,318; p<0,001), body mass index (r=-0,176 and r=-0,185; p=0,001). For the CAVI index, a relationship was found with the glucose level (r=0,192; p<0,001) and a sedentary lifestyle (r=-0,157; p=0,04), while for the START index — with the creatinine level (r=0,143; p=0,01).Conclusion. Patients with hypertension showed a high correlation between the novel START index and the CAVI score (r=0,823, p<0,001). The indicators had similar associations with risk factors, which is important for the subsequent practical application of the START index.