Results 61 to 70 of about 448 (100)

Descartes' rule of signs, Newton polygons, and polynomials over hyperfields

, 2020
We develop a theory of multiplicities of roots for polynomials over hyperfields and use this to provide a unified and conceptual proof of both Descartes' rule of signs and Newton's "polygon rule".Comment: 21 pages.
Baker, Matthew, Lorscheid, Oliver
core  

Extensions of Hyperfields

, 2019
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong hyperfield extensions.
openaire   +2 more sources

Inductive graded rings, hyperfields and quadratic forms

, 2023
The goal of this work is twofold: (i) to provide a detailed analysis of some categories of inductive graded ring - a concept introduced in [DM98] in order to provide a solution of Marshall's signature conjecture in the algebraic theory of quadratic forms; (ii) apply this analysis to deepen the connections between the category of special hyperfields ...
Roberto, Kaique Matias de Andrade, Mariano, Hugo Luiz   +1 more
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Convex geometry over ordered hyperfields

Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
We initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields arising as quotients of fields. We prove hyperfield analogues of Helly, Radon and Carathéodory theorems. We also show that arbitrary convex sets can be separated via hemispaces.
Maxwell, James, Smith, Ben
openaire   +2 more sources

The Riemannian Geometry Theory of Visually-Guided Movement Accounts for Afterimage Illusions and Size Constancy. [PDF]

Vision (Basel), 2022
Neilson PD, Neilson MD, Bye RT.
europepmc   +1 more source

A Riemannian Geometry Theory of Synergy Selection for Visually-Guided Movement. [PDF]

Vision (Basel), 2021
Neilson PD, Neilson MD, Bye RT.
europepmc   +1 more source

Hypervaluations on Hyperfields and Ordered Canonical Hypergroups

Journal of Mathematical Sciences and Informatics
We study the concept of hypervaluations on hyperfields. In particular, we show that any hypervaluation from a hyperfield onto an ordered canonical hypergroup is the composition of a hypervaluation onto an ordered abelian group (which induces the same valuation hyperring) and an order preserving homomorphism of hypergroups.
Linzi, Alessandro, Stojałowska, Hanna
openaire   +2 more sources

From monoids to hyperstructures: in search of an absolute arithmetic

, 2010
We show that the trace formula interpretation of the explicit formulas expresses the counting function N(q) of the hypothetical curve C associated to the Riemann zeta function, as an intersection number involving the scaling action on the adele class ...
Connes, Alain, Consani, Caterina
core  

Geometry of tropical extensions of hyperfields

Proceedings of the Royal Society of Edinburgh: Section A Mathematics
We study the geometry of tropical extensions of hyperfields, including the ordinary, signed, and complex tropical hyperfields. We introduce the framework of ‘enriched valuations’ as hyperfield homomorphisms to tropical extensions and show that a notable family of them are relatively algebraically closed.
James Maxwell, Ben Smith
openaire   +3 more sources

Field extensions, Derivations, and Matroids over Skew Hyperfields

arXiv, 2018
We show that a field extension $K\subseteq L$ in positive characteristic $p$ and elements $x_e\in L$ for $e\in E$ gives rise to a matroid $M^ $ on ground set $E$ with coefficients in a certain skew hyperfield $L^ $. This skew hyperfield $L^ $ is defined in terms of $L$ and its Frobenius action $ :x\mapsto x^p$.
openaire   +2 more sources