Constant of motion - Revision history

128.227.38.253: /* Derivation */

2015-01-05T22:37:56Z

Derivation

← Older revision		Revision as of 00:37, 6 January 2015
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	~~{{primary sources\|date=August 2012}}~~		Hi there. My name is Sophia Meagher even though it is not the name on my birth certificate. My day job is a travel agent. I am really fond of to go to karaoke but I've been taking on new issues recently. Mississippi is where her home is but her spouse wants them to transfer.<br><br>Feel free to surf to my weblog good psychic ([http://netwk.hannam.ac.kr/xe/data_2/85669 netwk.hannam.ac.kr])
	~~The '''Heath-Brown–Moroz''' constant ''C'',<ref>{{cite journal\|author=D~~. R. ~~Heath-Brown \| authorlink=Roger Heath-Brown \| coauthors=B~~.~~Z. Moroz \| title=The density~~ of ~~rational points~~ on the cubic surface ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub> \| journal=Mathematical Proceedings of the Cambridge Philosophical Society \| volume=125 \| pages=385–395 \| year=1999\|doi=10.~~1017/S0305004198003089 \| issue=3}}</ref> named for [[Roger Heath-Brown]] and [[Boris Moroz]],~~ is ~~defined as~~

	~~:<math>C=\prod_p\left(1-\frac{1}{p}\right)^7\left(1+\frac{7p+1}{p^2}\right) = 0.001317641... </math>~~

	where ~~''p'' runs over the [[Prime number\|primes]]~~.

	~~This constant is part of an [[asymptotic estimate]] for the distribution of [[rational point]]s of bounded [[height function\|height]] on the [[cubic surface]] ''X''~~<~~sub~~>0<~~/sub~~>~~<sup>3<~~/~~sup>=''X''<sub>1<~~/~~sub>''X''<sub>2</sub>''X''<sub>3</sub>~~. ~~Let ''H'' be a positive real number and ''N''(''H'') the number of solutions to the equation ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1<~~/~~sub>''X''<sub>2</sub>''X''<sub>3<~~/~~sub> with all the ''X''<sub>''i''<~~/~~sub> non-negative integers less than or equal to ''H'' and their [[greatest common divisor]] equal to 1~~. ~~Then~~

	~~:<math>N(H)= C \cdot \frac{H(\log H)^6} {4\times 6!} + O(H(\log H)^5)~~.~~</math>~~

	~~==References==~~
	~~<references/>~~

	~~{{DEFAULTSORT:Heath-Brown-Moroz constant}}~~
	~~[[Category:Mathematical constants~~]]


	~~{{numtheory-stub}}~~
	~~{{num-stub}}~~

en>Jftsang: /* Integral of motion */

2013-10-22T18:48:32Z

Integral of motion

← Older revision		Revision as of 20:48, 22 October 2013
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	~~I would like to introduce myself to you~~, ~~I am Andrew and my wife doesn~~'~~t like it at all~~. ~~Kentucky~~ is where I'~~ve always been living. She functions as a travel agent but quickly she~~'~~ll be on her own~~. ~~To perform lacross~~ is ~~some thing he would by no means give up~~.<br><br>~~Also visit my page; clairvoyant psychic,~~ [~~http~~:~~//myoceancounty~~.~~net~~/~~groups~~/~~apply~~-~~these~~-~~guidelines-when-gardening~~-~~and~~-~~grow/ mouse click the next article],~~		{{primary sources\|date=August 2012}}
			The '''Heath-Brown–Moroz''' constant ''C'',<ref>{{cite journal\|author=D. R. Heath-Brown \| authorlink=Roger Heath-Brown \| coauthors=B.Z. Moroz \| title=The density of rational points on the cubic surface ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub> \| journal=Mathematical Proceedings of the Cambridge Philosophical Society \| volume=125 \| pages=385–395 \| year=1999\|doi=10.1017/S0305004198003089 \| issue=3}}</ref> named for [[Roger Heath-Brown]] and [[Boris Moroz]], is defined as

			:<math>C=\prod_p\left(1-\frac{1}{p}\right)^7\left(1+\frac{7p+1}{p^2}\right) = 0.001317641... </math>

			where ''p'' runs over the [[Prime number\|primes]].

			This constant is part of an [[asymptotic estimate]] for the distribution of [[rational point]]s of bounded [[height function\|height]] on the [[cubic surface]] ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub>. Let ''H'' be a positive real number and ''N''(''H'') the number of solutions to the equation ''X''<sub>0</sub><sup>3</sup>=''X''<sub>1</sub>''X''<sub>2</sub>''X''<sub>3</sub> with all the ''X''<sub>''i''</sub> non-negative integers less than or equal to ''H'' and their [[greatest common divisor]] equal to 1. Then

			:<math>N(H)= C \cdot \frac{H(\log H)^6} {4\times 6!} + O(H(\log H)^5).</math>

			==References==
			<references/>

			{{DEFAULTSORT:Heath-Brown-Moroz constant}}
			[[Category:Mathematical constants]]


			{{numtheory-stub}}
			{{num-stub}}

en>Hmainsbot1: /* Relevance for quantum chaos */AWB general fixes and delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB (8097)

2012-07-27T22:42:47Z

Relevance for quantum chaos: AWB general fixes and delink dates per WP:DATELINK, WP:YEARLINK and MOS:UNLINKYEARS using AWB (8097)

New page

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