fundamental region

fundamental region

[¦fən·də¦ment·əl ′rē·jən]
(mathematics)
Any region in the complex plane that can be mapped conformally onto all of the complex plane.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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However, there are concerns the stalemate in Jubbaland, a fundamental region for war against terrorism, could spark a wider dispute between the neighbouring countries, Kenya and Ethiopia.Both Kenya and Ethiopia have deployed peacekeeping troops in Jubbaland, raising stakes on the outcome of Thursday's presidential election.
where [V.sub.Q] is the volume of the fundamental region (cell) Q.
For example, in the discussion of the complex trigonometric functions, it was very easy to demonstrate that the fundamental region -[pi]/2 [less than or equal to] Re(z) < [pi]/2 appears to map onto the plane under the sine function, but the geometric demonstration by no means proved that fact (see figure 11).
They begin by describing Hecke's main correspondence theorem and establish a couple of useful lemmas, then work through a fundamental region. They closely work through three cases, in which the lemma is greater than two, less than two, and equal to two, and describe Bochner's generalization of the main correspondence theorem of Hecke with related results and present identities equivalent to the functional equation and to the modular relation.
These are two four-sided polygons that tile the plane only in a nonperiodic way, that is, without a fundamental region that repeats periodically like the hexagonal tiling of a bathroom floor, or the amazing tesselations of the Dutch artist M.
Using three-inch-square pieces of poster board, they created two fundamental regions: one for a slide tessellation and one for a turn tessellation.
To consider transitional, reflective, and rotational symmetry, each student examined a sample of Escher's artwork and followed the activity of one of the fundamental regions as it is repeated in his artwork.

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