Results 61 to 70 of about 394 (102)

Geometry of the arithmetic site [PDF]

, 2015
We introduce the Arithmetic Site: an algebraic geometric space deeply related to the non-commutative geometric approach to the Riemann Hypothesis. We prove that the non-commutative space quotient of the adele class space of the field of rational numbers ...
Connes, Alain, Consani, Caterina
core  

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
openaire   +2 more sources

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

A Note on Intuitionistic Fuzzy Hypervector Spaces

, 2010
The notion of Intuitionistic fuzzy hypervector space has been generalized and a few basic properties on this concept are studied. It has been shown that the intersection and union of an arbitrary family of Intuitionistic fuzzy hypervector spaces are also
Roy, Sanjay, Samanta, T. K.
core  

Sphingosine-1-phosphate expression in human epiretinal membranes. [PDF]

PLoS One, 2022
Kim M, Kwon S, Jeon S, Jung BJ, Kim KS.
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

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

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

Root selections and 2^p-th root selections in hyperfields

Discussiones Mathematicae - General Algebra and Applications, 2019
In this paper we define root selections and 2p-th root selections for hyperfields: these are multiplicative subgroups whose existence is equivalent to the existence of a well behaved square root function and 2p-th root function, respectively. We proceed to investigate some basic properties of such root selections, and draw some parallels between the ...
openaire   +4 more sources