Related papers: Fixed-Point Problems in Discrete Tomography: Case …
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower bounds on the number of fixed points of a surface symplectomorphism (i.e. area-preserving map) in the given mapping class, both with and…
We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…
Focusing of atoms with light potentials is studied. In particular, we consider strongly confined, cylindrical symmetric potential, and demonstrate their applications in both red and blue-detuned focusing of atoms. We also study the…
The square peg problem asks whether every Jordan curve in the plane has four points which form a square. The problem has been resolved (positively) for various classes of curves, but remains open in full generality. We present two new…
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a self mapping on PN spaces by means of measure of discontinuity.
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the…
Our purpose of this paper is to focus on fixed point property in fuzzy metric space. To achieve our objective, we will introduce a new contraction condition to examine the fixed point for multi-valued mapping, then we will be investigating…
The discrete tomography of B-type and F-type icosahedral model sets is investigated, with an emphasis on reconstruction and uniqueness problems. These are motivated by the request of materials science for the unique reconstruction of…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
The affinely regular polygons in certain planar sets are characterized. It is also shown that the obtained results apply to cyclotomic model sets and, additionally, have consequences in the discrete tomography of these sets.
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…
We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near non-degenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of…
We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…