HO (complexity) - Revision history

en>Rjwilmsi: Added 1 dois to journal cites using AWB (10094)

2014-05-05T20:01:53Z

Added 1 dois to journal cites using AWB (10094)

← Older revision		Revision as of 22:01, 5 May 2014
Line 1:		Line 1:
	~~{{BLP sources\|date=February 2013}}~~		Hello, I'm Tamara, a 27 year old from Walwick, Great Britain.<br>My hobbies include (but are not limited to) Gymnastics, Ice hockey and watching Arrested Development.<br><br>Check out my web site - [http://demo.wpmlm.com/activity/p/446378/ Biking for modern life mountain bike sizing.]
	~~{{ Infobox scientist~~
	~~\| name = Mark Mahowald~~
	~~\| image = <!--(filename only)-->~~
	~~\| image_size =~~
	~~\| caption =~~
	~~\| birth_date = {{Birth date\|1931\|12\|1}}~~
	~~\| birth_place = [[Albany~~, ~~Minnesota]]~~
	~~\| death_date ={{Dda\|2013\|7\|20\|1931\|12\|1}}~~
	~~\| death_place = Illinois, United States~~
	~~\| nationality = {{flag\|United States}}~~
	~~\| fields = [[Mathematics]]~~
	~~\| workplaces = [[Northwestern University]]~~
	~~\| alma_mater = [[University of Minnesota]]~~
	~~\| doctoral_advisor = [[Bernard Russell Gelbaum]]~~
	~~\| doctoral_students = [[Michael J. Hopkins]]~~
	~~Martin Tangora~~
	~~\| known_for = [[Homotopy groups of spheres]]~~
	~~\| awards =~~
	}}
	~~'''Mark Edward Mahowald~~'~~'' (December 1~~, 1931 – July 20, 2013) was an [[United States\|American]] [[mathematician]] known for work in [[algebraic topology]].<ref>{{cite web\|url=http://www.legacy.com/obituaries/chicagotribune/obituary.aspx?n=mark-edward-mahowald&pid=165996488&fhid=2074#fbLoggedOut \|title=MARK EDWARD MAHOWALD Obituary: View MARK MAHOWALD's Obituary by Chicago Tribune \|publisher=Legacy.com \|date=2013-07-20 \|accessdate=2013-07-24}}</ref>

	~~==Life==~~
	Mahowald was born in Albany, Minnesota in 1931.<ref>http://books.google.ca/books?id=allYAAAAMAAJ&q=%22Mahowald,+Mark+edward%22+1931&dq=%22Mahowald,+Mark+edward%22+1931&hl=en&sa=X&ei=ue7xUYzAL6PfiAK5qoGYDg&ved=0CDcQ6AEwAg</ref> He received his Ph.D. from ~~[[University of Minnesota]] in 1955 under the direction of [[Bernard Russell Gelbaum]] with a thesis on ''Measure in Groups''. In the sixties~~, ~~he became professor at [[Syracuse University]] and around 1963 he went to [[Northwestern University]] in Chicago~~.

	~~==Work==~~
	Much of Mahowald's most important works concerns the [[homotopy groups of spheres]], especially using the [[Adams spectral sequence]] at the prime 2. He is known for constructing one of the first known infinite families of elements in the stable homotopy groups of spheres by showing that the classes <~~math~~>h_1h_j</math> survive the Adams spectral sequence for <math>j\geq 3</math>. In addition, he made extensive computations of the structure of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Barratt, Tangora and Kochman. Using these computations, he could show that a manifold of [[Kervaire invariant]] 1 exists in dimension 62.

	~~In addition, he contributed~~ to the chromatic picture of the homotopy groups of spheres: His earlier work contains much on the image of the [[J-homomorphism]] and recent work together with Goerss, Henn, Karamanov and Rezk does computations in stable homotopy localized at the [[Morava K-theory]] K(2).

	Besides the work on the homotopy groups of spheres and related spaces, he did important work on [[Thom spectrum\|Thom spectra]]. This work was used heavily in the proof of the [[nilpotence theorem]] by Devinatz, ~~[[Michael J. Hopkins\|Hopkins]]~~ and ~~Smith.~~

	~~==Awards and honors==~~
	~~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 2013-02-02.~~<~~/ref~~>

	~~==Selected publications==~~
	*M. E. Mahowald and M. C. Tangora, ''Some differentials in the Adams spectral sequence'', Topology 6 (1967) 349–369.
	*M. G. Barratt, M. E. Mahowald and M. C. Tangora, ''Some differentials in the Adams spectral sequence II'', Topology 9 (1970) 309–316.
	*S.O. Kochman and M. E. Mahowald, ''On the computation of stable stems'' in ''The Cech centennial: a Conference on Homotopy Theory, June 22–26, 1993''
	* M. E. Mahowald,'' A new infinite family in <math>_2\pi_*^S</math>'', Topology 16 (1977) 249–256.
	*P. Goerss, H-W. Henn, H.W., M. E. Mahowald and C. Rezk, ''A resolution of the K (2)-~~local sphere at the prime 3'', Annals of Mathematics 162 (2005), 777–822.~~

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

	~~== External links ==~~
	*[http://~~www~~.~~math~~.~~northwestern.edu/people/emeritiProfiles/mark.mahowald.html Homepage at the Northwestern University]~~
	*[http://~~www.math.rochester.edu~~/u/~~faculty~~/~~doug/mypapers/mahowalds-groups.pdf Miller, Ravenel about Mahowald's work on the homotopy groups of spheres, pdf file] (294 kB)~~

	~~{{Authority control\|VIAF=110574649}}~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]~~. ~~-->~~
	~~\| NAME = Mahowald, Mark~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = American mathematician~~
	~~\| DATE OF BIRTH = 1931~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH = July 20, 2013~~
	~~\| PLACE OF DEATH =~~
	}}
	~~{{DEFAULTSORT:Mahowald, Mark}}~~
	~~[[Category:1931 births]]~~
	~~[[Category:American mathematicians]]~~
	~~[[Category:University of Minnesota alumni]]~~
	~~[[Category:Northwestern University faculty]]~~
	~~[[Category:Fellows of the American Mathematical Society]]~~
	~~[[Category:2013 deaths]~~]

en>Arthur MILCHIOR: /* Definitions and notations */ Second was written instead of higher

2013-11-03T02:56:24Z

Definitions and notations: Second was written instead of higher

← Older revision		Revision as of 04:56, 3 November 2013
Line 1:		Line 1:
	~~Therefore~~, ~~we all are needed to consider each area~~ of ~~writing accurately to be sufficient our desire~~. ~~Essay writers UK handle such complex topics and subjects with great care and write~~ an ~~essay which addresses all the complex issues the essay carries~~. ~~All our customers are guaranteed of non plagiarized papers of the highest quality~~. ~~It is a journey that can begin only after a person realizes the need to use time more efficiently~~. ~~Unfortunately, many students are failing to write their paper on the tough topic of economics that are assigned~~ by ~~their professor~~. <br><br>~~For now you need to understand exactly what the question is asking you. Should you loved this short article and you want to receive details regarding [~~http://~~www~~.~~isaacwkim~~.~~com/xe~~/?~~document_srl~~=~~944444 buy essay for cheap] assure visit our own web page~~. ~~This is looked down upon as one~~ of the ~~major causes~~ of ~~getting bad grades~~. ~~The second step towards learning~~ the ~~fine art of writing essay is reading widely. But now that you have prepared thoroughly you will be able~~ to ~~relax and have some fun putting together your essay~~. ~~Within~~ the ~~present-day educational enviroment~~, ~~lecturers and lecturers generally stress college students with various educational~~ is ~~effective these types~~ of ~~as term papers, research papers, thesis, essays and several academic routines which can be necessary to be submitted~~ in ~~a very quite limited length~~ of ~~time.~~ <br><br>~~If one wants to write an essay~~, ~~but one does not know how~~ to ~~write one~~, ~~one can take essay writing help from an expert~~. ~~Students~~, ~~who buy essay paper writing from us, do keep faith~~ in ~~us because we promise them to get 100% plagiarism free essays~~. So,~~it is wise~~ to ~~explore lacking sides in your essay writing task by indulging more into~~ the ~~process. In writing academic essays, students have realized that we have example essays which give them enough skills~~ of ~~developing essays that are original. Article Source~~: ~~you have difficulties~~ with ~~writing essays~~, ~~pay a visit to essaysprofy~~. ~~<br><br>This is where lessons learned will be described and~~ the ~~importance of~~ the ~~topic emphasized. A narrative paper can also be a challenge to students because it requires a lot~~ of ~~time in drafting~~, ~~pondering~~ on the ~~details significance~~ and ~~presenting an outline~~ of the ~~experience~~. ~~However, essay writing helps improve the students understanding on a particular topic~~. ~~We provide a wide range~~ of ~~academic writing services to our valued customers worldwide cost effectively such as articles writing~~, ~~essay writing~~, ~~research papers writing~~, ~~essays writing~~, ~~argumentative writing~~, ~~business writing~~, ~~internet marketing writing~~, ~~health articles writing~~, ~~travel writing~~, ~~and so on~~. ~~An essay is a short piece of writing which deals with a given topic analytically from the Authors point of view~~. <br><br>~~The professional writers are devoted towards their work and to cross check~~, ~~we make the use of software~~. ~~The company has employed professional company writers who are trained on how to write academic documents in all academic areas~~. ~~In essay writing~~, ~~getting failing grades is the main fear of students but it is just an instigator of other apprehensions~~ - ~~as the writing process progresses~~, ~~the main concern branches out to more precise fears~~. ~~Instructional linguists employing this theoretical framework are worried along with the way language results signify the purposeful social things to do that folks interact in~~, and ~~with~~ the ~~way to present~~ the ~~learner together with~~ the ~~language resources necessary to fulfill their social roles~~. ~~A student gives their assignment to~~ the ~~essay writing service~~, ~~and they write it for them~~.		{{BLP sources\|date=February 2013}}
			{{ Infobox scientist
			\| name = Mark Mahowald
			\| image = <!--(filename only)-->
			\| image_size =
			\| caption =
			\| birth_date = {{Birth date\|1931\|12\|1}}
			\| birth_place = [[Albany, Minnesota]]
			\| death_date ={{Dda\|2013\|7\|20\|1931\|12\|1}}
			\| death_place = Illinois, United States
			\| nationality = {{flag\|United States}}
			\| fields = [[Mathematics]]
			\| workplaces = [[Northwestern University]]
			\| alma_mater = [[University of Minnesota]]
			\| doctoral_advisor = [[Bernard Russell Gelbaum]]
			\| doctoral_students = [[Michael J. Hopkins]]
			Martin Tangora
			\| known_for = [[Homotopy groups of spheres]]
			\| awards =
			}}
			'''Mark Edward Mahowald''' (December 1, 1931 – July 20, 2013) was an [[United States\|American]] [[mathematician]] known for work in [[algebraic topology]].<ref>{{cite web\|url=http://www.legacy.com/obituaries/chicagotribune/obituary.aspx?n=mark-edward-mahowald&pid=165996488&fhid=2074#fbLoggedOut \|title=MARK EDWARD MAHOWALD Obituary: View MARK MAHOWALD's Obituary by Chicago Tribune \|publisher=Legacy.com \|date=2013-07-20 \|accessdate=2013-07-24}}</ref>

			==Life==
			Mahowald was born in Albany, Minnesota in 1931.<ref>http://books.google.ca/books?id=allYAAAAMAAJ&q=%22Mahowald,+Mark+edward%22+1931&dq=%22Mahowald,+Mark+edward%22+1931&hl=en&sa=X&ei=ue7xUYzAL6PfiAK5qoGYDg&ved=0CDcQ6AEwAg</ref> He received his Ph.D. from [[University of Minnesota]] in 1955 under the direction of [[Bernard Russell Gelbaum]] with a thesis on ''Measure in Groups''. In the sixties, he became professor at [[Syracuse University]] and around 1963 he went to [[Northwestern University]] in Chicago.

			==Work==
			Much of Mahowald's most important works concerns the [[homotopy groups of spheres]], especially using the [[Adams spectral sequence]] at the prime 2. He is known for constructing one of the first known infinite families of elements in the stable homotopy groups of spheres by showing that the classes <math>h_1h_j</math> survive the Adams spectral sequence for <math>j\geq 3</math>. In addition, he made extensive computations of the structure of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Barratt, Tangora and Kochman. Using these computations, he could show that a manifold of [[Kervaire invariant]] 1 exists in dimension 62.

			In addition, he contributed to the chromatic picture of the homotopy groups of spheres: His earlier work contains much on the image of the [[J-homomorphism]] and recent work together with Goerss, Henn, Karamanov and Rezk does computations in stable homotopy localized at the [[Morava K-theory]] K(2).

			Besides the work on the homotopy groups of spheres and related spaces, he did important work on [[Thom spectrum\|Thom spectra]]. This work was used heavily in the proof of the [[nilpotence theorem]] by Devinatz, [[Michael J. Hopkins\|Hopkins]] and Smith.

			==Awards and honors==
			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 2013-02-02.</ref>

			==Selected publications==
			*M. E. Mahowald and M. C. Tangora, ''Some differentials in the Adams spectral sequence'', Topology 6 (1967) 349–369.
			*M. G. Barratt, M. E. Mahowald and M. C. Tangora, ''Some differentials in the Adams spectral sequence II'', Topology 9 (1970) 309–316.
			*S.O. Kochman and M. E. Mahowald, ''On the computation of stable stems'' in ''The Cech centennial: a Conference on Homotopy Theory, June 22–26, 1993''
			* M. E. Mahowald,'' A new infinite family in <math>_2\pi_*^S</math>'', Topology 16 (1977) 249–256.
			*P. Goerss, H-W. Henn, H.W., M. E. Mahowald and C. Rezk, ''A resolution of the K (2)-local sphere at the prime 3'', Annals of Mathematics 162 (2005), 777–822.

			==References==
			{{reflist}}

			== External links ==
			*[http://www.math.northwestern.edu/people/emeritiProfiles/mark.mahowald.html Homepage at the Northwestern University]
			*[http://www.math.rochester.edu/u/faculty/doug/mypapers/mahowalds-groups.pdf Miller, Ravenel about Mahowald's work on the homotopy groups of spheres, pdf file] (294 kB)

			{{Authority control\|VIAF=110574649}}

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Mahowald, Mark
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = American mathematician
			\| DATE OF BIRTH = 1931
			\| PLACE OF BIRTH =
			\| DATE OF DEATH = July 20, 2013
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Mahowald, Mark}}
			[[Category:1931 births]]
			[[Category:American mathematicians]]
			[[Category:University of Minnesota alumni]]
			[[Category:Northwestern University faculty]]
			[[Category:Fellows of the American Mathematical Society]]
			[[Category:2013 deaths]]

en>They: /* Externals links */

2012-08-12T02:26:33Z

Externals links

New page

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