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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> | |||
==Background== | |||
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. | |||
==Conjecture== | |||
Ragsdale's main conjecture is as follows. | |||
Assume that an [[algebraic curve]] of degree 2''k'' contains ''p'' even and ''n'' odd ovals. Ragsdale conjectured that | |||
:<math> p \le \tfrac32 k(k-1) + 1 \quad\text{and}\quad n \le \tfrac32 k(k-1). </math> | |||
She also posed the inequality | |||
:<math> | 2(p-n)-1 | \le 3k^2 - 3k + 1, </math> | |||
and showed that the inequality could not be further improved. This inequality was later proved by [[Ivan Petrovsky|Petrovsky]]. | |||
==Notes== | |||
<references/> | |||
==References== | |||
* {{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 }} | |||
[[Category:Conjectures]] | |||
[[Category:Real algebraic geometry]] | |||
Revision as of 07:15, 1 November 2012
The Ragsdale conjecture is a 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.[1]
Background
Her dissertation dealt with Hilbert's sixteenth problem, which was proposed in the year 1900, along with 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.
Conjecture
Ragsdale's main conjecture is as follows.
Assume that an algebraic curve of degree 2k contains p even and n odd ovals. Ragsdale conjectured that
She also posed the inequality
and showed that the inequality could not be further improved. This inequality was later proved by Petrovsky.
Notes
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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
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Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang