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Topic: Discrete category

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kernel category theory

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	[No title] (Site not responding. Last check: 2007-10-16)
		DA is isomorphic to the category of K0(K)(p)- comodules.
		Bousfield's category A(p) is isomorphic to the cate- gory DA of discrete A-modules.
		(3) DB is isomorphic to Bousfield's category B(p).
	hopf.math.purdue.edu /Clarke-Crossley-Whitehouse/ccwDiscrete.txt (6369 words)

	DMP: Definitions from Discrete Mathematics
		Apportionment may include division of discrete objects, as in the division of seats of a representative government among districts, or may involve division of continuous objects such as dividing a cake among a group of people.
		Estate division is a category of fair division which deals with determining a fair method for dividing an estate among a number heirs.
		A category of discrete mathematics which deals with whether a given problem has a solution or not.
	www.colorado.edu /education/DMP/def.html (3248 words)

	MATHS: Category Theory
		Category Theory is a way for talking about the relationships between the classes of objects modeled by mathematics and logic.
		The original use of the term category was in the idea of a 'categorical' axiom system - an axiom system which defined its objects so exactly that all objects that satisfied the axioms were isomorphic - they mapped into each other, one-to-one, preserving all the axioms and structure.
		A Category is a mixture of an algebra and a directed graph.
	www.csci.csusb.edu /dick/maths/math_25_Categories.html (3607 words)

	Discrete category - Wikipedia, the free encyclopedia
		In mathematics, especially category theory, a discrete category is a category whose only morphisms are the identity morphisms.
		Also, a category is discrete if and only if all of its subcategories are full.
		The limit of any functor from a discrete category into another category is called a product, while the colimit is called a coproduct.
	en.wikipedia.org /wiki/Discrete_category (154 words)

	RATIONAL NUMBER LEARNING AIDS: TRANSFER FROM CONTINUOUS MODELS TO DISCRETE MODELS
		The aid used was an egg carton which, if the subject views the holes as salient, is discrete; if, on the other hand, the subject focuses on the proportion of total area enclosed by the edges of each of the holes, then it is viewed as a continuous entity.
		It is not required that the discrete objects which comprise the unit be of the same size or even the same shape, since the appropriate measure of the unit an d subunit relates solely to the cardinality of the sets.
		Among the discrete tasks, the data suggests a slight trend favoring the experimental groups; and, among the continuous tasks, there appears to be a sharp difference favoring the experimental groups.
	education.umn.edu /rationalnumberproject/88_2.html (2929 words)

	Springer Online Reference Works
		If a category has products of arbitrary small families of objects and equalizers of pairs of morphisms, then it has limits for all functors defined on small categories.
		In most modern work in category theory, the unadorned name  "limit" ; is used for this concept (and the dual concept is called a colimit).
		Inverse and direct limits were first studied as such in the 1930's, in connection with topological concepts such as Čech cohomology; the general concept of limit was introduced in 1958 by D.M. Kan [a1].
	eom.springer.de /p/p075260.htm (370 words)

	The Math Forum - Math Library - Discrete Math (Site not responding. Last check: 2007-10-16)
		A centre whose aim is to carry out and promote research and teaching in discrete mathematics and computing, and to facilitate collaborative research with groups working in related areas in Australia and overseas.
		Discrete math problems from a variety of sources, including textbooks, math contests, NCTM books, and puzzle books, and real-life situations, designed to reflect different levels of difficulty.
		A glossary of discrete math terms, from "and" and "absorption law" through "characteristic equation," "negation," and "recurrence relation," to "universal bound law" and "vacuously true." Available for navigation without frames.
	mathforum.org /library/topics/discrete (2153 words)

	Empirical Arguments for Phonetic Discreteness
		For a small enough difference, moving the difference along the continuum, one should (on the discrete category view) find discrimination flat spots (where the sounds are within the same sensory class) alternating with discrimination bumps (across a boundary between the sensory steps).
		So the fact that there are sensory limits relevant to distinguishing phonetic categories from each other in no way justifies a claim that there is a discrete set that can be reliably identified.
		On the other hand, it is known that if you give subjects a great deal of practice on just a single speech stimulus, listener's can respond in ways that reveal that their auditory resolution approaches the sensory limits observed for simple tones [Kewley-Port et al., 1988].
	www.cs.indiana.edu /~port/pap/manaster/node4.html (1545 words)

	Goldblatt. Topoi: The Categorial Analysis of Logic (Site not responding. Last check: 2007-10-16)
		These categories are examples of preorders: categories in which there is at most one arrow between any two objects (identity corresponds to reflexivity and composition corresponds to transitivity).
		A category is complete if it has all limits, co-complete if it has all colimits, bi-complete if it is complete and co-complete, finitely complete if it has all finite limits, finitely co-complete if it has all finite colimits, and finitely bi-complete if it is finitely complete and finitely co-complete.
		For Cartesian closed categories, we have 0xA is initial for all A, an arrow A->0 implies A is initial, we can only have a zero object if the category is degenerate (all objects are isomorphic), any arrow 0->A is monic, A^1 is isomorphic to A, A^0 and 1^A are terminal.
	www.andrew.cmu.edu /user/cebrown/notes/goldblatt.html (7165 words)

	SEMISEEK Semiconductor Components\IC Manufacturers\By Category\Discrete (Site not responding. Last check: 2007-10-16)
		Philips Semiconductor We manufacture over 50 million integrated circuits (IC components) and discrete devices every day for a huge diversity of markets and applications.
		SGS/STMicroelectronics is a global independent semiconductor company which designs, develops, manufactures and markets a broad range of semiconductor integrated circuits ("ICs") and discrete devices used in a wide variety of microelectronic applications.
		These discrete electronic components are solid state switches (either on or off) which are used to modulate the flow of electrical currents and to limit voltages.
	www.semiseek.com /SEMISEEK/Pag00607.htm (176 words)

	MapCalc shading manager options for discrete maps
		Using MapCalc’s Shading Manager for Displaying Discrete Maps: While grid-based systems are best suited for processing and displaying continuous maps, there are several considerations for grid-based display of discrete map data.
		Category labels can be changed simply by clicking on the text and modifying them.
		When attempting to view a map, you should first consider its Data Type (Discrete or Continuous) then decide on the Display Type (Lattice or Grid and 2D or 3D) and finally the Color Intervals/Pallet (Shading Manager) to use.
	www.innovativegis.com /basis/Senarios/SMdiscrete_scenario.htm (682 words)

	pXtXr data: continuous formulation
		The basic spirit of this follows along with the discrete category misclassification formulation examples.
		These stories will adopt the CLBH "continuous" perspective, (which doesn't produce results much different from the discrete framework); that is, for purposes here I'm happy to grant the CLBH wish that judges can give a score of 3.11 to a paper (however impractical that may be).
		Once an individual's theta is drawn, then we need to construct that individual's score on a specified task, where the student's paper is assumed to be judged/rated with perfect accuracy To get the score from a perfectly judged paper simply add task wobble to theta.
	www-stat.stanford.edu /~rag/ed351/gtheory/pxtxrcont.html (711 words)

	Data Mining Glossary (Site not responding. Last check: 2007-10-16)
		That is, we are interested in knowing which category (from a finite set) a particular situation belongs to.
		For discrete class problems this is computed by summing the absolute difference between a binary vector that contains a 1 for the actual class value of an instance and 0's for all other classes and the predicted class probability distribution for each instance and then taking the average.
		For discrete class problems this is computed in a similar fashion to the mean absolute error.
	www.auknomi.com /glossary.html (1156 words)

	Subject Index
		category of complexes as a Frobenius category 681
		category of Grothendieck topoi as a category of fractions of localic groupoids 516
		category of homotopy classes of maps between fibrant-cofibrant objects 656
	www1.elsevier.com /homepage/saj/523281/subject.htm (1223 words)

	week202
		A rig category is basically the most general sort of category in which we can "add" and "multiply" as we do in a ring - but without negatives, hence the missing letter "n".
		It relates the category whose objects are 2-manifolds with a circle as boundary, and whose morphisms are 3-manifolds with corners going between these, to a braided monoidal category "freely generated by a quasitriangular Hopf algebra object".
		A 2-rig is a symmetric monoidal cocomplete category where the monoidal structure, which we call x, distributes over the colimits, which we think of as a generalized form of addition.
	math.ucr.edu /home/baez/week202.html (4106 words)

	Philosophy of Real Mathematics: Klein 2-Geometry IV
		These are categories with a vector space of objects, a vector space of morphisms, and with all the usual category operations (e.g.
		The category of vertical morphism is C. The category of horizontal morphisms is C_0//G_0, i.e.
		If we consider the category of subgroups of a given 2-group (well, should probably be a 2-category, and we haven't fully got a handle on sub2-groups yet) with inclusions the morphisms (and I suppose transformations of inclusions too, to be safe) then I would imagine the above construction describes the kernel as its own stabilizer.
	www.dcorfield.pwp.blueyonder.co.uk /2006/08/klein-2-geometry-iv.html (14127 words)

	, ergo we can't include 'quandaryheader.html' like we do elsewhere -->
		The Action/Adventure Games Awards seems to be a 'catch-all' category or the miscellaneous category for games that don't merit a category of their own.
		Leaving aside children's games which are a special item, if there were another discrete category for adventure games then along with family games there would be two categories to represent games that don't involve the player in combat or confrontation of some kind.
		The changes to the categories over the years show that AIAS have tried to be accommodating by changing things around, RPGs are a case in point.
	www.quandaryland.com /jsp/dispArticle.jsp?index=690 (843 words)

	OPM - Memorandum for Human Resources Directors (CPM 2003-05)
		Provide the number of LEOs whose LEO status is based on having frequent and direct contact with suspected or convicted criminals, but who are not correctional officers or correctional administrators in the direct chain of command (e.g., support staff at correctional institutions).
		For LEOs other than those identified in paragraph b, identify discrete categories of LEOs with similar duties and responsibilities.
		Identify discrete categories of non-LEOs with similar duties and responsibilities.
	www.opm.gov /OCA/compmemo/2003/2003-05.asp (1603 words)

	OneKIT :: Search results :: Discrete
		Discrete removable captions inform you about each image.
		An unlimited number of discrete PM schedules can be created by the user, making PM scheduling for different equipment types easy and efficient.
		Places tools over the image to 1) extract values from continuous or discrete point graphs tilted due to scanning, 2) measure distance and area on curved paths, 3) measure angle and straight-line distance, 4) record color values at multiple points of an image.
	www.onekit.com /store/search.html?query=Discrete (587 words)

	[No title]
		In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.
		http://hopf.math.purdue.edu/cgi-bin/generate?/Clarke-Crossley-Whitehouse/ccwDiscrete The discrete module category for the ring of K-theory operations Francis Clarke, Martin Crossley, Sarah Whitehouse We study the category of discrete modules over the ring of degree zero stable operations in p-local complex K-theory.
		We show that the p-local K-homology of any space or spectrum is such a module, and that this category is isomorphic to a category defined by Bousfield and used in his work on the K-local stable homotopy category (Amer.
	www.lehigh.edu /~dmd1/h0406 (581 words)

	Discrete Manufacturing Software, Hardware, Services and Research Papers - Fast Company
		Adonix X3 is a fully-integrated software application that is robust across manufacturing, distribution, warehousing, CRM and accounting.
		Designed for North American mid-sized manufacturers and distributors in discrete and process industries, Adonix X3 also incorporates supply chain management and finite capacity planning functionality.
		Epicor's manufacturing solutions are complete with rich functionality and powerful features, allowing you to reduce scrap and defects, identify and eliminate bottlenecks, and automate quoting, scheduling, and job costing.
	knowledgestorm.fastcompany.com /fastco/search/browse/1071/1071.jsp (692 words)

	What is discrete? - A Word Definition From the Webopedia Computer Dictionary (Site not responding. Last check: 2007-10-16)
		(1) In audio/sound terms discrete refers to multichannel audio or soundtrack being stored with each individual channel isolated from the other tracks.
		Digi-Key: Search Discrete Integrated Circuits - Broad-line distributor web site features real-time stock status and pricing, online ordering, RFQ, technical support, product datasheets and photos.
		Digi-Key: Dialight Discrete - Broad-line distributor web site features real-time stock status and pricing, online ordering, RFQ, technical support, product datasheets and photos.
	www.pcwebopedia.com /discrete.html (278 words)

	Textbookx.com - Discrete Mathematics for New Technology by Rowan Garnier at TextbookX.com
		Textbookx.com - Discrete Mathematics for New Technology by Rowan Garnier at TextbookX.com
		Discrete Mathematics for New Technology provides an accessible introduction to discrete mathematics.
		The approach is comprehensive but maintains an easy-to-follow progression from the basic mathematical ideas to more sophisticated concepts.
	www.textbookx.com /product_detail.php?detail_isbn=0750306521 (380 words)

	Toward Reformulating the Diagnosis of Schizophrenia -- Tsuang et al. 157 (7): 1041 -- American Journal of Psychiatry
		(negative symptoms are the fifth symptom in the category).
		of schizophrenia presents the disorder as a discrete condition.
		A final problem is that use of the category of schizotaxia risks
	ajp.psychiatryonline.org /cgi/content/full/157/7/1041 (6280 words)

	Dual Diagnosis and the Passive-Aggressive Personality Disorder
		The passive-aggressive (negativistic) personality disorder is located in Appendix B: "Criteria Sets and Axes Provided for Further Study" of the DSM-IV.
		It is being considered for inclusion in future revisions but was removed from the Axis II Personality Disorders (DSM-IIIR) because there is controversy regarding the category.
		177) notes that the term passive-aggressive clearly describes a discrete behavior, but it is not certain that it describes a discrete diagnostic category.
	www.toad.net /~arcturus/dd/papd.htm (5649 words)

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