A geometric look at the objective gravitational wave function reduction

Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction Function

A Geometric Look at Manipulation

We take a fresh look at voting theory, in particular at the notion of manipulation, by employing the geometry of the Saari triangle. This yields a geometric proof of the Gibbard/Satterthwaite theorem, and new insight into what it means to manipulate the vote. Next, we propose two possible strengthenings of the notion of manipulability (or weakenings of the notion of non-manipulability), and ana...

A geometric look at corner cutting

G. de Rham (1947), Un peu de math ematiques a propos d'une courbe plane, Elemente der Mathematik, 2(4):89{104. G. de Rham (1956), Sur une courbe plane, Journal de Math ematiques pures et appliqu ees, 35:25{42. 27 Figure 28: Each point in the shaded area carries a continuum of lines such that the associated aane standard cut produces C 1-curves without line segments. Hence for each contact point...

Wave Function as Geometric Entity

A special approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function...

A Differential-geometric Look at the Jacobi–davidson Framework

The problem of computing a p-dimensional invariant subspace of a symmetric positivedefinite matrix pencil of dimension n is interpreted as computing a zero of a tangent vector field on the Grassmann manifold of p-planes in R. The theory of Newton’s method on manifolds is applied to this problem, and the resulting Newton equations are interpreted as block versions of the Jacobi–Davidson correcti...