Related papers: Dilatation structures I. Fundamentals
Chords in musical harmony can be viewed as objects having shapes (major/minor/etc.) attached to base sets (pitch class sets). The base set and the shape set are usually given the structure of a group, more particularly a cyclic group. In a…
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…
This work is the first in a series of papers that, among other things, extends the formalism of diolic differential calculus, wherein a new context for obtaining differential calculus in vector bundles was established. Here we provide a…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
The concept of concrete regularity structure gives the algebraic backbone of the operations involved in the local expansions used in the regularity structure approach to singular stochastic partial differential equations. The spaces and the…
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
It is shown that a locally geometrical structure of arbitrarily curved Riemannian space is defined by a deformed group of its diffeomorphisms
Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian symmetric spaces. Keywords: braided sets,…
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them…
We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
Let M be a manifold, and G a Lie group which satisfies the unique extension property. An (M,G) manifold N is a manifold endowed with an atlas (U_i,f_i) where f_i is a diffeomorphism between U_i and an open set of M such that the coordinates…
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…