Related papers: Self-Referential Definition of Orthogonality
Although various polytomous item response models are considered to be ordinal models there seems no general definition of an ordinal model available. Alternative concepts of ordinal models are discussed and it is shown that they coincide…
Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories have a natural extriangulated structure and are appearing as…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
This paper introduces the notion of referring forms as a new metric for analyzing sequential circuits from a functional perspective. Sequential circuits are modeled as causal stream functions, the outputs of which depend solely on the past…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
An orthoset is a set equipped with a symmetric, irreflexive binary relation. With any (anisotropic) Hermitian space $H$, we may associate the orthoset $(P(H),\perp)$, consisting of the set of one-dimensional subspaces of $H$ and the usual…
We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give…
Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of…
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion…
The interior polynomial was originally defined for hypergraphs and later shown to coincide with the Ehrhart polynomial of the root polytope of an associated bipartite graph. In previous work, we derived an alternating cycle recursion…
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
A special class of orthogonal rational functions (ORFs) is presented in this paper. Starting with a sequence of ORFs and the corresponding rational functions of the second kind, we define a new sequence as a linear combination of the…
The no-go theorems of Bell and Kochen and Specker could be interpreted as implying that the notions of system and experimental context are fundamentally inseparable. In this interpretation, statements such as "spin is 'up' along direction…