相关论文: Metric Coordinate Systems

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…

We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of…

A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either invariant or transforms appropriately with respect to the action…

Matrix coordinate transformations are defined as substitution operators without requiring an ordering prescription or an inclusion function from the Abelian coordinate transformations. We construct transforming objects mimicking most of the…

The coordinate conditions for three exact solutions for the metric components of a coordinate system with constant acceleration or of a static plane symmetric gravitational field are presented. First, the coordinate condition that the…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

The Caratheodory and Kobayashi metrics have proved to be important tools in the function theory of several complex variables. But they are less familiar in the context of one complex variable. Our purpose here is to gather in one place the…

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant…

We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with the implications of algebro-geometric nature under the existence of a Hermitian metric with nonnegative…

We introduce the concept of monodromy coordinates for representing solutions to large polynomial systems. Representing solutions this way provides a time-memory trade-off in a monodromy solving algorithm. We describe an algorithm, which…

The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor…

In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of…

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -- diffeomorphisms -- moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry…

A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…

We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…

In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…

We show the existence of some special coordinate systems for expressing maps with branch points. These coordinates allow obtaining an explicit representation formula of branch immersions and understanding the regularity of some fundamental…