Related papers: A Logic of Strong Contact between Polytopes
We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…
A lattice polytope translated by a rational vector is called an almost integral polytope. In this paper we investigate Ehrhart quasi-polynomials of almost integral polytopes. We study the relationship between the shape of the polytopes and…
We consider a binary system of small and large objects in the continuous space interacting via a non-negative potential. By integrating over the small objects, the effective interaction between the large ones becomes multi-body. We prove…
Polytopes from subgraph statistics are important in applications and conjectures and theorems in extremal graph theory can be stated as properties of them. We have studied them with a view towards applications by inscribing large explicit…
We report a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. We study the contact area and the interfacial separation from small contact (low load) to full…
Contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with a relation called contact. The elements of the Boolean algebra are considered as formal representations of physical…
We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any…
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real…
We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact…
Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended…
Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular polytopes are by definition hereditary,…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and…
The present paper presents a new general conception of interaction between physical systems, differing significantly from that of both classical physics and quantum physics as generally understood. We believe this conception could provide…
The paper develops a novel analysis of mutual interactions between topology and soft topology. It is known that each soft topology produces a system of crisp (parameterized) topologies. The other way round is also possible. Namely, one can…
We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is…