Related papers: Oppositions in a line segment
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
An open set in C^n is pseudoconvex if and only if its intersection with every affine subspace of complex dimension two as seen as an open set in C^2 is pseudoconvex.
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we…
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
Exact solutions of Einstein's equations in 2+1-dimensional anti-de Sitter space containing any number of black holes are described. In addition to the black holes these spacetimes can possess ``internal'' structure. Accordingly the generic…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…
Exponential of exponential of almost every line in the complex plane is dense in the plane. On the other hand, for lines through any point, for a set of angles of Hausdorff dimension one, exponential of exponential of a line with angle from…
While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
Suppose that a finite-dimensional cube is orthogonally projected onto a central section of itself by a subspace of one dimension less. Up to dimension $9$, at least one vertex is projected onto the section, but for dimension $10$ or larger,…
A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} is defined. Some classifications of skew perspectives are presented.
We consider the set of pairs of orthogonal vectors in Hilbert space, which is also called the cross because it is the union of the horizontal and vertical axes in the Euclidean plane when the underlying space is the real line. Crosses,…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
A two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic. The body performs both translational and slow rotational motion. It is required to select the body, from a…
One often distinguishes between a line and a plane by saying that the former is one-dimensional while the latter is two. But, what does it mean for an object to have $d-$dimensions? Can we define a consistent notion of dimension rigorously…
A projective variety whose Gauss map has positive dimensional fibres corresponds to a special kind of scroll called \emph{Gaussian}. A Gaussian scroll is a member of a canonical derived \emph{ Gaussian flag}. We introduce a duality in the…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…