Related papers: Metric Coordinate Systems
The aim of this paper is to prove the existence of inductive and inverse limits of direct and inverse systems in a certain category of compact metric spaces as well as of compact metric groups. Some applications are presented.
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
Projective metrics on vector spaces over finite fields, introduced by Gabidulin and Simonis in 1997, generalize classical metrics in coding theory like the Hamming metric, rank metric, and combinatorial metrics. While these specific metrics…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces then we give the flag curvature formula of them. Also we study the special cases of…
The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but…
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…
Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more…
A physical metric is constructed as one that gives a coordinate independent result for the time delay in infinite order in the perturbation expansion in the gravitational constant. A compact form for the metric is obtained. One result is…
Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…
Field equations with general covariance are interpreted as equations for a target space describing physical space time co-ordinates, in terms of an underlying base space with conformal invariance. These equations admit an infinite number of…
The idea of gauging (i.e. making local) symmetries of a physical system is a central feature of many modern field theories. Usually, one starts with a Lagrangian for some scalar or spinor matter fields, with the Lagrangian being invariant…
Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
In this paper, the concept of the metric matrix is introduced to establish a concise and unified formulation for the inner product in barycentric coordinates. Building on this framework, we explore the intrinsic algebraic identities of…
One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…
Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are $\mathscr{C}^{s+1}$ for…
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…