the projective representation of the 3D scene. In other words, the projective representation of the scene can undergo a projective transformation (which eeectively translates the scene along the optical axes of the rst view) which is interchangeable with the camera motion from view to view. The in-terchangeability point is eeectively contained in the arguments of 3] about the geometric content ...

This work considers the minimization of a general convex function f(X) over the cone of positive semidefinite matrices whose optimal solution X⋆ is of low-rank. Standard first-order convex solvers require performing an eigenvalue decomposition in each iteration, severely limiting their scalability. A natural nonconvex reformulation of the problem factors the variable X into the product of a rec...

In this paper, we show that via a novel construction every rank-3 root system induces a root system of rank 4. Via the Cartan-Dieudonné theorem, an even number of successive Coxeter reflections yields rotations that in a Clifford algebra framework are described by spinors. In three dimensions these spinors themselves have a natural four-dimensional Euclidean structure, and discrete spinor group...

We prove global results about actions of cocompact lattices in higher-rank simple Lie groups on closed manifolds endowed with either a projective class connections or conformal pseudo-Riemannian metrics signature (p, q), $$\min (p,q) \ge 2$$ . Building recent article [17], provided that such structure is locally equivalent to its model $${\textbf{X}}$$ , the main question treated here completen...

Throughout this paper L will be an algebraically closed field and K an algebraically closed subfield such that the transcendence rank of L over K is at least 3. In [4] we considered the pregeometry G(L/K) = (L,clK), where, for Y a subset of L, the closure clK( Y) is the algebraic closure in L of the subfield generated by K and Y. In this paper we shall be concerned mainly with the geometry G(L/...

‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...

1992 Mathematisches Institut Universitt at zu KK oln Weyertal 86-90 D{5000 KK oln 41 (Lindenthal) Germany Telefon (0221) 470{3937 Telex 8882291 unik d Telefax (0221) 470{5160 Abstract There are two concepts of duality in combinatorial geometry. A set theoretical one, generalizing the structure of two orthocomplementary vector spaces and a lattice theoretical concept of an adjoint, that mimics d...