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Topic: Partial order

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	PlanetMath: partial order
		A partial order (often simply referred to as an order or ordering) is a relation
		A total order is a partial order that satisfies a fourth property known as comparability:
		This is version 14 of partial order, born on 2001-10-06, modified 2007-11-04.
	planetmath.org /encyclopedia/PartialOrder.html (144 words)

	Kids.Net.Au - Encyclopedia > Partially ordered set
		In mathematics, a partial order ≤ on a set X is a binary relation that is reflexive, antisymmetric and transitive, i.e., it holds for all a, b and c in X that:
		A chain is a linearly ordered subset of a poset.
		Partially ordered sets can be given a topology, for example, the Alexandrov topology, consisting of all upwards closed subsets.
	www.kids.net.au /encyclopedia-wiki/pa/Partially_ordered_set (802 words)

	Order Comics Online - Nostalgia Zone Comic Store - FAQ
		- Otherwise, if we are missing anything from the order, or if shipping comes to more than $9.50 for Canada and Mexico or $11.50 for the rest of the world, there will be no charge on the card until the order is verified with you via email.
		For foreign orders, the charge for Global Priority Mail shipping and handling is $9.50 to Canada and Mexico, and $11.50 to other countries for up to 8 or so comic books.
		This ships the order if some items are out of stock; you are only charged for items we send you.
	www.nostalgiazone.com /doc/order.html (928 words)

	RFC 1693 (rfc1693) - An Extension to TCP : Partial Order Service
		What is more appropriate for some applications is a partial order and/or partial reliability service where a subset of objects being communicated must arrive in the order transmitted, yet some objects may arrive in a different order, and some (well specified subset) of the objects may not arrive at all.
		Partial Order Connection The implementation of a protocol that provides partial order service requires, at a minimum, (1) communication of the partial ordering between the two endpoints, and (2) dynamic evaluation of the deliverability of objects as they arrive at the receiver.
		For the partial ordering to commence, the TCP must be made aware of the acceptable object orderings and reliability for both the send- side and receive-side of the connection for a given set of objects (hereafter referred to as a "period").
	www.faqs.org /rfcs/rfc1693.html (8491 words)

	Partially ordered set - ExampleProblems.com
		In mathematics, especially order theory, a partially ordered set (or poset for short) is a set equipped with a partial order relation.
		A partial order is a binary relation R over a set P which is reflexive, antisymmetric, and transitive, i.e., for all a, b and c in P, we have that:
		Strict partial orders are also useful because they correspond more directly to directed acyclic graphs (dags): every strict partial order is a dag, and the transitive closure of a dag is both a strict partial order and also a dag itself.
	www.exampleproblems.com /wiki/index.php?title=Partially_ordered_set&printable=yes (437 words)

	Citations: Partial Order Transport Service: An Analytic Model - Marasli, Amer, Conrad, Burch (ResearchIndex)
		Ordered transport protocols have to reorder ADUs before delivering them to the application thereby delaying the delivery of ADUs and resulting in a longer occupancy of the transport receiver s buffers.
		Partially reliable transport service provides a middle ground between these two in which the loss tolerance of each object can be specified individually.
		This analytic model is similar to the one presented in [5] to study the protocol Partial Order Connection (POC) 3 Its major difference is that, in this model, it is unnecessary for all of the objects that are transmitted to eventually be communicated.
	citeseer.ist.psu.edu /context/220263/15627 (808 words)

	Partial order
		A partial order is a binary relation R over a set P which is reflexive, antisymmetric and transitive.
		A partial order R on X is called a (total) order on X if for any x, y ∈ X one of the conditions is satisfied: x < y, x = y or x > y.
		In these contexts a strict (or irreflexive) partial order is a binary relation that is irreflexive and transitive, and therefore antisymmetric.
	www.brainyencyclopedia.com /encyclopedia/p/pa/partial_order.html (572 words)

	PA 765: Partial Correlation
		Partial correlation still requires meeting all the usual assumptions of Pearsonian correlation: linearity of relationships, the same level of relationship throughout the range of the independent variable ("homoscedasticity"), interval or near-interval data, and data whose range is not truncated.
		Partial Q is simply Q for those pairs of i and j that are tied on a dichotomous control variable, k.
		Partial association may be constructed in an analogous manner for other measures of association, such as gamma for ordinal data (Yule's Q is gamma for the 2x2 case).
	www2.chass.ncsu.edu /garson/pa765/partialr.htm (2423 words)

	Order Relation (Site not responding. Last check: )
		The properties common to orders we see in our daily lives have been extracted and are used to characterize the concepts of order.
		Example 1: The less-than-or-equal-to relation on the set of integers I is a partial order, and the set I with this relation is a poset.
		According to that definition a quasi order is a relation that is reflexive and transitive.
	www.cs.odu.edu /~toida/nerzic/content/relation/order/order.html (1120 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: )
		Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering.
		Orders appear everywhere - at least as far as mathematics and related areas, such as computer science, are concerned.
		Directed complete partial orders (dcpos), that guarantee the existence of suprema of all directed subsets and that are studied in domain theory.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=order_theory (3764 words)

	[No title]
		What is more appropriate for some applications is a partial order and/or partial reliability service where a subset of objects being communicated must arrive in the order transmitted, yet some objects may arrive in a different order, and some (well specified subset) of the objects may not arrive at all.
		Furthermore, it is conceivable for a host to support the sending-half (or receiving- half) of a partial order connection alone to reduce the size of the TCP as well as the effort involved in the implementation.
		Partial Order Connection The implementation of a protocol that provides partial order service requires, at a minimum, (1) communication of the partial ordering between the two endpoints, and (2) dynamic evaluation of the deliverability of objects as they arrive at the receiver.
	www.ietf.org /rfc/rfc1693.txt (8502 words)

	An Extension to TCP : Partial Order Service [RFC-Ref]
		A service which allows partial order delivery and partial reliability is one which requires some, but not all objects to be received in the order transmitted while also allowing objects to be transmitted unreliably (i.e., some may be lost).
		The authors envision the use of a partial order service within a connection-oriented, transport protocol such as TCP providing a further level of granularity to the transport user in terms of the type and quality of offered service.
		It may be considered a useful option for any transport protocol and we encourage researchers and practitioners to investigate further the most effective uses for partial ordering whether in a next-generation TCP, or another general purpose protocol such as XTP, or perhaps within a "special purpose" protocol tailored to a specific application and network profile.
	rfc-ref.org /RFC-TEXTS/1693/index.html (469 words)

	RFC 1693 - An Extension to TCP : Partial Order Service
		Introduction A service which allows partial order delivery and partial reliability is one which requires some, but not all objects to be received in the order transmitted while also allowing objects to be transmitted unreliably (i.e., some may be lost).
		What is more appropriate for some applications is a partial order and/or partial reliability service where a subset of objects being communicated must arrive in the order transmitted, yet some objects may arrive in a different order, and some (well specified subset) of the objects may not arrive at all.
		Partial Order Connection The implementation of a protocol that provides partial order service requires, at a minimum, (1) communication of the partial ordering between the two endpoints, and (2) dynamic evaluation of the deliverability of objects as they arrive at the receiver.
	www.packetizer.com /rfc/rfc1693 (8651 words)

	Well partial order (Site not responding. Last check: )
		This isa generalization to partial orders of well orders, which are total orders that have no infinite sequences that always go down.
		Any total order will be a well partial order if and only if it is awell order.
		So the set of positive integers (with the usual ordering)is a well partial order, but the set of all integers is not, because it contains the infinfinite descending sequence -1, -2, -3,...
	www.therfcc.org /well-partial-order-210696.html (416 words)

	Partial Order
		is reflexive, antisymmetric and transitive, R is a reflexive partial order.
		If R is a partial order on a set X, the notation x ≼ y is sometimes used to indicate that (x,y) Î R.
		The reason for the term “partial order” is that in general some elements in X may be incomparable.
	home.earthlink.net /~inforef/i3450prtlorder.htm (260 words)

	Roxen Community: RFC 1693 An Extension to TCP : Partial Order Service (Experimental) (Site not responding. Last check: )
		Partial order services are needed and can be employed as soon as a complete ordering is not mandatory.
		Of particular interest to our discussion of partial ordering is the fact that, while objects of a given media type generally must be received in order, there exists flexibility between the separate "streams" of multimedia data (where a "stream" represents the sequence of objects for a specific media type).
		The implementation of a protocol that provides partial order service requires, at a minimum, (1) communication of the partial ordering between the two endpoints, and (2) dynamic evaluation of the deliverability of objects as they arrive at the receiver.
	community.roxen.com /developers/idocs/rfc/rfc1693.html (9138 words)

	Volume 29 "Partial Order Methods in Verification;"
		Research in the last few decades on the connection between partial order semantics and interleaving semantics has resulted in a class of new verification techniques for distributed systems that are beginning to prove themselves to be of great practical value in routine industrial applications of formal verification techniques.
		Until recently partial order semantics had not been widely applied in practical verification due to a lack of maturity in the methodology of its use and a shortage of suitable tools for verification based on partial orders.
		Since total orders are a special case of partial orders, the move to the latter has freed verification system builders to employ new methods without having to abandon those sequential methods that have proved useful in concurrent verification.
	dimacs.rutgers.edu /Volumes/Vol29.html (1980 words)

	Partial differential equation Summary
		Partial differentiation is the mathematical act of taking the derivative of a function that depends on more than one variable with respect to one or more of those variables.
		Partial differentiation involves a process by which the derivatives of a function containing multiple independent variables are found by considering all but the variable of interest as fixed during differentiation.
		Partial differential equations are used to formulate and solve problems that involve unknown functions of several variables, such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, elasticity, or more generally any process that is distributed in space, or distributed in space and time.
	www.bookrags.com /Partial_differential_equation (3679 words)

	Search ScienceWorld
		An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x
		Separation of variables is a method of solving ordinary and partial differential equations.For an ordinary differential equation (dy)/(dx)==g(x)f(y), where f(y)is nonzero in a neighborhood of the initial value, the solution is given implicitly by int(dy)/(f(y))==intg(x)dx.
		Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements.
	scienceworld.wolfram.com /search/index.cgi?num=&q=Partial&start=20 (376 words)

	Minimaximal and maximinimal optimisation problems: a partial order-based approach
		We focus on graph-theoretic minimaximal and maximinimal optimisation problems that may be obtained from source optimisation problems using the partial order of set inclusion.
		Some examples of MM-reductions are given, involving several partial orders, and involving source optimisation problems from a variety of domains.
		Finally, we revisit the general framework for minimaximal and maximinimal optimisation problems, considering an alternative definition in which the partial order is defined on the set of all possible (not necessarily feasible) solutions.
	www.dcs.gla.ac.uk /~davidm/thesisabs/thesisabs.html (1202 words)

	Partial Order
		Such a partial order is called a weak (reflexive) partial order, and is what is usually mean by the term "Partial Order" when used without qualification.
		For every partial order there is an isomorphic partial order whose elements are sets and where the relationship is non-trivial containment.
		The correct output of the program is defined by a partial order (and a particularly easy one at that, since it is defined by 3 disjoint total orders).
	www.c2.com /cgi/wiki>?PartialOrder (689 words)

	World Web Math: Vector Calculus: Partial Differentiation
		A partial function is a one-variable function obtained from a function of several variables by assigning constant values to all but one of the independent variables.
		A partial derivative is the rate of change of a multi-variable function when we allow only one of the variables to change.
		To get an intuitive grasp of partial derivatives, suppose you were an ant crawling over some rugged terrain (a two-variable function) where the x-axis is north-south with positive x to the north, the y-axis is east-west and the z-axis is up-down.
	web.mit.edu /wwmath/vectorc/scalar/partial.html (706 words)

	Math Forums @ Math Goodies - partial order
		either a <= b or b <= a) then the partially ordered set (poset) is called totally ordered or chain.
		The set of natural numbers is not totally ordered since, for example, 3 and 5 are not comparable.
		An example of a totally ordered set is the set of real numbers with the relation <= being the ordinary 'less than or equal to' relation.
	www.mathgoodies.com /forums/topic.asp?ARCHIVE=true&TOPIC_ID=30416 (538 words)

	[No title]
		This is important for addressing problems both in the original version of POA (such as order sensitivity) and in standard progressive alignment programs (such as information loss in complex alignments, especially surrounding gap regions).
		Orders are built up over the course of a session, with the partial order being saved in a session file until it is complete.
		The keys of order elements in the session data array are the product names, and the values are the numbers of the items ordered by the user.
	www.lycos.com /info/partial-order.html (514 words)

	Partial Differentiation - HMC Calculus Tutorial
		Similarly, the rate of change of f with respect to y is called the partial derivative of f with respect to y and is denoted by f
		at each point in the region, so the order in which the differentiation is done does not matter.
		Using the subscript notation, the order of differentiation is from left to right.
	www.math.hmc.edu /calculus/tutorials/partialdifferentiation (371 words)

	TCP option 10, Partial Order Service Profile. (Site not responding. Last check: )
		A service which allows partial order delivery and partial reliability is one which requires some, but not all objects to be received in the order transmitted while also allowing objects to be transmitted unreliably (i.e., some may be lost).
		The realization of such a service requires, (1) communication and/or negotiation of what constitutes a valid ordering and/or loss-level, and (2) an algorithm which enables the receiver to ascertain the deliverability of objects as they arrive.
		For the partial ordering to commence, the TCP must be made aware of the acceptable object orderings and reliability for both the send- side and receive-side of the connection for a given set of objects (hereafter referred to as a "period").
	www.networksorcery.com /enp/protocol/tcp/option010.htm (287 words)

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