Numerical Implementation of the Fictitious Domain Method for Elliptic Equations

In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method

Investigation of the stability and convergence of difference schemes for the three-dimensional equations of the atmospheric boundary layer

In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is prove

Magna Carta – as the conceptual predecessor of the rule of law concept in the middle ages

The 1215 Magna Carta, or the Great Charter of the Liberties as a legal document, that according to its historical-philosophical origin is an idea embodiment about an origin of the king’s power from «a common law» which provided for «the universal recognition of mutual rights and duties» between the governor and his citizens. As for the historical-political origin, this document appeared as a result of resistance to lawlessness from the monarch as attempt to put the king into a certain legal framework. Finally, the philosophical-legal contents of this document, in the author’ opinion, gives the answer to the question: «Which should be supreme – the rule of law or will of a ruler?». Subsequently, provisions of the Great Charter had a great influence on the development of such human rights, as the right to life and the right to freedom, and also many procedural guarantees which in turn played an important role in the formation of the rule of law concept

THE ROLE OF SCHOOL EDUCATION IN MODERN YOUTH EDUCATION.

In this article, state documents similar to the "State general national program for the development of school education", "Regulation on education", "National program of personnel training" deal with training schools with professional personnel, increasing the quality of education and training, creating its effective system, and other issues. adjusted

Effects of vestibular rehabilitation in patients with unilateral vestibular hypofunction

Purpose: To investigate the effect of physiotherapy on the balance parameters and fall risk in patients with unilateral vestibular hypofunction (UVH). Patients and Methods: Thirty patients diagnosed with UVH were included in the study. The number of falls, Visual Analog Scale, Modified Clinical Test for Sensory Interaction in Tandem and Balance, and dynamic visual acuity assessments was performed before and after treatment. The patients were included in an individual treatment program for 8 weeks. Physiotherapy sessions were given at 2-week intervals. Along with the level of development of the treatment applied to the patients, it was requested perform a home exercise program with ten repetitions three times a day. Results: After 8 weeks of vestibular rehabilitation, it was observed that the balance parameters of the participants improved and the number of falls decreased. Statistically significant results were obtained in the Eyes-closed Tandem test (P = 0.001). Significant changes occurred in the modified Clinical Test results for Sensory Interaction in Balance from 0.37 +/- 0.19 s to 0.93 +/- 0.11 s (P = 0.001). Vestibular symptoms and dynamic visual acuity scores also improved after treatment (P = 0.001). Conclusion: It was concluded that the physiotherapy program applied to our patients with UVH positively affected fall risk and significantly improved balance parameters

Internal boundary layer in a singularly perturbed problem of fractional derivative

This paper is devoted to the study of internal boundary layer. Such motions are often associated with effect of boundary layer, i.e. low flow viscosity affects only in a narrow parietal layer of a streamlined body, and outside this zone the flow is as if there is no viscosity - the so-called ideal flow. Number of exponentials in the boundary layer is determined by the number of non-zero points of the limit operator spectrum. In the paper we consider the case when spectrum of the limit operator vanishes at the point To study the problem the Lomov regularization method is used. The original problem is regularized and the main term of asymptotics of the problem solution is constructed as the low viscosity tends to zero. Numerical results of solutions are obtained for different values of low viscosity

The Ignored Parameter in the Diagnosis of Obstructive Sleep Apnea Syndrome: The Oxygen Desaturation Index

Objective: The apnea-hypopnea index (AHI) does not provide information about the apnea depth and length. We aimed to evaluate the correlation of the oxygen desaturation index (ODI) with AHI and the subjective symptoms because it is known that hypoxia plays an important role in morbidity and complications of obstructive sleep apnea syndrome (OSAS).Methods: We reviewed the data of patients who applied to our clinic between 2010 and 2014 and underwent polysomnography (PSG) with a diagnosis of suspected sleep apnea. The demographic and anthropometric data of the patients were recorded. Epworth sleepiness scale (ESS) and values of AHI and ODI were analyzed in PSG.Results: A total of 321 patients were divided into four groups, according to AHI as follows: 82 (25.5%) common snoring, 77 (24%) mild obstructive sleep apnea (OSA), 71 (22.1%) moderate OSA, and 91 (28.3%) severe OSA. A strong correlation was detected between AHI and ODI (p<0.005 and r=0.904) in all patient groups. There was a positive correlation between AHI and ESS (p<0.05 and r=0.435), but the correlation of ESS with ODI was stronger than that with AHI (p<0.05 and r=0.504).Conclusion: The subjective symptoms of sleep apnea syndrome seem to be closely related to oxygen desaturations. Hypoxia during apnea periods of OSA is important; therefore, we suggest that ODI is as valuable as AHI in diagnosing and grading the OSAS

Development of artemia resources in the western basin of the Aral sea

Researchers from the Republic of Karakalpakstan are conducting continuous monitoring on the Aral Sea, studying artemia from various perspectives, as it is an interesting object from both a biological and applied perspective. This work is also being carried out jointly with the P.P. Shirshov Institute of Oceanology of the Russian Academy of Sciences. This paper presents the results of long-term comprehensive scientific research conducted on the Aral Sea. The main material for the study was our own collection of hydrobiological samples collected from the Western basin of the Aral Sea. As a result of the research, the dynamics of artemia resource development has been determined

Creation of machine and tractor enterprises with application of logistics principles in village councils of Kyrgyzstan

This paper deals with the issues of creating machine and tractor enterprises (MTE) using the logistics principles in the village councils of the Kyrgyz Republic. The main restraining factors for creation and construction of the MTE have been identified. The regional peculiarity of this problem is analyzed and solutions with detailed calculations and scientific research were proposed. On the basis of many years of scientific research the problem tree of absence and creation of MTE in the village councils of the Kyrgyz Republic was compiled. The results of the study, specific recommendations on creation of MTE with the application of logistics principles in the village councils of the Kyrgyz Republic are arranged and given in the design matrix of this project. The criteria for success in the successful implementation of this project have been determined