Описание вращений в трёхмерном пространстве с помощью методов геометрической алгебры с реализацией на языке Python

This paper provides a brief overview of the basic theoretical information from geometric algebra and modules for Python, in particular the clifford module. During the presentation of the theoretical material, much attention was paid to the mathematical apparatus of geometric algebra. Classical methods of rotations on the plane and in space were studied: complex numbers, matrices and quaternions. Geometric algebra is based on the concept of a multivector and a geometric product. With the help of a special kind of multivector, rotations in spaces of any dimension are described in a uniform way. The mathematical apparatus of geometric algebra is relatively simple to master and therefore has gained great popularity in various applied fields. One of these areas is computer graphics. The fact is that with the help of a special kind of multivector, it becomes possible to uniformly describe rotations and reflections in spaces of any dimension. Potentially, this method of describing rotations can displace the method based on quaternions and biquaternions, since it is algorithmically not more complicated, but allows for a much clearer geometric interpretation. The paper provides an overview of a number of Python programming language libraries: libraries implementing algebraic operations, quaternions, libraries for visualization and libraries for geometric algebra. There are also a number of examples of using multivectors to describe rotations and reflections and their implementation using the Python Clifford module. Programs were written that implement rotations on the plane in various ways, they were also visualized in 2D and in 3D.В данной работе даётся краткий обзор основных теоретических сведений из геометрической алгебры и модулей для языка Python, в частности модуля clifford. В ходе изложения теоретического материала большое внимание было уделено математическому аппарату геометрической алгебры. Были изучены классические методы поворотов на плоскости и в пространстве: комплексные числа, матрицы и кватернионы. Геометрическая алгебра основывается на понятии мультивектора и геометрического произведения. С помощью мультивектора специального вида описываются вращения в пространствах любой размерности единообразным способом. Математический аппарат геометрической алгебры сравнительно прост для освоения и поэтому обрёл большую популярность в различных прикладных областях. Одной из таких областей является компьютерная графика. Дело в том, что с помощью мультивектора специального вида становится возможным единообразно описать вращения и отражения в пространствах любой размерности. Потенциально этот способ описания вращений может вытеснить способ, основанный на кватернионах и бикватернионах, так как алгоритмически не сложнее, но допускает намного более ясную геометрическую интерпретацию. В работе дан обзор ряда библиотек языка программирования Python: библиотеки, реализующие алгебраические операции, кватернионы, библиотеки для визуализации и библиотеки для геометрической алгебры. Также приводится ряд примеров использования мультивекторов для описания вращений и отражений и их реализация с помощью модуля Clifford языка Python. Были написаны программы, реализующие повороты на плоскости различными способами, также они были визуализированы в 2D и в 3D

The formation of risk groups for development of occupational diseases during the pre-employment and periodic medical examinations to conduct recreational activities

Research objective. The purpose ofthe study was to develop methodology for the formation of groups at risk of developing chronic diseases and complex of measures for their prevention when carrying out a compulsory medical examination of workers. Materials and methods. The results of periodic medical examinations for 2012 were analyzed according to 19 the final acts and reports 61 subjects ofthe Russian Federation. The results ofthe examination ofthe connection between disease and occupation were analyzed according to 50 examination protocols ofthe Burnasyan Federal Medical Biophysical Center of Federal Medical Biological Agency during 200-2010. Results. Based on the results ofthe conducted analysis methodology was developed to assess the risk of occupational disease fully meets the current legislative and regulatory framework of the Russian Federation and enable the individual and group level: to assess the risk of occupational diseases (high, medium, low, no); to identify possible nosological forms of diseases that should be expected, in accordance with the current list of occupational diseases; — to predict the presence or absence of responsibility employer for any case of occupational disease; to generate the necessary recommendations to the employer for the prevention of occupational diseases among workers. Conclusion. The method of formation of risk groups for development of occupational diseases recommended for medical organizations, conducting preliminary and periodic medical examinations

MUCOPOLYSACCHARIDOSIS TYPE II

Article is devoted to one of the orphan diseases — mucopolysaccharidosis (MPS), which is the result of any lysosomal enzyme deficiency (which determines the type of illness). The most common is the MPS type II (Hunter syndrome), developing as a result of deficiency of the enzyme alpha-L-iduronosulphatsulphataze. The authors are observing the largest group of children with this pathology in the Russian population — 40 patients. On the example of their own clinical cases the only existing on the date the pathogenetic treatment is provided — replacement therapy with idursulphase that significantly improves the disease prognosis.Key words: MPS, types, Hunter syndrome, clinical course, diagnosis, treatment, prognosis, children

MUCOPOLYSACCHARIDOSIS TYPE II

Article is devoted to one of the orphan diseases — mucopolysaccharidosis (MPS), which is the result of any lysosomal enzyme deficiency (which determines the type of illness). The most common is the MPS type II (Hunter syndrome), developing as a result of deficiency of the enzyme alpha-L-iduronosulphatsulphataze. The authors are observing the largest group of children with this pathology in the Russian population — 40 patients. On the example of their own clinical cases the only existing on the date the pathogenetic treatment is provided — replacement therapy with idursulphase that significantly improves the disease prognosis.Key words: MPS, types, Hunter syndrome, clinical course, diagnosis, treatment, prognosis, children

СРАВНИТЕЛЬНАЯ ХАРАКТЕРИСТИКА ЭФФЕКТИВНОСТИ ПРИМЕНЕНИЯ PROROOT И BIODENTINE В СТОМАТОЛОГИЧЕСКОЙ ПРАКТИКЕ

Today, new tricalcium silicate cements (TSC) can provide biocompatibility with improved performance properties. This review of the literature was aimed at a comparative assessment of the physicochemical properties of biological activity (ProRoot MTA and Biodentine).На сегодняшний день новые трикальцийсиликатные цементы (TSC) могут обеспечивать биосовместимость с улучшенными рабочими свойствами. Этот обзор литературы был направлен на сравнительную оценку физико-химических свойств, биологической активности TSC (ProRoot MTA и Biodentine)

ВЗАИМОСВЯЗЬ БОЛЕЗНИ ПАРКИНСОНА И БРУКСИЗМА

This article aims to address the relationship between Parkinson's disease and bruxism. Although the etiology and pathogenesis of these diseases has not been fully studied, due to the alleged polytelogenicity of these conditions, in particular stress factors and dopamine metabolic disturbances, a high probability of their mutual development is possible. Through a review of the literature, an analysis of these pathologies was made and an assumption was made about the possible connection between these diseases.В данной статье ставится задача рассмотреть взаимосвязь между болезнью Паркинсона и бруксизмом. Хотя этиологии и патогенезы этих заболеваний до конца не изучены, за счёт предполагаемой полиэтилогичности этих состояний, в частности стрессовых факторов и нарушения обмена дофамина, возможна высокая вероятность их взаимного развития. Посредством обзора литературы был совершен анализ данных патологий и приведено предположение о возможной связи этих заболеваний