Related papers: A Minimalist Approach to Rolling Wheels
Rollings of reductive homogeneous spaces are investigated. More precisely, for a reductive homogeneous space $G / H$ with reductive decomposition $\mathfrak{g} = \mathfrak{h} \oplus \mathfrak{m}$, we consider rollings of $\mathfrak{m}$ over…
A wheel that is capable of producing thrust and maintaining vehicle internal integrity is presented. The wheel can be seen as an organic extension to the central unit (eg the vehicle) it is attached to, that is, the system and the wheel can…
Rubber friction is of major practical importance in applications such as tires, rubber seals, and footwear. This review article focuses on the theory and experimental studies of rubber friction on substrates with random roughness. We…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
We study the geometry of the space of rational curves on smooth complete intersections of low degree, which pass through a given set of points on the variety. The argument uses spreading out to a finite field, together with an adaptation to…
In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently, these conjectures have been established in the course of…
Given two regular graphs with consistent rotation maps, we produce a constructive method for a consistent rotation map on their Cartesian product. This method will be given as a simple set of rules of addition and table look ups. We assume…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
We study periodic Brownian paths, wrapped around the surface of a cylinder. One characteristic of such a path is its width square, $w^2$, defined as its variance. Though the average of $w^2$ over all possible paths is well known, its full…
Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the…
In his paper from 1996 on quadratic forms Heath-Brown developed a version of the circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight, and approximated…
A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…
A body moves in a medium composed of noninteracting point particles; interaction of particles with the body is absolutely elastic. It is required to find the body's shape minimizing or maximizing resistance of the medium to its motion. This…
We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh-B\'enard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary…
In his paper from 1996 on quadratic forms Heath-Brown developed a version of circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight. The weight function is…
We achieve compositions rules for the geometric parameters of the composed rotations, which is in a certain sense analogous to the well known Rodrigues formula. We also obtain a necessary and sufficient condition for a composition of two…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
Let $P$ be a connected bounded region in the plane formed out of $2 \times 2$ blocks joined by their sides. Peng and Rascoussier conjectured that all minimum-turn Hamiltonian cycles of $P$ exhibit a certain regular structure. We prove this…
In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories…
Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only if the universally…