We briefly review the basics of Weyl geometry and its natural extension by a general linear ”distortion” of the metric connection by a vector field. A special class of the connections has torsion but retains the Weyl’s semi-metricity condition. We present ghost-free gravitational theories in this geometrical setup and highlight their possible cosmological applications, such as new self-tuning s...

There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which squared-norm Hessian a nonzero multiple quadratic form defining Euclidean metric. Solutions are constructed in all dimensions and solutions classified dimension at most $4$. Techniques given determining when two linearly conformally inequivalent.

Abstract We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. first extend to the family of theories first-order formulation that we recently developed for Horndeski Remarkably, find dynamics is equivalent general relativity (GR) evolving a, distinct, effecti...

Due to a significant increase in the number of spacecrafts low orbit, problem planning observations by radio instruments acquires importance. The paper shows that this can be reduced optimization observation time. Two metrics for plan quality evaluation are proposed (minimum value metric and geometric mean metric). It was suggested 3 algorithms planning: maximization arithmetic mean, minimizati...

This paper concerns the interplay between the complex structure of a Riemann surface and the essentially Euclidean geometry induced by a quadratic differential. One aspect of this geometry is the " trajectory structure" of a quadratic differential which has long played a central role in Teichmfiller theory starting with Teichmiiller's proof of the existence and uniqueness of extremal maps. Ahlf...

This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

Many strategies for similarity search in image databases assume a metric and quadratic form-based similarity model where an optimal lower bounding distance function exists for filtering. These strategies are mainly two-step, with the initial "filter" step based on a spatial or metric access method followed by a "refine" step employing expensive computation. Recent research on robust matching me...

The success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data. It is often beneficial to learn such a metric from the input training data, instead of using a default one such as the Euclidean distance. In this work, we propose a boosting-based technique, termed BOOSTMETRIC, for learning a quadratic...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...