Две статьи Д.С. Широкова по проекту зеркальной лаборатории опубликованы в международных журналах

Две статьи Д.С. Широкова по проекту зеркальной лаборатории «Кватернионы, геометрические алгебры и приложения» опубликованы в международных журналах:

• D. S. Shirokov, “On Rank of Multivectors in Geometric Algebras”, Mathematical Methods in the Applied Sciences (WoS Q1), 2025, arXiv: 2412.02681, https://doi.org/10.1002/mma.10946

Аннотация: We introduce the notion of rank of multivector in Clifford geometric algebras of arbitrary dimension without using the corresponding matrix representations and using only geometric algebra operations. We use the concepts of characteristic polynomial in geometric algebras and the method of SVD. The results can be used in various applications of geometric algebras in computer science, engineering, and physics.

• D. S. Shirokov, “Calculation of Spin Group Elements Revisited”, International Journal of Geometric Methods in Modern Physics (Scopus Q2), 2025, arXiv: 2412.02772, https://doi.org/10.1142/S0219887825400316

Аннотация: In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then explicitly using matrices, quaternions, and split-quaternions in the cases of all possible signatures (p,q) of space up to dimension n=p+q=3. The different formalisms are convenient for different possible applications in physics, engineering, and computer science.