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Topic: Diagram chasing

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	tScholars.com \| Commutative diagram
		Diagram chasing is a method of mathematical proof used especially in homological algebra.
		Given a commutative diagram, a proof by diagram chasing involves formally using the properties of the diagram, such as injective or surjective maps, or exact sequences.
		Examples of proofs by diagram chasing include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.
	www.tscholars.com /encyclopedia/Diagram_chasing (240 words)

	Diagram chasing - Wikipedia, the free encyclopedia
		Diagram chasing is a method of mathematical proof used especially in homological algebra.
		Given a commutative diagram, a proof by diagram chasing involves formally using the properties of the diagram, such as injective or surjective maps, or exact sequences.
		Examples of proofs by diagram chasing include the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.
	en.wikipedia.org /wiki/Diagram_chasing (99 words)

	Nine lemma - Wikipedia, the free encyclopedia
		In mathematics, the nine lemma is a statement about commutative diagrams and exact sequences valid in any abelian category, as well as in the category of groups.
		is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well.
		The nine lemma can be proved by direct diagram chasing, or by applying the snake lemma (to the two bottom rows in the first case, and to the two top rows in the second case).
	en.wikipedia.org /wiki/Nine_lemma (133 words)

	Chasing rope light - US Patent 6502955 (Site not responding. Last check: 2007-10-22)
		A chasing rope light includes a flexible core tube which has a plurality of cavities transversely and spacedly formed thereon, a pair of conductive wires longitudinally extended along the core tube, and a pair of illuminating units.
		The present invention relates to rope light, and more particularly to a chasing rope light which is adapted to minimize the use of the wire, so as to maintain a multicircuit of the rope light for performing various lighting effects such as chasing and fading effect.
		7, the chasing rope light 1 according to a second preferred embodiment of the present invention is illustrated, a plurality of cavities 11' are transversely and spacedly formed on the core tube 10', wherein the illuminators 31A', 31 B' from two illuminating units 30A', 30B' are alternately and transversely disposed in the cavities 11'.
	www.patentstorm.us /patents/6502955.html (1695 words)

	Chasing rope light - US Patent 6527412 (Site not responding. Last check: 2007-10-22)
		A chasing rope light, as recited in claim 2, wherein said core tube is a hollow tube defining an axial tubular cavity to receive said first, second, third, and fourth illuminating units therein, and the first, second and third conductive wires are longitudinally extended along said outer circumference of said core tube.
		A chasing rope light, as recited in claim 1, wherein said core tube is a hollow tube defining an axial tubular cavity to receive said first, second and third illuminating units therein, and the first, second and third conductive wires are longitudinally extended along said outer circumference of said core tube.
		7, the chasing rope light 1 according to a second preferred embodiment of the present invention is illustrated, a plurality of cavities 11' are transversely and spacedly formed on the core tube 10', wherein the illuminators 31A', 31B' from two illuminating units 30A', 30B' are alternately and transversely disposed in the cavities 11'.
	www.patentstorm.us /patents/6527412.html (1915 words)

	Diagram chasing (Site not responding. Last check: 2007-10-22)
		One ends up "chasing" elements around the diagram, until the desired element is constructed.
		Examples of proofs by diagram chasing include the Five lemma, the Snake lemma, the zig-zag lemma, and the Nine lemma.
		It is licensed under the GNU free documentation license.
	www.ufaqs.com /wiki/en/di/Diagram%20chasing.htm (92 words)

	Lesson 7: Basic Capturing Techniques
		Diagram 7-16 shows when fl tries to save his stone, but white keeps atari him on alternate sides, forcing fl to go in a zigzag way, until white 23 captures all the fl stones.
		Diagram 7-17 is a replica of Diagram 7-15, with six diagonal lines added.
		The triangle stone in Diagram 7-18 and Diagram 7-19 is known as a ladder block.
	unkx80.netfirms.com /weiqi/howtoplaygo/howtoplaygo07.htm (1607 words)

	[Ganoksin] Jewelry Making - Some Basic notes on Chasing Tools
		When you see chasing tool shafts that are twisted back and forth in a decorative pattern this is usually copying of Asian tools which are often made of brass and twisted.
		Chasing tools can be slid into a handle almost their entire length to function as burnishers.
		Chasing and dapping tools can be clamped onto the end of a hammer handle as temporary small shaping hammers if a suitable clamping device is constructed onto the end of a hammer handle.
	www.ganoksin.com /borisat/nenam/chasing.htm (661 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		A Knight or a Cannon cannot perpetually chase a confined Rook, disregard whether the confined Rook is protected or not.
		In Diagrams 64 and 65, the Black Rook is confined by the Red Cannon and cannot leave the fourth file.
		Therefore, the Red Rook is perpetually chasing the Black Rook and that is a violation of the rule.
	www.clubxiangqi.com /rules/d63to66.htm (187 words)

	[No title]
		A diagram thus contrasts with a single drawn figure (of a saint, for example), in which there is no intention that one should follow from part to part and infer anything.
		Nor can the diagram explicitly show forces and their transmission, or the direction in which a part is intended to move.
		For the usual Platonist reasons, he thinks physical diagrams are unsuitable: "the circle in sensible things is inferior in precision, infected with straightness, and falls short of the purity of immaterial circles".
	web.maths.unsw.edu.au /~jim/image.html (16210 words)

	[No title]
		The Young diagram of weight d is an arrangement of d squares (boxes) associated to a given partition in the obvious way.
		.,.* fil), 3 the (skew) diagram* ~=~ = (fi1 + ff1,.
		This diagram commutes: the commutativity of the first square follows from the naturality of ~, and the commutativity of the second from the compati- bility of a family.
	hopf.math.purdue.edu /Chalupnik/cohsdr.txt (8238 words)

	category, surjective, groups, exact, homology, object, monomorphism, unknown, prove, small, shall, notation, morphisms ...
		Consider the following commutative diagram in any Abelian category (such as the category of Abelian groups or the category of vector spaces over a given field) or in the category of groups.
		The method of proof we shall use is commonly referred to as diagram chasing.
		To perform diagram chasing, we assume that we are in a category of modules over some ring, so that we may speak of elements of the objects in the diagram and think of the morphisms of the diagram as functions (in fact, homomorphisms) acting on those elements.
	www.alphasearch.org /Five-lemma.html (893 words)

	IIIA Research Reports 1998 (Site not responding. Last check: 2007-10-22)
		This paper shows diagrams as an alternative formal notation for pure logic programming which not only emphasizes some structural features of logical statements, but could also be useful to conduct visual inferences and to communicate them.
		We explore two interesting features provided by its diagrammatic nature: First, the ability of intuitively keeping track ---within a diagram--- of the proof that is built while solving a query, and second, the possibility to represent the several different alternatives to answer a query within a unique diagram.
		In this paper we formally analize commutative diagrams and diagram chasing from the perspective of `diagrammatic reasoning', and present them as an instance of the abstract notion of `entailment system' within Meseguer's General Logics framework.
	www.iiia.csic.es /Reports/1998/Index.html (4414 words)

	NationMaster - Encyclopedia: Category Theory (Site not responding. Last check: 2007-10-22)
		Diagram chasing is a visual method of arguing with abstract 'arrows', and has appeared in a Hollywood film, as Jill Clayburgh proved the snake lemma (at the start of It's My Turn, 1980).
		Topos theory is a form of abstract sheaf theory, with geometric origins, and leads to ideas such as pointless topology.
		Jill Clayburgh (born April 30, 1944) is an American actress of stage, motion pictures, and television.
	www.nationmaster.com /encyclopedia/Category-Theory (845 words)

	Five lemma -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		The method of proof we shall use is commonly referred to as (Click link for more info and facts about diagram chasing) diagram chasing.
		Let d be an element of the (Click link for more info and facts about inverse image) inverse image under p of t(c'); d exists since p is surjective.
		By commutativity of the diagram, u(p(d)) = q(j(d)).
	www.absoluteastronomy.com /encyclopedia/F/Fi/Five_lemma.htm (607 words)

	World Class Coaching Newsletter
		On his first touch the next player in line, who is at the second cone, chases and attempts to disrupt the player’s run at the goalkeeper.
		On that player’s first touch, the front players in the outside lines chase the player with the ball and attempt to disrupt his run to goal.
		Organize the players as shown in diagram 4 with a defender in front of each goal and defenders behind each goal ready to rotate in.
	www.worldclasscoaching.com /freesamples/mayjune99.html (467 words)

	Physics: An Introduction Chapter 9 -- Warm-Ups
		The red ball in the diagram is chasing after the blue ball.
		A red ball is propelled forward and collides with a blue ball initially at rest.
		After the collision, the balls' trajectories are as shown in the diagram.
	cwx.prenhall.com /bookbind/pubbooks/walker2/chapter9/essay1/deluxe-content.html (428 words)

	C&EN: BOOKS - CHEMISTRY'S QUIXOTIC BEGINNINGS
		Yet within a little more than a half-century, a language was developed that assigned a separate name and diagram to every organic compound, a language so sophisticated that the name and diagram suggested the properties and often the ways the substance could be made from simpler molecules.
		Suddenly, thousands of new substances were being made in the laboratory, and chemistry became almost unique among the sciences in creating much of the world of materials that was the object of its studies.
		Although Loschmidt's 1861 diagram for aniline suggests a six-carbon benzene ring, Buckingham doesn't make it clear that Loschmidt's large circle merely represented a six-carbon cluster whose internal arrangement Loschmidt said he didn't know.
	pubs.acs.org /cen/books/8251/8251books1.html (1690 words)

	[No title]
		To establish that such functions exist you would have to instead chase things around from the domain to the codomain, and that's not such a nice task.
		Then you input any other sequences of functions, such that every function in your diagram is accounted for.
		You can enter in a function as a part of a few sequences, but you only need to cover your diagram, not every possible composition series.
	www.maths.tcd.ie /~icecube/exact.c (364 words)

	Chapter 1 - Modelling (Site not responding. Last check: 2007-10-22)
		Objects in the story can also be positioned on the diagram to imply some kind of group or relationship, and that is the main reason for using collaboration diagrams.
		Both sequence diagrams and collaboration diagrams are known as interaction diagrams, as they display the interaction between objects.
		Sequence diagrams are clearer, but it is difficult to get many objects and interactions on the same page, whereas a collaboration diagram is far more densely packed.
	www.softwarearchitect.biz /chapter1/chapter1_8.htm (660 words)

	Asian Chinese Chess Rules
		Chase - A piece moves to a position where it can capture an opponent's piece, which is not the King, in the next move.
		Similar definitions also apply to "one check and one chase", "one check and one idle", "one threatening to checkmate and one chase", "one threatening to checkmate and one idle", "several check and one threatening to checkmate", and "several check and one idle".
		In "Two chase and one chase back", the "two chase" side is "perpetually chasing" and has to change.
	www.clubxiangqi.com /rules/asiarule.htm (3266 words)

	Diagram chasing - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-22)
		Diagram chasing - Encyclopedia, History, Geography and Biography
		This page was last modified 01:31, 11 Jan 2005.
		This encyclopedia, history, geography and biography article about Diagram chasing contains research on
	www.arikah.net /encyclopedia/Diagram_chasing (119 words)

	ArtLex's Ch page
		Chasing might be done in order to remove the imperfections and rough spots on a bronze
		Chasing might also be done in order to ornament metal surfaces by embossing or hollowing with tools.
		Also see adze, chase, chipping out, ciseau, ciselet, drove, flat chisel, gouge, pick, pitcher, point, staple, and tooth.
	www.artlex.com /ArtLex/Ch.html (4058 words)

	Five lemma (Site not responding. Last check: 2007-10-22)
		The five lemma can be thought of as a combination of two other theorems, the four lemmas, which are dual to each other.
		Consider the following commutative diagram in any Abelian category (such as the category of Abelian groups or the category of vector spaces over a given field), or in the category of groups.
		To perform diagram chasing, we assume that we are in a category of modules over some ring, so thatwe may speak of elements of the objects in the diagram and think of the morphisms of the diagram as functions (in fact, homomorphisms) acting on those elements.
	www.therfcc.org /five-lemma-210909.html (607 words)

	Nine lemma (Site not responding. Last check: 2007-10-22)
		In mathematics, the Nine Lemma is a statement about commutative diagrams and exact sequences valid in any abelian category,as well as in the category of groups.
		is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well.Likewise, if all columns as well as the two top rows are exact, then the bottom row is exact as well.
		The Nine Lemma can be proved by direct diagram chasing, or by applying the snake lemma (to thetwo bottom rows in the first case, and to the two top rows in the second case).
	www.therfcc.org /nine-lemma-210912.html (121 words)

	CS 303E: Type Chasing in Assignment #1001 (Fall 2004)
		In BlueJ class diagrams, classes are shown as labeled boxes, and some of the key relationships between classes are shown via arrows.
		Now, let's consider a class diagram for the classes that should be defined after Part 1 of Assignment #1001.
		Type Chasing: These are the fundamental questions of type-chasing, which I'll define as determining where the hell I'm supposed to access/define this method/variable.
	www.cs.utexas.edu /users/sarvela/cs303e/assignments/type-chasing.html (2356 words)

	Stormtrack - Links
		Chase With Safety, Courtesy, and Responsibility -- Charles Doswell/Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma.
		Mississippi State University Chase Team -- The North Mississippi Severe Storms Intercept Team (NOMISSIT) is an organization dedicated to improving the quality and timeliness of severe local storm information utilized by local civil defense organizations, law enforcement, and the general public.
		Storm Chasers of America -- we are a network of chasers dedicated to the storm chasing enthusiasts and those new to the hobby from all across the United States.
	www.stormtrack.org /links (3520 words)

	Clothes Dryer News and Tips clothes dryer parts diagram
		If you are chasing the most informative help pertaining to clothes dryer parts diagram.
		Sometimes when you're trying to find better-quality advice concerning clothes dryer parts diagram, you'll find it easier said than done unscrambling quality advice from ill-advised clothes dryer parts diagram suggestions and help so it is imperative to know ways of moderating the information presented to you.
		This may reveal the operators clothes dryer parts diagram identifications The fastest way to determine who owns the clothes dryer parts diagram website is to look on the 'about' page or 'contact' page.
	www.clothes-dryer.info /clothes-dryer-parts-diagram.htm (245 words)

	Kestrel Institute - Research Staff - Dusko Pavlovic - Math and Logic papers
		In a sense, this approach seems complementary to the known combinatorial colouring procedures.
		Maps II: chasing diagrams in categorical proof theory
		Diagram chasing comes about in algebra of proofs.
	www.kestrel.edu /home/people/pavlovic/math.html (435 words)

	Abstract nonsense - Wikipedia, the free encyclopedia
		Rather than enter an elaborate discussion on particulars of arguments, mathematicians will use the expression Such and such is true by abstract nonsense.
		Typical instances are arguments involving diagram chasing, application of the definition of universal property, definition of natural transformations between functors, use of the Yoneda lemma and so on.
		Other, possibly less flattering, characterizations of abstract reasoning have been recorded, although they have not acquired the status of mathematical jargon.
	en.wikipedia.org /wiki/Abstract_nonsense (205 words)

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