Related papers: Oppositions in a line segment

We extend the results of our previous work on the conformal invariant description of two relativistic point particles. We consider here the most general lagrangian by using a conformal tensor $h_{\mu\nu}$, transforming as a Wilson line, and…

The projective line over a field carries structure of a groupoid with a certain correspondence between objects and arrows. We discuss to what extent the field can be reconstructed from the groupoid.

A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many…

Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial…

This paper is an edited and shortened version of Chapter 6 from the thesis of the author. First the one dimensional orthogonal derivative will be extended to the two-dimensional case. In the two-dimensional case we have to define the region…

We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…

Let $P$ be a finite poset of width two, i.e., with no three-element antichain. We associate with $P$ a skew Young diagram $\Upsilon(P)$ and discuss some of the properties of the map $\Upsilon$. In particular, if we regard $\Upsilon(P)$ as a…

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…

The two-dimensional surface of a bi-axial ellipsoid is characterized by the lengths of its major and minor axes. Longitude and latitude span an angular coordinate system across. We consider the egg-shaped surface of constant altitude above…

We define a new $E_{\infty}$ operad based on surfaces with foliations which contains $E_k$ sub-operads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes -thus making…

We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from…

The paper deals with partial and weak preference relations defined on infinite-dimensional vector spaces and compatible with algebraic operations. By a partial preference we mean an asymmetric and transitive binary relation, while a weak…

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the…

We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an…

Let $K$ be a convex body (a non-empty compact convex set) in $n$-dimensional Euclidean space. A set $B$ is called a barrier (or an `opaque set') for $K$ if every line that intersects $K$, also intersects $B$. Although this concept was…

An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define…

An automorphism of a spherical building is called domestic if it maps no chamber to an opposite chamber. In this paper we classify domestic automorphisms of spherical buildings of classical type.

A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the $\pi$-property in terms of norms of compositions of projections is found.

In this paper we consider two types of dimension that can be defined for products of one-dimensional topologically totally transcendental (t.t.t) structures. The first is topological and considers the interior of projections of the set onto…

Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in $R^3$, we abstract the notion of an oriented congruence structure. This is a 3-dimensional CR manifold $(M,H, J)$ with a preferred…