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	Disjoint union - Wikipedia, the free encyclopedia
		In set theory, a disjoint union (or discriminated union) is a union of a collection of sets whose members are pairwise disjoint.
		This notation is meant to be suggestive of the fact that the cardinality of the disjoint union is the sum of the cardinalities of the terms in the family.
		In the language of category theory, the disjoint union is the coproduct in the category of sets.
	en.wikipedia.org /wiki/Disjoint_union (339 words)

	PlanetMath: disjoint union (Site not responding. Last check: 2007-11-07)
		This is also often called being pairwise disjoint and is a much stronger condition than that the intersection of all the images is empty.
		Of course, there are many categories where this usage is unnatural: In the category of pointed sets, the coproduct will be the disjoint union with the distinguished points identified.
		This is version 4 of disjoint union, born on 2004-03-01, modified 2004-03-23.
	planetmath.org /encyclopedia/DisjointUnion.html (214 words)

	Disjoint sets - Wikipedia, the free encyclopedia
		In mathematics, two sets are said to be disjoint if they have no element in common.
		Formally, two sets A and B are disjoint if their intersection is the empty set, i.e.
		A collection of sets is pairwise disjoint or mutually disjoint if any two distinct sets in the collection are disjoint.
	en.wikipedia.org /wiki/Disjoint (204 words)

	Class notes CS251B -- Winter 1997
		Disjoint sets structures are yet another new abstract data type (A.D.T.) for which we must now define a mathematical model and a series of related operations.
		Disjoint sets, sometimes called partitions, are the model of this A.D.T. A partition is a collection of disjoint sets such that the union of the sets is the entire space.
		A disjoint set forest consists of a collection of parent pointer trees taken together representing a collection of sets, a partition.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic24 (1992 words)

	Disjoint Flows
		We evaluate this by varying the number of nodes in the network from 2 to 30 and introducing a flow between disjoint pairs of nodes -- the number of flows varies from 1 to 15.
		Figure 9: Disjoint Flows: The throughput of each flow on increasing the number of flows.
		These random choices do not lead to a perfectly balanced allocation, and therefore there is still unused spectrum even when there are 13 flows in the system, as shown by the continuing positive slope of the curve in Figure 9.
	www.cs.cornell.edu /people/ranveer/multinet/ssch/Disjoint_Flows.html (301 words)

	The Disjoint Sum
		Given two sets, A and B, we define their disjoint sum, A+B, to be the collection of symbols of form (a,) with a in A or of form (,b) with b in B. If A and B are ordered, we can extend their orders to A+B by deeming every (a,) to come before every (,b).
		Given two functions (Af:C) and (Bg:D), we define their disjoint sum, f+g, to be (A+Bf+g:C+D) mapping any (a,) to (f(a),) and any (,b) to (,g(b)).
		It should be noted that the standard embeddings of A and B in A+B compose with this to yield f and g as appropriate: in this sense, A+B is a minimal set via embeddings of A and B in which one may factorise any pair of functions, as above.
	www.chaos.org.uk /~eddy/math/disjoint.html (603 words)

	Approximation Algorithms for Disjoint Paths Problems - Kleinberg (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible.
		Disjoint paths on a surface (context) - Robertson, Seymour - 1988
		2 Disjoint paths in a planar graph --- a general theorem (context) - Ding, Schrijver et al.
	citeseer.ist.psu.edu /kleinberg96approximation.html (1647 words)

	Boost Disjoint Sets (Site not responding. Last check: 2007-11-07)
		This is class that provides disjoint sets operations with union by rank and path compression.
		This rearranges the representatives such that the representative of each set is the element with the smallest ID.
		Precondition: the disjoint sets structure must be compressed.
	www.boost.org /libs/disjoint_sets/disjoint_sets.html (450 words)

	ASPN : Python Cookbook : Grouping objects into disjoint sets (Site not responding. Last check: 2007-11-07)
		This recipe provides a lightweight way to group arbitrary objects together into disjoint sets when a full-blown graph data structure would be overkill.
		Objects can be joined using.join(), tested for connectedness using.joined(), and all disjoint sets can be retreived using.get().
		I've used this class to group vector objects on page images, and group sets of webpages by their links, but there are many other conceivable applications.
	aspn.activestate.com /ASPN/Cookbook/Python/Recipe/387776 (455 words)

	The Disjoint-paths Problem
		In this case, it is especially desirable to establish more than one disjoint path between each pair of vertices.
		Multiple disjoint paths can increase the effective bandwidth between pairs of nodes, reduce congestion in the network and increase the probability of receiving the information.
		Furthermore, the most efficient way of transmitting information consisting of a high volume of data (e.g., multimedia applications) is achieved by maintaining, during the whole duration of the connection, disjoint paths of exclusive dedication.
	tracer.lcc.uma.es /problems/DisjPaths/disjpaths.html (382 words)

	Disjoint Paths in Densely Embedded Graphs - Kleinberg, Tardos (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		We are given a large network, and pairs of nodes that wish to communicate over paths through the network --- the goal is to simultaneously connect as many of these pairs as possible in such a way that no two communication paths share an edge in the network.
		35 Approximations for the disjoint paths problem in high-diamet..
		9 Disjoint circuits of prescribed homotopies in a graph on a c..
	citeseer.ist.psu.edu /kleinberg95disjoint.html (665 words)

	Fireworks disjoint rollover
		It is impossible to use hotspots for links on disjoint rollovers without them being active across all frames.
		Frame 2 contains the second state of the buttons, the second state of the disjoint rollover, plus an arrow to which we'll add a hotspot.
		Frame 3 contains the third state of the disjoint rollover, plus an arrow to which we'll attach a hotspot.
	www.playingwithfire.com /tool_tips/rollem.html (328 words)

	Disjoint Union (Site not responding. Last check: 2007-11-07)
		The disjoint union operation is used to form a new domain from two existing domains.
		The disjoint union of Id and Article contains pairs of values, the second item in each pair is a "1" if the first item came from Id and a "2" if the first item came from article.
		These are in fact some of the domains of the language L1 which we are using to illustrate some of this course.
	scom.hud.ac.uk /scomtlm/cas810/notes/djoin.html (378 words)

	PhilSci Archive - Asymptotically disjoint quantum states
		A nonpure quantum state can be interpreted as a classical mixture if and only if its components are disjoint.
		Here, two pure quantum states are called disjoint if there exists an element of the center of the algebra of observables such that its expectation values with respect to these states are different.
		Such asymptotically disjoint quantum states lead to regular decision problems while exactly disjoint states evoke singular problems which engineers reject as improperly posed.
	philsci-archive.pitt.edu /archive/00000949 (163 words)

	K-th Shortest Path Problem
		So, if we are interested to know which is each one of the k-th shortest disjoint paths, we have to construct a new network, whose set of arcs is the set of arcs for which the flow is one.
		The algorithm is exemplified with the network on the left, where the initial node (s) is 1, the terminal node (t) is 4 and the number close to each arc represents its cost (or distance...).
		Note that the shortest path in the original network - {1, (1,2), 2, (2,3), 3, (3,4), 4} - is not one of the two shortest disjoint paths.
	www.mat.uc.pt /~eqvm/OPP/KSPP/KSPP.html (853 words)

	The CIDOC CRM (Site not responding. Last check: 2007-11-07)
		In the sequence, disjointness declarations are required whereever applicable.
		In Monterey a proposal was accepted to declare all disjoint classes in order to aid comprehnsion of the CRM (See issue 66), and Martin has now produced a draft list of disjoint class declarations.
		Even though Persitent Items (or endurants) have a limited existence in time, because they may be destroyed, lost or forgotten, we regard them as disjoint from Temporal Enties, as their persistent identity allows to relate Temporal Entities in which they participate.
	zeus.ics.forth.gr /cidoc/issues.php?id=92 (1217 words)

	DISJOINT (Site not responding. Last check: 2007-11-07)
		In a disjoint representation of a multi-valued function every minterm is covered only one.
		The main advantages of this method over the existing ones is drastically reduced memory requirement and the posibility of the fast computation of spectra for functions which can be represented by relatively few disjoint terms.
		Disjoint program accepts the standard truth table format for input, and the output is also in the truth table format.
	www.ee.pdx.edu /polo/DIADES/docs/disjoint.html (199 words)

	[No title]
		for type(L, Disjoint) read: the classes in L are pairwise disjoint.
		for disjointUnionOf(X, Y) read: X is the disjoint union of the classes in the list Y: (a) for any c1 and c2 in Y, disjointWith(c1, c2), and (b) i.e.
		(Range disjointUnionOf Disjoint) %% A class that is the disjoint union of a list of pairwise disjoint classes is the union of that list.
	www-ksl.stanford.edu /people/dlm/DAML-Ont-kif-axioms-001107.doc (2866 words)

	Graphs with (Edge) Disjoint Links in Every Spatial Embedding (Site not responding. Last check: 2007-11-07)
		In an attempt to find an analog of this theorem for the vertex disjoint linking property, we found different types of graphs that contain non-splittable links that share no vertices and no edges in every spatial embedding.
		A graph is said to have the vertex disjoint linking property if, in every spatial embedding, there exists a pair of non-splittable links that share no vertices.
		Some examples of graphs that have this property are disjoint copies of Petersen graphs, expansions of disjoint copies of Petersen graphs, and a finite set of graphs that we have found with this property that do not contain at least two disjoint copies of Petersen graphs.
	www.clarkson.edu /dor/sure/Sure2000/lalonde.htm (758 words)

	Sonic Garden :: Disjoint
		Disjoint: to separate; Referring to the idea that in the beginning of time there was a great mass of energy which most people would call God.
		It disjointed tiny fractions of itself and scattered them throughout all planes of existence, binding them in life until death, when they will then return back to the great mass of energy.
		So, he bought a bass because of his love for music and to be a part of Disjoint.
	www.sonicgarden.com /sonic-web/artist.cfm?artistid=16032 (653 words)

	disjoint union - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "disjoint union" is defined.
		Disjoint Union : Eric Weisstein's World of Mathematics [home, info]
		disjoint union : FOLDOP - Free On Line Dictionary Of Philosophy [home, info]
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=disjoint+union (104 words)

	Dreamweaver disjoint rollovers
		How do I turn them into disjoint rollovers in Dreamweaver?" --G.L. Go ahead and mouse over the buttons on the left to see how the rollovers function.
		NOTE: for the image swaps to function properly, it is necessary for each pair of button state images and each pair of disjoint rollover state images to have the same dimensions.
		Without clicking O.K., which would close the dialog box, scroll to the unique name of the image that represents the normal state of your disjoint rollover and highlight it.
	www.playingwithfire.com /tool_tips/disjoint.html (347 words)

	Solving the Shortest Edge Disjoint or Capacited Undirected Paths Problems (Site not responding. Last check: 2007-11-07)
		The edge disjoint paths problem is, given an undirected graph G=(V,A) and K pairs of vertices of G, to decide if there are K mutually edge disjoint paths of G linking the pairs.
		Let us consider lengths associated with each edge of A. The problem of finding K edge disjoint paths with a minimum total length is at least as difficult as the edge disjoint paths problem so it is a NP-hard problem.
		Now let us add capacities uij imposed on any edge [i,j] of A. The shortest capacited paths problem (SCPP) is to find K paths linking K given pairs of vertices of G with a minimum total length and such as an edge [i,j] of A belongs to no more than uij paths.
	rosowww.epfl.ch /ismp97/ismp_abs_552.html (324 words)

	dBforums - disjoint reports
		not have to be fixed on a specific column or row but can be disjoint.
		A disjoint report allows dimension members and measures to be placed in any
		The advantage of using disjoint reports over the tradition pivot table is
	www.dbforums.com /showthread.php?t=779249 (172 words)

	Finite groups in MAPLE5 (Site not responding. Last check: 2007-11-07)
		the permutation matrix associated to a permutation in disjoint cycle notation using
		For example, the cyclic permutation (1,2,3) is written [[1,2,3]] and the disjoint product (1,2)*(3,4,5) is written [[1,2],[3,4,5]].
		We can take a permutation, say written as a list 32415 (so 1 is sent to 4, 2 is left alone,...), convert it to a disjoint cycle, and then permute the corresponding columns of a martix):
	web.usna.navy.mil /~wdj/symm_gp.html (889 words)

	disjoint - OneLook Dictionary Search
		Disjoint : Hormel Glossary of Kitchen and Food Terms [home, info]
		Phrases that include disjoint: disjoint union, disjoint sets, disjoint set, mutually disjoint, almost disjoint, more...
		Words similar to disjoint: disarticulate, disjoin, disjointed, disjointing, dissassociate, dissociate, disunite, divorce, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=disjoint (209 words)

	Disjoint Union (Site not responding. Last check: 2007-11-07)
		Disjoint union is like set union, but each element is ``tagged'' with the set that it originally came from.
		The disjoint union of two types is a type defined by:
		The ML constructors for disjoint union types are
	www.cs.cornell.edu /Info/Projects/NuPrl/cs611/fall94notes/cn4/paragraph3_1_1_2_2.html (110 words)

	Disjoint Sets (Site not responding. Last check: 2007-11-07)
		Two disjoint events are also called mutually exclusive events.
		For example, if you sample patients randomly from a clinic, then the event that the patient was male is disjoint from the event that the patient had a diagnosis of cervical cancer.
		Knowing that one of two disjoint events occurred provides information about the occurrence of the other - namely that the other did not occur.
	www.mathepi.com /stat/prob/disjoint.html (142 words)

	Re: Adding disjoint sum types to SML
		D > >why not take their disjoint sum in the type system: > >fun foobar A = 1 >
		foobar D = 4 > >val foobar : fn (alpha + beta) -> int > >where the + designates we are taking the (necessarily disjoint) sum >of types alhpa and beta.
		There are certainly some semantic issues that you'd need to work out first.
	www.talkaboutprogramming.com /group/comp.lang.ml/messages/6423.html (277 words)

	A Linear Time Algorithm for the Arc Disjoint Menger Problem in Planar Directed Graphs (Site not responding. Last check: 2007-11-07)
		Given a graph $G=(V,E)$ and two vertices $s,t\in V$, $s\neq t$, the Menger problem is to find a maximum number of disjoint paths connecting $s$ and $t$.
		Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively.
		For planar graphs the edge disjoint Menger problem has been solved to optimality, while the fastest algorithm for the arc disjoint version is Weihe's general maximum flow algorithm for planar networks, which has running time ${\cal O}(V \log V)$.
	dmawww.epfl.ch /roso.mosaic/ismp97/ismp_abs_844.html (144 words)

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