Clausius theorem - Revision history

en>Anaxial: Reverted 1 edit by 180.215.71.105 (talk): Unexplained deletion. using TW

2014-12-26T02:09:34Z

Reverted 1 edit by 180.215.71.105 (talk): Unexplained deletion. using TW

← Older revision		Revision as of 04:09, 26 December 2014
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	~~'''Jeffrey Clark Lagarias''' (born November, 1949 in [[Pittsburgh, Pennsylvania\|Pittsburgh]], [[Pennsylvania]], [[USA]]) is a [[mathematician]] and professor at the [[University of Michigan]]~~.		Hi there. Let me start by [http://www.alemcheap.fi/people/anhipkiss alemcheap.fi] introducing the author, [http://www.hurtdating.com/groups/candida-albicans-tips-you-have-to-remember/ home std test] her title is Myrtle Cleary. Managing people is what I do and the salary has been really satisfying. One of the things she loves most is to do aerobics and over the counter std test now she is attempting to make money with it. [http://www.mydr.com.au/sexual-health/herpes-your-questions-answered California] is where I've always been residing and I adore each std testing at home working day residing here.<br><br>my blog post :: [http://www.bluecomtech.com/3dp/index.php?document_srl=701711&mid=bbs_firmware http://www.bluecomtech.com/3dp/index.php?document_srl=701711&mid=bbs_firmware]

	~~== Education ==~~
	~~While in high school in 1966, Lagarias studied [[astronomy]] at the [~~[~~Summer Science Program]].~~

	~~He completed an S.B. and S.M. in Mathematics at the [[Massachusetts Institute of Technology]] in 1972.<ref name=cv>{{cite web\|title=Jeffrey C. Lagarias\|url=~~http://www.~~math.lsa.umich~~.~~edu~~/~~~lagarias/PROFESSIONAL/VITA~~/~~vita2013a~~.~~pdf\|work=CV}}</ref> The title of his thesis was "Evaluation of certain character sums".<ref name=cv/> He was a [[Putnam Fellow~~]~~] at MIT in 1970.<ref name=cv/> He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of~~ the ~~class group of a quadratic field"~~, ~~in 1974.<ref name=cv/><ref name=um>{{cite web\|title=Jeffrey Lagarias, Professor\|url=~~http://www.~~math.lsa.umich~~.~~edu~~/~~people~~/~~facultyDetail.php?uniqname=lagarias\|publisher=University of Michigan}}<~~/~~ref> His advisor for both his masters and Ph.D was [[Harold Stark]~~].~~<ref name=cv/>~~

	~~== Career ==~~
	~~In 1975 he joined [[AT&T Bell Laboratories]]~~ and ~~eventually became [[Distinguished Member of Technical Staff]]. Since 1995, he~~ has been ~~a Technology Consultant at AT&T Research Laboratories~~. ~~In 2002, he moved to [[Michigan]]~~ to ~~work at the University and settle down with his family.~~

	~~While his recent work has been in [[theoretical computer science]], his original training was in analytic [[algebraic number theory]]. He has since worked in many areas, both pure and applied,~~ and ~~considers himself a mathematical generalist.~~ ~~Lagarias discovered an elementary problem that~~ is ~~equivalent~~ to ~~the [[Riemann hypothesis]], namely whether~~
	~~for all ''n'' > 0, we have~~

	~~:<math> \sigma(n) \le H_n + e^{H_n} \ln H_n \, </math>~~

	with ~~equality only when ''n'' = 1~~. ~~Here ''H''<sub>''n''</sub> is the ''n''th [~~[~~harmonic number]], the sum of the reciprocals of the first <math> n </math> positive integers, and ''σ''(''n'') is the [[divisor function]], the sum of the positive divisors of ''n''.<ref>~~http://~~front~~.~~math~~.~~ucdavis~~.~~edu~~/~~math.NT~~/~~0008177</ref>~~
	~~He disproved [[Keller's conjecture~~]~~] in dimensions at least 10.~~
	~~Lagarias has also done work on the [[Collatz conjecture]] and [[Li~~'~~s criterion]].~~

	~~==Awards~~ and ~~honors==~~
	~~In 1987 he received a [[Lester R. Ford]] award from the [[Mathematical Association of America]]~~.<~~ref~~>~~http://oldweb.cecm.sfu.ca/CMS-95W/lagarias.html~~<~~/ref>~~

	~~In 2012 he became a fellow of the [[American Mathematical Society]].<ref~~>[http://www.~~ams~~.~~org~~/~~profession~~/~~fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27~~.~~</ref>~~

	== ~~External links ==~~
	*{{MathGenealogy \|id=36350}}
	*[http://www.~~math.lsa.umich~~.~~edu~~/~~~lagarias~~/ ~~Jeffrey Clark Lagarias homepage], University of Michigan~~

	~~== References ==~~
	~~{{reflist}}~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]~~. ~~-->~~
	~~\| NAME~~ = ~~Lagarias, Jeffrey~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION~~ = ~~American mathematician~~
	~~\| DATE OF BIRTH = 1949~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH =~~
	~~\| PLACE OF DEATH =~~
	}}
	~~{{DEFAULTSORT:Lagarias, Jeffrey}}~~
	~~[[Category:1949 births]]~~
	~~[[Category:Living people]]~~
	~~[[Category:People from Pittsburgh, Pennsylvania]]~~
	~~[[Category:Massachusetts Institute of Technology alumni]]~~
	~~[[Category:Scientists at Bell Labs]]~~
	~~[[Category:20th-century mathematicians]]~~
	~~[[Category:21st-century mathematicians]]~~
	~~[[Category:Number theorists]]~~
	~~[[Category:American computer scientists]]~~
	~~[[Category:Theoretical computer scientists]]~~
	~~[[Category:University of Michigan faculty]]~~
	~~[[Category:Putnam Fellows]]~~
	~~[[Category:Summer Science Program]]~~
	~~[[Category:Fellows of the American Mathematical Society]~~]

en>GoingBatty: fixed CS1 errors: dates using AWB (9884)

2014-01-23T02:57:42Z

fixed CS1 errors: dates using AWB (9884)

← Older revision		Revision as of 04:57, 23 January 2014
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	The title of the ~~writer~~ is ~~Numbers but it~~'~~s not the most masucline title out there~~. ~~North Dakota~~ is ~~where me~~ and ~~my husband reside~~. ~~For years he~~'s ~~been working as a meter reader~~ and it's ~~something~~ he ~~truly appreciate~~. ~~Playing baseball is~~ the ~~hobby~~ he ~~will by no means quit doing~~.<br><br>~~Here is my web site -~~ [http://www.~~sddch~~.~~org~~/~~?document_srl~~=~~345265 over~~ the ~~counter std test~~]		'''Jeffrey Clark Lagarias''' (born November, 1949 in [[Pittsburgh, Pennsylvania\|Pittsburgh]], [[Pennsylvania]], [[USA]]) is a [[mathematician]] and professor at the [[University of Michigan]].

			== Education ==
			While in high school in 1966, Lagarias studied [[astronomy]] at the [[Summer Science Program]].

			He completed an S.B. and S.M. in Mathematics at the [[Massachusetts Institute of Technology]] in 1972.<ref name=cv>{{cite web\|title=Jeffrey C. Lagarias\|url=http://www.math.lsa.umich.edu/~lagarias/PROFESSIONAL/VITA/vita2013a.pdf\|work=CV}}</ref> The title of his thesis was "Evaluation of certain character sums".<ref name=cv/> He was a [[Putnam Fellow]] at MIT in 1970.<ref name=cv/> He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974.<ref name=cv/><ref name=um>{{cite web\|title=Jeffrey Lagarias, Professor\|url=http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=lagarias\|publisher=University of Michigan}}</ref> His advisor for both his masters and Ph.D was [[Harold Stark]].<ref name=cv/>

			== Career ==
			In 1975 he joined [[AT&T Bell Laboratories]] and eventually became [[Distinguished Member of Technical Staff]]. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories. In 2002, he moved to [[Michigan]] to work at the University and settle down with his family.

			While his recent work has been in [[theoretical computer science]], his original training was in analytic [[algebraic number theory]]. He has since worked in many areas, both pure and applied, and considers himself a mathematical generalist. Lagarias discovered an elementary problem that is equivalent to the [[Riemann hypothesis]], namely whether
			for all ''n'' > 0, we have

			:<math> \sigma(n) \le H_n + e^{H_n} \ln H_n \, </math>

			with equality only when ''n'' = 1. Here ''H''<sub>''n''</sub> is the ''n''th [[harmonic number]], the sum of the reciprocals of the first <math> n </math> positive integers, and ''σ''(''n'') is the [[divisor function]], the sum of the positive divisors of ''n''.<ref>http://front.math.ucdavis.edu/math.NT/0008177</ref>
			He disproved [[Keller's conjecture]] in dimensions at least 10.
			Lagarias has also done work on the [[Collatz conjecture]] and [[Li's criterion]].

			==Awards and honors==
			In 1987 he received a [[Lester R. Ford]] award from the [[Mathematical Association of America]].<ref>http://oldweb.cecm.sfu.ca/CMS-95W/lagarias.html</ref>

			In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref>

			== External links ==
			*{{MathGenealogy \|id=36350}}
			*[http://www.math.lsa.umich.edu/~lagarias/ Jeffrey Clark Lagarias homepage], University of Michigan

			== References ==
			{{reflist}}

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Lagarias, Jeffrey
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = American mathematician
			\| DATE OF BIRTH = 1949
			\| PLACE OF BIRTH =
			\| DATE OF DEATH =
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Lagarias, Jeffrey}}
			[[Category:1949 births]]
			[[Category:Living people]]
			[[Category:People from Pittsburgh, Pennsylvania]]
			[[Category:Massachusetts Institute of Technology alumni]]
			[[Category:Scientists at Bell Labs]]
			[[Category:20th-century mathematicians]]
			[[Category:21st-century mathematicians]]
			[[Category:Number theorists]]
			[[Category:American computer scientists]]
			[[Category:Theoretical computer scientists]]
			[[Category:University of Michigan faculty]]
			[[Category:Putnam Fellows]]
			[[Category:Summer Science Program]]
			[[Category:Fellows of the American Mathematical Society]]

118.68.192.45: /* History */

2012-08-24T03:36:17Z

History

New page

The title of the writer is Numbers but it's not the most masucline title out there. North Dakota is where me and my husband reside. For years he's been working as a meter reader and it's something he truly appreciate. Playing baseball is the hobby he will by no means quit doing.<br><br>Here is my web site - [http://www.sddch.org/?document_srl=345265 over the counter std test]