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AIP Conference Proceedings
Vol. 2328: ICMM-2020.
AIP Publishing LLC, 2021.
9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL MODELING: Dedicated to the 75th Anniversary of Professor V.N. Vragov
Shirokov D., , in : AIP Conference Proceedings. Vol. 2328: ICMM-2020.: AIP Publishing LLC, 2021. Ch. 060001. P. 060001-1-060001-4.
In this note, we present basis-free definitions of subspaces of fixed grades of real Clifford algebras of arbitrary dimension. We do not use fixed basis of Clifford algebra and use only the properties of commutators and anticommutators. ...
Added: April 2, 2021
Madera A. G., Компьютерные исследования и моделирование 2019 Т. 11 № 4 С. 613-630
A hierarchical method of mathematical and computer modeling of interval-stochastic thermal processes in complex electronic systems for various purposes is developed. The developed concept of hierarchical structuring reflects both the constructive hierarchy of a complex electronic system and the hierarchy of mathematical models of heat exchange processes. Thermal processes that take into account various physical ...
Added: November 1, 2019
Shirokov D., Advances in Applied Clifford Algebras 2018 Vol. 28 No. 3 P. 1-16
We present a new class of covariantly constant solutions of the Yang–Mills equations. These solutions correspond to the solution of the field equation for the spin connection of the general form. ...
Added: July 6, 2018
Shirokov D., Marchuk N., Reports on Mathematical Physics 2016 Vol. 78 No. 3 P. 305-326
We find general solutions of some field equations (systems of equations) in pseudo-Euclidian spaces (so-called primitive field equations). These equations are used in the study of the Dirac equation and Yang-Mills equations. These equations are invariant under orthogonal O(p,q) coordinate transformations and invariant under gauge transformations, which depend on some Lie groups. In this paper ...
Added: September 27, 2016
Petrov A.P., Maslov A. I., Tsaplin N. A., Mathematical Models and Computer Simulations 2016 Vol. 8 No. 4 P. 401-408
In this paper, a mathematical model is developed for information warfare in society whereby an individual chooses between two suggested viewpoints. The model is based on the traditional Rashevsky framework of imitative behavior. A primary analysis of the model is conducted. The model has the form of a nonlinear integro-differential equation in which the unknown ...
Added: October 12, 2016
Covolo T., Journal of Noncommutative Geometry 2015 Vol. 9 No. 2 P. 543-565
We develop the theory of linear algebra over a (Z2)n-commutative algebra (n∈N), which includes the well-known super linear algebra as a special case (n=1). Examples of such graded-commutative algebras are the Clifford algebras, in particular the quaternion algebra H. Following a cohomological approach, we introduce analogues of the notions of trace and determinant. Our construction ...
Added: September 28, 2015
Zakhariev I., Aksenov S. A., Logashina I. V., Letters on Materials 2017 № 1 С. 49-54
The paper is oriented toward the problem of determination of rheological characteristics of a material by free bulging testing. This information about the material behavior is used for design of gas forming technologies for production of complex shell parts used in aerospace industry. Realization of such technologies requires pressure forming regimes which can be calculated ...
Added: March 14, 2017
Nikitin A. A., Галкин Е. Г., Moscow University Computational Mathematics and Cybernetics 2020 Vol. 44 No. 2 P. 61-68
A study is performed of the main approaches to investigating the stochastic process of
population dynamics. Continuous time and space and immovable individuals are used to derive a
denumerable system of integrodifferential equations corresponding to the dynamics of the spatial
momentum of this process. A way to find an approximate solution using the momentum approach is
described. ...
Added: April 27, 2020
Shmatko N., Katchanov Y. L., / Cornell University. Series math "arxiv.org". 2013. No. v.1.
The paper puts forth an axiomatic description of the complexity of an object of sociological investigation. The proposed axioms allow us to determine complexity within the framework of mathematical sociology such as the variational principle, which is formed relative to the state of the object of sociological investigation. On the basis of this principle ...
Added: June 13, 2013
Галкин Е. Г., Зеленков В. К., Nikitin A. A., International Journal of Open Information Technologies 2019 Т. 7 № 12 С. 18-23
This publication begins a series of works devoted to the comparison of the results of numerical methods for solving integral equations and the results of computer simulations using Poisson processes. The pros and cons of these two approaches are highlighted. The main subject of study is the model of two-species communities proposed in the works ...
Added: December 8, 2019
Akaev A., Sadovnichii V. A., Korotayev A. et al., М. : Институт социально-политических исследований РАН, 2012
В данной книге авторы предлагают новую методологию долгосрочного социально-экономического моделирования и прогнозирования, основанную на кондратьевских больших циклах экономической конъюнктуры. Использование методологии позволяет обнаружить точки кризисов, рецессий и бифуркаций и тем самым повышает точность и надежность прогноза. Методология применяется для системного анализа мировой динамики и построения сценариев развития России. ...
Added: October 22, 2014
Галкин Е. Г., Nikitin A. A., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2020 № 2 С. 11-18
The article presents the main approaches to the study of the stochastic process of population dynamics with continuous time and space and with fixed individuals, a countable system of integro-differential equations corresponding to the dynamics of spatial moments of this process is derived, and a method for finding an approximate solution using the method of ...
Added: February 18, 2020
Kham T., Социальные и гуманитарные науки: теория и практика 2019 № 1(3) С. 167-183
The article examines the problems of defining the term computer simulations of scientific experiments. The first part analyzes the original method for classifying variations of terms proposed by Duran as the most successful for demonstrating significant existing contradictions among philosophers regarding the place and role of computer simulations in the philosophy of science. In the ...
Added: December 11, 2019
Shirokov D., Advances in Applied Clifford Algebras 2019 Vol. 29 No. 50 P. 1-12
We present a method of computing elements of spin groups in the case of arbitrary dimension. This method generalizes Hestenes method for the case of dimension 4. We use the method of averaging in Clifford’s geometric algebra previously proposed by the author. We present explicit formulas for elements of spin group that correspond to the ...
Added: July 22, 2019
Shirokov D., Theoretical and Mathematical Physics 2013 Vol. 175 No. 1 P. 454-474
We discuss a generalized Pauli theorem and its possible applications for describing n-dimensional (Dirac, Weyl, Majorana, and Majorana–Weyl) spinors in the Clifford algebra formalism. We give the explicit form of elements that realize generalizations of Dirac, charge, and Majorana conjugations in the case of arbitrary space dimensions and signatures, using the notion of the Clifford ...
Added: March 11, 2015
Sadovnichii V. A., Akaev A., Korotayev A. et al., М. : Издательский Дом "Наука", 2014
В коллективной монографии представлены результаты моделирования развития стран БРИКС, полученные к настоящему времени в рамках исследований по проекту «Математическое моделирование глобальной и региональной динамики в условиях модернизации системы науки и образования» Программы фундаментальных исследований Президиума РАН «Экономика и социология науки и образования». ...
Added: October 23, 2014
Malkov S. Y., Meshcherina K., Korotayev A., BioSystems 2020 Vol. 198 P. 104231
This paper proposes a methodological approach to analyzing the evolution of the stability of socioeconomic systems and to assessing the risk of their possible destabilization based on the use of mathematical modeling methods. In this paper, a basic model is presented allowing us to describe the joint dynamics of processes in the economic, organizational, and ...
Added: August 20, 2020
Михайлов А. П., Petrov A., Маревцева Н. А. et al., Математическое моделирование 2014 Т. 26 № 3 С. 65-74
Работа посвящена развитию системы моделей распространения информации в социуме. В качестве надстройки над базовой моделью предложены четыре новых механизма, влияющие на процесс распространения информации. Для модели со всеми четырьмя механизмами получены достаточные условия устойчивости так называемого безадептного состояния ...
Added: October 18, 2014
Shirokov D., Advances in Applied Clifford Algebras 2015 Vol. 25 No. 3 P. 707-718
In this paper we prove isomorphisms between 5 Lie groups (of arbitrary dimension and fixed signatures) in Clifford algebra and classical matrix Lie groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms of corresponding Lie algebras. ...
Added: March 12, 2015
Shirokov D., Наноструктуры. Математическая физика и моделирование 2013 Т. 9 № 1 С. 93-104
В работе доказаны утверждения, которые обобщают так называемую фундаментальную теорему Паули о гамма-матрицах. Рассмотрены алгебры Клиффорда над полем вещественных и комплексных чисел произвольной размерности. Для произвольных двух наборов из четного или нечетного числа элементов, удовлетворяющих определяющим антикоммутационным соотношениям алгебры Клиффорда, доказаны обобщения теоремы Паули. Предъявлены алгоритмы для вычисления элемента, осуществляющего связь между двумя наборами. ...
Added: July 22, 2019
Shirokov D., Advances in Applied Clifford Algebras 2015 Vol. 25 No. 1 P. 227-244
We formulate generalizations of Pauli’s theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for computing elements of spin groups that correspond to elements of orthogonal groups as double cover. ...
Added: March 11, 2015
Shirokov D., Marchuk N., Advances in Applied Clifford Algebras 2008 Vol. 18 No. 2 P. 237-254
For the complex Clifford algebra <img /> (p, q) of dimension n = p + q we define a Hermitian scalar product. This scalar product depends on the signature (p, q) of Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With the aid of Hermitian idempotents we suggest a new construction of, so called, normal matrix representations of Clifford algebra elements. These ...
Added: June 16, 2015
Shirokov D., Advances in Applied Clifford Algebras 2010 Vol. 20 No. 2 P. 411-425
In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudo-unitary groups. Our main techniques are Clifford algebras. We have found 12 types of subalgebras of Lie algebras of pseudo-unitary groups. ...
Added: June 16, 2015
Соомере Т., Kurkina O. E., Фундаментальная и прикладная гидрофизика 2011 Т. 4 № 4 С. 43-57
The properties of extreme wave storms in the Darss Sill area, SW Baltic Sea, are analysed based on waverider data for 1991-2010 and long-term numerical simulations. The long-term significant wave height is HS ~0.7 m and the most frequent wave periods 2-4 s. The largest measured HS is 4.46 m. The typical measured and modelled ...
Added: September 21, 2012