Displaying 1421 – 1440 of 2516

Showing per page

On the diffeomorphic type of the complement to a line arrangement in a projective plane

Fedor Bogomolov, Viktor Kulikov (2012)

Open Mathematics

We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011,...

On the existence of wavelets for non-expansive dilation matrices.

Darrin Speegle (2003)

Collectanea Mathematica

Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation lattice...

Currently displaying 1421 – 1440 of 2516