Related papers: Ladder operators and rational extensions
We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
In 1981, Andr\'e Joyal provided a combinatorial interpretation of the algebra of formal power series, a central gadget in the toolkit of enumerative combinatorics. In Joyal's theory of species of structures, combinatorial species (like…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler…
We construct various multiple categories, based on generalised Ehresmann quintets. The main construction is a multiple category whose objects are all the `lax' multiple categories; the transversal arrows are their strict multiple functors…
We prove the equivalence of VOA tensor categories and conformal net tensor categories for the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type $ADE$ discrete series $W$-algebras; their tensor…
In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with…
We classify the irreducible modules of a rational Lorentzian lattice vertex operator algebra (LLVOA) based on an even, self-dual Lorentzian lattice $\Lambda\subset\mathbb{R}^{m,n}$ of signature $(m,n)$. We show that the set of isomorphism…
We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category.…
The space of linear differential operators on a smooth manifold $M$ has a natural one-parameter family of $Diff(M)$ (and $Vect(M)$)-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case…
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…