Related papers: Old and new about equidistant sets and generalized…
We examine certain phenomena in $C^1$-dynamics from a viewpoint of shadowing and improve a known result on hyperbolic sets. We also review a result on the stability of attractor boundaries from the same viewpoint and derive several…
We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
In classical Euclidean geometry, there are several equivalent definitions of conic sections. We show that in the hyperbolic plane, the analogues of these same definitions still make sense, but are no longer equivalent, and we discuss the…
Observing a linear superposition principle, a family of new minimal hypersurfaces in Euclidean space is found, as well as that linear combinations of generalized helicoids induce new algebraic minimal cones of arbitrarily high degree.
Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead…
There were obtained some properties of weakly m-convex sets. Various kinds of the problem of shadow were investigated. There was obtained the lower estimation for the number of balls that are necessary to create a shadow at the point of the…
This study investigates a generalisation of the Pythagorean theorem to the lengths of conic arcs constructed symmetrically on the sides of a right triangle. It is demonstrated that the theorem remains valid whenever the conic eccentricity…
We tackle the problem of learning the geometry of multiple categories of deformable objects jointly. Recent work has shown that it is possible to learn a unified dense pose predictor for several categories of related objects. However,…
Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures…
We study hyperbolized versions of cohomological equations that appear with cocycles by isometries of the euclidean space. These (hyperbolized versions of) equations have a unique continuous solution. We concentrate in to know whether or not…
Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In…
The theme of this paper is the multiplicity of the consistent sets appearing in the consistent histories approach to quantum mechanics. We propose one criterion for choosing preferred families among them: that the physically realizable…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
Classical shadows (CS) has recently emerged as an important framework to efficiently predict properties of an unknown quantum state. A common strategy in CS protocols is to parametrize the basis in which one measures the state by a random…
In this paper we continue the study of the geometrical features of a functional approach to classical mechanics proposed some time ago. In particular we try to shed some light on a N=2 "universal" supersymmetry which seems to have an…
When considering geometry, one might think of working with lines and circles on a flat plane as in Euclidean geometry. However, doing geometry in other spaces is possible, as the existence of spherical and hyperbolic geometry demonstrates.…
It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding…
In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…