Neptune - Revision history

en>Tetra quark: revert: neptune is more massive

2015-01-12T14:56:07Z

revert: neptune is more massive

← Older revision		Revision as of 16:56, 12 January 2015
Line 1:		Line 1:
	~~Taisha will be~~ the name ~~she loves in order~~ to ~~called with and she totally digs that~~ make. ~~What Would like enjoy doing is canoeing~~ and ~~I am going~~ to ~~never stop doing thought~~. ~~Administering databases been recently my normal work~~ for a ~~bit~~ of ~~time~~. ~~My husband fuel tank chose~~ to ~~exist in Kansas even so will must move every year or pair~~. ~~You~~ can ~~always find her website here:~~ http://~~www~~.~~youtube.com~~/~~watch~~?~~v=9hqIGzHNPdA~~<br><br>~~my web~~ blog ~~[http://www~~.~~youtube~~.~~com/watch?v=9hqIGzHNPdA zyto compass reviews]~~		If you are looking for a specific plugin, then you can just search for the name of the plugin. Good luck on continue learning how to make a wordpress website. This CMS has great flexibility to adapt various extensions and add-ons. If you need a special plugin for your website , there are thousands of plugins that can be used to meet those needs. The top 4 reasons to use Business Word - Press Themes for a business website are:. <br><br>

			Creating a website from scratch can be such a pain. If a newbie missed a certain part of the video then they could always rewind. Several claim that Wordpress just isn't an preferred tool to utilise when developing a professional site. They provide many such popular products which you can buy for your baby. If you have any questions with regards to where and how to use [http://dinky.in/?WordpressDropboxBackup438804 wordpress dropbox backup], you can make contact with us at our 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>The entrepreneurs can easily captivate their readers by using these versatile themes. Browse through the popular Wordpress theme clubs like the Elegant Themes, Studio Press, Woo - Themes, Rocket Theme, Simple Themes and many more. This platform can be customizedaccording to the requirements of the business. These frequent updates have created menace in the task of optimization. After that the developer adds the unordered list for navigations. <br><br>The disadvantage is it requires a considerable amount of time to set every thing up. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. A higher percentage of women are marrying at older ages,many are delaying childbearing until their careers are established, the divorce rate is high and many couples remarry and desire their own children. The most important plugins you will need are All-in-One SEO Pack, some social bookmarking plugin, a Feedburner plugin and an RSS sign up button. If your blog employs the permalink function, This gives your SEO efforts a boost, and your visitors will know firsthand what's in the post when seeing the URL. <br><br>Many developers design websites and give them to the clients, but still the client faces problems to handle the website. If you operate a website that's been built on HTML then you might have to witness traffic losses because such a site isn't competent enough in grabbing the attention of potential consumers. The days of spending a lot of time and money to have a website built are long gone. Word - Press is an open source content management system which is easy to use and offers many user friendly features. You can check out the statistics of page of views for your web pages using free tools that are available on the internet.

en>Ryulong: /* Naming */

2014-03-03T10:16:29Z

Naming

← Older revision		Revision as of 12:16, 3 March 2014
Line 1:		Line 1:
	~~In [[topology]] a mathematical discipline, a '''prime manifold''' is an ''n''-[[manifold (topology)\|manifold]] that cannot~~ be ~~expressed as a non-trivial [[connected sum]] of two ''n''-manifolds. Non-trivial means that neither of~~ the ~~two is an [[n-sphere\|''n''-sphere]].~~		Taisha will be the name she loves in order to called with and she totally digs that make. What Would like enjoy doing is canoeing and I am going to never stop doing thought. Administering databases been recently my normal work for a bit of time. My husband fuel tank chose to exist in Kansas even so will must move every year or pair. You can always find her website here: http://www.youtube.com/watch?v=9hqIGzHNPdA<br><br>my web blog [http://www.youtube.com/watch?v=9hqIGzHNPdA zyto compass reviews]
	~~A similar notion is that of an '''''irreducible''''' ''n''-manifold, which is one~~ in which any embedded (''n'' − 1)-sphere bounds an embedded ''n''-[[ball (topology)\|ball]]. Implicit in this definition is the use of a suitable [[category theory\|category]], such as the category of [[differentiable manifold]]s or the category of [[piecewise-linear manifold]]s.

	The notions of irreducibility in algebra and manifold theory are related. An irreducible manifold is prime, although the converse does not hold. From an algebraist's perspective, prime manifolds should be called "irreducible"; however the topologist (in particular the 3-manifold topologist) finds the definition above more useful. The only compact, connected 3-manifolds that are prime but not irreducible are the trivial 2-sphere [[fiber bundle\|bundle]] over the circle S<sup>1</sup> and the twisted 2-sphere bundle over S<sup>1</sup>.

	~~According to [[Prime decomposition (3-manifold)\|a theorem]] of [[Hellmuth Kneser]]~~ and ~~[[John Milnor]], every [[compact space\|compact]], [[orientability\|orientable]] [[3-manifold]] is the [[connected sum]] of a unique ([[up to]] [[homeomorphism]]) collection of prime 3-manifolds.~~

	~~== Definitions ==~~
	~~Let us consider specifically [[3-manifold]]s.~~

	~~=== Irreducible manifold ===~~
	A 3-manifold is '''irreducible''' if any smooth sphere bounds a ball. More rigorously, a [[differentiable manifold\|differentiable]] [[connected space\|connected]] 3-manifold <math>M</math> is irreducible if every differentiable [[submanifold]] <math>S</math> [[homeomorphic]] to a [[n-sphere\|sphere]] bounds a subset <math>D</math> (that ~~is, <math>S=\partial D </math>) which is homeomorphic to the closed [[ball (topology)\|ball]]~~
	~~:<math>D^3 = \{x\in\R^3\ \|\ \|x\|\leq 1\}~~. ~~</math>~~
	~~The assumption of differentiability of <math>M</math>~~ is not important, because every topological 3-manifold has a unique differentiable structure. The assumption that the sphere is ''smooth'' (that is, that it is a differentiable submanifold) is however important: indeed the sphere must have a [[tubular neighborhood]].

	~~A 3-manifold that is not irreducible is '''reducible'''.~~

	~~===Prime manifolds===~~
	A connected 3-manifold <math>M</math> is '''prime''' if it cannot be obtained as a [[connected sum]] <math>N_1\# N_2 </math> of two manifolds neither of which is the 3-sphere <math>S^3</math> (or, equivalently, neither of which is the homeomorphic to ~~<math>M</math>)~~.

	~~== Examples ==~~
	~~=== Euclidean space ===~~
	~~Three-dimensional [[Euclidean space]] <math> \R^3 </math> is irreducible: all smooth 2-spheres in it bound balls.~~

	~~On the other hand, [[Alexander's horned sphere]] is a non-smooth sphere in <math>\R^3</math> that does not bound~~ a ~~ball. Thus the stipulation that the sphere be smooth is necessary.~~

	~~=== Sphere, lens spaces ===~~
	The [[3-sphere]] <math>S^3</math> is irreducible. The [[product space]] <math>S^2\times S^1</math> is not irreducible, since any 2-sphere <math>S^2\times \{pt\} </math> (where 'pt' is some point of <math>S^1</math>) has a connected complement which is not a ball (it is the product of ~~the 2-sphere and a line)~~.

	~~A [[lens space]] <math>L(p,q) </math> with <math>p\neq 0 </math> (and thus not the same as <math>S^2\times S^1 </math>) is irreducible.~~

	~~== Prime manifolds and irreducible manifolds ==~~
	A 3-manifold is irreducible if and only if it is prime, except for two cases: the product <math>S^2\times S^1</math> and the [[non-orientable]] [[fiber bundle]] of the 2-sphere over the circle <math>S^1</math> are both prime but not irreducible.

	~~=== From irreducible~~ to ~~prime ===~~
	~~An irreducible manifold <math>M</math> is prime. Indeed, if we express <math>M</math> as a connected sum~~
	~~:<math>M=N_1\#N_2, </math>~~
	then <math>M</math> is obtained by removing a ball each from <math>N_1</math> and from <math>N_2</math>, and then gluing the two resulting 2-spheres together. These two (now united) 2-spheres form a 2-sphere in ~~<math>M</math>. The fact that <math>M</math> is irreducible means that this 2-sphere~~ must ~~bound a ball. Undoing the gluing operation, either <math>N_1</math>~~ or ~~<math>N_2</math> is obtained by gluing that ball to the previously removed ball on their borders. This operation though simply gives a 3-sphere~~. ~~This means that one of the two factors <math>N_1</math> or <math>N_2</math> was in fact a (trivial) 3-sphere, and <math>M</math> is thus prime.~~

	~~=== From prime to irreducible ===~~
	~~Let <math>M</math> be a prime 3-manifold, and let <math>S</math> be a 2-sphere embedded in it. Cutting on <math>S</math> one may obtain just one manifold <math> N </math> or perhaps one~~ can only obtain two manifolds <math>M_1</math> and <math>M_2</math>. In the latter case, gluing balls onto the newly created spherical boundaries of these two manifolds gives two manifolds <math>N_1</math> and <math>N_2</math> such that
	:~~<math>M = N_1\#N_2. <~~/~~math>~~
	~~Since <math>M<~~/~~math> is prime, one of these two, say <math>N_1</math>, is <math>S^3</math>~~. ~~This means <math>M_1</math> is <math>S^3</math> minus a ball, and is therefore a ball itself~~. ~~The sphere <math>S<~~/~~math> is thus the border of a ball, and since we are looking at the case where only this possibility exists (two manifolds created) the manifold <math>M</math> is irreducible.~~

	~~It remains to consider the case where it is possible to cut <math>M</math> along <math>S</math> and obtain just one piece,~~ <~~math~~>N<~~/math~~>~~. In that case there exists a closed simple~~ [[curve]] <math>\gamma </math> in <math>M</math> intersecting <math>S</math> at a single point. Let <math> R </math> be the union of the two [[tubular neighborhood]]s of <math>S</math> and <math>\gamma </math>. The boundary <math>\partial R</math> turns out to be a 2-sphere that cuts <math>M</math> into two pieces, <math>R</~~math> and the complement of <math>R<~~/~~math>~~. ~~Since <math>M</math> is prime and <math>R</math> is not a ball, the complement must be a ball~~. ~~The manifold <math>M<~~/math> that results from this fact is almost determined, and a careful analysis shows that it is either <math>S^2\times S^1</math> or else the other, non-orientable, [[fiber bundle]] of <math>S^2</math> over <math>S^1</math>.

	~~== Bibliography ==~~
	* {{cite book\|author=[[William Jaco]]\|title= Lectures on 3-manifold topology \| isbn = ~~0-8218-1693-4}}~~

	~~== See also ==~~
	* [[3-manifold]]
	* [[Connected sum]]
	* [[Prime decomposition (3-manifold)]]

	~~[[Category:Manifolds]~~]

en>Kwamikagami: fmt using AWB

2014-02-02T06:48:48Z

fmt using AWB

← Older revision		Revision as of 08:48, 2 February 2014
Line 1:		Line 1:
			In [[topology]] a mathematical discipline, a '''prime manifold''' is an ''n''-[[manifold (topology)\|manifold]] that cannot be expressed as a non-trivial [[connected sum]] of two ''n''-manifolds. Non-trivial means that neither of the two is an [[n-sphere\|''n''-sphere]].
			A similar notion is that of an '''''irreducible''''' ''n''-manifold, which is one in which any embedded (''n'' − 1)-sphere bounds an embedded ''n''-[[ball (topology)\|ball]]. Implicit in this definition is the use of a suitable [[category theory\|category]], such as the category of [[differentiable manifold]]s or the category of [[piecewise-linear manifold]]s.

			The notions of irreducibility in algebra and manifold theory are related. An irreducible manifold is prime, although the converse does not hold. From an algebraist's perspective, prime manifolds should be called "irreducible"; however the topologist (in particular the 3-manifold topologist) finds the definition above more useful. The only compact, connected 3-manifolds that are prime but not irreducible are the trivial 2-sphere [[fiber bundle\|bundle]] over the circle S<sup>1</sup> and the twisted 2-sphere bundle over S<sup>1</sup>.

	~~It involves expertise and knowledge~~ of ~~various tools~~ and ~~technologies used for creating websites. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog~~, ~~splash page~~, ~~capture page or any other site you like. Should you go with simple HTML or use~~ a ~~platform like Wordpress~~. ~~Keep reading for some great Word~~ - ~~Press ideas you can start using today~~. ~~You can customize the appearance with PSD to Word~~ - ~~Press conversion~~ ''. <br><br>The ~~Internet~~ is a ~~vast open market where businesses and consumers congregate~~. ~~If you are~~ a ~~positive thinker businessman then today you~~ have ~~to put your business online~~. ~~Some plugins ask users to match pictures~~ or ~~add numbers~~, ~~and although effective~~, ~~they appear unprofessional and unnecessary~~. ~~Being able to help with your customers can make~~ a ~~change~~ in ~~how~~ a ~~great deal work, repeat online business, and referrals you'll~~ be ~~given~~. ~~Aided by the completely foolproof j~~ - ~~Query color selector~~, ~~you~~'~~re able to change the colors~~ of ~~factors of your theme~~ a the ~~click on~~ the ~~screen~~, with ~~very little previous web site design experience.~~ <br><br>It is ~~also popular because willing surrogates~~,~~as well as egg~~ and ~~sperm donors,~~are ~~plentiful~~. To sum up, ~~ensure that the tactics are aiming to increase the ranking~~ and ~~attracting~~ the ~~maximum intended traffic in the major search engines~~. ~~If Gandhi was empowered with~~ a ~~blogging system, every event~~ in ~~his life would have been minutely documented so~~ that ~~it could be recounted to~~ the ~~future generations. Every single Theme might be unique~~, ~~providing several alternatives for webpage owners~~ to ~~reap~~ the ~~benefits of in an effort to instantaneously adjust~~ their ~~web page appear~~. ~~Customization~~ of ~~web layout~~ is ~~easy due~~ to ~~the availability of huge selection of templates.~~ <br><br>~~There has been~~ a ~~huge increase~~ in the ~~number~~ of ~~developers releasing free premium Word - Press themes over the years~~. ~~For more information on [http:~~//~~www~~.~~bitmyurl~~.~~com~~/~~wordpressdropboxbackup19080 wordpress backup plugin] have~~ a ~~look~~ at the ~~website. High Quality Services: These companies help you in creating high quality Word - Press websites. However, you may not be able to find a theme that~~ is ~~in sync with your business~~. It ~~supports backup scheduling and allows you~~ to ~~either download~~ the ~~backup file or email~~ it to ~~you~~. ~~The Pakistani culture is~~ in ~~demand of~~ a ~~main surgical treatment~~. <br><br>~~Instead, you can easily just include it with our bodies integration field in e - Panel.~~ s ~~ability to use different themes~~ and ~~skins known as Word - Press Templates or Themes~~. The ~~days of spending~~ a ~~lot~~ of ~~time~~ and ~~money to have~~ a ~~website built are long gone~~. ~~Word - Press~~ is ~~an open source content management system which~~ is ~~easy to use and offers many user friendly features. You can check out~~ the ~~statistics~~ of ~~page of views for your web pages using free tools that are available~~ on ~~the internet.~~		According to [[Prime decomposition (3-manifold)\|a theorem]] of [[Hellmuth Kneser]] and [[John Milnor]], every [[compact space\|compact]], [[orientability\|orientable]] [[3-manifold]] is the [[connected sum]] of a unique ([[up to]] [[homeomorphism]]) collection of prime 3-manifolds.

			== Definitions ==
			Let us consider specifically [[3-manifold]]s.

			=== Irreducible manifold ===
			A 3-manifold is '''irreducible''' if any smooth sphere bounds a ball. More rigorously, a [[differentiable manifold\|differentiable]] [[connected space\|connected]] 3-manifold <math>M</math> is irreducible if every differentiable [[submanifold]] <math>S</math> [[homeomorphic]] to a [[n-sphere\|sphere]] bounds a subset <math>D</math> (that is, <math>S=\partial D </math>) which is homeomorphic to the closed [[ball (topology)\|ball]]
			:<math>D^3 = \{x\in\R^3\ \|\ \|x\|\leq 1\}. </math>
			The assumption of differentiability of <math>M</math> is not important, because every topological 3-manifold has a unique differentiable structure. The assumption that the sphere is ''smooth'' (that is, that it is a differentiable submanifold) is however important: indeed the sphere must have a [[tubular neighborhood]].

			A 3-manifold that is not irreducible is '''reducible'''.

			===Prime manifolds===
			A connected 3-manifold <math>M</math> is '''prime''' if it cannot be obtained as a [[connected sum]] <math>N_1\# N_2 </math> of two manifolds neither of which is the 3-sphere <math>S^3</math> (or, equivalently, neither of which is the homeomorphic to <math>M</math>).

			== Examples ==
			=== Euclidean space ===
			Three-dimensional [[Euclidean space]] <math> \R^3 </math> is irreducible: all smooth 2-spheres in it bound balls.

			On the other hand, [[Alexander's horned sphere]] is a non-smooth sphere in <math>\R^3</math> that does not bound a ball. Thus the stipulation that the sphere be smooth is necessary.

			=== Sphere, lens spaces ===
			The [[3-sphere]] <math>S^3</math> is irreducible. The [[product space]] <math>S^2\times S^1</math> is not irreducible, since any 2-sphere <math>S^2\times \{pt\} </math> (where 'pt' is some point of <math>S^1</math>) has a connected complement which is not a ball (it is the product of the 2-sphere and a line).

			A [[lens space]] <math>L(p,q) </math> with <math>p\neq 0 </math> (and thus not the same as <math>S^2\times S^1 </math>) is irreducible.

			== Prime manifolds and irreducible manifolds ==
			A 3-manifold is irreducible if and only if it is prime, except for two cases: the product <math>S^2\times S^1</math> and the [[non-orientable]] [[fiber bundle]] of the 2-sphere over the circle <math>S^1</math> are both prime but not irreducible.

			=== From irreducible to prime ===
			An irreducible manifold <math>M</math> is prime. Indeed, if we express <math>M</math> as a connected sum
			:<math>M=N_1\#N_2, </math>
			then <math>M</math> is obtained by removing a ball each from <math>N_1</math> and from <math>N_2</math>, and then gluing the two resulting 2-spheres together. These two (now united) 2-spheres form a 2-sphere in <math>M</math>. The fact that <math>M</math> is irreducible means that this 2-sphere must bound a ball. Undoing the gluing operation, either <math>N_1</math> or <math>N_2</math> is obtained by gluing that ball to the previously removed ball on their borders. This operation though simply gives a 3-sphere. This means that one of the two factors <math>N_1</math> or <math>N_2</math> was in fact a (trivial) 3-sphere, and <math>M</math> is thus prime.

			=== From prime to irreducible ===
			Let <math>M</math> be a prime 3-manifold, and let <math>S</math> be a 2-sphere embedded in it. Cutting on <math>S</math> one may obtain just one manifold <math> N </math> or perhaps one can only obtain two manifolds <math>M_1</math> and <math>M_2</math>. In the latter case, gluing balls onto the newly created spherical boundaries of these two manifolds gives two manifolds <math>N_1</math> and <math>N_2</math> such that
			:<math>M = N_1\#N_2. </math>
			Since <math>M</math> is prime, one of these two, say <math>N_1</math>, is <math>S^3</math>. This means <math>M_1</math> is <math>S^3</math> minus a ball, and is therefore a ball itself. The sphere <math>S</math> is thus the border of a ball, and since we are looking at the case where only this possibility exists (two manifolds created) the manifold <math>M</math> is irreducible.

			It remains to consider the case where it is possible to cut <math>M</math> along <math>S</math> and obtain just one piece, <math>N</math>. In that case there exists a closed simple [[curve]] <math>\gamma </math> in <math>M</math> intersecting <math>S</math> at a single point. Let <math> R </math> be the union of the two [[tubular neighborhood]]s of <math>S</math> and <math>\gamma </math>. The boundary <math>\partial R</math> turns out to be a 2-sphere that cuts <math>M</math> into two pieces, <math>R</math> and the complement of <math>R</math>. Since <math>M</math> is prime and <math>R</math> is not a ball, the complement must be a ball. The manifold <math>M</math> that results from this fact is almost determined, and a careful analysis shows that it is either <math>S^2\times S^1</math> or else the other, non-orientable, [[fiber bundle]] of <math>S^2</math> over <math>S^1</math>.

			== Bibliography ==
			* {{cite book\|author=[[William Jaco]]\|title= Lectures on 3-manifold topology \| isbn = 0-8218-1693-4}}

			== See also ==
			* [[3-manifold]]
			* [[Connected sum]]
			* [[Prime decomposition (3-manifold)]]

			[[Category:Manifolds]]

en>Bibcode Bot: Adding 1 arxiv eprint(s), 0 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2012-08-21T01:31:44Z

Adding 1 arxiv eprint(s), 0 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

New page

It involves expertise and knowledge of various tools and technologies used for creating websites. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. Should you go with simple HTML or use a platform like Wordpress. Keep reading for some great Word - Press ideas you can start using today. You can customize the appearance with PSD to Word - Press conversion ''. The Internet is a vast open market where businesses and consumers congregate. If you are a positive thinker businessman then today you have to put your business online. Some plugins ask users to match pictures or add numbers, and although effective, they appear unprofessional and unnecessary. Being able to help with your customers can make a change in how a great deal work, repeat online business, and referrals you'll be given. Aided by the completely foolproof j - Query color selector, you're able to change the colors of factors of your theme a the click on the screen, with very little previous web site design experience. It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. If Gandhi was empowered with a blogging system, every event in his life would have been minutely documented so that it could be recounted to the future generations. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. Customization of web layout is easy due to the availability of huge selection of templates. There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. For more information on [http://www.bitmyurl.com/wordpressdropboxbackup19080 wordpress backup plugin] have a look at the website. High Quality Services: These companies help you in creating high quality Word - Press websites. However, you may not be able to find a theme that is in sync with your business. It supports backup scheduling and allows you to either download the backup file or email it to you. The Pakistani culture is in demand of a main surgical treatment. Instead, you can easily just include it with our bodies integration field in e - Panel. s ability to use different themes and skins known as Word - Press Templates or Themes. The days of spending a lot of time and money to have a website built are long gone. Word - Press is an open source content management system which is easy to use and offers many user friendly features. You can check out the statistics of page of views for your web pages using free tools that are available on the internet.