Modularity (networks) - Revision history

en>Pnoursalehi: moved to network science category

2014-12-04T17:48:45Z

moved to network science category

← Older revision		Revision as of 19:48, 4 December 2014
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152.78.40.207 at 14:15, 25 February 2014

2014-02-25T14:15:48Z

← Older revision		Revision as of 16:15, 25 February 2014
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	In [[geometry]], the '''radius of curvature''', ''R'', of a curve at a point is a measure of the [[radius]] of the [[circular arc]] which best approximates the curve at that point. It is the inverse of the [[curvature]].

	~~In the case of a [[space curve]], the radius of curvature is the length of the [[curvature vector]].~~

	~~In the case~~ of ~~a [[plane curve]], then ''R'' is~~ the ~~[[absolute value]] of~~		The main advantage of using the blog is that anyone can use the Word - Press blog and customize the elements in the theme regardless to limited knowledge about internet and website development. Should you have just about any questions regarding where in addition to the way to employ [http://urlon.com.br/wordpress_backup_175590 wordpress dropbox backup], you are able to call us with our own internet site. It is used by around 25% of all new websites, and there are more than 27 thousand plugins currently available. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. This particular wordpress plugin is essential for not only having the capability where you improve your position, but to enhance your organic searches for your website. <br><br>You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. Several claim that Wordpress just isn't an preferred tool to utilise when developing a professional site. You can up your site's rank with the search engines by simply taking a bit of time with your site. That's a total of 180$ for each Wordpress theme if you sell 3 links and keep the designer link for your own website, or 240$ if you sell all links. <br><br>But before choosing any one of these, let's compare between the two. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. We can active Akismet from wp-admin > Plugins > Installed Plugins. Provide the best and updated information to the web searchers and make use of these wonderful free themes and create beautiful websites. Customization of web layout is easy due to the availability of huge selection of templates. <br><br>If all else fails, please leave a comment on this post with the issue(s) you're having and help will be on the way. The SEOPressor Word - Press SEO Plugin works by analysing each page and post against your chosen keyword (or keyword phrase) and giving a score, with instructions on how to improve it. Specialty about our themes are that they are easy to load, compatible with latest wordpress version and are also SEO friendly. Word - Press is the most popular open source content management system (CMS) in the world today. Digital digital cameras now function gray-scale configurations which allow expert photographers to catch images only in black and white. <br><br>Yet, overall, less than 1% of websites presently have mobile versions of their websites. I'm a large fan of using Word - Press to create pretty much any sort of web page. This allows updates to be sent anyone who wants them via an RSS reader or directly to their email. Extra investment in Drupal must be bypassed as value for money is what Drupal provides. Customers within a few seconds after visiting a site form their opinion about the site.

	~~: <math>\frac{ds}{d\varphi} = \frac{1}{\kappa},</math>~~

	~~where ''s''~~ is the ~~arc length from a fixed point on~~ the ~~curve, ''φ'' is~~ the ~~[[tangential angle]]~~ and ~~<math>\scriptstyle\kappa</math> is~~ the [~~[curvature#Curvature\|curvature]~~].

	~~If the curve~~ is ~~given in [[Cartesian coordinates]] as ''y(x)''~~, ~~then~~ the ~~radius~~ of ~~curvature~~ is ~~(assuming~~ the ~~curve is differentiable up~~ to ~~order 2):~~

	: <~~math~~>~~R =\left\| \frac { \left(1 + y'^{\,2}\right)^{3/2}}{y''}\right\|,~~
	~~\qquad\mbox{where}\quad~~
	~~y' = \frac{dy}{dx},\quad y'' = \frac{d^2y}{dx^2},~~<~~/math~~>
	and ~~\| ''z'' \| denotes~~ the ~~absolute value of ''z''~~.

	~~If the curve~~ is ~~given [[parametric equation\|parametrically]]~~ by ~~functions '~~'x(t)'' and ~~''y(t)'', then~~ the ~~radius of curvature is~~
	~~:<math>R = \;\left\|\frac{ds}{d\varphi}\right\| \;= \;\left\|\frac {\big({\dot{x}^2 + \dot{y}^2}\big)^{3/2}}{\dot {x}\ddot{y} - \dot{y}\ddot{x}}\right\|,~~
	~~\qquad\mbox{where}\quad~~
	~~\dot{x} = \frac{dx}{dt},\quad\ddot{x} = \frac{d^2x}{dt^2},\quad~~
	~~\dot{y} = \frac{dy}{dt}~~,~~\quad\ddot{y} = \frac{d^2y}{dt^2}~~.<~~/math~~>

	~~Heuristically, this result can be interpreted as~~
	:<~~math~~> ~~R = \frac{\left\|\mathbf{v}\right\|^3}{\left\| \mathbf{v} \times \mathbf{ \dot v} \right\|}~~,
	~~\qquad\mbox{where}\quad~~
	~~\left\| \mathbf{v} \right\| = \left\| (\dot x~~, ~~\dot y) \right\| = R \frac{d\varphi}{dt}.</math>~~

	~~==Examples==~~
	~~===Semicircles~~ and ~~circles===~~

	~~For a [[semi-circle]] of radius ''a''~~ in the ~~upper half~~-~~plane~~
	~~: <math~~>
	~~y=\sqrt{a^2-x^2}, \quad~~
	~~y'=\frac{-x}{\sqrt{a^2-x^2}}, \quad~~
	~~y''=\frac{-a^2}{(a^2-x^2)^{3/2}},\quad~~
	~~R=\|-a\| =a.~~
	~~</math~~>

	~~[[Image:Ellipse evolute~~.~~svg\|\|right\|thumb\|240px\|An ellipse (red)~~ and ~~its [[evolute]] (blue). The dots are~~ the ~~vertices~~ of ~~the ellipse, at the points of greatest~~ and ~~least curvature~~.]]

	~~For a semi-circle~~ of ~~radius ''a'' in~~ the ~~lower half-plane~~
	: <~~math~~>
	~~y=-\sqrt{a^2-x^2}~~, ~~\quad~~
	~~R=\|a\|=~~a.
	~~</math>~~
	The ~~[[circle]] of radius ''~~a~~'' has a radius of curvature equal~~ to ~~''a''~~.

	~~===Ellipses===~~

	~~In an [[ellipse]]~~ with ~~major axis 2''a''~~ and ~~minor axis 2''b'',~~ the ~~[[Vertex~~ (~~curve~~)~~\|vertices]] on~~ the ~~major axis have the smallest radius of curvature of any points~~ <~~math~~>~~\left( R = \frac{b^2}{a} \right)~~ <~~/math~~>, ~~and the vertices on the minor axis~~ have ~~the largest radius~~ of ~~curvature~~ of any ~~points <math>\left( R = \frac{~~a~~^2}{b} \right) </math>~~.

	~~== See also ==~~

	* [[Osculating circle]]

	~~==References==~~
	*{{cite book \|title = Differential Geometry of Curves and Surfaces\|first = Manfredo\|last = do Carmo\| id = ISBN 0-13-212589-7 \| year = 1976}}

	~~[[Category:Curvature (mathematics)]]~~
	~~[[Category:Curves]]~~
	~~[[Category:Integral calculus]]~~
	~~[[Category:Multivariable calculus]]~~
	~~[[Category:Theoretical physics]]~~

en>Ruby Murray: Reverted edits by 117.192.50.100 (talk) to last version by 64.121.31.29

2013-12-27T16:21:04Z

Reverted edits by 117.192.50.100 (talk) to last version by 64.121.31.29

← Older revision		Revision as of 18:21, 27 December 2013
Line 1:		Line 1:
			In [[geometry]], the '''radius of curvature''', ''R'', of a curve at a point is a measure of the [[radius]] of the [[circular arc]] which best approximates the curve at that point. It is the inverse of the [[curvature]].

			In the case of a [[space curve]], the radius of curvature is the length of the [[curvature vector]].

	[~~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~~=~~Elizbeth+Cola&Submit~~=~~Go Elizbeth Cola~~] is the ~~title folks use to simply call me~~ and ~~I absolutely appreciate this identify~~. ~~Administering databases has been my working day job for~~ a ~~although and I~~'~~ll be promoted quickly~~. ~~Playing badminton is the only interest his wife doesn~~'~~t approve~~ of. ~~Wyoming is in which he~~'~~s been living for several years but he desires to move because~~ of ~~his household.~~<br><br>~~Feel free to visit my blog ..~~. [~~http~~:~~//paediatricdental.yolasite.com/ paediatric dentist~~]		In the case of a [[plane curve]], then ''R'' is the [[absolute value]] of

			: <math>\frac{ds}{d\varphi} = \frac{1}{\kappa},</math>

			where ''s'' is the arc length from a fixed point on the curve, ''φ'' is the [[tangential angle]] and <math>\scriptstyle\kappa</math> is the [[curvature#Curvature\|curvature]].

			If the curve is given in [[Cartesian coordinates]] as ''y(x)'', then the radius of curvature is (assuming the curve is differentiable up to order 2):

			: <math>R =\left\| \frac { \left(1 + y'^{\,2}\right)^{3/2}}{y''}\right\|,
			\qquad\mbox{where}\quad
			y' = \frac{dy}{dx},\quad y'' = \frac{d^2y}{dx^2},</math>
			and \| ''z'' \| denotes the absolute value of ''z''.

			If the curve is given [[parametric equation\|parametrically]] by functions ''x(t)'' and ''y(t)'', then the radius of curvature is
			:<math>R = \;\left\|\frac{ds}{d\varphi}\right\| \;= \;\left\|\frac {\big({\dot{x}^2 + \dot{y}^2}\big)^{3/2}}{\dot {x}\ddot{y} - \dot{y}\ddot{x}}\right\|,
			\qquad\mbox{where}\quad
			\dot{x} = \frac{dx}{dt},\quad\ddot{x} = \frac{d^2x}{dt^2},\quad
			\dot{y} = \frac{dy}{dt},\quad\ddot{y} = \frac{d^2y}{dt^2}.</math>

			Heuristically, this result can be interpreted as
			:<math> R = \frac{\left\|\mathbf{v}\right\|^3}{\left\| \mathbf{v} \times \mathbf{ \dot v} \right\|},
			\qquad\mbox{where}\quad
			\left\| \mathbf{v} \right\| = \left\| (\dot x, \dot y) \right\| = R \frac{d\varphi}{dt}.</math>

			==Examples==
			===Semicircles and circles===

			For a [[semi-circle]] of radius ''a'' in the upper half-plane
			: <math>
			y=\sqrt{a^2-x^2}, \quad
			y'=\frac{-x}{\sqrt{a^2-x^2}}, \quad
			y''=\frac{-a^2}{(a^2-x^2)^{3/2}},\quad
			R=\|-a\| =a.
			</math>

			[[Image:Ellipse evolute.svg\|\|right\|thumb\|240px\|An ellipse (red) and its [[evolute]] (blue). The dots are the vertices of the ellipse, at the points of greatest and least curvature.]]

			For a semi-circle of radius ''a'' in the lower half-plane
			: <math>
			y=-\sqrt{a^2-x^2}, \quad
			R=\|a\|=a.
			</math>
			The [[circle]] of radius ''a'' has a radius of curvature equal to ''a''.

			===Ellipses===

			In an [[ellipse]] with major axis 2''a'' and minor axis 2''b'', the [[Vertex (curve)\|vertices]] on the major axis have the smallest radius of curvature of any points <math>\left( R = \frac{b^2}{a} \right) </math>, and the vertices on the minor axis have the largest radius of curvature of any points <math>\left( R = \frac{a^2}{b} \right) </math>.

			== See also ==

			* [[Osculating circle]]

			==References==
			*{{cite book \|title = Differential Geometry of Curves and Surfaces\|first = Manfredo\|last = do Carmo\| id = ISBN 0-13-212589-7 \| year = 1976}}

			[[Category:Curvature (mathematics)]]
			[[Category:Curves]]
			[[Category:Integral calculus]]
			[[Category:Multivariable calculus]]
			[[Category:Theoretical physics]]

en>Bibcode Bot: Adding 2 arxiv eprint(s), 3 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2012-08-31T10:17:55Z

Adding 2 arxiv eprint(s), 3 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

New page

[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=Elizbeth+Cola&Submit=Go Elizbeth Cola] is the title folks use to simply call me and I absolutely appreciate this identify. Administering databases has been my working day job for a although and I'll be promoted quickly. Playing badminton is the only interest his wife doesn't approve of. Wyoming is in which he's been living for several years but he desires to move because of his household.<br><br>Feel free to visit my blog ... [http://paediatricdental.yolasite.com/ paediatric dentist]