Ultrametric space - Revision history

en>Yobot: WP:CHECKWIKI error fixes using AWB (10090)

2014-04-30T17:10:03Z

WP:CHECKWIKI error fixes using AWB (10090)

← Older revision		Revision as of 19:10, 30 April 2014
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	~~In [[complex analysis]], a branch of [[mathematics]], an '''isolated singularity'''~~ is ~~one that has no other [[mathematical singularity\|singularities]] close to it. In other words, a [[complex~~ number~~]] ''z<sub>0</sub>'' is an isolated singularity~~ of a ~~function ''f'' if there exists an [[open set\|open]] [[disk (mathematics)\|disk]] ''D'' centered at ''z<sub>0</sub>'' such that ''f''~~ is ~~[[holomorphic~~ function~~\|holomorphic]] on ''D'' \ {z<sub>0</sub>}~~, ~~that is~~, ~~on the [[Set (mathematics)\|set]] obtained from ''D'' by taking ''z<sub>0</sub>'' out.~~		Your Basal Metabolic rate (BMR) is the number of calories your body burns a day while in a resting state. The Basal Metabolic Rate is a function of your Gender, Age, Height, and Weight. This amount is essentially the number of calories which you'd burn should you did nothing but sit on the sofa and watch TV all day. Generally speaking, If you are a Male, the BMR might be higher than a Female's BMR. Additionally, being young, heavier, and/or taller will strengthen a BMR.<br><br>One pound = 3500 calories. Maintaining a caloric deficit of 500 calories every [http://safedietplans.com/bmr-calculator bmr calculator] day for one week could indicate you lose a pound (if the illustration does her circuit training, and consumes about 1700 total calories which day, then she's prepared her 500 calorie deficit). For anybody who's ever dieted, though, the equations is maddeningly inconsistent. Sure, eat less and move more, plus you need to lose fat. But that doesn't always happen. Why not?<br><br>If the basal metabolic rate is 2,300 calories a day, 1,200 calories of food intake is not enough food for you to function correctly. Doing this for too long will damage the metabolism! Having a healthy body at a healthy weight plus acceptable body fat percentage are the most important elements. You desire a healthy, lean body that will give you the best chance to reside healthy for a extended time.<br><br>The suggested regime is three months and will extend to six months in some difficult instances. The oil can be selected by regulars too whom wish To keep their figure and prevent accumulation of fat.<br><br>So how do we learn how various calories you need? There is not any magic amount which fits everybody. Many factors have a role in determining what the proper number is for we. Some of these factors include age, present fat, activity level, height, and bmr.<br><br>To calculate the BMR, try utilizing this free online calculator: http://www.caloriesperhour.com/index_burn.html . When we have a results, jot them down on a piece of paper for reference.<br><br>Nutritionists employ the first 2 formulas because a guideline to compute standard calorie needs. They do not compute extra calories used inside exercise. The last one computes the calories different body weight need based on activity level.

	~~Formally~~, and ~~within~~ the ~~general scope~~ of ~~[[functional analysis]], an isolated singularity for a function <math>f</math> is any~~ '~~'topologically isolated'' point within an open set where~~ the ~~function is defined~~.

	~~Every singularity of~~ a ~~[[meromorphic function]] is isolated~~, but isolation of singularities is not alone sufficient to guarantee a function is meromorphic. Many important tools of complex analysis such as [[Laurent series]] and the [[residue theorem]] require that all relevant singularities of the ~~function~~ be ~~isolated~~.
	~~There are three types of singularities: removable singularities~~, ~~poles~~ and ~~essential singularities.~~

	~~==Examples==~~

	*The function <math>\frac {1} {z}</~~math> has 0 as an isolated singularity~~.

	*The [[cosecant]] function <~~math~~>~~\csc \left(\pi z\right)~~<~~/math~~> ~~has every [[integer]] as an isolated singularity.~~

	=~~=Nonisolated singularities==~~
	~~Other than isolated singularities, complex functions of one variable may exhibit other singular behaviour~~. ~~Namely, two kinds~~ of ~~nonisolated singularities exist~~:

	* '''Cluster points''', i.~~e. [[limit points~~]~~] of isolated singularities:~~ if ~~they are all poles~~, ~~despite admitting [[Laurent series]] expansions on each of them~~, ~~no such expansion is possible at its limit~~.

	* '''Natural boundaries''', i.e. ~~any non-isolated set (e.g~~. ~~a curve) which functions can~~ not ~~be [[analytic continuation\|analytically continued]] around (or outside them if they are closed curves in the [[Riemann sphere]]).~~

	~~===Examples===~~
	~~[[Image:Natural_boundary_example.gif\|thumb\|right\|256px\|The natural boundary of this power series is the unit circle (read examples).]]~~
	*The function <~~math~~>~~\tan\left(\frac{1}{z}\right)~~<~~/math~~> is ~~meromorphic in <math>\mathbb{C}\backslash\{0\}</math>~~, ~~with simple poles in <math>z_n=\left(\frac{\pi}{2}+n\pi\right)^{-~~1~~}</math>~~, for ~~every <math> n\in\mathbb{N}_0</math>~~. ~~Since <math>z_n\rightarrow 0</math>~~, ~~every punctured disk centred in <math>0</math> has an infinite number of singularities within, so no Laurent espansion is available~~ for <~~math~~>~~\tan\left(\frac{1}{z}\right)~~<~~/math~~> ~~around <math>0</math>, which~~ is in ~~fact a cluster point~~ of ~~its~~.

	*The function <~~math~~>~~\csc \left(\frac {\pi} {z}\right)~~<~~/math~~> ~~has a singularity at 0 which~~ is ''not~~'' isolated, since there are additional singularities at~~ the ~~[[Multiplicative inverse\|reciprocal]]~~ of ~~every [[integer]] which are located arbitrarily close to 0 (though the singularities at~~ these ~~reciprocals are themselves isolated)~~.

	*The function here defined as the [[Maclaurin series]] <~~math~~>~~\sum_{n=0}^{\infty}z^{2^n}~~<~~/math~~> ~~converges inside~~ the ~~open unit disk centred at <math>0</math> and has the unit circle as its natural boundary.~~

	~~==See also ==~~
	* [[Pole (complex analysis)]]
	* [[Essential singularity]]
	* [[Removable singularity]]

	~~== External links ==~~
	* {{MathWorld \| urlname= Singularity \| title= Singularity}}
	* [http://~~math~~.~~fullerton~~.~~edu~~/~~mathews/c2003/SingularityZeroPoleMod~~.html ~~Singularities Zeros~~, ~~Poles by John H~~. ~~Mathews]~~

	~~[[Category:Complex analysis]]~~

152.19.55.168: /* Properties */

2013-11-22T17:14:34Z

Properties

← Older revision		Revision as of 19:14, 22 November 2013
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	~~Hola~~. ~~The~~ [~~http:~~//~~search.usa.gov/search?query=author%27s author~~'~~s] name is Eusebio although he never really enjoyed~~ that ~~name. The ideal hobby for him with his kids is which will drive and he~~'~~s also been doing it for quite some time. Auditing~~ is ~~how he supports his family.~~ [~~http://Www.Google.Co.uk/search?hl=en~~&~~gl=us~~&~~tbm=nws&q=Massachusetts&gs_l=news Massachusetts~~] ~~is where that he and his wife survive. He~~'~~s been working around his website for some time now. Check the game out here: http://circuspartypanama.com~~<br><br>		In [[complex analysis]], a branch of [[mathematics]], an '''isolated singularity''' is one that has no other [[mathematical singularity\|singularities]] close to it. In other words, a [[complex number]] ''z<sub>0</sub>'' is an isolated singularity of a function ''f'' if there exists an [[open set\|open]] [[disk (mathematics)\|disk]] ''D'' centered at ''z<sub>0</sub>'' such that ''f'' is [[holomorphic function\|holomorphic]] on ''D'' \ {z<sub>0</sub>}, that is, on the [[Set (mathematics)\|set]] obtained from ''D'' by taking ''z<sub>0</sub>'' out.

	~~My blog post~~: ~~clash~~ of ~~clans hack cydia~~ ([http://~~circuspartypanama~~.~~com click hyperlink~~])		Formally, and within the general scope of [[functional analysis]], an isolated singularity for a function <math>f</math> is any ''topologically isolated'' point within an open set where the function is defined.

			Every singularity of a [[meromorphic function]] is isolated, but isolation of singularities is not alone sufficient to guarantee a function is meromorphic. Many important tools of complex analysis such as [[Laurent series]] and the [[residue theorem]] require that all relevant singularities of the function be isolated.
			There are three types of singularities: removable singularities, poles and essential singularities.

			==Examples==

			*The function <math>\frac {1} {z}</math> has 0 as an isolated singularity.

			*The [[cosecant]] function <math>\csc \left(\pi z\right)</math> has every [[integer]] as an isolated singularity.

			==Nonisolated singularities==
			Other than isolated singularities, complex functions of one variable may exhibit other singular behaviour. Namely, two kinds of nonisolated singularities exist:

			* '''Cluster points''', i.e. [[limit points]] of isolated singularities: if they are all poles, despite admitting [[Laurent series]] expansions on each of them, no such expansion is possible at its limit.

			* '''Natural boundaries''', i.e. any non-isolated set (e.g. a curve) which functions can not be [[analytic continuation\|analytically continued]] around (or outside them if they are closed curves in the [[Riemann sphere]]).

			===Examples===
			[[Image:Natural_boundary_example.gif\|thumb\|right\|256px\|The natural boundary of this power series is the unit circle (read examples).]]
			*The function <math>\tan\left(\frac{1}{z}\right)</math> is meromorphic in <math>\mathbb{C}\backslash\{0\}</math>, with simple poles in <math>z_n=\left(\frac{\pi}{2}+n\pi\right)^{-1}</math>, for every <math> n\in\mathbb{N}_0</math>. Since <math>z_n\rightarrow 0</math>, every punctured disk centred in <math>0</math> has an infinite number of singularities within, so no Laurent espansion is available for <math>\tan\left(\frac{1}{z}\right)</math> around <math>0</math>, which is in fact a cluster point of its.

			*The function <math>\csc \left(\frac {\pi} {z}\right)</math> has a singularity at 0 which is ''not'' isolated, since there are additional singularities at the [[Multiplicative inverse\|reciprocal]] of every [[integer]] which are located arbitrarily close to 0 (though the singularities at these reciprocals are themselves isolated).

			*The function here defined as the [[Maclaurin series]] <math>\sum_{n=0}^{\infty}z^{2^n}</math> converges inside the open unit disk centred at <math>0</math> and has the unit circle as its natural boundary.

			==See also ==
			* [[Pole (complex analysis)]]
			* [[Essential singularity]]
			* [[Removable singularity]]

			== External links ==
			* {{MathWorld \| urlname= Singularity \| title= Singularity}}
			* [http://math.fullerton.edu/mathews/c2003/SingularityZeroPoleMod.html Singularities Zeros, Poles by John H. Mathews]

			[[Category:Complex analysis]]

130.216.46.16: /* Properties */ Recoded into LaTeX

2012-07-30T04:41:36Z

Properties: Recoded into LaTeX

New page

Hola. The [http://search.usa.gov/search?query=author%27s author's] name is Eusebio although he never really enjoyed that name. The ideal hobby for him with his kids is which will drive and he's also been doing it for quite some time. Auditing is how he supports his family. [http://Www.Google.Co.uk/search?hl=en&gl=us&tbm=nws&q=Massachusetts&gs_l=news Massachusetts] is where that he and his wife survive. He's been working around his website for some time now. Check the game out here: http://circuspartypanama.com<br><br>

My blog post: clash of clans hack cydia ([http://circuspartypanama.com click hyperlink])