Related papers: Chersiphron & Son Engineers
In this paper we show that states, transitions and behavior of concurrent systems can often be modeled as sheaves over a suitable topological space. In this context, geometric logic can be used to describe which local properties (i.e.…
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…
The discovery of the Diary of Merer (papyri Wadi al-Jarf) allows us to see the Egyptian calendar applied in a logbook. The diary is dated to the 26th year of reign of Khufu and describes Merer and his crew transporting the limestone blocks…
Skyrmions and domain walls are typical spin textures of significant technological relevance to magnetic memory and logic applications, where they are used as carriers of information. The unique topology of skyrmions makes them to display…
The modular curves serve as excellent objects for testing conjectures in arithmetic geometry. They possess a natural geometric definition in contrast with rather nontrivial structure. On the other hand, they are well-studied from the…
One of the key problems in active materials is the control of shape through actuation. A fascinating example of such control is the elephant trunk, a long, muscular, and extremely dexterous organ with multiple vital functions. The elephant…
Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.
By the methods of the synthetic geometry we investigate properties of objects generated from a complete quadrangle and a line, which lies in its plane. We start with a problem from the book of Sharygin "Problems in Plane Geometry". We…
The architectural complexes composed by the two main pyramids of Giza together with their temples are investigated from an inter-disciplinary point of view, taking into account their astronomical alignments as well as their relationships…
In this work, we will explore some polygons that individually are capable of filling the plane in an aperiodic way. These polygons were recently discovered by some researchers and constitute a great discovery for Mathematics. We will…
We briefly review the basic structure of modern--day technicolor theories. We then discuss the signatures for technicolor as they were in its early days, the searches that have been recently performed at the Tevatron and LEP colliders, and…
Simple ideas that shed new light on the physics of rotation as it concerns two famous experiments: The Wilson and Wilson, and the Michelson and Morley experiments.
We calculate the integer cohomology ring and stable tangent bundle of a family of compact, 3-Sasakian 7-manifolds constructed by Boyer, Galicki, Mann, and Rees. Previously only the rational cohomology ring was known. The most important part…
Graphene has been considered by many as a revolutionary material with electronic and structural properties that surpass conventional semiconductors and metals. Due to its superlative qualities, graphene is being considered as the reference…
Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.
Puzzle solving is a difficult problem in its own right, even when the pieces are all square and build up a natural image. But what if these ideal conditions do not hold? One such application domain is archaeology, where restoring an…
Rubber rolling (no-slip and no-twist) of a convex body on the plane under the influence of gravity is a SE(2) Chaplygin system, that reduces to the sphere of Poisson vectors. I comment upon an observation by A.V Borisov and I.S. Mamaev…
Painting is a fluid mechanical process. The action of covering a solid surface with a layer of a viscous fluid is one of the most common human activities; virtually all man-made surfaces are painted to provide protection against the…
Let $\pi: X \to Y$ be a morphism of projective varieties and suppose that $\alpha$ is a pseudo-effective numerical cycle class satisfying $\pi_*\alpha = 0$. A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha$ is a limit of…