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Topic: Least element

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Greatest element

Supremum

Dedekind completion

Natural number

Binary operation

Symmetry group

Group theory

Perfect graph

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	Magnetic material - Patent 5549766
		A part of the element A is possibly replaced by H. The element Co(cobalt) serves to increase a content of Co and Fe in the principal phase so as to improve the saturation magnetic flux density of the magnetic material.
		The element Fe(iron) is a principal element of the composition.
		An element M which is at least one element selected from the group consisting of Si, Ti, Cr, V, Mo, W, Mn, Ni, Ga and Al may partly replace the elements Fe so that the ratio of the principal phase, i.e., TbCu.sub.7 phase, to the whole magnetic compound may be increased.
	www.freepatentsonline.com /5549766.html (6706 words)

	ELEMENT: 118 Ununoctium
		Element 118 and its immediate decay product, element 116, were discovered at Berkeley Lab's 88-Inch Cyclotron by bombarding targets of lead with an intense beam of high-energy krypton ions.
		Although both new elements almost instantly decay into other elements, the sequence of decay events is consistent with theories that have long predicted an "island of stability" for nuclei with approximately 114 protons and 184 neutrons.
		Elements 118 and 116 were discovered by accelerating a beam of krypton-86 ions to an energy of 449 million electron volts and directing the beam into targets of lead-208.
	www.radiochemistry.org /periodictable/elements/118.html (1071 words)

	2.1 Augmented BNF (Site not responding. Last check: 2007-11-03)
		Elements enclosed in parentheses are treated as a single element.
		Default values are 0 and infinity so that *"(element)"** allows any number, including zero; "1element" requires at least* one; and "1*2element" allows one or two.
		Therefore, where at least one element is required, at least one non-null element must be present.
	www.freesoft.org /CIE/RFC/2068/7.htm (484 words)

	Suprema
		In mathematics, the supremum of an ordered set S is the least element that is greater than or equal to each element of S.
		In analysis the supremum or least upper bound of a set S of real numbers is denoted by sup(S) and is defined to be the smallest real number that is greater than or equal to every number in S.
		The difference between the supremum of a set and the greatest element of a set may not be immediately obvious.
	www.sfcrowsnest.com /scifinder/a/Suprema.php (1757 words)

	United States Patent: 4,999,687
		For a logic element with two input terminals (A, B) a particular electrical state thus is A=1, B=0, and a further particular state is A=0, B=1, where 1 and 0 are used in conventional fashion.
		The combination 100 is an embodiment of the inventive logic element, with numerals 101, 102, and 103 referring, respectively to emitter, barrier, and collector of the RST device, numerals 1040, 1041 and 1042 referring to the input terminals, and numerals 105, 106 and 107 referring to the output terminals, load resistor, and voltage source, respectively.
		All logic elements according to the invention have the property that their output is logic 1 only if all inputs are at the same logic state (1 or 0), and is zero whenever all inputs are not at the same logic state.
	www.ece.sunysb.edu /~serge/pat11.html (3606 words)

	Element 118
		The new "superheavy" elements were discovered at Berkeley Laboratory's 88-inch cyclotron by bombarding targets of lead-208 with a high energy and high intensity beam of krypton-86 ions—at an average current of 2 trillion ions per second.
		This daughter element 116 is also radioactive and alpha-decays into an isotope of element 114.
		Although both elements almost instantly decay into other elements, the announcement is important because it supports theories of an "island of stability" for nuclei (in which the decay lasts for a period of time instead of decaying instantly).
	www.infoplease.com /spot/element118.html (303 words)

	Order Relation
		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)

	Greatest element - Wikipedia, the free encyclopedia
		In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S which is greater than or equal to any other element of S.
		This also demonstrates that the existence of a least upper bound (the number 1 in this case) does not imply the existence of a greatest element either.
		Greatest elements of a partially ordered subset must not be confused with maximal elements of such a set which are elements that are not smaller than any other element.
	en.wikipedia.org /wiki/Greatest_element (402 words)

	Declogging process for filtration installation and improved filtration installation - Patent 4292053
		Filtration apparatus according to claim 8 wherein each filtration cell comprises a plurality of said filtering elements and wherein said inlet enclosure comprises wall means partially separating the filtering elements of each filtration cell from one another.
		The filtering element has an upstream face which is met by the dust-laden gas and a downstream face, the dust being deposited then on said upstream face.
		Furthermore, it is frequent for a filtration installation to operate in an explosive environment, that is to say that either the gas, or the dust, or the gas and the dust may form under certain conditions an explosive medium.
	www.freepatentsonline.com /4292053.html (2464 words)

	Math Notes - Well-Ordering Principle
		Let S be a non-empty subset of a well-ordered set, and let b be the least element. Let b’ be another least element. The proof will show that b = b’.
		Since b is a least element and b’ is a least element, let b and b’ be distinct elements such that:
		Corollary to Theorem 1: If b is a least element of set S, and b’ £ b then b = b’.
	home.att.net /~p.konieczko/mathwell.html (315 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 6 of maximal element, born on 2002-03-02, modified 2006-10-28.
	planetmath.org /encyclopedia/LeastElement.html (111 words)

	2.1 Augmented BNF
		Elements separated by a bar ("I") are alternatives, e.g., "yes
		The full form is "#element" indicating at least and at most elements, each separated by one or more commas (",") and optional linear whitespace (LWS).
		That is, "(element),, (element)" is permitted, but counts as only two elements.
	www.freesoft.org /CIE/RFC/1945/7.htm (507 words)

	Chemistry : Periodic Table : ununquadium : key information
		Element 114 was reported informally in January 1999 following experiments towards the end of December 1998 involving scientists at Dubna (Joint Institute for Nuclear Research) in Russia apparently using isotopes supplied by scientists at the Lawrence Livermore National Laboratory, USA.
		As only about three atoms of element 114 has ever been made (through nuclear reaction involving fusing a calcium atom with a plutonium atom) isolation of an observable quantity has never been achieved, and may well never be.
		This isotope of element 116, is also radioactive and undergoes further α-decay processes to an isotope of element 114 and so on down to at least element 106.
	www.webelements.com /webelements/elements/text/Uuq/key.html (364 words)

	Course Summary
		Reflexive property: (a,a) is an element of R for every a in A. Symmetric property: if (a,b) is an element of R, (b,a) is an element of R. Antisymmetric property: if (a,b) is an element of R and (b,a) is an element of R, then a=b.
		An element a is the greatest element if b<=a for all b in S. An element a is the least element if a<=b for all b in S. Greatest and least elements are unique when they exist.
		An element that is greater than all the elements in a subset A of a poset is called an upper bound of A.
	sweb.uky.edu /~jcscov0/dmath_4.htm (1397 words)

	Radix Sort
		In the first pass, the elements of the array are sorted by the least significant decimal digit.
		The key characteristic of the radix sort is that the second pass is done in such a way that it does not destroy the effect of the first pass.
		E.g., there are no elements that have a 0 as the least-significant digit; there are two elements that have a 1 as the least-significant digit; and so on.
	www.brpreiss.com /books/opus4/html/page518.html (732 words)

	Radio Control Car Action - Team Orion Element 19T (Site not responding. Last check: 2007-11-03)
		At each end of the brush hood there's a polarized, aluminum brush heat sink; one is anodized red, and the other is fl to show which is the positive side and which is the negative side.
		Last, but not least, the Element is available with standard brushes or laydown brushes and brush hoods; our test motor had laydown brushes.
		The Element is available with standard or laydown brushes and brush hoods; it also has distinctive, unique green-anodized brush-hood heat sinks.
	www.rccaraction.com /rc/articles/element19t.asp (410 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)

	queue<T, Sequence>
		Returns a mutable reference to the element at the front of the queue, that is, the element least recently inserted.
		Returns a const reference to the element at the front of the queue, that is, the element least recently inserted.
		Returns a mutable reference to the element at the back of the queue, that is, the element most recently inserted.
	www.sgi.com /tech/stl/queue.html (476 words)

	Method for selecting a constructed element of a drawing to generate similar elements (US5513310)
		A menu may be displayed after selecting an element in order for the user to modify various parameters for the similar element.
		constructing a representation of at least one element, said at least one element possessing a plurality of attributes, each of said plurality of attributes being dependent on at least one parameter set by at least one computer command that generated said at least one element;
		automatically reproducing at least one other independent element sharing similar attributes as at least one of said constructed element and said at least one reference element using said at least one of said at least one computer command and said at least one parameter retrieved from said memory.
	www.delphion.com /details?patent_number=5513310 (572 words)

	Transfinite number Summary
		In this case, the least element is 'a'.
		If v and w are both in X and v ; w as elements in X, then v ; w as elements of Q. A similar statement holds for Y. If v is an element of X and w is an element of Y, then x ; w.
		If x and y are ordinal numbers then x y means that there is function f from X to Y that maps the least element of X to the least element of Y and if w is the successor of v then f(w) is the successor of f(v).
	www.bookrags.com /Transfinite_number (1152 words)

	Workshop on Scheme: Finding the kth least element of a vector
		Problem: Given a vector, a position in that vector, and a predicate that expresses a total ordering on a domain that includes the elements of that vector, identify the element that would occupy the specified position if the vector were completely sorted.
		At each step, the last element of the sub-vector is chosen as the pivot, and the rest of the sub-vector is partitioned.
		In either of these cases, the sub-vector to be searched has been reduced by at least one element (since it does not include the pivot).
	www.math.grin.edu /~stone/events/scheme-workshop/kth-least.html (473 words)

	PlanetMath: properties of well-ordered sets
		is either empty or has a least element, then
		cannot be chosen bijective, then it can at least be chosen such that its image is a section.
		Cross-references: empty set, maps, restrictions, equation, minimal element, sequences, monotonically decreasing, maximal element, image, surjective, injective, contradiction, mapping, inclusion, structure, order morphism, bijective, poset, well-ordered, least element, strictly, subset, totally ordered set, easy to see, properties, orderings
	planetmath.org /encyclopedia/Section4.html (450 words)

	Sorting
		Selection sort maintains a growing `front' section of the array which is (i)sorted and (ii)less than the remainder of the array.
		At each step, the smallest element in the `remainder' is selected and moved to enlarge the `front' section.
		At some intermediate stage, a[1..i-1] is sorted and, on an element by element basis, less than everything in a[i..N].
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Sort (237 words)

	HsqlHeap (HSQLDB 1.8.0RC10 API) (Site not responding. Last check: 2007-11-03)
		In this context, a Heap is simply a collection-like ADT that allows addition of elements and provides a way to remove the least element, given some implementation-dependent strategy for imposing an order over its elements.
		Retrieves the least element from this Heap, without removing it.
		Retrieves the least element from this Heap, removing it in the process.
	hsqldb.sourceforge.net /alphadocs/devsrc/org/hsqldb/lib/HsqlHeap.html (234 words)

	Math 135: Solutions to Homework Set # 11
		is an ordinal and is the least upper bound of
		has no greatest element, then its least upper bound cannot be an element.
		has a greatest element, then that greatest element is the least upper bound,
	math.berkeley.edu /~scanlon/m135s03/sol11/sol11.html (250 words)

	Principles of Programming Languages: Lecture 6 Supplement
		The special element bot approximates all functions as well as all numbers.
		In general, every computable function mapping a cpo D to D has a least fixed-point.
		The Full Domain of LC We made the simplifying assumption that functions are never passed as arguments or returned as values in describing the domain of LC above.
	www.cs.rice.edu /~taha/teaching/04F/311/Notes/97/6.5.html (614 words)

	Chemistry : Periodic Table : ununoctium : key information
		Earlier, a team of Berkeley Lab scientists announced in 1999 the observation of what appeared to be element 118 but retracted the claim after several confirmation experiments failed to reproduce the results.
		The element 118 nucleus was said to decay less than a millisecond after its formation by emitting an α-particle resulting in an isotope of element 116 (mass number 289, containing 116 protons and 173 neutrons).
		This isotope of element 116 undergoes further α-decay processes to an isotope of element 114 and so on down to at least element 106 (seaborgium).
	www.webelements.com /webelements/elements/text/Uuo/key.html (483 words)

	select kth element (Site not responding. Last check: 2007-11-03)
		Two approaches are a modified distribution sort or select and partition.
		Note: The select-and-partition approximately divides in half the number of elements which must be considered at each step.
		The modified distribution sort divides by m the number of elements at each step.
	www.nist.gov /dads/HTML/selectkth.html (108 words)

	FSA Reference Manual (Site not responding. Last check: 2007-11-03)
		El is the least element occurring in Bbbtree, using the standard ordering of terms.
		El is the largest element occurring in Bbbtree, using the standard ordering of terms.
		BbbtreeB is the result of removing the least element Least from BbbtreeA, in the standard ordering of terms.
	web.mit.edu /course/6/6.863/fsa6/Manual/node22.html (373 words)

	TreeSet (Site not responding. Last check: 2007-11-03)
		The elements are ordered using their natural ordering, or by a
		Adds the specified element to this set if it is not already present.
		If the user attempts to add an element to the set that violates this constraint (for example, the user attempts to add a string element to a set whose elements are integers), the
	gee.cs.oswego.edu /dl/concurrent/dist/docs/java/util/TreeSet.html (2053 words)

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