Different implementations of Clifford algebra: spinors, quaternions, and geometric algebra, are used to describe physical and technical systems. The geometric algebra formalism is a relatively new ...approach, destined to be used primarily by engineers and applied researchers. In a number of works, the authors examined the implementation of the geometric algebra formalism for computer algebra systems. In this article, the authors extend elliptic geometric algebra to hyperbolic space-time algebra. The results are illustrated by different representations of Maxwell’s equations. Using a computer algebra system, Maxwell’s vacuum equations in the space-time algebra representation are converted to Maxwell’s equations in vector formalism. In addition to practical application, the authors would like to draw attention to the didactic significance of these studies.
In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer ...geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed.
Asymptote-based scientific animation Gevorkyan, Migran N.; Korolkova, Anna V.; Kulyabov, Dmitry S.
Discrete and continuous models and applied computational science,
12/2023, Letnik:
31, Številka:
2
Journal Article
Recenzirano
Odprti dostop
This article discusses a universal way to create animation using Asymptote the language for vector graphics. The Asymptote language itself has a built-in library for creating animations, but its ...practical use is complicated by an extremely brief description in the official documentation and unstable execution of existing examples. The purpose of this article is to eliminate this gap. The method we describe is based on creating a PDF-file with frames using Asymptote, with further converting it into a set of PNG images and merging them into a video using FFmpeg. All stages are described in detail, which allows the reader to use the described method without being familiar with the used utilities.
The cross section of atomic electron Compton scattering γ+e→γ′+e′ was measured in the 4.400–5.475 GeV photon beam energy region by the PrimEx collaboration at Jefferson Lab with an accuracy of 2.6% ...and less. The results are consistent with theoretical predictions that include next-to-leading order radiative corrections. The measurements provide the first high precision test of this elementary QED process at beam energies greater than 0.1 GeV.
Julia language features for processing statistical data Gevorkyan, Migran N.; Korolkova, Anna V.; Kulyabov, Dmitry S.
Discrete and continuous models and applied computational science,
03/2023, Letnik:
31, Številka:
1
Journal Article
Recenzirano
Odprti dostop
The Julia programming language is a specialized language for scientific computing. It is relatively new, so most of the libraries for it are in the active development stage. In this article, the ...authors consider the possibilities of the language in the field of mathematical statistics. Special emphasis is placed on the technical component, in particular, the process of installing and configuring the software environment is described in detail. Since users of the Julia language are often not professional programmers, technical issues in setting up the software environment can cause difficulties that prevent them from quickly mastering the basic features of the language. The article also describes some features of Julia that distinguish it from other popular languages used for scientific computing. The third part of the article provides an overview of the two main libraries for mathematical statistics. The emphasis is again on the technical side in order to give the reader an idea of the general possibilities of the language in the field of mathematical statistics.
Hyperbolic complex numbers are used in the description of hyperbolic spaces. One of the well-known examples of such spaces is the Minkowski space, which plays a leading role in the problems of the ...special theory of relativity and electrodynamics. However, such numbers are not very common in different programming languages. Of interest is the implementation of hyperbolic complex in scientific programming languages, in particular, in the Julia language. The Julia language is based on the concept of multiple dispatch. This concept is an extension of the concept of polymorphism for object-oriented programming languages. To implement hyperbolic complex numbers, the multiple dispatching approach of the Julia language was used. The result is a library that implements hyperbolic numbers. Based on the results of the study, we can conclude that the concept of multiple dispatching in scientific programming languages is convenient and natural.
The article is an overview. We carry out the comparison of actual machine learning libraries that can be used the neural networks development. The first part of the article gives a brief description ...of TensorFlow, PyTorch, Theano, Keras, SciKit Learn libraries, SciPy library stack. An overview of the scope of these libraries and the main technical characteristics, such as performance, supported programming languages, the current state of development is given. In the second part of the article, a comparison of five libraries is carried out on the example of a multilayer perceptron, which is applied to the problem of handwritten digits recognizing. This problem is well known and well suited for testing different types of neural networks. The study time is compared depending on the number of epochs and the accuracy of the classifier. The results of the comparison are presented in the form of graphs of training time and accuracy depending on the number of epochs and in tabular form.
Total RNA from the bone marrow of healthy donor rats was injected to experimental rats 6 h, 2 h, or 30 min prior to a single γ-irradiation in the sublethal dose of 6 Gy. Injection total RNA 30 min ...prior to the exposure most effectively restored erythropoiesis in experimental animals. In 5 days, reticulocyte count in these animals 30-fold surpassed the control (injection of 0.9% NaCl). In 12 days, the content of new erythroblastic islands in the bone marrow in rats injected with the total RNA 2 h or 30 min prior to irradiation increased significantly and erythropoiesis recovery activation was observed.
In addition to their role in physiological and reparative regeneration of tissues, lymphoid cells are involved in the implementation of protective and adaptive reactions not related to immune ...response. The present review addresses the role of lymphocytes in organism reactivity changes upon hypoxia and hyperthermia and in modification of metabolic activity of cells. Mechanisms that underlie the control of resistibility to ionizing radiation and neoplastic processes by the lymphocytes and the role of lymphocytes in adaptive response development and enhancement of the organism’s resistance to stressful impacts are discussed.
Methodological derivation of the eikonal equation Fedorov, Arseny V.; Stepa, Christina A.; Korolkova, Anna V. ...
Discrete and continuous models and applied computational science,
12/2023, Letnik:
31, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Usually, when working with the eikonal equation, reference is made to its derivation in the monograph by Born and Wolf. The derivation of this equation was done rather carelessly. Understanding this ...derivation requires a certain number of implicit assumptions. For a better understanding of the eikonal approximation and for methodological purposes, the authors decided to repeat the derivation of the eikonal equation, explicating all possible assumptions. Methodically, the following algorithm for deriving the eikonal equation is proposed. The wave equation is derived from Maxwell’s equation. In this case, all conditions are explicitly introduced under which it is possible to do this. Further, from the wave equation, the transition to the Helmholtz equation is carried out. From the Helmholtz equation, with the application of certain assumptions, a transition is made to the eikonal equation. After analyzing all the assumptions and steps, the transition from the Maxwell’s equations to the eikonal equation is actually implemented. When deriving the eikonal equation, several formalisms are used. The standard formalism of vector analysis is used as the first formalism. Maxwell’s equations and the eikonal equation are written as three-dimensional vectors. After that, both the Maxwell’s equations and the eikonal equation use the covariant 4-dimensional formalism. The result of the work is a methodically consistent description of the eikonal equation.
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