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Signed Tropicalization of Polar Cones. [PDF]
J Optim Theory ApplAkian M +3 more
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Immunometabolic resistors of aging in long-lived golden spiny mice. [PDF]
Sci AdvKim HH +12 more
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Classification of Krasner Hyperfields of Order 4
Acta Mathematica Sinica, English Series, 2020Let \(H\) be a non-empty set. A map from \(H\times H\) into the non-empty subsets of \(H\) is called a hyperoperation. The image of \((a,b)\) is denoted by \(ab\). Various notions generalize, one way or another, basic properties of groups. One such notion are polygroups. The authors study \(n\)-polygroups, where \(ab\) has at most \(n\) elements.
Iranmanesh, Mahdeyeh +3 more
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Hyperaffine planes over hyperfields
Journal of Geometry, 1995The authors first study hyperaffine planes coordinatized over planar hyperfields. The main purpose of the paper is to show that if an abstract hyperaffine plane satisfies certain additional conditions 1-11, then there exists a hyperfield such that the coordinate plane over this hyperfield is isomorphic to the given hyperaffine plane.
Procesi Ciampi, R., Rota, R.
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IFAC Proceedings Volumes, 1983
Abstract Basically, σ- hyperfields on σ- complete De Morgan algebras are introduced and explored. Measurable spaces (topological spaces) are extended to hypermeasurable spaces (hypertopological spaces) constructed considering σ- hyperfields. Random sets are then given a pure measure theoretical definition and, finally, random fuzzy sets are ...
Wang Pei-Zhuang, E. Sanchez
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Abstract Basically, σ- hyperfields on σ- complete De Morgan algebras are introduced and explored. Measurable spaces (topological spaces) are extended to hypermeasurable spaces (hypertopological spaces) constructed considering σ- hyperfields. Random sets are then given a pure measure theoretical definition and, finally, random fuzzy sets are ...
Wang Pei-Zhuang, E. Sanchez
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Theory of hyperrings and hyperfields
Algebra and Logic, 1985The notion of hyperfield was introduced by \textit{M. Krasner} [Colloq. d'Algèbre Supérieure, CBRM, Bruxelles 1956, 129-206 (1959; Zbl 0085.265)] who raised the following question: Are all hyperfields isomorphic to quotient hyperfields? He also raised an analogous question for hyperrings.
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Generalisations of Tropical Geometry over Hyperfields
2022Hyperfields are structures that generalise the notion of a field by way of allowing the addition operation to be multivalued. The aim of this thesis is to examine generalisations of classical theory from algebraic geometry and its combinatorial shadow, tropical geometry.
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Journal of Algebraic Hyperstructures and Logical Algebras
The first use of the largest class of hyper-structures, the Hv-structures, and their fundamental relations was to define the general hyper-field. Moreover, the enormous number Hv-structures defined on the same set, admits a partial order and has a lot of applications in pure mathematics and other sciences.
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The first use of the largest class of hyper-structures, the Hv-structures, and their fundamental relations was to define the general hyper-field. Moreover, the enormous number Hv-structures defined on the same set, admits a partial order and has a lot of applications in pure mathematics and other sciences.
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1984
The concepts of (semi) hypergroups, hyperrings or hyperfields H differ from the ones of (semi) groups, rings, fields by replacing the operations of addition and multiplication by maps from H×H into the collection of nonempty subsets of H . A hyperring (H,∘,□) is complete if both (H,∘) and (H,□) are complete. The author gives examples for these concepts
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The concepts of (semi) hypergroups, hyperrings or hyperfields H differ from the ones of (semi) groups, rings, fields by replacing the operations of addition and multiplication by maps from H×H into the collection of nonempty subsets of H . A hyperring (H,∘,□) is complete if both (H,∘) and (H,□) are complete. The author gives examples for these concepts
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Design issues of a hyperfield fisheye lens
SPIE Proceedings, 2004This paper discusses the design of a 310 degree fisheye lens. Particular attention is paid to color correction and lens edge overlap. Other issues in the design of fisheye lenses are addressed such as the distortion/mapping, illumination, and overall aberration correction.
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