Ward-Fonten\'e Differential Universal Algebras
Ronald Orozco L\'opez
TL;DR
This paper introduces Ward-Fontené differential universal algebras that unify various calculi on sequences, including simplicial polytopic calculus and Bell number calculus, enabling generalized Leibniz rules.
Contribution
It constructs a new algebraic framework that generalizes differential calculus rules across multiple sequence-based calculi.
Findings
Unified calculus on sequences via Ward-Fontené algebra
Derived product ψ-rule and Leibniz rule in this framework
Applied to simplicial polytopic calculus and Bell numbers
Abstract
In this paper a Ward-Fonten\'e differential universal algebra is constructed. In this algebra it is possible to obtain a product -rule and a general -rule of Leibniz for any calculus on sequences. In particular, the simplicial polytopic calculus and the calculus on Bell numbers are introduced.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Algebraic structures and combinatorial models · Advanced Topics in Algebra