Публикации
Публикации 2024 года по проекту 24-00-001 "Алгебры Клиффорда и приложения":
- E. R. Filimoshina, D. S. Shirokov, “A Note on Centralizers and Twisted Centralizers in Clifford Algebras”. Adv. Appl. Clifford Algebras, 34:50, 2024, https://doi.org/10.1007/s00006-024-01345-8, arXiv: 2404.15169
- E. R. Filimoshina, D. S. Shirokov, “On generalization of Lipschitz groups and spin groups”, Mathematical Methods in the Applied Sciences, 47(3), 1375–1400, 2024, https://doi.org/10.1002/mma.8530 (Список журналов А, WoS Q1), arXiv: 2205.06045.
- K. S. Abdulkhaev, D. S. Shirokov, “Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras”, Advances in Applied Clifford Algebras, 32 (2022), 57, 27 pp., https://doi.org/10.1007/s00006-022-01232-0 (Список журналов C, WoS Q2), arXiv: 2205.13449.
- E. R. Filimoshina, D. S. Shirokov, "On Some Lie Groups in Degenerate Clifford Geometric Algebras", Advances in Applied Clifford Algebras, 33 (2023), 44, 29 pp., https://doi.org/10.1007/s00006-023-01290-y (Список журналов C, WoS Q2), arXiv: 2301.06842.
- K. S. Abdulkhaev, D. S. Shirokov, “On Explicit Formulas for Characteristic Polynomial Coefficients in Geometric Algebras”, Advances in Computer Graphics. CGI 2021. Lecture Notes in Computer Science, 13002, eds. N. Magnenat-Thalmann et al., Springer, Cham, 2021, 670–681. https://doi.org/10.1007/978-3-030-89029-2_50.
- E. R. Filimoshina, D. S. Shirokov, “On some Lie groups in degenerate geometric algebras”, ICACGA 2022. Lecture Notes in Computer Science, 13771, Springer, Cham, 2024, 186–198. https://doi.org/10.1007/978-3-031-34031-4_16.
Книги:
- Д. С. Широков, Лекции по алгебрам Клиффорда и спинорам, Лекц. курсы НОЦ, 19, МИАН, М., 2012, 180 с., PDF-файл.
- Н. Г. Марчук, Д. С. Широков, Теория алгебр Клиффорда и спиноров, Красанд, Москва, 2020, 560 с., http://urss.ru/cgi-bin/db.pl?lang=Ru&blang=ru&page=Book&id=263794.
- Н. Г. Марчук, Д. С. Широков, Введение в теорию алгебр Клиффорда, Фазис, Москва, 2012, 590 с.
- D. S. Shirokov, “Clifford algebras and their applications to Lie groups and spinors”, Lectures, Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June 2 - 7, 2017), eds. Ivaïlo Mladenov and Akira Yoshioka, Avangard Prima, Sofia, Bulgaria, 2018, 11–53 , arXiv:1709.06608.
- Д. С. Широков, Основы теории алгебр Клиффорда и спиноров, Математический институт им. В. А. Стеклова РАН, 11 февраля - 6 мая 2021, записи лекций.
- D. S. Shirokov, “On Singular Value Decomposition and Polar Decomposition in Geometric Algebras”, Advances in Computer Graphics. CGI 2023. Lecture Notes in Computer Science (Shanghai, 28 August – 01 September 2023), 14498, eds. Sheng, B., Bi, L., Kim, J., Magnenat-Thalmann, N., Thalmann, D., Springer, Cham, 2024, 391–401.
- D. S. Shirokov, “Noncommutative Vieta theorem in Clifford geometric algebras”, Mathematical Methods in the Applied Sciences, 2023, 1–16, https://doi.org/10.1002/mma.9221 (Список журналов А, WoS Q1), arXiv: 2301.06848.
- D. S. Shirokov, “Development of the method of averaging in Clifford geometric algebras”, Mathematics, 11:16 (2023), 3607, 18 pp., arXiv: 1409.8163
- D. S. Shirokov, “Classification of all constant solutions of SU(2) Yang–Mills equations with arbitrary current in pseudo-Euclidean space R^{p,q}”, Modern Physics Letters A, 38:20n21 (2023), 2350096, 54 pp., arXiv: 1912.04996
- D. S. Shirokov, “On Noncommutative Vieta Theorem in Geometric Algebras”, Empowering Novel Geometric Algebra for Graphics and Engineering. ENGAGE 2022. Lecture Notes in Computer Science, 13862, eds. Hitzer, E., Papagiannakis, G., Vasik, P., Springer, Cham, 2023, 28–37.
- Д. С. Широков, “Гиперболическое сингулярное разложение при исследовании уравнений Янга–Миллса и Янга–Миллса–Прока”, Ж. вычисл. матем. и матем. физ., 62:6 (2022), 1042–1055; D. S. Shirokov, “Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations”, Computational Mathematics and Mathematical Physics, 62:6 (2022), 1007–1019.
- D. S. Shirokov, “On inner automorphisms preserving fixed subspaces of Clifford algebras”, Advances in Applied Clifford Algebras, 31 (2021), 30, 23 pp., arXiv: 2011.08287.
- D. S. Shirokov, “On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension”, Computational and Applied Mathematics, 40 (2021), 173, 29 pp., arXiv: 2005.04015.
- D. S. Shirokov, “Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension”, Advances in Applied Clifford Algebras, 31 (2021), 70, 19 pp., arXiv: 2109.01816.
- D. S. Shirokov, “A note on subspaces of fixed grades in Clifford algebras”, AIP Conference Proceedings, ISBN: 978-0-7354-4072-2 (Yakutsk, Russia, July 27 - August 1, ICMM-2020), 2328, AIP Publishing, 2021, 060001.
- D. S. Shirokov, “A note on the hyperbolic singular value decomposition without hyperexchange matrices”, Journal of Computational and Applied Mathematics, 391 (2021), 113450, arXiv: 1812.02460.
- D. S. Shirokov, “On solutions of the Yang-Mills equations in the algebra of h-forms”, Journal of Physics: Conference Series (International Conference «Marchuk Scientific Readings 2021» (MSR-2021) 4-8 October 2021, Novosibirsk, Russian Federation), 2099, IOP Publishing, 2021, 012015.
- D. S. Shirokov, “On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space R^n”, Journal of Nonlinear Mathematical Physics, 27:2 (2020), 199–218 , arXiv: 1804.04620.
- N. G. Marchuk, D. S. Shirokov, “Local Generalization of Pauli`s Theorem”, Azerb. J. Math., 10:1 (2020), 38–56 https://azjm.org/volumes/1001/pdf/1001-3.pdf, arXiv: 1201.4985.
- Н. Г. Марчук, Д. С. Широков, “О некоторых уравнениях, моделирующих уравнения Янга-Миллса”, Физика элементарных частиц и атомного ядра, 51:4 (2020), 676–685 www1.jinr.ru/Pepan/v-51-4/38_Marchuk.pdf ; N. G. Marchuk, D. S. Shirokov, “On some equations modeling the Yang-Mills equations”, Physics of Particles and Nuclei, 51:4 (2020), 589–594.
- D. S. Shirokov, “On Basis-Free Solution to Sylvester Equation in Geometric Algebra”, Advances in Computer Graphics. CGI 2020. Lecture Notes in Computer Science, 12221, eds. Magnenat-Thalmann N. et al., Springer, Cham, 2020, 541–548.
- D. S. Shirokov, “Calculation of elements of spin groups using method of averaging in Clifford`s geometric algebra”, Advances in Applied Clifford Algebras, 29 (2019), 50, 12 pp., arXiv: 1901.09405.
- D. S. Shirokov, “Classification of Lie algebras of specific type in complexified Clifford algebras”, Linear and Multilinear Algebra, 66:9 (2018), 1870–1887 , arXiv: 1704.03713.
- D. S. Shirokov, “Covariantly constant solutions of the Yang-Mills equations”, Advances in Applied Clifford Algebras, 28 (2018), 53, 16 pp., arXiv: 1709.07836.
- D. S. Shirokov, “Method of averaging in Clifford Algebras”, Advances in Applied Clifford Algebras, 27:1 (2017), 149–163 , arXiv: 1412.0246.
- N. G. Marchuk, D. S. Shirokov, “Constant Solutions of Yang-Mills Equations and Generalized Proca Equations”, Journal of Geometry and Symmetry in Physics, 42 (2016), 53–72 , arXiv: 1611.03070.
- D. S. Shirokov, “On Some Lie Groups Containing Spin Group in Clifford Algebra”, Journal of Geometry and Symmetry in Physics, 42 (2016), 73–94 , arXiv: 1607.07363.
- N.G. Marchuk, D.S. Shirokov, “General solutions of one class of field equations”, Rep. Math. Phys., 78:3 (2016), 305–326 , arXiv: 1406.6665.
- D. S. Shirokov, “Calculations of elements of spin groups using generalized Paulis theorem”, Advances in Applied Clifford Algebras, 25:1 (2015), 227–244 , arXiv: 1409.2449.
- Д. С. Широков, “Свертки по рангам и кватернионным типам в алгебрах Клиффорда”, Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 19:1 (2015), 117–135.
- D. S. Shirokov, “Symplectic, Orthogonal and Linear Lie Groups in Clifford Algebra”, Advances in Applied Clifford Algebras, 25:3 (2015), 707-718 , arXiv: 1409.2452.
- Д. С. Широков, “Теорема Паули при описании n-мерных спиноров в формализме алгебр Клиффорда”, ТМФ, 175:1 (2013), 11–34; D. S. Shirokov, “Pauli theorem in the description of n-dimensional spinors in the Clifford algebra formalism”, Theoret. and Math. Phys., 175:1 (2013), 454–474.
- Д. С. Широков, “Использование обобщëнной теоремы Паули для нечëтных элементов алгебры Клиффорда для анализа связей между спинорными и ортогональными группами произвольных размерностей”, Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 1(30) (2013), 279–287.
- Д. С. Широков, “Обобщение теоремы Паули на случай алгебр Клиффорда”, Школа-семинар "Взаимодействие математики и физики: новые перспективы для студентов, аспирантов и молодых исследователей (Москва, Математический институт им. В.А.Стеклова РАН, 22–30 августа 2012), Наноструктуры. Математическая физика и моделирование, 9, № 1, 2013, 93–104.
- D. S. Shirokov, “Quaternion typification of Clifford algebra elements”, Adv. Appl. Clifford Algebr., 22:1 (2012), 243–256 , arXiv: 0806.4299.
- D. S. Shirokov, “Development of the method of quaternion typification of Clifford algebra elements”, Adv. Appl. Clifford Algebr., 22:2 (2012), 483–497 , arXiv: 0903.3494.
- D. S. Shirokov, “Concepts of trace, determinant and inverse of Clifford algebra elements”, Progress in analysis. Proceedings of the 8th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Moscow, Russia, August 22–27, 2011. Volume 1., v. 1, eds. Burenkov, V. I. (ed.); Goldman, M. L. (ed.); Laneev, E. B. (ed.); Stepanov, V. D. (ed.), Moscow: Peoples’ Friendship University of Russia (ISBN 978-5-209-04582-3/hbk), 2012, 187-194 , 8 pp., arXiv: 1108.5447.
- D. S. Shirokov, “On some relations between spinor and orthogonal groups”, p-Adic Numbers Ultrametric Anal. Appl., 3:3 (2011), 212–218.
- D. S. Shirokov, “Quaternion types of Clifford algebra elements, basis-free approach”, Proceedings of 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (Weimar, Germany, 15–20 July), Bauhaus-University Weimar, 2011, 9 pp. , arXiv: 1109.2322.
- Д. С. Широков, “Обобщение теоремы Паули на случай алгебр Клиффорда”, Докл. РАН, 440:5 (2011), 607–610; D. S. Shirokov, “Extension of Pauli's theorem to Clifford algebras”, Dokl. Math., 84:2 (2011), 699–701.
- Д. С. Широков, “Теорема о норме элементов спинорных групп”, Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2011, № 1(22), 165–171.
- D. S. Shirokov, “A classification of Lie algebras of pseudo-unitary groups in the techniques of Clifford algebras”, Adv. Appl. Clifford Algebr., 20:2 (2010), 411–425 , arXiv: 0705.3368.
- Д. С. Широков, “Классификация элементов алгебр Клиффорда по кватернионным типам”, Докл. РАН, 427:6 (2009), 758–760; D. S. Shirokov, “Classification of elements of Clifford algebras according to quaternionic types”, Dokl. Math., 80:1 (2009), 610–612.
- N. G. Marchuk, D. S. Shirokov, “Unitary spaces on Clifford algebras”, Adv. Appl. Clifford Algebr., 18:2 (2008), 237–254 , arXiv: 0705.1641.
Нашли опечатку?
Выделите её, нажмите Ctrl+Enter и отправьте нам уведомление. Спасибо за участие!
Сервис предназначен только для отправки сообщений об орфографических и пунктуационных ошибках.