Related papers: The Tensorial Connections
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on…
A mechanical model was developed to describe the behaviour of a device able to transform vibrations into rotations, named Vibrot. The theoretical model, developed in the newtonian formulation of mechanics, was able to reproduce…
Objects are made of parts, each with distinct geometry, physics, functionality, and affordances. Developing such a distributed, physical, interpretable representation of objects will facilitate intelligent agents to better explore and…
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
This document aims to give a self-contained account of the parts of abelian group theory that are most relevant for algebraic topology. It is almost purely expository, although there are some slightly unusual features in the treatment of…
This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
We study some topological properties of attractors.
In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a…
In this paper we discuss curvature tensors in the context of Absolute Parallelism geometry. Different curvature tensors are expressed in a compact form in terms of the torsion tensor of the canonical connection. Using the Bianchi identities…
A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…
We introduce the notion of operadic torsors and operadic quasi-torsors. We show that if an operadic (quasi-)torsor between two operads exists, then these operads are (quasi-)isomorphic. As an application we present the (arguably) shortest…
Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.
The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…
We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding…
In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.