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The effect of symmetry on the Rieman...

Myers, Jeanine L.

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The effect of symmetry on the Riemann map.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The effect of symmetry on the Riemann map./
作者:	Myers, Jeanine L.
面頁冊數:	100 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-08(E), Section: B.
Contained By:	Dissertation Abstracts International74-08B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3559122
ISBN:	9781303040849

The effect of symmetry on the Riemann map.
Myers, Jeanine L.

The effect of symmetry on the Riemann map. - 100 p.

Source: Dissertation Abstracts International, Volume: 74-08(E), Section: B.

Thesis (Ph.D.)--University of Arkansas, 2013.

The Riemann mapping theorem guarantees the existence of a conformal mapping or Riemann map in the complex plane from the open unit disk onto an open simply-connected domain, which is not all of the complex plane. Although its existence is guaranteed, the Riemann map is rarely known except for special domains like half-planes, strips, etc. Therefore, any information we can determine about the Riemann map for any class of domains is interesting and useful.

ISBN: 9781303040849Subjects--Topical Terms:

515831
Mathematics.

The effect of symmetry on the Riemann map.
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245 1 4 $a The effect of symmetry on the Riemann map.
300 $a 100 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-08(E), Section: B.
500 $a Advisers: Loredana Lanzani; Andrew S. Raich.
502 $a Thesis (Ph.D.)--University of Arkansas, 2013.
520 $a The Riemann mapping theorem guarantees the existence of a conformal mapping or Riemann map in the complex plane from the open unit disk onto an open simply-connected domain, which is not all of the complex plane. Although its existence is guaranteed, the Riemann map is rarely known except for special domains like half-planes, strips, etc. Therefore, any information we can determine about the Riemann map for any class of domains is interesting and useful.
520 $a This research investigates how symmetry affects the Riemann map. In particular, we define domains with symmetries called Rectangular Domains or RDs. The Riemann map of an RD has real-valued coefficients, as opposed to complex-valued, and therefore we can determine the sign of the coefficients of the Taylor series about the origin of the Riemann map, f(z), from the unit disk onto RDs determined by f(0)=0 and f'(0)>0. We focus on the form of the Riemann map for specific RD polygons. These include rhombi, rectangles and non-equilateral octagons which have 2-fold symmetries. We also investigate equilateral polygons with more than 2-fold symmetries such as squares (rotated diamond), regular polygons, and equilateral octagons.
590 $a School code: 0011.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
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710 2 $a University of Arkansas. $b Mathematics. $3 2096727
773 0 $t Dissertation Abstracts International $g 74-08B(E).
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792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3559122