Results 11 to 20 of about 692 (164)
THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC
Journal of the Institute of Mathematics of Jussieu, 2023 AbstractThe Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is trivial when the curve is hyperelliptic with a marked Weierstrass point. The image of the Ceresa cycle under a certain cycle class map provides a class in étale cohomology called the Ceresa class.
Daniel Corey +2 more
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Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields
Mathematics, 2021 Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings.
Francisco José Valverde-Albacete +1 more
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On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]
, 2021 This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the fundamental theorem of tropical differential ...
Boulier, François +3 more
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Public-Key Cryptography Based on Tropical Circular Matrices
Applied Sciences, 2022 Some public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since the multiplication is actually an ordinary addition of numbers and there is no ordinary multiplication of numbers
Huawei Huang, Chunhua Li, Lunzhi Deng
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The Singular Value Decomposition over Completed Idempotent Semifields
Mathematics, 2020 In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD).
Francisco J. Valverde-Albacete +1 more
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Independent Rainbow Domination Numbers of Generalized Petersen Graphs P(n,2) and P(n,3)
Mathematics, 2020 We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P ( n , k ) for certain values of n , k ∈ N . By suitably adjusting and applying a well established technique of tropical algebra (path
Boštjan Gabrovšek +2 more
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Hokkaido Mathematical Journal, 2009 The construction of a tropical hypersurface is given by modeling the classical construction of a complex hypersurface. A tropical meromorphic function of finite type is shown to be a tropical rational function. One also has tropical nullstellensatz.
Illia Itenberg +2 more
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Matrix Tri-Factorization Over the Tropical Semiring
IEEE Access, 2023 Tropical semiring has proven successful in several research areas, including optimal control, bioinformatics, discrete event systems, and decision problems. Previous studies have applied a matrix two-factorization algorithm based on the tropical semiring
Amra Omanovic, Polona Oblak, Tomaz Curk
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TROPICAL ALGEBRAIC SETS, IDEALS AND AN ALGEBRAIC NULLSTELLENSATZ [PDF]
International Journal of Algebra and Computation, 2008 This paper introduces the foundations of the polynomial algebra and basic structures for algebraic geometry over the extended tropical semiring. Our development, which includes the tropical version for the fundamental theorem of algebra, leads to the reduced polynomial semiring — a structure that provides a basis for developing a tropical analogue to ...
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Algebraic properties of generic tropical varieties [PDF]
Algebra & Number Theory, 2010 We show that the algebraic invariants multiplicity and depth of a graded ideal in the polynomial ring are closely connected to the fan structure of its generic tropical variety in the constant coefficient case. Generically the multiplicity of the ideal is shown to correspond directly to a natural definition of multiplicity of cones of tropical ...
Römer, Tim, Schmitz, Kirsten
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