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| The '''Ragsdale conjecture''' is a [[mathematics|mathematical]] [[conjecture]] that concerns the possible arrangements of real [[algebraic curves]] embedded in the [[projective plane]]. It was proposed by [[Virginia Ragsdale]] several years after 1900 and was disproved in 1979.<ref>{{cite journal| last=Viro | first=Oleg Ya. | authorlink=Oleg Viro | year=1980 | title=Кривые степени 7, кривые степени 8 и гипотеза Рэгсдейл | trans_title=Curves of degree 7, curves of degree 8 and the hypothesis of Ragsdale | journal=[[Doklady Akademii Nauk SSSR]] | volume=254 | issue=6 | pages=1306–1309}} Translated in {{cite journal| journal=Soviet Mathematics - Doklady | volume=22 | pages=566–570 | year=1980}}</ref>
| | Emilia Shryock is my title but you can call me anything you like. One of the things she loves most is to do aerobics and now she is trying to make money with it. Years in the past we moved to Puerto Rico and my family members enjoys it. Hiring is my profession.<br><br>Feel free to visit my web blog: [http://www.ddaybeauty.com/node/14766 at home std testing] |
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| ==Background==
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| Her dissertation dealt with [[Hilbert's sixteenth problem]], which was proposed in the year 1900, along with [[Hilbert's problems|22 other unsolved problems of the 19th century]]. Ragsdale conjectured a particular upper bound on the number of topological circles of a certain type, along with the basis of evidence. The conjecture was held of high importance in the field of real algebraic geometry for nearly a century. Later [[Oleg Viro]] and [[Ilya Itenberg]] produced [[counterexamples]] to the Ragsdale conjecture, although the problem of finding a sharp upper bound remains unsolved.
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| ==Conjecture==
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| Ragsdale's main conjecture is as follows.
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| Assume that an [[algebraic curve]] of degree 2''k'' contains ''p'' even and ''n'' odd ovals. Ragsdale conjectured that
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| :<math> p \le \tfrac32 k(k-1) + 1 \quad\text{and}\quad n \le \tfrac32 k(k-1). </math>
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| She also posed the inequality
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| :<math> | 2(p-n)-1 | \le 3k^2 - 3k + 1, </math> | |
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| and showed that the inequality could not be further improved. This inequality was later proved by [[Ivan Petrovsky|Petrovsky]].
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| ==Notes==
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| <references/>
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| ==References==
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| * {{cite web |url=http://www.agnesscott.edu/LRiddle/women/ragsdale.htm |title=Virginia Ragsdale |accessdate=2007-03-09 |last=De Loera |first=Jesús |coauthors=Frederick J. Wicklin |year=2006 |work=Biographies of Women Mathematicians }}
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| [[Category:Conjectures]]
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| [[Category:Real algebraic geometry]]
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Latest revision as of 11:08, 12 November 2014
Emilia Shryock is my title but you can call me anything you like. One of the things she loves most is to do aerobics and now she is trying to make money with it. Years in the past we moved to Puerto Rico and my family members enjoys it. Hiring is my profession.
Feel free to visit my web blog: at home std testing