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Topic: Directed complete partial order

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Domain theory

	several replies re: chains vs. directed sets
		Directed completeness is a more mathematically elegant condition; it is particularly useful when one is working with compact elements.
		I think the advantage of chains is its conceptual simplicity: it is a linear order.
		Plotkin in his `Pisa Notes' indicated that for omega-algebraic cpos chains and directed sets are interchangeable.
	www.seas.upenn.edu /~sweirich/types/archive/1991/msg00104.html (339 words)

	Order theory - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-06)
		Orders appear everywhere - at least as far as mathematics and related areas, such as computer science, are concerned.
		These are graphss where the vertices are the elements of the poset and the ordering relation is indicated by both the edges and the relative positioning of the vertices.
		It is reasonable to require that functions between partially ordered sets have certain additional properties, that are related to the ordering relations of the two sets.
	encyclopedia.learnthis.info /o/or/order_theory.html (3998 words)

	Complete partial order - Wikipedia, the free encyclopedia
		For any poset, the set of all non-empty filters, ordered by subset inclusion, is a dcpo, even a cpo if the poset has a greatest element.
		Every finite poset is directed complete, every finite poset with a least element is a cpo.
		All complete lattices are of course also directed complete and thus provide numerous (though not particularly instructive) examples for dcpos.
	en.wikipedia.org /wiki/Complete_partial_order (629 words)

	The Avalon Project : General Orders No. 100 (Site not responding. Last check: 2007-11-06)
		Martial Law does not cease during the hostile occupation, except by special proclamation, ordered by the commander in chief; or by special mention in the treaty of peace concluding the war, when the occupation of a place or territory continues beyond the conclusion of peace as one of the conditions of the same.
		Its most complete sway is allowed - even in the commander's own country - when face to face with the enemy, because of the absolute necessities of the case, and of the paramount duty to defend the country against invasion.
		When humanity induces the adoption of the rules of regular war to ward rebels, whether the adoption is partial or entire, it does in no way whatever imply a partial or complete acknowledgement of their government, if they have set up one, or of them, as an independent and sovereign power.
	www.yale.edu /lawweb/avalon/lieber.htm (7205 words)

	Domain theory (Site not responding. Last check: 2007-11-06)
		Due to their importance for the theory, dcpos with a least element are called complete partial orders or just cpos.
		Adding even further completeness properties one obtains continuous lattices and algebraic lattices, which are just complete lattices with the respective properties.
		All of these classes of orders can be cast into various categories of dcpos, using functions which are monotone, Scott-continuous, or even more specialized as morphisms.
	domain-theory.kiwiki.homeip.net (2197 words)

	Banc of America Securities LLC: Admin. Proc. Rel. No. 34-49386 / March 10, 2004
		The staff also directed the firm to produce, in electronic form, all e-mail for three of the seven individuals whose e-mail previously had been requested.
		The staff demanded that BAS immediately produce a complete copy of the E-mail Exchange, including the copy reflecting all the BCC recipients, and directed BAS to provide a detailed explanation why these documents were not included in the firm's prior e-mail productions.
		Although the documents and information concerning the Compliance Department's inquiry were responsive to the November 6, 2002 request and to the Commission's Section 21(a) Order, BAS failed to produce the e-mails concerning the inquiry to the staff and failed to disclose the information in its response to the Section 21(a) Order.
	www.sec.gov /litigation/admin/34-49386.htm (4172 words)

	CSAIL Publications
		Partially observable Markov decision processes (POMDPs) are a well studied paradigm for programming autonomous robots, where the robot sequentially chooses actions to achieve long term goals efficiently.
		A directed excitatory chain with a global inhibitory network, for which experimental evidence exists, was found to produce waves of activity similar to those observed in RA; this similarity included one particularly important feature of the measured activity, synchrony between the onset of bursting in one neuron and the offset of bursting in another.
		We first motivate the problem by presenting theoretical bounds for the connectivity improvement of partially mobile networks and then present superior empirical results under a variety of different scenarios in which the mobile nodes in our ad-hoc network are embedded with adaptive routing policies and learned movement policies.
	www.ai.mit.edu /research/publications/browse/completebrowse.shtml (15133 words)

	Amazon.com: One Palestine, Complete: Jews and Arabs Under the British Mandate: Books: Tom Segev,Haim Watzman (Site not responding. Last check: 2007-11-06)
		Both parties fanatically believe they have an inalienable historical right to statehood on the land in question and both regard Jerusalem as a holy city.
		Tom Segev is one of Israel's most notable historians and journalists--one of the few to strive for any sense of objectivity in his writings--so a new book by him is always worth waiting for.
		One Palestine, Complete is a detailed account of Palestine under British rule from 1917 to 1948, the critical period in the modern history of the region that led up to the creation of the state of Israel.
	www.amazon.com /One-Palestine-Complete-British-Mandate/dp/0805048480 (4065 words)

	Amended Supreme Court Rules 751, 756, and 759 and New Rules 790 thru 799, entered 9/29/05; eff. immediately
		A restoration ordered under this rule shall be effective seven days after entry of the court’s order allowing the petition provided that the petitioner produces to the Administrator within the seven days verification from the Director of MCLE that the attorney has complied with MCLE requirements as set forth in Rule 790
		The course must be completed within one year of the newly admitted attorney’s admission to practice in Illinois.
		Partial credit shall be earned for qualified activities of less than 60 minutes duration.
	www.state.il.us /court/SupremeCourt/Rules/Amend/2005/MRAmend092905.htm (7714 words)

	Defence of Poesie (Ponsonby, 1595)
		Olney was directed to halt sale and turn over his remaining copies to Ponsonby, who replaced the title page with his own and sold the copies along with his own printing.
		Aristotle had made a place for rhetoric within dialectic by claiming that dialectic is simply the use of complete syllogisms to understand truth while rhetoric is the use of partial syllogisms to attain specific ends, such as convincing a jury of one's innocence, regardless of one's actual guilt (Rhetoric).
		There is no Art{17} delivered unto mankind that hath not the workes of nature for his principall object, without which they could not consist, and on which they so depend, as they become Actors and Plaiers, as it were of what nature will have set forth.
	darkwing.uoregon.edu /~rbear/defence.html (13374 words)

	Cooper ( Interaction Design
		This contradiction, where the user's goals and the program's tasks are in direct opposition is symptomatic of the failure of our current design methods to work effectively.
		If the client, for example, hasn't yet established where an order should be shipped, and the program rejects the order because it lacks a valid shipping address, the software has achieved the task of data integrity while utterly failing to achieve the goal of recording the client's order.
		Instead of leaving the partial weeks at the beginning and ending of the month blank, they color them gray and show the appointments scheduled in them.
	www.cooper.com /articles/art_goal_directed_design.htm (4416 words)

	OpenBSD ordering
		Bulk orders from OpenBSD Europe to locations in Western Europe, should be directed to kd85.com bvba (Belgium), or by using the European SECURE Web Ordering Form.
		This insurance may be paid either at time of order (you must so specify in the comment section of the order), or, at the rate of $6 CDN, it may be paid after you find that the item has gone missing, and upon requesting the replacement.
		Partial shipments: Sometimes a T-shirt of a certain size might not be in stock.
	www.openbsd.org /orders.html (2352 words)

	A Partial Order on Classical and Quantum States - Coecke, Martin (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation.
		In order to understand when a trajectory moves with respect to this order and especially when it is that domain theoretic kinematics...
		A partial order on classical and quantum states.
	citeseer.comp.nus.edu.sg /603928.html (579 words)

	Order theory (Site not responding. Last check: 2007-11-06)
		However, they have the additional property of being total, i.e., for all distinct a and b in P, we have that: :''a'' ≤ b or b ≤ a (totality) These orders can also be called linear orders or chains.
		Formally, an element m is a least element if: : m ≤ a, for all elements a of of the order.
		Formally, an element m is minimal if: : a ≤ m implies a = m, for all elements a of the order.
	order-theory.kiwiki.homeip.net (4028 words)

	Lab Lunch Talks 1997
		It would be more interesting to study relative completeness where one considers an arbitrary expressive assertion language.
		We conjecture that such an alternative definition of relative completeness is better than the traditional version in that it may prevent certain (all?) incompleteness results.
		A classic fixpoint theorem of Tarski says that any monotonic function on a directed-complete partial order with least element has a least fixpoint.
	www.lfcs.inf.ed.ac.uk /events/lablunch/1997.html (1165 words)

	Star Wars: Episode III \| Inside Del Rey's Episode III Library
		When he's on the set, or directing animatics, he goes from a gut instinct.
		And just in general watching Lucas direct was an incredible treat, being there able to interact with the sets (playing with the knobs and buttons) and being able to talk to the crew...
		As George says in the book, depending on what order you watch the movies -- saga order or the order they were released -- you get a different story.
	www.starwars.com /episode-iii/release/publishing/f20050330/indexp6.html (960 words)

	WiFi Speed Spray
		You'll receive a complete refund within 10-12 weeks.
		WiFi Speed Spray™ is safe and effective when used as directed.
		However, the product is known to the State of California to cause cancer; developmental toxicity; and/or male pattern baldness.
	www.j-walk.com /other/wifispray (472 words)

	Mathematical Structures: Directed complete partial orders (Site not responding. Last check: 2007-11-06)
		A directed complete partial order is a poset P = (P, ≤) such that every directed subset of P has a least upper bound: ∀D ⊆ P (D ≠ Ø and ∀x,y ∈ D ∃z ∈ D (x,y ≤ z) ⇒ ∃z ∈ P(z =
		Let P and Q be directed complete partial orders.
		A morphism from P to Q is a function f : P→Q that is Scott-continuous, which means that f preserves all directed joins: z =
	math.chapman.edu /cgi-bin/structures.pl?Directed_complete_partial_orders (117 words)

	Investing Glossary Rule 144 complete sell order firm
		Restricts solicitation of buyers to Complete the sell Order of an insider (unless the Firm is already a buyer); signified by a flashing "E" On Quotron.
		Highlight Investments Inc. makes no representations or warrantees whatsoever, expressed or implied, as to the accuracy, completeness, timeliness, appropriateness, suitability or fitness for any purpose or use of such Third party products, services and information, methods for payment, customer and technical support or web presence or any of their presentations or representations.
		Such links are provided for reference only and were independently developed by parties other than Highlight Investments Inc. Highlight Investments Inc. is not responsible for the contents of any such linked sites and does not assume any responsibility for the accuracy or appropriateness of the information contained at such sites.
	www.marketvolume.com /glossary/r0344.asp (4161 words)

	Modern History Sourcebook: Thomas Browne (1605-1682): Religio Medici, 1643
		'Tis not partiality, but equity in God, Who deals with us but as our natural Parents: those that are able of Body and Mind He leaves to their deserts; to those of weaker merits He imparts a larger portion, and pieces out the defect of one by the excess of the other.
		Yet a moderate and peaceable discretion may so state and order the matter, that they may be all Kings, and yet make but one Monarchy, every one exercising his Soveraignty and Prerogative in a due time and place, according to the restraint and limit of circumstance.
		There are many (questionless), canonized on earth, that shall never be Saints in Heaven; and have their names in Histories and Martyrologies, who in the eyes of God are not so perfect Martyrs as was that wise Heathen, Socrates, that suffered on a fundamental point of Religion, the unity of God.
	www.fordham.edu /halsall/mod/1643Browne-religio.html (15963 words)

	Mathematical Structures: History of Directed complete partial orders (Site not responding. Last check: 2007-11-06)
		Mathematical Structures: History of Directed complete partial orders
		A \emph{directed complete partial order} is a poset $\mathbf{P}=\left\langle P,\leq \right\rangle $
		Let $\mathbf{P}$ and $\mathbf{Q}$ be directed complete partial orders.
	math.chapman.edu /cgi-bin/structures?action=history;id=Directed_complete_partial_orders (201 words)

	List of order topics - Wikipedia, the free encyclopedia
		An alphabetical list of many notions of order theory can be found in the order theory glossary.
		Order topology of a total order (open interval topology)
		This page was last modified 23:05, 7 August 2006.
	en.wikipedia.org /wiki/List_of_order_topics (94 words)

	The Partial Preterist Archive - Books and Articles
		B) This class begins near the beginning of the "dark ages," turning into today's contemporary "Partial Preterism" during the Reformation era in the hands of Grotius and Hammond.
		God describes the passing of the order as a passing of heaven and earth.
		When this union of two peoples into one is completed, the mystery of God is finished (cf.
	www.preteristarchive.com /PartialPreterism/index.html (6066 words)

	Mathematical Structures: Directed complete partial orders (Site not responding. Last check: 2007-11-06)
		\end{definition} \begin{morphisms} Let $\mathbf{P}$ and $\mathbf{Q}$ be directed complete partial orders.
		A morphism from $\mathbf{P}$ to $\mathbf{Q}$ is a function $f:P\rightarrow Q$ that is \emph{Scott-continuous}, which means that $f$ preserves all directed joins: $z=\bigvee D\implies f(z)= \bigvee f[D]$ \end{morphisms} \begin{basic_results} \end{basic_results} \begin{examples} \begin{example} $\left\langle \mathbb{R},\leq \right\rangle $, the real numbers with the standard order.
		$\begin{array}{lr} f(1)= and1\\ f(2)= and\\ f(3)= and\\ f(4)= and\\ f(5)= and\\ f(6)= and\\ \end{array}$ \end{finite_members} \hyperbaseurl{http://math.chapman.edu/structures/files/} \parskip0pt \begin{subclasses}\ \href{Complete_semilattices.pdf}{Complete semilattices} \end{subclasses} \begin{superclasses}\ \href{Directed_partial_orders.pdf}{Directed partial orders} \end{superclasses} \begin{thebibliography}{10} \bibitem{Ln19xx} \end{thebibliography} \end{document} %
	math.chapman.edu /cgi-bin/structures?Directed_complete_partial_orders (244 words)

	Mathematical Structures: Algebraic posets (Site not responding. Last check: 2007-11-06)
		An algebraic poset is a directed complete partial order P = (P, ≤) such that
		The set of compact elements of P is denoted by K(P).
		Last edited May 28, 2003 4:39 pm (diff)
	math.chapman.edu /cgi-bin/structures.pl?Algebraic_posets (107 words)

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