Angular momentum operator - Revision history

50.148.202.105: /* Derivation using ladder operators */

2015-01-11T05:29:54Z

Derivation using ladder operators

← Older revision		Revision as of 07:29, 11 January 2015
Line 1:		Line 1:
	~~Hi there. Let me start by introducing~~ the ~~writer, her name is Myrtle Cleary. California is where her home~~ is but ~~she needs to move because of her family members~~. ~~Body building~~ is 1 of the things I adore most. Hiring is her ~~working~~ day occupation now but she's usually ~~needed~~ her own company.<br><br>~~Here is my web site :: over the counter std test (~~[http://~~citymama~~.com~~.ua~~/~~profile_info.php?ID=38588 go right here~~])		The title of the author is Figures but it's not the most masucline title out there. To gather coins is 1 of the things I adore most. Hiring is her day occupation now but she's usually wanted her own company. For a whilst I've been in South Dakota and my mothers and fathers reside nearby.<br><br>My blog post ... [http://torontocartridge.com/uncategorized/the-ideal-way-to-battle-a-yeast-infection/ home std test kit]

en>Bulbul99: The theorem explains, but not causes, QM behavior.

2014-02-21T18:05:24Z

The theorem explains, but not causes, QM behavior.

← Older revision		Revision as of 20:05, 21 February 2014
Line 1:		Line 1:
	~~{{about\|the formalism for [[ubiquitous computing]]\|graphs whose edges alternate between two kinds of vertices\|Bipartite graph}}~~		Hi there. Let me start by introducing the writer, her name is Myrtle Cleary. California is where her home is but she needs to move because of her family members. Body building is 1 of the things I adore most. Hiring is her working day occupation now but she's usually needed her own company.<br><br>Here is my web site :: over the counter std test ([http://citymama.com.ua/profile_info.php?ID=38588 go right here])
	~~__NOTOC__~~

	~~A '''bigraph''' (often used in the plural '''bigraphs''') can be modelled as the superposition of a [[Graph (mathematics)\|graph]] (~~the ''link graph'') and a set of [[Tree (mathematics)\|trees]] (the ''place graph'').<ref name="intro">''[http://www.itu.dk/research/pls/wiki/index.php/A_Brief_Introduction_To_Bigraphs A Brief Introduction To Bigraphs]'', [[IT University of Copenhagen]], ~~Denmark.</ref><ref~~ name~~="milner">Milner, Robin. ''[http://www.cl.cam.ac.uk/archive/rm135/uam-theme.html The Bigraphical Model]'', [[University of Cambridge Computer Laboratory]], UK.</ref>~~

	~~Each [[Node (mathematics)\|node]] of the bigraph~~ is ~~part of a graph and also part of some tree that describes how the nodes are nested~~. Bigraphs can be conveniently and formally displayed as [[diagram]]s.<ref name="intro" /> They have applications in the modelling of distributed systems for [[ubiquitous computing]] and can be used to describe [[Mobile agent\|mobile]] interactions. They have also been used by [[Robin Milner]] in an attempt to subsume [[Calculus of Communicating Systems]] (CCS) and [[Pi calculus\|π-calculus]].<ref name="milner" /> They have been studied in the context of [[category theory]].<ref>{{cite journal
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphs and Their Algebra~~
	~~\|journal=[[Electronic Notes in Theoretical Computer Science]]~~
	~~\|volume=209~~
	~~\|pages=5–19~~
	~~\|year=2008~~
	~~\|note=Proceedings of the LIX Colloquium on Emerging Trends in Concurrency Theory (LIX 2006)~~
	~~\|doi=10.1016/j.entcs.2008.04.002}}</ref>~~

	~~==Anatomy of a bigraph==~~

	Aside from nodes and (hyper-)edges, a bigraph may have associated with it one or more ''regions'' which are roots in the place forest, and zero or more ''holes'' in the place graph, into which other bigraph regions may be inserted. Similarly, to nodes we may assign ''controls'' that define identities and an arity (the number of ''ports'' for a given node to which link-graph edges may connect). These controls are drawn from a bigraph ''signature''. In the link graph we define ''inner'' and ''outer'' names, which define the connection points at which coincident names may be fused to form a single link.

	~~==Foundations==~~

	~~A bigraph~~ is ~~a 5-tuple:~~

	~~<math>(V,E,ctrl,prnt,link) : \langle k,X \rangle \to \langle m,Y \rangle,</math>~~

	where ~~<math>V</math> is a set of nodes, <math>E</math> is a set of edges, <math>ctrl</math>~~ is ~~the ''control map'' that assigns controls~~ to ~~nodes, <math>prnt</math> is the ''parent map'' that defines the nesting~~ of ~~nodes, and <math>link</math>~~ is ~~the ''link map'' that defines the link structure.~~

	The notation <math>\langle k,X \rangle \to \langle m,Y \rangle</math> indicates that the bigraph has <math>k</math> ''holes'' (sites) and a set of inner names <math>X</math> and <math>m</math> ''regions'', with a set of ''outer names'' <math>Y</math>. These are respectively known as the ''inner'' and ''outer'' interfaces of the ~~bigraph~~.

	~~Formally speaking, each bigraph~~ is ~~an arrow in a symmetric partial [[monoidal category]] (~~usually ~~abbreviated ''spm-category'') in which the objects are these interfaces~~.<~~ref~~>~~{{cite conference~~
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphical Categories~~
	~~\|series=[[Lecture Notes in Computer Science]]~~
	~~\|volume=5710~~
	~~\|pages=30–36~~
	~~\|year=2009~~
	~~\|booktitle=CONCUR 2009 - ''Concurrency Theory''~~
	~~\|publisher=Springer-Verlag~~
	~~\|doi=10.1007/978-3-642-04081-8_3}}~~<~~/ref~~> ~~As a result, the composition of bigraphs~~ is ~~definable in terms of the composition of arrows in~~ the ~~category.~~

	~~==See also==~~
	* [[Bisimulation]]
	* [[Combinatorial species]]

	~~==Bibliography==~~
	* {{cite book
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=The Space and Motion of Communicating Agents~~
	~~\|publisher=[[Cambridge University Press]]~~
	~~\|year=2009~~
	~~\|isbn=0521738334~~
	~~\|note=(200 pages)}}~~
	* {{cite conference
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphical reactive systems, (invited paper)~~
	~~\|booktitle=CONCUR 2001 – Concurrency Theory, Proc. 12th International Conference~~
	~~\|volume=2154~~
	~~\|series=[[Lecture Notes in Computer Science]]~~
	~~\|publisher=[[Springer-Verlag]]~~
	~~\|year=2001~~
	~~\|pages=16–35~~
	~~\|doi=10.1007/3-540-44685-0_2}}~~
	* {{cite conference
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphs as a Model for Mobile Interaction~~ (~~invited paper)~~
	~~\|booktitle=ICGT 2002: First International Conference on Graph Transformation~~
	~~\|series=[[Lecture Notes in Computer Science]]~~
	~~\|publisher=Springer-Verlag~~
	~~\|volume=2505~~
	~~\|year=2002~~
	~~\|pages=8–13~~
	~~\|doi=10.1007/3-540-45832-8_3~~
	}}
	* {{cite book
	~~\|first1=Søren~~
	~~\|last1=Debois~~
	~~\|first2=Troels Christoffer~~
	~~\|last2=Damgaard~~
	~~\|chapter=Bigraphs by Example~~
	~~\|id={{citeseerx\|10.1.1.73.176}}~~
	~~\|title=IT University Technical Report Series TR-2005-61~~
	~~\|publisher=[[IT University of Copenhagen]]~~
	~~\|location=Denmark~~
	~~\|year=2005~~
	~~\|isbn=87-7949-090-5}}~~

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

	~~==External links==~~
	* [http://~~www~~.~~itu~~.dk/~~~mikkelbu/research/bigraphsbib/ Bibliography on Bigraphs]~~

	~~[[Category:Formal methods]]~~
	~~[[Category:Theoretical computer science]~~]

en>Sbyrnes321: some edits for clarity

2014-01-30T14:40:29Z

some edits for clarity

← Older revision		Revision as of 16:40, 30 January 2014
Line 1:		Line 1:
	~~Andrew Berryhill is what his wife~~ [http://www.~~herandkingscounty~~.~~com~~/~~content~~/~~information-and-facts-you-must-know-about-hobbies love psychic readings~~] ~~loves to contact him and he totally digs that~~ name. ~~For years she~~'~~s been residing in Kentucky but her spouse desires them to transfer. To climb is something she~~ [http://www.~~khuplaza~~.~~com~~/~~dent~~/~~14869889 free psychic~~] ~~would by no means give up~~. ~~Invoicing~~ is ~~what I do~~ for ~~a residing but I've usually wanted my own business~~.<br><br>~~Feel free~~ to ~~visit my homepage~~ - ~~best psychics~~ - ~~[http~~://~~Myoceancounty~~.~~net~~/~~groups~~/~~apply~~-these-~~guidelines~~-~~when~~-~~gardening~~-and-~~grow~~/ ~~view~~] -		{{about\|the formalism for [[ubiquitous computing]]\|graphs whose edges alternate between two kinds of vertices\|Bipartite graph}}
			__NOTOC__

			A '''bigraph''' (often used in the plural '''bigraphs''') can be modelled as the superposition of a [[Graph (mathematics)\|graph]] (the ''link graph'') and a set of [[Tree (mathematics)\|trees]] (the ''place graph'').<ref name="intro">''[http://www.itu.dk/research/pls/wiki/index.php/A_Brief_Introduction_To_Bigraphs A Brief Introduction To Bigraphs]'', [[IT University of Copenhagen]], Denmark.</ref><ref name="milner">Milner, Robin. ''[http://www.cl.cam.ac.uk/archive/rm135/uam-theme.html The Bigraphical Model]'', [[University of Cambridge Computer Laboratory]], UK.</ref>

			Each [[Node (mathematics)\|node]] of the bigraph is part of a graph and also part of some tree that describes how the nodes are nested. Bigraphs can be conveniently and formally displayed as [[diagram]]s.<ref name="intro" /> They have applications in the modelling of distributed systems for [[ubiquitous computing]] and can be used to describe [[Mobile agent\|mobile]] interactions. They have also been used by [[Robin Milner]] in an attempt to subsume [[Calculus of Communicating Systems]] (CCS) and [[Pi calculus\|π-calculus]].<ref name="milner" /> They have been studied in the context of [[category theory]].<ref>{{cite journal
			\|first=Robin
			\|last=Milner
			\|title=Bigraphs and Their Algebra
			\|journal=[[Electronic Notes in Theoretical Computer Science]]
			\|volume=209
			\|pages=5–19
			\|year=2008
			\|note=Proceedings of the LIX Colloquium on Emerging Trends in Concurrency Theory (LIX 2006)
			\|doi=10.1016/j.entcs.2008.04.002}}</ref>

			==Anatomy of a bigraph==

			Aside from nodes and (hyper-)edges, a bigraph may have associated with it one or more ''regions'' which are roots in the place forest, and zero or more ''holes'' in the place graph, into which other bigraph regions may be inserted. Similarly, to nodes we may assign ''controls'' that define identities and an arity (the number of ''ports'' for a given node to which link-graph edges may connect). These controls are drawn from a bigraph ''signature''. In the link graph we define ''inner'' and ''outer'' names, which define the connection points at which coincident names may be fused to form a single link.

			==Foundations==

			A bigraph is a 5-tuple:

			<math>(V,E,ctrl,prnt,link) : \langle k,X \rangle \to \langle m,Y \rangle,</math>

			where <math>V</math> is a set of nodes, <math>E</math> is a set of edges, <math>ctrl</math> is the ''control map'' that assigns controls to nodes, <math>prnt</math> is the ''parent map'' that defines the nesting of nodes, and <math>link</math> is the ''link map'' that defines the link structure.

			The notation <math>\langle k,X \rangle \to \langle m,Y \rangle</math> indicates that the bigraph has <math>k</math> ''holes'' (sites) and a set of inner names <math>X</math> and <math>m</math> ''regions'', with a set of ''outer names'' <math>Y</math>. These are respectively known as the ''inner'' and ''outer'' interfaces of the bigraph.

			Formally speaking, each bigraph is an arrow in a symmetric partial [[monoidal category]] (usually abbreviated ''spm-category'') in which the objects are these interfaces.<ref>{{cite conference
			\|first=Robin
			\|last=Milner
			\|title=Bigraphical Categories
			\|series=[[Lecture Notes in Computer Science]]
			\|volume=5710
			\|pages=30–36
			\|year=2009
			\|booktitle=CONCUR 2009 - ''Concurrency Theory''
			\|publisher=Springer-Verlag
			\|doi=10.1007/978-3-642-04081-8_3}}</ref> As a result, the composition of bigraphs is definable in terms of the composition of arrows in the category.

			==See also==
			* [[Bisimulation]]
			* [[Combinatorial species]]

			==Bibliography==
			* {{cite book
			\|first=Robin
			\|last=Milner
			\|title=The Space and Motion of Communicating Agents
			\|publisher=[[Cambridge University Press]]
			\|year=2009
			\|isbn=0521738334
			\|note=(200 pages)}}
			* {{cite conference
			\|first=Robin
			\|last=Milner
			\|title=Bigraphical reactive systems, (invited paper)
			\|booktitle=CONCUR 2001 – Concurrency Theory, Proc. 12th International Conference
			\|volume=2154
			\|series=[[Lecture Notes in Computer Science]]
			\|publisher=[[Springer-Verlag]]
			\|year=2001
			\|pages=16–35
			\|doi=10.1007/3-540-44685-0_2}}
			* {{cite conference
			\|first=Robin
			\|last=Milner
			\|title=Bigraphs as a Model for Mobile Interaction (invited paper)
			\|booktitle=ICGT 2002: First International Conference on Graph Transformation
			\|series=[[Lecture Notes in Computer Science]]
			\|publisher=Springer-Verlag
			\|volume=2505
			\|year=2002
			\|pages=8–13
			\|doi=10.1007/3-540-45832-8_3
			}}
			* {{cite book
			\|first1=Søren
			\|last1=Debois
			\|first2=Troels Christoffer
			\|last2=Damgaard
			\|chapter=Bigraphs by Example
			\|id={{citeseerx\|10.1.1.73.176}}
			\|title=IT University Technical Report Series TR-2005-61
			\|publisher=[[IT University of Copenhagen]]
			\|location=Denmark
			\|year=2005
			\|isbn=87-7949-090-5}}

			==References==
			{{reflist}}

			==External links==
			* [http://www.itu.dk/~mikkelbu/research/bigraphsbib/ Bibliography on Bigraphs]

			[[Category:Formal methods]]
			[[Category:Theoretical computer science]]

en>Xqbot: r2.7.3) (Robot: Adding fr:Moment cinétique (mécanique quantique)

2012-07-30T17:29:21Z

r2.7.3) (Robot: Adding fr:Moment cinétique (mécanique quantique)

New page

Andrew Berryhill is what his wife [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies love psychic readings] loves to contact him and he totally digs that name. For years she's been residing in Kentucky but her spouse desires them to transfer. To climb is something she [http://www.khuplaza.com/dent/14869889 free psychic] would by no means give up. Invoicing is what I do for a residing but I've usually wanted my own business.<br><br>Feel free to visit my homepage - best psychics - [http://Myoceancounty.net/groups/apply-these-guidelines-when-gardening-and-grow/ view] -

← Older revision		Revision as of 20:05, 21 February 2014
Line 1:		Line 1:
	~~{{about\|the formalism for [[ubiquitous computing]]\|graphs whose edges alternate between two kinds of vertices\|Bipartite graph}}~~		Hi there. Let me start by introducing the writer, her name is Myrtle Cleary. California is where her home is but she needs to move because of her family members. Body building is 1 of the things I adore most. Hiring is her working day occupation now but she's usually needed her own company.<br><br>Here is my web site :: over the counter std test ([http://citymama.com.ua/profile_info.php?ID=38588 go right here])
	~~__NOTOC__~~

	~~A '''bigraph''' (often used in the plural '''bigraphs''') can be modelled as the superposition of a [[Graph (mathematics)\|graph]] (~~the ''link graph'') and a set of [[Tree (mathematics)\|trees]] (the ''place graph'').<ref name="intro">''[http://www.itu.dk/research/pls/wiki/index.php/A_Brief_Introduction_To_Bigraphs A Brief Introduction To Bigraphs]'', [[IT University of Copenhagen]], ~~Denmark.</ref><ref~~ name~~="milner">Milner, Robin. ''[http://www.cl.cam.ac.uk/archive/rm135/uam-theme.html The Bigraphical Model]'', [[University of Cambridge Computer Laboratory]], UK.</ref>~~

	~~Each [[Node (mathematics)\|node]] of the bigraph~~ is ~~part of a graph and also part of some tree that describes how the nodes are nested~~. Bigraphs can be conveniently and formally displayed as [[diagram]]s.<ref name="intro" /> They have applications in the modelling of distributed systems for [[ubiquitous computing]] and can be used to describe [[Mobile agent\|mobile]] interactions. They have also been used by [[Robin Milner]] in an attempt to subsume [[Calculus of Communicating Systems]] (CCS) and [[Pi calculus\|π-calculus]].<ref name="milner" /> They have been studied in the context of [[category theory]].<ref>{{cite journal
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphs and Their Algebra~~
	~~\|journal=[[Electronic Notes in Theoretical Computer Science]]~~
	~~\|volume=209~~
	~~\|pages=5–19~~
	~~\|year=2008~~
	~~\|note=Proceedings of the LIX Colloquium on Emerging Trends in Concurrency Theory (LIX 2006)~~
	~~\|doi=10.1016/j.entcs.2008.04.002}}</ref>~~

	~~==Anatomy of a bigraph==~~

	Aside from nodes and (hyper-)edges, a bigraph may have associated with it one or more ''regions'' which are roots in the place forest, and zero or more ''holes'' in the place graph, into which other bigraph regions may be inserted. Similarly, to nodes we may assign ''controls'' that define identities and an arity (the number of ''ports'' for a given node to which link-graph edges may connect). These controls are drawn from a bigraph ''signature''. In the link graph we define ''inner'' and ''outer'' names, which define the connection points at which coincident names may be fused to form a single link.

	~~==Foundations==~~

	~~A bigraph~~ is ~~a 5-tuple:~~

	~~<math>(V,E,ctrl,prnt,link) : \langle k,X \rangle \to \langle m,Y \rangle,</math>~~

	where ~~<math>V</math> is a set of nodes, <math>E</math> is a set of edges, <math>ctrl</math>~~ is ~~the ''control map'' that assigns controls~~ to ~~nodes, <math>prnt</math> is the ''parent map'' that defines the nesting~~ of ~~nodes, and <math>link</math>~~ is ~~the ''link map'' that defines the link structure.~~

	The notation <math>\langle k,X \rangle \to \langle m,Y \rangle</math> indicates that the bigraph has <math>k</math> ''holes'' (sites) and a set of inner names <math>X</math> and <math>m</math> ''regions'', with a set of ''outer names'' <math>Y</math>. These are respectively known as the ''inner'' and ''outer'' interfaces of the ~~bigraph~~.

	~~Formally speaking, each bigraph~~ is ~~an arrow in a symmetric partial [[monoidal category]] (~~usually ~~abbreviated ''spm-category'') in which the objects are these interfaces~~.<~~ref~~>~~{{cite conference~~
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphical Categories~~
	~~\|series=[[Lecture Notes in Computer Science]]~~
	~~\|volume=5710~~
	~~\|pages=30–36~~
	~~\|year=2009~~
	~~\|booktitle=CONCUR 2009 - ''Concurrency Theory''~~
	~~\|publisher=Springer-Verlag~~
	~~\|doi=10.1007/978-3-642-04081-8_3}}~~<~~/ref~~> ~~As a result, the composition of bigraphs~~ is ~~definable in terms of the composition of arrows in~~ the ~~category.~~

	~~==See also==~~
	* [[Bisimulation]]
	* [[Combinatorial species]]

	~~==Bibliography==~~
	* {{cite book
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=The Space and Motion of Communicating Agents~~
	~~\|publisher=[[Cambridge University Press]]~~
	~~\|year=2009~~
	~~\|isbn=0521738334~~
	~~\|note=(200 pages)}}~~
	* {{cite conference
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphical reactive systems, (invited paper)~~
	~~\|booktitle=CONCUR 2001 – Concurrency Theory, Proc. 12th International Conference~~
	~~\|volume=2154~~
	~~\|series=[[Lecture Notes in Computer Science]]~~
	~~\|publisher=[[Springer-Verlag]]~~
	~~\|year=2001~~
	~~\|pages=16–35~~
	~~\|doi=10.1007/3-540-44685-0_2}}~~
	* {{cite conference
	~~\|first=Robin~~
	~~\|last=Milner~~
	~~\|title=Bigraphs as a Model for Mobile Interaction~~ (~~invited paper)~~
	~~\|booktitle=ICGT 2002: First International Conference on Graph Transformation~~
	~~\|series=[[Lecture Notes in Computer Science]]~~
	~~\|publisher=Springer-Verlag~~
	~~\|volume=2505~~
	~~\|year=2002~~
	~~\|pages=8–13~~
	~~\|doi=10.1007/3-540-45832-8_3~~
	}}
	* {{cite book
	~~\|first1=Søren~~
	~~\|last1=Debois~~
	~~\|first2=Troels Christoffer~~
	~~\|last2=Damgaard~~
	~~\|chapter=Bigraphs by Example~~
	~~\|id={{citeseerx\|10.1.1.73.176}}~~
	~~\|title=IT University Technical Report Series TR-2005-61~~
	~~\|publisher=[[IT University of Copenhagen]]~~
	~~\|location=Denmark~~
	~~\|year=2005~~
	~~\|isbn=87-7949-090-5}}~~

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

	~~==External links==~~
	* [http://~~www~~.~~itu~~.dk/~~~mikkelbu/research/bigraphsbib/ Bibliography on Bigraphs]~~

	~~[[Category:Formal methods]]~~
	~~[[Category:Theoretical computer science]~~]