Related papers: Diagrams and discrete extensions for finitary 2-re…
The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…
We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we prove that every simple transitive $2$-representation of the…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of…
The present paper provides a method for finding partial differential equations satisfied by the Feynman integrals for diagrams of various types, using the Griffiths theorem on the reduction of poles of rational differential forms. As an…
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…
In this paper we introduce the concept of polynomial diagrams and its area for special polynomials.We study the properties of polynomial area diagrams. The formula for the area of an arbitrary polynomial diagram.
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…
Properties of morphisms represented by so-called 'string diagrams' of monoidal categories (and their braided and symmetric derivatives), mainly their resistance in value to isotopic deformation, have made the usage of graphical calculi…
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…
Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in…
We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
The differential representation is a novel formalism for studying boundary correlators in $(d+1)$-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of…
In a series of three papers we develop an end space theory for digraphs. Here in the second paper we introduce the topological space $|D|$ formed by a digraph $D$ together with its ends and limit edges. We then characterise those digraphs…
We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…
We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of…