1 citations · 1 across the 7 of their papers we have counts for
8 papers
Biunit pairs in semiheaps and associated semigroups
Bernard Rybołowicz, Carlos Zapata-Carratalá
Biunit pairs are introduced as pairs of elements in a semiheap that generalize the notion of unit. Families of functions generalizing involutions and conjugations, called switches…
Measurand Spaces and Dimensioned Hamiltonian Mechanics
Carlos Zapata-Carratala
In this paper we introduce a generalization of Hamiltonian mechanics that replaces configuration spaces, conventionally regarded simply as smooth manifolds, with line bundles over…
Heaps of Fish: arrays, generalized associativity and heapoids
Carlos Zapata-Carratala, Xerxes D. Arsiwalla, Taliesin Beynon
In this paper we investigate a ternary generalization of associativity by defining a diagrammatic calculus of hypergraphs that extends the usual notions of tensor networks, categor…
An Invitation to Higher Arity Science
Carlos Zapata-Carratala, Xerxes D. Arsiwalla
Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic operations, to compositions of processes, to network models, binary structures are deepl…
Poly-Jacobi Manifolds: the Dimensioned Approach to Jacobi Geometry
Carlos Zapata-Carratala
The standard formulation of Jacobi manifolds in terms of differential operators on line bundles, although effective at capturing most of the relevant geometric features, lacks a cl…
Dimensioned Algebra: the mathematics of physical quantities
Carlos Zapata-Carratala
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not devel…