43,058 research outputs found
The Finite Field Kakeya Problem
A Besicovitch set in AG(n,q) is a set of points containing a line in every
direction. The Kakeya problem is to determine the minimal size of such a set.
We solve the Kakeya problem in the plane, and substantially improve the known
bounds for n greater than 4.Comment: 13 page
On pattern structures of the N-soliton solution of the discrete KP equation over a finite field
The existence and properties of coherent pattern in the multisoliton
solutions of the dKP equation over a finite field is investigated. To that end,
starting with an algebro-geometric construction over a finite field, we derive
a "travelling wave" formula for -soliton solutions in a finite field.
However, despite it having a form similar to its analogue in the complex field
case, the finite field solutions produce patterns essentially different from
those of classical interacting solitons.Comment: 12 pages, 3 figure
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