Related papers: Seven mutually touching infinite cylinders
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…
The aim of this paper is to show that the existence of attracting sets for quasiperiodically forced systems can be extended to appropriate skew-products on the cylinder, homotopic to the identity, in such a way that the general system will…
We study the set of visible lattice points in multidimensional hypercubes. The problems we investigate mix together geometric, probabilistic and number theoretic tones. For example, we prove that almost all self-visible triangles with…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
Cylindric algebras, or concept algebras in another name, form an interface between algebra, geometry and logic; they were invented by Alfred Tarski around 1947. We prove that there are 2 to the alpha many varieties of geometric (i.e.,…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…
We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial…
We present a topological method of obtaining the existence of infinite number of symmetric periodic orbits for systems with reversing symmetry. The method is based on covering relations. We apply the method to a four-dimensional reversible…
The convex feasibility problem asks to find a point in the intersection of a collection of nonempty closed convex sets. This problem is of basic importance in mathematics and the physical sciences, and projection (or splitting) methods…
This article discusses the question - how to estimate the number of solutions of algebraic Diophantine equations with natural coefficients using Circular method developed by Hardy and Littlewood. This paper considers the estimate of the…
In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om scheme…
The class of traveling wave solutions of the sine-Gordon equation is known to be in 1-1 correspondence with the class of (necessarily singular) pseudospherical surfaces in Euclidean space with screw-motion symmetry: the pseudospherical…
We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact…
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their…
In this paper we describe a 1-dimensional family of initial conditions \Sigma that provides reduced periodic solution of the three body problem. This family \Sigma contains a bifurcation point and extend the periodic solution described in…
We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…
The hypercube \( Q_n \) contains a Hamiltonian path joining \( x \) and \( y \) (where $x$ and $y$ from the opposite partite set) containing \( P \) if and only if the induced subgraph of \( P \) is a linear forest, where none of these…
Given a closed $n$-manifold, we consider the set of simple homotopy types of $n$-manifolds within its homotopy type, called its simple homotopy manifold set. We characterise it in terms of algebraic K-theory, the surgery obstruction map,…