17 research outputs found
On Invariant Notions of Segre Varieties in Binary Projective Spaces
Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1,
2) that are direct products of copies of PG(1, 2), being any positive
integer, are established and studied. We first demonstrate that there exists a
hyperbolic quadric that contains \Segrem(2) and is invariant under its
projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into
\PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant
under \Stab{m}{2} as well. Such a basis can be split into two subsets whose
spans are either real or complex-conjugate subspaces according as is even
or odd. In the latter case, these spans can, in addition, be viewed as
indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m
- 1, 2). This spread is also related with a \Stab{m}{2}-invariant
non-singular Hermitian variety. The case is examined in detail to
illustrate the theory. Here, the lines of the invariant spread are found to
fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7,
2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and
Cryptograph
Gauged motion in general relativity and in Kaluza-Klein theories
In a recent paper [1] a new generalization of the Killing motion, the {\it
gauged motion}, has been introduced for stationary spacetimes where it was
shown that the physical symmetries of such spacetimes are well described
through this new symmetry. In this article after a more detailed study in the
stationary case we present the definition of gauged motion for general
spacetimes. The definition is based on the gauged Lie derivative induced by a
threading family of observers and the relevant reparametrization invariance. We
also extend the gauged motion to the case of Kaluza-Klein theories.Comment: 42 pages, revised version, typos correction along with some minor
changes, Revtex forma
On the Behavior of Spatial Critical Points under Gaussian Blurring: A Folklore Theorem and Scale-Space Constraints
The main theorem we present is a version of a "Folklore Theorem" from scale-space theory for nonnegative compactly supported functions from R to R. The theorem states that, if we take the scale in scale-space sufficiently large, the Gaussian-blurred function has only one spatial critical extremum, a maximum, and no other critical points