Related papers: The Tensorial Connections
We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We…
These notes are the second part of the tensor calculus documents which started with the previous set of introductory. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when…
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
Under mechanical deformation, most materials exhibit both elastic and fluid (or plastic) responses. No existing formalism derived from microscopic principles encompasses both their fluid-like and solid-like aspects. We define the {\it…
On a main class of the almost contact manifolds with B-metric, it is described the family of the linear connections preserving the manifold's structures by 4 parameters. In this family there are determined the canonical-type connection and…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and…
In this series of papers I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
A topical overview on the state of the art and science of superconducting materials is presented. The relation of atomic structure and suggested superconductivity mechanisms as well as possible applications are discussed for the various…
New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of…
This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.
This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable…
I have performed an experiment which is a variant of the one suggested recently by F. O. Minotti and T. E. Raptis. The aim of this experiment is to check the generation of a pulsed gravitational potential by a transient magnetic field as…
We review recent developments in the theory of Thompson group representations related to knot theory.