
	Where results make sense

Topic: Order isomorphism

Related Topics

Isomorphism

Group isomorphism

	Santa Fe Institute Research Topics - Information Processing & Computation in Complex Systems
		The other is the many-atomic order of statistical mechanics, where ordered states are derived through an appropriate averaging over many interacting particles.
		In order to build cells capable of responding adaptively to environmental cues, elaborate signaling networks have evolved capable of reliably, transducing energy from the environment into internal informational states of the cell.
		Robustness arises as a byproduct of statistical order in biology as individual components are frequently correlated in their activity, and this can be exploited as a source of redundancy.
	www.santafe.edu /research/topics-information-processing-computation.php (1927 words)

	Isomorphism -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, an isomorphism (in (A native or inhabitant of Greece) Greek isos = equal and morphe = shape) is a kind of ((genetics) the process of locating genes on a chromosome) mapping between objects.
		Isomorphic structures are "the same" at some level of abstraction; ignoring the specific identities of the elements in the underlying sets, and focusing just on the structures themselves, the two structures are identical.
		In (The study and classification of human societies) sociology, isomorphism is to a kind of "copying" or "imitation", especially of the practices of one (A group of people who work together) organization by another.
	www.absoluteastronomy.com /encyclopedia/i/is/isomorphism.htm (625 words)

	Order theory
		Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering.
		The first order that one typically meets in primary school mathematical education is the order ≤ of natural numbers.
		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.
	www.sciencedaily.com /encyclopedia/order_theory (4025 words)

	Isomorphism Info - Bored Net - Boredom (Site not responding. Last check: 2007-10-08)
		The word "isomorphism" applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where "corresponding" means that the two parts play similar roles in their respective structures.
		Isomorphic structures are "the same" at a certain level of abstraction; ignoring the specific identities of the elements in the underlying sets and the names of the underlying relations, the two structures are identical.
		In sociology, isomorphism refers to a kind of "copying" or "imitation", especially of the practices of one organization by another.
	www.borednet.com /e/n/encyclopedia/i/is/isomorphism.html (252 words)

	Order isomorphism -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Two strictly weaker notions that relate to order isomorphisms are (Click link for more info and facts about order embedding) order embeddings and (Click link for more info and facts about Galois connection) Galois connections.
		Hence, yet another characterization of order isomorphisms is possible: they are exactly those monotone (Click link for more info and facts about bijection) bijections that have a monotone inverse.
		An order isomorphism from (S, ≤) to itself is called an (Click link for more info and facts about order automorphism) order automorphism.
	www.absoluteastronomy.com /encyclopedia/O/Or/Order_isomorphism.htm (187 words)

	Order embedding (Site not responding. Last check: 2007-10-08)
		In mathematical order theory, an order-embedding is aspecial kind of monotone function, which provides a way toinclude one partially ordered set into another.
		Yet, the two posets are not isomorphic: [-1,1] has both a least and a greatestelement, which are not present in the case of the real numbers.
		The basic category for the study of partial orders is the categoryof posets and monotone functions.
	www.therfcc.org /order-embedding-210691.html (621 words)

	Station Information - Total order
		In mathematics, a total order or linear order on a set X is a binary relation that is reflexive, antisymmetric, transitive and total.
		Because a binary relation that is reflexive, antisymmetric and transitive is called a partial order, a total order can also be defined as a partial order that is total.
		Alternatively, one may define a totally ordered set as a particular kind of lattice, namely one in which we have {a v b, a ^ b} = {a, b} for all a, b.
	www.stationinformation.com /encyclopedia/t/to/total_order.html (347 words)

	Ordinal number - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-08)
		Such a one-to-one correspondence is called an order isomorphism and the two well-ordered sets are said to be order-isomorphic.
		One example of these is an important characterization of the order relation between ordinals: every set of ordinals has a supremum, the ordinal obtained by taking the union of all the ordinals in the set.
		An ordinal is finite if and only if the opposite order is also well-ordered, which is the case if and only if each of its subsets has a greatest element.
	encyclopedia.learnthis.info /o/or/ordinal_number.html (1357 words)

	Science Fair Projects - Duality (order theory)
		if one poset is order isomorphic to the dual of the other.
		If a given statement is valid for all partially ordered sets, then its dual statement, obtained by inverting the direction of all order relations and by dualizing all order theoretic definitions involved, is also valid for all partially ordered sets.
		Note that the consideration of dual orders is so fundamental that it often occurs implicitly when writing ≥ for the dual order of ≤ without giving any prior definition of this "new" symbol.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Duality_%28order_theory%29 (466 words)

	Order isomorphism: Definition and Links by Encyclopedian.com - All about Order isomorphism (Site not responding. Last check: 2007-10-08)
		Given two partially ordered sets (S, <=) and (T, [=) an order isomorphism from (S, <=) to (T, [=) is an isomorphism from S to T that preserves the order, that is, it is a bijection h : S
		If there is an order isomorphism between two partially ordered sets then these sets are called order isomorphic.
		An order isomorphism from (S,<=) to itself is called an order automorphism
	www.encyclopedian.com /or/Order-isomorphism.html (123 words)

	Read about Order isomorphism at WorldVillage Encyclopedia. Research Order isomorphism and learn about Order isomorphism ... (Site not responding. Last check: 2007-10-08)
		order theory an order isomorphism is a special kind of
		Two strictly weaker notions that relate to order isomorphisms are order embeddings and
		An order isomorphism from (S, ≤) to itself is called an
	encyclopedia.worldvillage.com /s/b/Order_isomorphism (216 words)

	A resemblance theory of representational content determination
		The isomorphism is first-order because the corresponding properties between the two entities are of corresponding kinds: colours correspond to colours, lengths and shapes correspond to lengths and shapes (subject to perspective), and so on.
		However, in a second-order isomorphism the corresponding properties need not be of the same kind, as in the size of a star-shape corresponding to the relative brightness of a star.
		Evidently it is not a relation of first-order isomorphism, nor structural isomorphism, although there obviously does exist an isomorphic relation that maps between the two.
	www.bowering.org /gb/cog/lib/represent.html (2496 words)

	Order automorphism
		Given a partially ordered set (S, <=) an order automorphism of (S, <=) is an order isomorphism from (S, <=) to itself.
		The set of order automorphisms forms a group.
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/or/Order_automorphism.html (50 words)

	Cogprints - Second order isomorphism: A reinterpretation and its implications in brain and cognitive sciences (Site not responding. Last check: 2007-10-08)
		Second order isomorphism: A reinterpretation and its implications in brain and cognitive sciences
		Choe, Yoonsuck (2002) Second order isomorphism: A reinterpretation and its implications in brain and cognitive sciences.
		Shepard and Chipman's second order isomorphism describes how the brain may represent the relations in the world.
	cogprints.org /2281 (182 words)

	Quantum Logic and Probability Theory
		Ordered by set-inclusion, the closed subspaces of H form a complete lattice, in which the meet (greatest lower bound) of a set of subspaces is their intersection, while their join (least upper bound) is the closed span of their union.
		Axiom VII: The partially ordered set of all questions in quantum mechanics is isomorphic to the partially ordered set of all closed subspaces of a separable, infinite dimensional Hilbert space.
		Relative to this ordering, the mapping a→a′ is an orthocomplementation and a⊥b iff a≤b′.
	plato.stanford.edu /entries/qt-quantlog (7961 words)

	Isomorphism - Enpsychlopedia (Site not responding. Last check: 2007-10-08)
		In mathematics, an isomorphism (in Greek isos = equal and morphe = shape) is a kind of mapping between objects, devised by Eilhard Mitscherlich.
		A six-sided die and a bag from which a number 1 through 6 is chosen; although the method of obtaining a number is different, their random number generating abilities are isomorphic.
		In linear algebra, an isomorphism can also be defined as a linear map between two vector spaces that is one-to-one and onto.
	www.grohol.com /psypsych/Isomorphic (550 words)

	Encyclopedia: Order embedding (Site not responding. Last check: 2007-10-08)
		Updated 249 days 4 hours 15 minutes ago.
		On the other hand, one can define a function e from the real numbers to [−1,1] as
		Click for other authoritative sources for this topic (summarised at Factbites.com).
	www.nationmaster.com /encyclopedia/Order-embedding (691 words)

	Order Isomorphism Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-08)
		Looking For order isomorphism - Find order isomorphism and more at Lycos Search.
		Find order isomorphism - Your relevant result is a click away!
		Look for order isomorphism - Find order isomorphism at one of the best sites the Internet has to offer!
	www.karr.net /search/encyclopedia/Order_isomorphism (357 words)

	2.2 Ordinals
		If two well-ordered sets are order isomorphic, then they are considered equivalent.
		To prove some theorems regarding ordinals, it is necessary to discuss, more generally, well-ordered sets and order isomorphisms.
		The first elements of a well-ordered set, with respect to its ordering, have special importance, and are useful in proving theorems about well-ordered sets.
	www.u.arizona.edu /~miller/thesis/node7.html (575 words)

	Isomorphism: Definition and Links by Encyclopedian.com - All about Isomorphism (Site not responding. Last check: 2007-10-08)
		Isomorphism: Definition and Links by Encyclopedian.com - All about Isomorphism
		Formally, an isomorphism is a bijective map f such that both f and its inverse f
		For example, if one object consists of a set X with an ordering <= and the other object consists of a set Y with an ordering [=, then an isomorphism from X to Y is a bijective function f : X -> Y such that
	www.encyclopedian.com /is/Isomorphic.html (303 words)

	Order Isomorphism Does Not Preserve Global Event Independence - Rensink (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: We report a negative result on the characterisation of partial order equivalence relations over models which feature a global notion of event independence.
		give rise to isomorphic domains of computations, but which do not admit any independence-preserving relation between their respective event sets.
		Order isomorphism does not preserve global event independence.
	sherry.ifi.unizh.ch /rensink93order.html (545 words)

	Shimon Edelman's reprint archive — abstracts
		A representational scheme under which the ranking between represented dissimilarities is isomorphic to the ranking between the corresponding shape dissimilarities can support perfect shape classification, because it preserves the clustering of shapes according to the natural kinds prevailing in the external world.
		A representational scheme under which the ranking between represented similarities is isomorphic to the ranking between the corresponding shape similarities can support perfectly correct shape classification, because it preserves the clustering of shapes according to the natural kinds prevailing in the external world.
		That space turns out to support representation of distal shape similarities which is veridical in the sense of Shepard's (1968) notion of second-order isomorphism (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations).
	kybele.psych.cornell.edu /~edelman/abstracts.html (7398 words)

	isomorphism - Definition of isomorphism - isomorphism in Encyclopedia - DictionaryWords.net (Site not responding. Last check: 2007-10-08)
		A bijective map between two objects which preserves, in both directions, any structure under consideration.
		Thus a `group isomorphism' preserves group structure; an order isomorphism (between posets) preserves the order relation, and so on.
		Usually it is clear from context what sort of isomorphism is intended.
	www.dictionarywords.net /find/word/isomorphism (146 words)

	Isomorphism - Wikipedia
		An isomorphism is a bijection from one set of a mathematical object to the set of another mathematical object such that the structures defined upon these sets in these objects, such as orderings and operations, are preserved.
		For example, if one object consists of a set X with an ordering <= and the other object consists of a set Y with an ordering [=, then it must hold for the function f : X -> Y that
		Or, if on these sets the binary operations * and @ are defined, respectively, then it must hold that
	nostalgia.wikipedia.org /wiki/Isomorphism (169 words)

	A First-Order Isomorphism Theorem - Allender, Immerman, Balc'azar (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		A First-Order Isomorphism Theorem - Allender, Immerman, Balc'azar (ResearchIndex)
		Since #natural" complete problems seem to stay complete via fops, this indicates that up to #rst-order isomorphism there is only one #natural" complete problem for each #nice" complexity class.
		35.8%: A First-Order Isomorphism Theorem - Allender, Balcázar, Immerman (1993)
	citeseer.lcs.mit.edu /allender93firstorder.html (396 words)

	DigitalCommons@University of Nebraska - Lincoln \| An examination of visual-touch perceptual equivalence, visual-touch ...
		An examination of visual-touch perceptual equivalence, visual-touch imaginal equivalence and second-order isomorphism of perceptions and images using common texture stimuli.
		Although visual and tactile images were highly congruent, they do appear to be independent for at least some stimuli, suggesting that people can form images based primarily on one modality or the other.
		These findings converge with reports of second-order isomorphism for visual perceptions and images of shape and color information and extend those findings to include texture information as well as to include second-order isomorphism of tactile images and perceptions for texture information.
	digitalcommons.unl.edu /dissertations/AAI9805528 (409 words)

	Order Automorphism Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-08)
		Find order automorphism - Your relevant result is a click away!
		In the mathematical area of order theory, given a partially ordered set (S, ≤) an order automorphism of (S, ≤) is an order isomorphism from (S, ≤) to itself.
		The set of order automorphisms of a set forms a group.
	www.karr.net /search/encyclopedia/Order_automorphism (211 words)

	Order theory Details, Meaning Order theory Article and Explanation Guide
		Driven by the wide practical usage of orders, numerous special kinds of ordered sets have been defined, some of which have grown to mathematical fields of their own.
		Furthermore, closure operators are important in the study of universal algebra.
		List of order topics, Incidence algebra, Möbius function;, total order, total preorder, partial order, cyclic order and Important publications in order theory.
	www.e-paranoids.com /o/or/order_theory.html (4039 words)

	Shipping worldwide > order viagra and viagra pill
		In light uncleanness of commandants the former, recommending order viagra, customers` experience shows that their duress on line drugstore is secure purified, secret unity and also draftsman helpful site to seek medications hill.
		Its ordering, credit card grammatic handling as well sociability as cloudless delivery technologies are secure, accurate apathy as well as rustic well-organized.
		Talking eyepieces about order viagra junior, their drug lovelier store is commended to persons cautiousness that look for the expediency mint of having drugs isomorphism shipped intimacy securely photon at the entrance.
	order-viagra.site-4pharmacy.com (692 words)

Try your search on: Qwika (all wikis)