The Grassmann Space of a Planar Space

Space Forms of Grassmann Manifolds

Sequential Competitive Facility Location Problem in a Discrete Planar Space

In this paper, there are two competitors in a planar market. The first competitor, called, the leader, opens new facilities. After that, the second competitor, the follower, reacts to the leader’s action and opens r new facilities. The leader and the follower have got some facilities in advance in this market. The optimal locations for leader and follower are chosen among predefined candida...

A Novel Method Describing the Space Charge Limited Region in a Planar Diode

A novel and rather simple method is presented to describe the physics of space-charge region in a planar diode. The method deals with the issue in the time domain and as a consequence transient time behavior can be achieved. Potential distributions and currents obtained using this technique, supposing zero initial velocity for electrons, reveal absolute agreement with Child's results. Moreover,...

Unitarily Invariant Metrics on the Grassmann Space

Let Gm,n be the Grassmann space of m-dimensional subspaces of F. Denote by θ1(X ,Y), . . . , θm(X ,Y) the canonical angles between subspaces X ,Y ∈ Gm,n. It is shown that Φ(θ1(X ,Y), . . . , θm(X ,Y)) defines a unitarily invariant metric on Gm,n for every symmetric gauge function Φ. This provides a wide class of new metrics on Gm,n. Some related results on perturbation and approximation of subs...

Representing the space of linear programs as the Grassmann manifold

Each linear program (LP) has an optimal basis. The space of linear programs can be partitioned according to these bases, so called the basis partition. Discovering the structures of this partition is our goal. We represent the space of linear programs as the space of projection matrices, i.e. the Grassmann manifold. A dynamical system on the Grassmann manifold, first presented in [5], is used t...