Results 11 to 20 of about 5,854 (265)
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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On the apolar algebra of a product of linear forms [PDF]
Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020 Apolarity is a important tool in commutative algebra and algebraic geometry which studies a form, f, by the action of polynomial differential operators on f. The quotient of all polynomial differential operators by those which annihilate f is called the apolar algebra of f.
Michael DiPasquale +2 more
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On the pulsating (m,c)-Fibonacci sequence
Heliyon, 2021 In this paper, we study new ideas in the generalization of additive and multiplicative pulsating Fibonacci sequences. Then, we construct two types of pulsating Fibonacci sequences of the mth order.
Kittipong Laipaporn +2 more
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Reconstruction of Forms by Linear Algebra [PDF]
Nexus Network Journal, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marchetti, Elena, Costa, Luisa Rossi
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On the group of automorphisms of the algebra of plural numbers
Дифференциальная геометрия многообразий фигур, 2023 The algebra of dual numbers was first introduced by V. K. Clifford in 1873. The algebras of plural and dual numbers are analogous to the algebra of complex numbers. Dual numbers form an algebra, but not a field, because only dual numbers with a real part
A. Ya. Sultanov +2 more
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Definability of linear equation systems over groups and rings [PDF]
Logical Methods in Computer Science, 2013 Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from ...
Anuj Dawar +4 more
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Differential forms and Lie algebra cohomology for algebraic linear groups [PDF]
Illinois Journal of Mathematics, 1962 In the study of the rational cohomology theory of algebraic linear groups, the differential forms, constructed from the algebra of the rational representative functions on the group, play a major role in providing the link between the group cohomology and the Lie algebra cohomology [5].
Hochschild, G., Kostant, B.
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Linear maps preserving G-unitary operators in Hilbert space
Arab Journal of Mathematical Sciences, 2015 Let H be a complex Hilbert space and B(H) the algebra of all bounded linear operators on H. We give the concrete forms of surjective continuous unital linear maps from B(H) onto itself that preserve G-unitary operators.
Abdellatif Chahbi, Samir Kabbaj
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Hilbert polynomials of the algebras of $SL_ 2$-invariants
Karpatsʹkì Matematičnì Publìkacìï, 2018 We consider one of the fundamental problems of classical invariant theory, the research of Hilbert polynomials for an algebra of invariants of Lie group $SL_2$.
N.B. Ilash
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Hierarchical Zonotopal Power Ideals [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors.
Matthias Lenz
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