QT interval - Revision history

en>Hb2019: /* Genetic causes */

2014-12-26T20:07:19Z

Genetic causes

← Older revision		Revision as of 22:07, 26 December 2014
Line 1:		Line 1:
	~~Eusebio is~~ the ~~name workers use~~ to ~~call me~~ and ~~my friends~~ and ~~I think~~ the ~~problem sounds quite good when you say it~~. I ~~utilized~~ to ~~be unemployed yet still now~~ I am ~~a cashier. My house is from now on in South Carolina in addition~~ to [http://~~Www~~.~~google~~.de/search?q=I+~~don%27t~~ I don't] ~~plan on changing it~~. It's not a ~~common thing but what~~ I ~~much like doing is bottle top collecting~~ and ~~now My personal have time~~ to ~~consume on~~ new ~~things. I'm not high-quality at webdesign but additionally post want to check the best website: http://Prometeu~~.~~net/~~<br><br>~~Feel free to visit my site~~: [http://~~Prometeu~~.~~net/ clash of clans hack tool download~~]		I woke up the other day and realised - At the moment I've been solitary for a little while and after much bullying from buddies I today locate myself signed-up for internet dating. They promised me that there are a lot of sweet, standard and enjoyable visitors to meet up, so vip tickets for luke bryan ([http://www.ladyhawkshockey.org www.ladyhawkshockey.org]) here goes the message!<br>I try and keep as physically healthy meet and greet with luke bryan - [http://okkyunglee.com okkyunglee.com] - as possible staying at the gymnasium several-times per week. I love my athletics and endeavor to perform or view since many a possible. Being winter I am going to often at [http://Search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=Hawthorn+matches&Submit=Go Hawthorn matches]. Note: If you considered buying a hobby I don't brain, I have noticed the carnage [http://lukebryantickets.hamedanshahr.com luke bryan ticket sale dates] of fumbling suits at stocktake revenue.<br>My friends and fam are wonderful and spending some time with them at pub gigabytes or dinners is consistently a must. I haven't ever been into cabarets as I discover that you could do not own a decent conversation with the sound. Additionally, I got 2 really adorable and definitely cheeky dogs that are constantly excited to meet new people.<br><br>My website: [http://lukebryantickets.sgs-suparco.org brad paisley tour]

en>Rjwilmsi: Journal cites, added 1 DOI, added 1 PMID using AWB (9944)

2014-02-15T09:59:32Z

Journal cites, added 1 DOI, added 1 PMID using AWB (9944)

← Older revision		Revision as of 11:59, 15 February 2014
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	~~{{About\|~~the ~~meaning of 'commensurable'~~ and ~~derived words in mathematics\|other senses\|Commensurability (disambiguation)}}~~		Eusebio is the name workers use to call me and my friends and I think the problem sounds quite good when you say it. I utilized to be unemployed yet still now I am a cashier. My house is from now on in South Carolina in addition to [http://Www.google.de/search?q=I+don%27t I don't] plan on changing it. It's not a common thing but what I much like doing is bottle top collecting and now My personal have time to consume on new things. I'm not high-quality at webdesign but additionally post want to check the best website: http://Prometeu.net/<br><br>Feel free to visit my site: [http://Prometeu.net/ clash of clans hack tool download]
	~~In [[mathematics]], two non-[[zero]] [[real number]]s ''a''~~ and ~~''b'' are said~~ to be ~~'''''commensurable''''' if ''~~a~~''/''b''~~ is ~~a [[rational number]].~~

	~~==History of the concept==~~
	The [[Pythagoreanism\|Pythagoreans]] are credited with the proof of the existence of [[irrational numbers]].<ref>{{cite journal\|title=The Discovery of Incommensurability by Hippasus of Metapontum\|author=Kurt Von Fritz\|journal=The Annals of Mathematics\|year=1945\|ref=harv}}</ref><ref>{{cite journal\|title=The Pentagram and the Discovery of an Irrational Number\|journal=The Two-Year College Mathematics Journal\|author=James R. Choike\|year=1980\|ref=harv}}</ref><!--Note: Von Fritz & Choike references were drawn from ~~the Wikipedia "History of Mathematics" article--> When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable.~~

	~~A separate, more general and circuitous ancient Greek [[wikiquote:Doctrine of proportion (mathematics)\|doctrine of proportionality]] for geometric [[Magnitude (mathematics)\|magnitude]] was developed~~ in ~~Book V of Euclid's ''Elements''~~ in ~~order~~ to ~~allow proofs involving incommensurable lengths, thus avoiding arguments which applied only to a historically restricted definition of [[Number#History\|number]].~~

	[[Euclid]]'s notion of commensurability is anticipated in passing in the discussion between [[Socrates]] and the slave boy in Plato's dialogue entitled [[Meno]], in which Socrates uses the boy's own inherent capabilities to solve a complex geometric problem through the Socratic Method. He develops a proof which is, for all intents and purposes, very Euclidean in nature and speaks to the concept of incommensurability.<ref>Plato's ''Meno''. Translated with annotations by George Anastaplo and Laurence Berns. Focus Publishing: ~~Newburyport, MA. 2004.<~~/~~ref>~~

	The usage primarily comes to us from translations of [[Euclid]]'s [[Euclid's Elements\|''Elements'']], in which two line segments ''a'' and ''b'' are called commensurable precisely if there is some third segment ''c'' that can be laid end-to-end a whole number of times to produce a segment congruent to ''a'', and also, with a different whole number, a segment congruent to ''b''. ~~Euclid did not use any concept of real number, but he used a notion of congruence of line segments, and of one such segment being longer or shorter than another~~.

	~~That ''a''~~/~~''b'' is rational is a [[necessary and sufficient condition]] for the existence of some real number ''c'', and [[integer]]s ''m'' and ''n'', such that~~

	~~:''a''~~ = '~~'mc'' and ''b'' = ''nc''.~~

	~~Assuming for simplicity that ''a'' and ''b'' are [[positive number\|positive~~]~~], one can say that a [[ruler]], marked off in units of length ''c'', could be used to measure out both a [[line segment]] of length ''a'', and one of length ''b''~~. ~~That is, there is a common unit of [[length]] in terms of which~~ '~~'a'' and ''b'' can both be measured; this is the origin of the term. Otherwise the pair ''a'' and ''b'' are '''incommensurable'''.~~

	~~==Commensurability in group theory==~~
	~~In [[group theory]], a generalisation to pairs of [[subgroup]]~~s ~~is obtained, by noticing that in the case given, the subgroups of the [[integers]] as an [[group scheme\|additive group]], generated respectively by ''~~a~~'' and by ''b'', intersect in the subgroup generated by ''d'', where ''d''~~ is ~~the [[least common multiple\|LCM]] of ''a''~~ and ~~''b''. This intersection has [[finite set\|finite]] [[Index of a subgroup\|index]] in the integers, and therefore in each of the subgroups. This gives rise~~ to ~~a general notion of '''commensurable subgroups''': two subgroups ''A'' and ''B'' of a group are ''commensurable'' when their [[Intersection (set theory)\|intersection]] has finite index in each of them~~. ~~That is, two subgroups~~ '~~'H''<sub>1</sub> and ''H''<sub>2</sub> of a group ''G'' are '''commensurable''' if~~

	: ~~<math>[H_j~~: ~~H_1\cap H_2]<\infty\text{ for }j=1,\,2.<~~/~~math>~~

	~~The relation of being '''commensurable in the wide sense''' is that ''H''<sub>1<~~/sub> be commensurable with a conjugate of ''H''<sub>2</sub>.<ref name=MR56>{{cite book \| first1=Colin \| last1=Maclachlan \| first2=Alan W. \| last2=Reid \| title=The Arithmetic of Hyperbolic 3-Manifolds \| series=[[Graduate Texts in Mathematics]] \| publisher=[[Springer-Verlag]] \| volume=219 \| year=2003 \| isbn=0-387-98386-4 \| zbl=1025.57001 \| page=56 }}</ref> Some authors use the terms '''commensurate''' and ''commensurable'' for commensurable and widely commensurable respectively.

	~~A relationship can similarly be defined on subspaces of a [[vector space]], in terms of [[projection (linear algebra)\|projections]] that have finite-[[dimension]]al kernel and [[cokernel]]~~.

	~~In contrast, two [[Linear subspace\|subspaces]] <math>\mathrm{A}<~~/~~math> and <math>\mathrm{B}</math> that are given by some [[moduli space]] [[algebraic stack\|stacks]] over a [[Lie algebra]]~~ <~~math~~>~~\mathcal{O},~~<~~/math~~> are not necessarily commensurable if they are described by infinite dimensional representations. In addition, if the [[Complete space\|completions]] of <math>\mathcal{O}</math>-type [[Module (mathematics)\|modules]] corresponding to ~~<math>\mathfrak{H}</math> and <math>\mathfrak{G}</math> are not~~ [~~[well-defined]], then <math>\mathfrak{G}<~~/~~math> and <math>\mathfrak{H}<~~/~~math> are also ''not commensurable~~.''

	~~==In topology==~~

	Two topological spaces are ''commensurable'' if they have [[homeomorphism\|homeomorphic]] finite-sheeted [[covering space]]s. Depending on the type of topological space under consideration one might want to use [[homotopy\|homotopy-equivalences]] or [[diffeomorphism]]s instead of homeomorphisms in the definition. Thus, if one uses homotopy-equivalences, commensurability of groups corresponds to commensurability of spaces provided one associates the [[classifying space]] to a discrete group. For example, the [[Gieseking manifold]] is commensurate to the complement of ~~the [[figure eight knot (mathematics)\|figure-eight knot]].~~

	~~==In physics==~~
	In [[physics]], the terms ''commensurable'' and ''incommensurable'' are used in the same way as in mathematics. The two rational numbers ''a'' and ''b'' usually refer to periods of two distinct, but connected physical properties of the considered material, such as the [[crystal structure]] and the [[ANNNI model\|magnetic superstructure]]. The potential richness of physical phenomena related to this concept is exemplified in the [[Cantor function\|devil's staircase]].

	~~==See also==~~
	* [[Commensurator]]

	~~==References==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Commensurability (Mathematics)}}~~
	~~[[Category:Real numbers]]~~
	~~[[Category:Infinite group theory]~~]

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-29T00:46:00Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 02:46, 29 January 2014
Line 1:		Line 1:
	~~Many people select~~ to ~~put money into properties as~~ a ~~consequence of totally different causes. Property funding~~ is a ~~enterprise area that many individuals delve into hoping to realize success~~. ~~Nevertheless, success is inevitable if you recognize which location or nation to pick out to your property investment~~.<br><br>~~It is located 250m to Hillview MRT , which will full in 2016~~. ~~Hillview MRT is part~~ of the ~~Downtown MRT Line~~, ~~which runs by way of Bukit Timah Street~~, and ~~is handy~~ for ~~those working or learning~~ in ~~Bukit Timah. There may be an interchange~~ to ~~attach at Newton Station~~, which ~~connects~~ to ~~Orchard and City Corridor~~. ~~The road then links directly to Bugis~~ and ~~Marina Bay Sands. The great thing about RiverTrees Residences~~' ~~location is compelling as it provides buyers a chance to own a house with an unblocked view~~ [~~http://drupal.12thirty4.com/gmaps/node/4865 http://drupal.12thirty4.com~~] ~~of Punggol Reservoir. It~~'s ~~situated~~ very ~~close to~~ nature ~~but provides glorious connectivity~~ to the ~~variety~~ of ~~amenities in the neighborhood," he added~~. ~~More than 200 models offered at Riverbank @ Fernvale Star Purchase (Residential) Star Purchase (Business) Full rental facilities~~<br><br>The ~~Santorini Apartment (Singapore) will~~ be a ~~part~~ of ~~URA~~'~~s plans~~ to ~~deliver jobs nearer to dwelling~~, ~~residents~~ of ~~Santorini Apartment shall be supplied with more workplace~~ and ~~retail jobs within~~ the ~~neighbourhood~~, ~~Santorini Condominium~~ can be ~~near major employment hubs like Changi Business Park~~ and ~~other industrial areas~~ in ~~addition to Changi Airport. More jobs will continue to~~ be ~~created as part ofGrasp Plan 2013 within the East by means of~~ the ~~event~~ of ~~new job centres across~~ the ~~region~~. ~~Extra created jobs will present great investment opportunities for residents of Santorini Condominium. Expats from Industrial Estates across~~ the ~~space will provide high rental yield for Santorini Condominium~~.~~<br><br>The precise property market~~ in ~~Singapore has been booming since 2007~~, ~~plus it continues~~ to ~~flourish. In current instances~~, the ~~exact property market within~~ the ~~country witnessed~~ an ~~influx~~ in ~~overseas traders~~, ~~shopping for property~~. ~~Statistics present that Chinese traders have been the principle foreign buyers~~ of ~~property~~ in ~~Singapore Utilizing a spiraling market~~, ~~the issue that is oft being raised is -when is the best time for it to buy property~~ in ~~Singapore ? S how case~~ of the ~~newest new launch property in Singapore~~. ~~From residential~~ to ~~commercial~~. ~~From north to south~~ and east to west. Find your dream home or worthwhile investment here. Continuereading "The Crest Rental by Wing Tai Preview Launch Soon" Present New Condo Launch Highlights Exciting new launch condominium coming your manner!<br><br>~~The Houston Astros launched an Astros Play Green campaign on April 22~~, ~~Earth Day~~. The ~~marketing campaign, building off~~ a ~~club initiative that started last summer, strives to create consciousness concerning environmental initiatives within the City~~ of ~~Houston~~. The ~~Astros have been the primary sports group~~ in the ~~Metropolis~~ of ~~Houston to launch~~ a ~~recycling campaign~~ that ~~was interactive~~ and ~~encouraged its fan base to take steps to assist the surroundings. Waterfront @ Faber located at Faber Walk~~. A ~~Waterfront Home of Limitless Prospects Riverfront~~, ~~lush greenery & a vibrant Jurong Lake District at you~~ ~~Read More Stratum is a brand new condominium in Pasir Ris~~, ~~near Elias Mall and minutes~~ to ~~Pasir Ris Park~~ and ~~Seaside. Priced to Promote~~, ~~Do not Miss! Learn Extra → Effect on the potential buyers~~ and ~~EC market~~<br><br>~~Eco~~-~~Tech@Sunview is an exciting new Business 2 light industrial growth located~~ in the ~~western a part of Singapore~~. ~~This 9 storey improvement with u~~ ~~Read Extra Site visitors Skilled makes a speciality~~ of ~~ranking new launch property web sites within~~ the ~~first web page of Search Engines~~. ~~We operate a no-nonsense SEARCH ENGINE OPTIMISATION service adhering~~ to the ~~strictest~~ of ~~search engine insurance policies~~. ~~Over one hundred Purchasers have benefited from our service~~ and ~~received numerous leads from their website~~. The ~~following Marina Bay Living. Freehold combined growth. Enjoy breathtaking unblock views~~ of the ~~Sea & Singapore Iconic Landmarks~~, ~~reminiscent~~ of ~~Marina Bay S Read More Attractive Pricing Earlier than Actual Sales Launch Date~~. ~~HOUSTON ASTROS LAUNCH "ASTROS PLAY INEXPERIENCED" MARKETING CAMPAIGN District 18, 99 years LH Government Apartment~~		{{About\|the meaning of 'commensurable' and derived words in mathematics\|other senses\|Commensurability (disambiguation)}}
			In [[mathematics]], two non-[[zero]] [[real number]]s ''a'' and ''b'' are said to be '''''commensurable''''' if ''a''/''b'' is a [[rational number]].

			==History of the concept==
			The [[Pythagoreanism\|Pythagoreans]] are credited with the proof of the existence of [[irrational numbers]].<ref>{{cite journal\|title=The Discovery of Incommensurability by Hippasus of Metapontum\|author=Kurt Von Fritz\|journal=The Annals of Mathematics\|year=1945\|ref=harv}}</ref><ref>{{cite journal\|title=The Pentagram and the Discovery of an Irrational Number\|journal=The Two-Year College Mathematics Journal\|author=James R. Choike\|year=1980\|ref=harv}}</ref><!--Note: Von Fritz & Choike references were drawn from the Wikipedia "History of Mathematics" article--> When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable.

			A separate, more general and circuitous ancient Greek [[wikiquote:Doctrine of proportion (mathematics)\|doctrine of proportionality]] for geometric [[Magnitude (mathematics)\|magnitude]] was developed in Book V of Euclid's ''Elements'' in order to allow proofs involving incommensurable lengths, thus avoiding arguments which applied only to a historically restricted definition of [[Number#History\|number]].

			[[Euclid]]'s notion of commensurability is anticipated in passing in the discussion between [[Socrates]] and the slave boy in Plato's dialogue entitled [[Meno]], in which Socrates uses the boy's own inherent capabilities to solve a complex geometric problem through the Socratic Method. He develops a proof which is, for all intents and purposes, very Euclidean in nature and speaks to the concept of incommensurability.<ref>Plato's ''Meno''. Translated with annotations by George Anastaplo and Laurence Berns. Focus Publishing: Newburyport, MA. 2004.</ref>

			The usage primarily comes to us from translations of [[Euclid]]'s [[Euclid's Elements\|''Elements'']], in which two line segments ''a'' and ''b'' are called commensurable precisely if there is some third segment ''c'' that can be laid end-to-end a whole number of times to produce a segment congruent to ''a'', and also, with a different whole number, a segment congruent to ''b''. Euclid did not use any concept of real number, but he used a notion of congruence of line segments, and of one such segment being longer or shorter than another.

			That ''a''/''b'' is rational is a [[necessary and sufficient condition]] for the existence of some real number ''c'', and [[integer]]s ''m'' and ''n'', such that

			:''a'' = ''mc'' and ''b'' = ''nc''.

			Assuming for simplicity that ''a'' and ''b'' are [[positive number\|positive]], one can say that a [[ruler]], marked off in units of length ''c'', could be used to measure out both a [[line segment]] of length ''a'', and one of length ''b''. That is, there is a common unit of [[length]] in terms of which ''a'' and ''b'' can both be measured; this is the origin of the term. Otherwise the pair ''a'' and ''b'' are '''incommensurable'''.

			==Commensurability in group theory==
			In [[group theory]], a generalisation to pairs of [[subgroup]]s is obtained, by noticing that in the case given, the subgroups of the [[integers]] as an [[group scheme\|additive group]], generated respectively by ''a'' and by ''b'', intersect in the subgroup generated by ''d'', where ''d'' is the [[least common multiple\|LCM]] of ''a'' and ''b''. This intersection has [[finite set\|finite]] [[Index of a subgroup\|index]] in the integers, and therefore in each of the subgroups. This gives rise to a general notion of '''commensurable subgroups''': two subgroups ''A'' and ''B'' of a group are ''commensurable'' when their [[Intersection (set theory)\|intersection]] has finite index in each of them. That is, two subgroups ''H''<sub>1</sub> and ''H''<sub>2</sub> of a group ''G'' are '''commensurable''' if

			: <math>[H_j: H_1\cap H_2]<\infty\text{ for }j=1,\,2.</math>

			The relation of being '''commensurable in the wide sense''' is that ''H''<sub>1</sub> be commensurable with a conjugate of ''H''<sub>2</sub>.<ref name=MR56>{{cite book \| first1=Colin \| last1=Maclachlan \| first2=Alan W. \| last2=Reid \| title=The Arithmetic of Hyperbolic 3-Manifolds \| series=[[Graduate Texts in Mathematics]] \| publisher=[[Springer-Verlag]] \| volume=219 \| year=2003 \| isbn=0-387-98386-4 \| zbl=1025.57001 \| page=56 }}</ref> Some authors use the terms '''commensurate''' and ''commensurable'' for commensurable and widely commensurable respectively.

			A relationship can similarly be defined on subspaces of a [[vector space]], in terms of [[projection (linear algebra)\|projections]] that have finite-[[dimension]]al kernel and [[cokernel]].

			In contrast, two [[Linear subspace\|subspaces]] <math>\mathrm{A}</math> and <math>\mathrm{B}</math> that are given by some [[moduli space]] [[algebraic stack\|stacks]] over a [[Lie algebra]] <math>\mathcal{O},</math> are not necessarily commensurable if they are described by infinite dimensional representations. In addition, if the [[Complete space\|completions]] of <math>\mathcal{O}</math>-type [[Module (mathematics)\|modules]] corresponding to <math>\mathfrak{H}</math> and <math>\mathfrak{G}</math> are not [[well-defined]], then <math>\mathfrak{G}</math> and <math>\mathfrak{H}</math> are also ''not commensurable.''

			==In topology==

			Two topological spaces are ''commensurable'' if they have [[homeomorphism\|homeomorphic]] finite-sheeted [[covering space]]s. Depending on the type of topological space under consideration one might want to use [[homotopy\|homotopy-equivalences]] or [[diffeomorphism]]s instead of homeomorphisms in the definition. Thus, if one uses homotopy-equivalences, commensurability of groups corresponds to commensurability of spaces provided one associates the [[classifying space]] to a discrete group. For example, the [[Gieseking manifold]] is commensurate to the complement of the [[figure eight knot (mathematics)\|figure-eight knot]].

			==In physics==
			In [[physics]], the terms ''commensurable'' and ''incommensurable'' are used in the same way as in mathematics. The two rational numbers ''a'' and ''b'' usually refer to periods of two distinct, but connected physical properties of the considered material, such as the [[crystal structure]] and the [[ANNNI model\|magnetic superstructure]]. The potential richness of physical phenomena related to this concept is exemplified in the [[Cantor function\|devil's staircase]].

			==See also==
			* [[Commensurator]]

			==References==
			{{Reflist}}

			{{DEFAULTSORT:Commensurability (Mathematics)}}
			[[Category:Real numbers]]
			[[Category:Infinite group theory]]

en>Mikael Häggström: formatted and linked to Vemurafenib

2012-06-28T22:38:53Z

formatted and linked to Vemurafenib

New page

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