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Topic: Minimal element

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	Extreme value - Wikipedia, the free encyclopedia
		In the case of a general partial order one should not confuse a least element (smaller than all other) and a minimal element (nothing is smaller).
		Likewise, a greatest element of a poset is an upper bound of the set which is contained within the set, whereas a maximal element m of a poset A is an element of A such that if m ≤ b (for any b in A) then m = b.
		In a totally ordered set, or chain, all elements are mutually comparable, so such a set can have at most one minimal element and at most one maximal element.
	en.wikipedia.org /wiki/Minimum (428 words)

	Springer Online Reference Works
		A minimal element of the partially ordered set of ideals of a given type of some algebraic system.
		In a semi-group with minimal left ideals every left ideal contains a minimal left ideal, and the union of all minimal left ideals (which are pairwise disjoint) is the kernel of the semi-group.
		The presence of minimal ideals in a primitive ring makes it close to a matrix ring in the following sense: A primitive ring with a non-zero socle is isomorphic to a dense subring of the ring of all linear transformations of some vector space over a skew-field, containing all transformations of finite rank.
	eom.springer.de /m/m063830.htm (648 words)

	Element Operations
		Given an element a from an algebraic field or order L, returns the characteristic polynomial of the element over R if given or the subfield or suborder F otherwise where F is the field or order over which L is defined as an extension.
		Given an element a from an algebraic field or order L, returns the minimal polynomial of the element over R if given otherwise the subfield or suborder F where F is the field or order over which L is defined as an extension.
		For an element a of an algebraic field F, a sequence of coefficients of length degree of F with respect to the basis is returned.
	www.umich.edu /~gpcc/scs/magma/text634.htm (1704 words)

	[No title]
		The first element of the pair is found by adding the minimal element to each of the partial pull-off sequences.
		When all the elements have been removed from the poset, purplpst is the standard form and the first pull-off sequence in pairlst gives an inverse isomorphism from the poset to this form.
		The second argument is an element of the poset that is a green bubble.
	www.unc.edu /~rap/Posets/Word/chapt5.doc (5208 words)

	Maximal element - Wikipedia, the free encyclopedia
		In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set is an element of S that is not smaller than any other element in S.
		This example also shows that maximal elements are usually not unique and that it is possible for an element to be both maximal and minimal at the same time.
		Yet, in a totally ordered set, the terms maximal element and greatest element coincide, which is why both terms are used interchangeably in fields like analysis where only total orders are considered.
	en.wikipedia.org /wiki/Maximal_element (416 words)

	CSE 3315 - Homework 3 (Site not responding. Last check: 2007-10-14)
		Therefore, a is a minimal element [(b, a)
		A containing the minimal elements of R. Note that for R to be a partial order, it will contain (a, a) for every element a
		M in the form (a, x) - the minimal element(s) are the "ancestors" of all other elements; and of course there can be no (x, a) for any minimal a, since R must be antisymmetric.
	home.flash.net /~kennieg/cse3315/hw03.htm (355 words)

	Order Relation (Site not responding. Last check: 2007-10-14)
		The elements in a finite poset can be ordered linearly in a number of ways while preserving the partial order.
		It is based on the fact that a finite poset has at least one minimal element.
		The basic idea of the topological sorting is to first remove a minimal element from the given poset, and then repeat that for the resulting set until no more elements are left.
	www.cs.odu.edu /~toida/nerzic/content/relation/order/order.html (1120 words)

	Language In the Field (Site not responding. Last check: 2007-10-14)
		It is the minimal unit in the sound system which is not a sound per se, but a distinctive element within that sound system.
		Therefore, a phoneme is the abstract element of sound, identified as being distinctive in a particular language.
		It took even longer than that before formal linguistics, as the study of the abstract linguistic forms and their internal relations (phonology, morphology and syntax), opened some space for functional linguistics, which is primarily concerned with the forms of language in reference to their social function in communication (semantics and sociolinguistics).
	www.aucegypt.edu /academic/anth/anth352/language_in_the_field.htm (1027 words)

	PlanetMath: maximal element
		) have no least element, but infinitely many minimal elements (the primes.) In neither case is there a greatest or maximal element.
		have no least element or minimal element, and no maximal or greatest element.
		This is version 5 of maximal element, born on 2002-03-02, modified 2006-04-24.
	planetmath.org /encyclopedia/LeastElement.html (120 words)

	Orðasafn: M
		maximum element stærsta stak, efsta stak, hæsta stak, síðasta stak, = greatest element, = largest element, = last element, = maximum 2, -> max.
		minimal residue algildisminnsta leif, = least absolute remainder.
		minimal system of generators óminnkanlegt spannmengi, ósmækkanlegt spannmengi, óminnkanlegt spannandi mengi, ósmækkanlegt spannandi mengi, = irreducible generating set, = minimal generating set, = minimal set of generators.
	www.hi.is /~mmh/ord/safn/safnM.html (2128 words)

	Ordered Sets : Software Foundations : Thomas Alspaugh : UCI
		EU has a minimum element under the prefix relation ≤, and that minimum is 01, so E={01} has a LUB of 01 in S.
		The second set has three minimal elements, and an edge is drawn down from each of the three minimal elements of Q to each of the five maximal elements of P.
		The second set is an antichain, so all its elements are trivially minimal, and an edge is drawn down from each of the five minimal elements of P to the single maximal element of Q.
	www.ics.uci.edu /~alspaugh/foundations/orderedSet.html (2579 words)

	Publications of Jinchao Xu
		For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid.
		A new Z-type nonconforming finite element, in n spatial dimensions with n 2, is proposed.
		Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on a posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations.
	www.math.psu.edu /xu/papers.html (11552 words)

	Working with Elements of a Braid Group
		Given elements u and v belonging to the same braid group B, return the right-lcm of u and v, that is, the with respect to succeq minimal element d of B satisfying d succeq u and d succeq v, where succeq is defined as above.
		Given a set or a sequence S containing elements of a braid group B, return the left-gcd of the elements of S, that is, the with respect to preceq minimal element d of B satisfying s preceq d for all s in S, where preceq is defined as above.
		Given a set or a sequence S containing elements of a braid group B, return the right-lcm of the elements of S, that is, the with respect to succeq minimal element d of B satisfying d succeq s for all s in S, where succeq is defined as above.
	www.math.lsu.edu /magma/text462.htm (6729 words)

	Post-transcriptional Cosuppression of Ty1 Retrotransposition -- Garfinkel et al. 165 (1): 83 -- Genetics
		elements that are transcriptionally repressed or fused to the
		elements in the genome are inhibited for retrotransposition
		A Ty1 element is represented by a solid rectangle and an LTR by a horizontal triangle.
	www.genetics.org /cgi/content/full/165/1/83 (7925 words)

	Transcript-Selective Translational Silencing by Gamma Interferon Is Directed by a Novel Structural Element in the ...
		The 29-nt GAIT element confers the translational silencing response to a heterologous transcript in vitro and in vivo.
		GAIT element from the IRE, the histone 3'-UTR element, and the
		The evolution of the GAIT element is not
	mcb.asm.org /cgi/content/full/23/5/1509 (6362 words)

	Functional characterization of the interferon regulatory element in the enhancer 1 region of the hepatitis B virus ...
		Functional characterization of the interferon regulatory element in the enhancer 1 region of the hepatitis B virus genome -- Alcantara et al.
		Functional characterization of the interferon regulatory element in the enhancer 1 region of the hepatitis B virus genome
		an interferon-stimulated response element in the context of
	nar.oxfordjournals.org /cgi/content/full/30/9/2068 (4909 words)

	Gap Junctional Communication Modulates Gene Transcription by Altering the Recruitment of Sp1 and Sp3 to ...
		Either removal of the CT element (dCT) or mutation of the CT element (mtCT) in the context of the homologous promoter abrogated the gap junction sensitivity of the reporter to Cx45 overexpression.
		Minimal effects on Sp1 or Sp3 protein levels were observed by Cx45 transfection.
		CT element, Sp3 is a repressor and inhibits Sp1-induced transactivation,
	www.jbc.org /cgi/content/full/278/27/24377 (6948 words)

	Minimal XML in a Nutshell (Site not responding. Last check: 2007-10-14)
		Minimal XML is a subset of XML 1.0; including features essential for data interchange applications, and excluding non-essential features that are arcane, legacy-related, problematic for data interchange applications, or redundant.
		Minimal XML documents must be encoded in either UTF-8 or UTF-16.
		In Minimal XML, element names that cannot satisfy the XML 1.0 Name production are reserved.
	xml.coverpages.org /minxmlspec20000413.html (461 words)

	Robotics Institute: Modifying Soft Tissue Models: Progressive Cutting with Minimal New Element Creation
		The cutting surface follows the free form path of the user's motion, and generates a minimal set of new elements to replace intersected tetrahedra.
		Intersected elements are progressively cut to minimize the lag between the user's motion and model modification.
		A linear finite element model is used to model deformation of the soft tissue.
	www.ri.cmu.edu /pubs/pub_3457.html (290 words)

	Frequently Asked Questions About Standardized Terminologies (Site not responding. Last check: 2007-10-14)
		What is the difference between a minimal data element set and a standardized terminology?
		Answer: The minimal data element sets in nursing designate only what data should be collected, e.g.
		Other minimal data element sets may contain both the data needed as well as the terminology needed to collect it.
	www.nursingworld.org /npii/faq.htm (886 words)

	Math 3309_10639
		Note: (1) problem 7.17 uses the Principle of Mathematical Induction II, page 13; (2) the predecessor set of an element is defined in problem 7.31 and used in 7.32; (3) from problems 7.47 and 7.52, we may conclude that an ordered set with one maximal (minimal) element may not have a last (first) element.
		Be certain that you go through the practice exercises regarding minimal and maximal elements, first and last elements, and infimum and supremum.
		Note that an ordered set may have no minimal element, or may have more than one minimal element; this is also true for maximal elements.
	cms.dt.uh.edu /faculty/BecerraL/Spring2004/3312_calendar.htm (2054 words)

	Maximal and Minimal Elements (Site not responding. Last check: 2007-10-14)
		A maximal element of A is any element t of
		A minimal element of A is any element
		elements are 8 and 10 and the minimal elements
	www.enm.bris.ac.uk /research/aigroup/enjl/als/tsld047.htm (27 words)

	Ordered Sets (Site not responding. Last check: 2007-10-14)
		An example of a strict partial order is given by the relation ⊂ as it's a binary relation that is transitive and totally irreflexive, meaning that for each x, x~R x.
		If an element, m, of a linear order is a such that for all x, m R x, then m is a minimal element.
		If every non-empty subset of a linear ordered set has a minimal element then it is well-ordered.
	www.jboden.demon.co.uk /SetTheory/order.html (246 words)

	The Cellular TATA Binding Protein Is Required for Rep-Dependent Replication of a Minimal Adeno-Associated Virus Type 2 ...
		The p5 element is contained in the lower DNA band.
		Novel cis-acting replication element in the adeno-associated virus type 2 genome is involved in amplification of integrated rep-cap sequences.
		Asymmetric replication in vitro from a human sequence element is dependent on adeno-associated virus Rep protein.
	jvi.asm.org /cgi/content/full/79/17/11082 (7726 words)

	Selection and design of high-affinity RNA ligands for HIV-1 Rev.
		We have used in vitro selection to isolate minimal, high-affinity RNA ligands for the Rev protein of HIV-1.
		We have designed and synthesized a short (37 nt) RNA molecule that incorporates this motif; this RNA ligand has from three- to fivefold tighter binding than the full-length wt element, and up to 16-fold tighter than minimal wt RBEs.
		A guanosine:guanosine pairing that is postulated to occur in the wt element has been altered to other base pairings in the context of our optimized minimal element.
	www.aegis.com /aidsline/1994/apr/M9440027.html (439 words)

	Maximal and minimal elements.
		The Hasse diagram of a (finite) poset is a useful tool for finding maximal and minimal elements: they are respectively top and bottom elements of the diagram.
		Note, however, that this example is quite special: there is a unique maximal element and a unique minimal element.
		as its least element and has no greatest element.
	ndp.jct.ac.il /tutorials/Discrete/node34.html (93 words)

	MAPK and JNK transduction pathways can phosphorylate Sp1 to activate the uPA minimal promoter element and endogenous ...
		HeLa cells were transfected with a reporter construct in which the luciferase gene was driven by the minimal promoter element of the uPA gene.
		Variation in transcriptional activation is expressed as fold induction relative to the minimal promoter construct alone.
		A regulatory element that mediates co-operation between a PEA3/AP-1 element and an AP-1 site is required for phorbol ester induction of urokinase enhancer activity in HepG2 hepatoma cells.
	www.bloodjournal.org /cgi/content/full/104/1/256 (5518 words)

	MinMax (CoMa Container Classes)
		Find the maximal element in a container with respect to the given ordering.
		Find the minimal element in a container with respect to the given ordering.
		- container where to search for the minimal element.
	www.math.tu-berlin.de /CCC/doc/ccc/util/MinMax.html (233 words)

	Robotics Institute: Progressive Cutting with Minimal New Element Creation of Soft Tissue Models for Interactive ...
		This thesis deals with the modification of finite element models used in surgical simulation.
		Also, within the framework the interactive simulator demonstrated, the user is able to palpate, grasp, and puncture the model.
		Mor, Progressive Cutting with Minimal New Element Creation of Soft Tissue Models for Interactive Surgical Simulation, doctoral dissertation, tech.
	www.ri.cmu.edu /pubs/pub_3881.html (359 words)

	Database Leasing Information - MEDLINE Minimal Data Element Set
		The following elements are the minimum set required for MEDLINE by NLM under the Quality Assurance provisions of the License Agreement to Lease Databases in Machine- Readable Form.
		These requirements pertain to any version of MEDLINE made available by the Licensee.
		All elements with an "X" in the Search Status column must be directly searchable on Licensee's system.
	www.nlm.nih.gov /databases/license/min_data.html (144 words)

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