Publications (2021–2024)
2024
On Generalization of Lipschitz Groups and Spin Groups
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 (WoS Q1), arXiv: 2205.06045.
On SVD and Polar Decomposition in Real and Complexified Clifford Algebras
D. S. Shirokov, “On SVD and Polar Decomposition in Real and Complexified Clifford Algebras”, Advances in Applied Clifford Algebras, 34 (2024), 23, 20 pp., arXiv: 2404.11920
A Class of Field Equations for Neutrinos with Nonzero Masses
N. G. Marchuk, “A Class of Field Equations for Neutrinos with Nonzero Masses”, Theoret. and Math. Phys., 219:3 (2024), 897–912.
On Some Lie Groups in Degenerate Geometric Algebras
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.
A Note on Centralizers and Twisted Centralizers in Clifford Algebras
E. R. Filimoshina, D. S. Shirokov, “A Note on Centralizers and Twisted Centralizers in Clifford Algebras”. Adv. Appl. Clifford Algebras, 34:50, 2024, arXiv: 2404.15169
On Singular Value Decomposition and Polar Decomposition in Geometric Algebras
D. S. Shirokov, “On Singular Value Decomposition and Polar Decomposition in Geometric Algebras”, Advances in Computer Graphics. CGI 2023. Lecture Notes in Computer Science, 14498, Springer, Cham, 2024, 391–401.
Noncommutative Vieta Theorem in Clifford Geometric Algebras
D. S. Shirokov, “Noncommutative Vieta Theorem in Clifford Geometric Algebras”, Mathematical Methods in the Applied Sciences, 47(14), 2024, 11305–11320, arXiv: 2301.06848
2023
On Some Lie Groups in Degenerate Clifford Geometric Algebras
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. (WoS Q2), arXiv: 2301.06842
Classification of All Constant Solutions of SU(2) Yang–Mills Equations with Arbitrary Current in Pseudo-Euclidean Space R^{p,q}
D. S. Shirokov, “Classification of All Constant Solutions of SU(2) Yang–Mills Equations with Arbitrary Current in Pseudo-Euclidean Space Rp,q”, Modern Physics Letters A, 38:20n21 (2023), 2350096 , 54 pp., arXiv: 1912.04996
On Noncommutative Vieta Theorem in Geometric Algebras
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, Springer, Cham, 2023, 28–37
Field Theory Equations and Clifford Algebras"
N.G. Marchuk. "Field Theory Equations and Clifford Algebras" (in Russian). URSS, Moscow, 2023, 344 pp.
Development of the Method of Averaging in Clifford Geometric Algebras
D. S. Shirokov, “Development of the Method of Averaging in Clifford Geometric Algebras”, Mathematics, 11:16 (2023), 3607 , 18 pp., arXiv: 1409.8163
2022
Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras
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. (WoS Q2), arXiv: 2205.13449.
Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations
“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
2021
On Explicit Formulas for Characteristic Polynomial Coefficients in Geometric Algebras
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.
A Note on Subspaces of Fixed Grades in Clifford Algebras
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.
On Solutions of the Yang-Mills Equations in the Algebra of h-forms
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.
On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras
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
On Computing the Determinant, Other Characteristic Polynomial Coefficients, and Inverse in Clifford Algebras of Arbitrary Dimension
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
Sketch of a Gauge Model of Gravity with SU(2) Symmetry in Minkowski Space
Nikolay Marchuk, “Sketch of a Gauge Model of Gravity with SU(2) Symmetry in Minkowski Space”, Adv. Appl. Clifford Algebr., 31 (2021), 75 , 14 pp.
A Note on the Hyperbolic Singular Value Decomposition without Hyperexchange Matrices
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
Basis-free Solution to Sylvester Equation in Clifford Algebra of Arbitrary Dimension
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
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