Related papers: Anisotropic Grand Lorentz Spaces
A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to…
We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and completeness and hence the measure theoretic requirements are…
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…
Let $A$ be a simple algebra over a field $F$. Under a mild cardinality assumption on $F$, we determine the greatest possible dimension for an $F$-affine subspace of $A$ that is included in the group of units $A^\times$, and we describe the…
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…
In this article, we review some aspects of gravitational field and cosmology based on Finsler and Finsler-like generalized metric structures. The geometrical framework of these spaces allows further investigation of locally-anisotropic…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
Let $n,p,r$ be positive integers with $n \geq p\geq r$. A rank-$\overline{r}$ subset of $n$ by $p$ matrices (with entries in a field) is a subset in which every matrix has rank less than or equal to $r$. A classical theorem of Flanders…
It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of the class GH in a sufficiently small neighborhood of a generic…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
With the increasing wealth of high-quality astronomical and cosmological data and the manifold departures from General Relativity in principle conceivable, the development of generalized parametrization frameworks that unify gravitational…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
Many elliptic boundary value problems exhibit an interior regularity property, which can be exploited to construct local approximation spaces that converge exponentially within function spaces satisfying this property. These spaces can be…
We study a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain…