1 citations · 2 across the 8 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…
Jacobi Geometry and Hamiltonian Mechanics: the Unit-Free Approach
Carlos Zapata-Carratala
We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely id…
A Landscape of Hamiltonian Phase Spaces: on the foundations and generalizations of one of the most powerful ideas of modern science
Carlos Zapata-Carratala
In this thesis we revise the concept of phase space in modern physics and devise a way to explicitly incorporate physical dimension into geometric mechanics. A historical account o…