194 research outputs found
Eilenberg Theorems for Free
Eilenberg-type correspondences, relating varieties of languages (e.g. of
finite words, infinite words, or trees) to pseudovarieties of finite algebras,
form the backbone of algebraic language theory. Numerous such correspondences
are known in the literature. We demonstrate that they all arise from the same
recipe: one models languages and the algebras recognizing them by monads on an
algebraic category, and applies a Stone-type duality. Our main contribution is
a variety theorem that covers e.g. Wilke's and Pin's work on
-languages, the variety theorem for cost functions of Daviaud,
Kuperberg, and Pin, and unifies the two previous categorical approaches of
Boja\'nczyk and of Ad\'amek et al. In addition we derive a number of new
results, including an extension of the local variety theorem of Gehrke,
Grigorieff, and Pin from finite to infinite words
Algebraic geometry over algebraic structures II: Foundations
In this paper we introduce elements of algebraic geometry over an arbitrary
algebraic structure. We prove Unification Theorems which gather the description
of coordinate algebras by several ways.Comment: 55 page
Brane and string field structure of elementary particles
The two quantizations of QFT,as well as the attempt of unifying it with
general relativity,lead us to consider that the internal structure of an
elementary fermion must be twofold and composed of three embedded internal
(bi)structures which are vacuum and mass (physical) bosonic fields decomposing
into packets of pairs of strings behaving like harmonic oscillators
characterized by integers mu corresponding to normal modes at mu (algebraic)
quanta.Comment: 50 page
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