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Topic: Ordered sequence

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	Ordinal number - Wikipedia, the free encyclopedia
		For example, the ordinal 42 is the order type of the ordinals less than it, i.e., the ordinals from 0 (the smallest of all ordinals) to 41 (the immediate predecessor of 42), and it is generally identified as the set {0,1,2,…,41}.
		A well-ordered set is an ordered set in which every non-empty subset has a least element: this is equivalent (at least in the presence of the axiom of dependent choices) to just saying that the set is totally ordered and there is no infinite decreasing sequence, something which is perhaps easier to visualize.
		Any ordinal can be made into a topological space by endowing it with the order topology (since, being well-ordered, an ordinal is in particular totally ordered): in the absence of indication to the contrary, it is always that order topology which is meant when an ordinal is thought of as a topological space.
	en.wikipedia.org /wiki/Ordinal (4254 words)

	Sequence - Free net encyclopedia (Site not responding. Last check: 2007-10-30)
		In mathematics, a sequence is a list of objects (or events) arranged in a "linear" fashion, such that the order of the members is well defined and significant.
		A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements.
		If the terms of the sequence are a subset of an ordered set, then a monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing.
	www.netipedia.com /index.php/Sequence (804 words)

	Ordinal number
		Ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. The mathematician Georg Cantor showed in 1897 how to extend this concept beyond the natural numbers to the infinite and how to do arithmetic with these transfinite ordinals.
		Viewed this way, every natural number is a well-ordered set: the set 4 for instance has the elements 0,1,2,3 which are of course ordered as 0<1<2<3 and this is a well-order.
		One example of these is an important characterization of the order relation between ordinals: every set of ordinals has a supremum, the ordinal gotten by taking the union of all the ordinals in the set.
	www.ebroadcast.com.au /lookup/encyclopedia/or/Ordinal.html (1239 words)

	Tools: Protein Identification using de novo Peptide Sequence Data
		Ordered sequence tags (runs of amino acids for which the order is known) are designated by single letter amino acid codes that are not enclosed in square brackets.
		Disordered sequence tags (runs of amino acids for which the order is unknown) are designated by single letter amino acid codes that are enclosed in square brackets.
		The user can require that all, some, or none of the ordered sequence tags be present for a match to be shown.
	proteomics.mcw.edu /denovoid/help.jsp (452 words)

	Ordered
		If the type is only partially ordered, it will be undefined for some values of the type, whereas if it is totally ordered, it will be defined for all values.
		Here the type officer is fully ordered, because the less-than operator is defined for all values of officers, while the type soldier is partially ordered, since the less-than operators are only defined for privates.
		A scalar type is an ordered type whose values form a fully ordered sequence.
	www.sei.cmu.edu /community/easel/lrm/Ordered.html (1674 words)

	A High-Resolution Radiation Hybrid Map of the Human Genome Draft Sequence -- Olivier et al. 291 (5507): 1298 -- Science
		be the draft sequence order as the Celera sequence order.
		Comparison of STS order in the draft sequence and the Celera sequence with the order in the TNG map.
		Although the fact that the draft sequence of individual clones is often in unordered and unoriented fragments might reduce the hit rate somewhat below that of finished sequence, the effect should be minimal given that we require an alignment of only 100 base pairs or greater to call a positive hit.
	www.sciencemag.org /cgi/content/full/291/5507/1298 (4967 words)

	FanFiction.Net : Dictionary & Thesaurus (Site not responding. Last check: 2007-10-30)
		having or evincing a systematic arrangement; especially, having elements succeeding in order according to rule; as, an ordered sequence; an ordered pair.
		To put in order; to reduce to a methodical arrangement; to arrange in a series, or with reference to an end.
		[1913 Webster] Order arms (Mil.), the command at which a rifle is brought to a position with its butt resting on the ground; also, the position taken at such a command.
	www.fanfiction.net /dictionary.php?word=Ordered (238 words)

	[No title]
		Values specified by or elements, that are not present in context, are represented as an empty sequence.
		If argument of a function is described as a set, then when a sequence with matching elements is given, it should be compacted with preserved order before evaluation: each subsequent duplicate value should be removed.
		ordered-or or — ordered or and or return boolean true, if at least one argument has boolean value true: some arguments may be invalid.
	www.oasis-open.org /archives/xacml/200208/doc00007.doc (876 words)

	Addition Sequence
		An addition sequence is a sequence starting with a certain value 'a' where each element is the sum of two prior elements (not specifically the two just before it like the FibonacciSequence, neither specifically two different elements):
		I think the next step is to prove that given any addition sequence, and given some prime p_i that is a factor of the final desired number, there is some ordered addition sequence that does have a SPLIT that either has the same or fewer number of steps.
		Given some ordered addition sequence that does not have a split (in other words, a_n = a_0 + a_i), it can be converted to an ordered addition sequence (with the same or fewer number of steps), and also has a split, by...
	c2.com /cgi/wiki?AdditionSequence (985 words)

	Computer software - Wikipedia, the free encyclopedia
		The concept of reading different sequences of instructions into the memory of a device to control computations was invented by Charles Babbage as part of his difference engine.
		Software is an ordered sequence of instructions for changing the state of the computer hardware in a particular sequence.
		In particular, it may require additional software from a software library in order to be complete.
	en.wikipedia.org /wiki/Computer_software (1663 words)

	SEQ Home Page
		The basic model of a sequence is a set of records mapped to an ordered domain of ``positions''.
		All the sequence operators are extended to work with groups of similar sequences, instead of with single sequences.
		One of the important observations is that accessing sequence data in a single stream is probably very efficient, and evaluation strategies should take this into account.
	www.cs.cornell.edu /Info/People/praveen/projects/seq.html (1194 words)

	Index Ofa Sub Set
		Determine the index of the B in the sequence of all subsets of A ordered lexicographically.
		The ordered sequence of subsets of A is
		Determine the index of the B in the sequence of all subsets of the same cardinality of A ordered lexicographically.
	c2.com /cgi/wiki?IndexOfaSubSet (894 words)

	Do I have this definition right? (and a suprise bonus question on sequences!)
		I have always thought that it was enough to define a sequence to be a countable set- so that there was some order for the set- but it didn't matter which of the infinite number of possible orderings you chose.
		sequences with orderings are also crucial for defining countable ordinals.
		a set of ordered pairs whose first elements are the positive integers, and each pair is still ordered, no matter what sequence the ordered pairs are presented in.
	www.physicsforums.com /showthread.php?t=76889 (794 words)

	Dr. Dobb's \| Standard C/C++ \| April 15, 2003
		In either case, the sequence is said to be ordered by a rule if no pair of elements in the sequence breaks the rule.
		An ordering algorithm rearranges elements as needed to impose the desired ordering on a sequence.
		If the sequence is larger than the buffer, the second function falls back on a classic divide-and-conquer strategy to reduce the problem to one of manageable size.
	www.ddj.com /dept/cpp/184403241?pgno=6 (1913 words)

	System for managing information in a three dimensional workspace - Patent 5312478
		Thus, the long sequence of keystrokes is reduced to the short sequence of keystrokes that calls the macro.
		The system includes means for organizing information into an ordered sequence of worksheets in a workspace; means for selecting a plurality of worksheets from the ordered sequence of worksheets; and means for displaying on the display screen a perspective presentation of the selected worksheets.
		It shifts the sequence of integers representing columns A through G to the right by one element and it stores FF in all of the elements that now represent the new column B. The resulting stored sequence is shown by state IV in FIG.
	www.freepatentsonline.com /5312478.html (15782 words)

	Method of determining an ordered sequence of subfragments of a nucleic acid fragment by hybridization of ... (Site not responding. Last check: 2007-10-30)
		The sequence of a given nucleic acid fragment is read by the hybridization and assembly of positively hybridizing exactly complementary oligonucleotide probes through overlapping subfragments.
		A method for determining an ordered sequence of one or more subfragments of a nucleic acid fragment by ordering oligonucleotide probe sequences which are complementary to subfragments of said nucleic acid fragment, comprising the steps of:
		(c) ordering said subset of oligonucleotide probes by compiling overlapping sequences of said subset of oligonucleotide probes which are exactly complementary to one or more subfragments of said nucleic acid fragment, thereby determining the ordered sequence of one or more subfragments of a nucleic acid fragment.
	www.delphion.com /details?pn10=US05492806 (467 words)

	Sequence
		A utility class that provides access to small sequence of items that grow at the end and require quick ordered and indexed access.
		raptor_sequence is optimised to append to the end of the sequence.
		After this operation, sequence src will be empty (zero size) but will have the same item capacity as before.
	librdf.org /raptor/api/raptor-section-sequence.html (322 words)

	More on Ordinal Numbers
		A set S is an ordinal if and only if S is totally ordered with respect to set containment and every element of S is also a subset of S. (Here, "set containment" is another name for the subset relationship.) Such a set S is automatically well-ordered with respect to set containment.
		This relies on the axiom of well foundation: every nonempty set S has an element a which is disjoint from S. Note that the natural numbers are ordinals by this definition.
		For example, in the topological space ω1+1, the element ω1 is in the closure of the subset ω1 even though no sequence of elements in ω1 has the element ω1 as its limit.
	www.artilifes.com /ordinal-numbers.htm (1747 words)

	[No title]
		Calculate_mins computes the ordered sequence M. The elements of M are the numbers that would have been extracted by “Extract_min” commands in the given input sequence of “Insert” and “Extract_min” commands.
		M should preserve the order in which the numbers were extracted.
		Note that while processing the “Extract_min” command from the input, your program does not necessarily need to update the set S and sequence M to reflect the true online state of S and M. Only after the “Calculate_mins” command is processed the sequence M is required to be updated.
	www.cs.technion.ac.il /~ct234218/20-2/exs/wet1/wet1.doc (486 words)

	Method for tracking a video object in a time-ordered sequence of image frames - Patent 6724915
		The present invention is related to the field of digital video processing and analysis, and more specifically, to a method and apparatus for tracking a video object in an ordered sequence of two-dimensional images, including obtaining the trajectory of the video object in the sequence of images.
		Video object descriptors are generated by a generating tool which decomposes frames of video sequences and tracks movement of objects in those frames so as to generate a frame sequential file of video object descriptors.
		In order to find the best marker location, the location that gives the least mean square error MSE or the maximum correlation C value, in the current frame 250, logarithmic or exhaustive search strategies are applied in 3-D space, (z,d.sub.x,d.sub.y) space.
	www.freepatentsonline.com /6724915.html (6417 words)

	Searching all possible paths
		A computer outputting representations for the members of an infinite set gives an ordering to the members that is not present in the original set.
		This is not the same as the set of all ordered sequences of integers needed to specify the position of every node in the tree.
		is the map between an unordered sequence of integers and the ordered sequence defined in the above paragraph.
	www.mtnmath.com /whatrh/node55.html (879 words)

	Interleaving Fibonacci Numbers
		The sequence of Fibonacci numbers is defined by the initial values f
		For example, given the even-ordered sequence 0, 1, 3, 8, 21, 55, 144, … we could simply apply the “greedy algorithm” by expressing each term as the sum of the maximum number of the immediately preceding terms.
		This shows that another way of arriving at the recurrence for the kth Fibonacci numbers is to solve for the (k-2)th degree polynomial that gives, when multiplied by the characteristic polynomial of the Fibonacci sequence, a polynomial whose only non-zero coefficients are for powers that are multiples of k.
	www.mathpages.com /home/kmath285/kmath285.htm (514 words)

	Integrated and Sequence-Ordered BAC- and YAC-Based Physical Maps for the Rat Genome -- Krzywinski et al. 14 (4): 766 -- ... (Site not responding. Last check: 2007-10-30)
		Representation of sequence positions of map contigs in the manually edited fingerprint map (green) and merged map (blue) on the first 100 Mb of Chromosomes 1-5.
		If a contig is localized to disparate regions of the sequence assembly and appears to be correctly constructed, its glyph is red.
		Representation of consistency between the order of YACs in the YAC physical map and sequence assembly.
	www.genome.org /cgi/content/full/14/4/766 (8161 words)

	Applications
		That is, the ordered pair is comprised of the coefficient of the
		The advantage of using the sequence of ordered pairs to represent such a polynomial is that we can omit from the sequence those pairs that have a zero coefficient.
		Of course, the worst-case running time of the polynomial differentiation will depend on the way that the sequence of ordered pairs is implemented.
	www.brpreiss.com /books/opus5/html/page189.html (566 words)

	Groups and sequences
		Encyclopedia of Integer Sequences which count orbits of an infinite permutation group acting on n-sets or n-tuples of elements of the permutation domain.
		The purpose of this paper is to document all examples known to the author of such sequences occurring in the Encyclopedia of Integer Sequences.
		Structures such as graphs and partial orders can be described by a single binary relation, but in general we do not restrict the arities of the relations, and also permit an infinite number of relations.
	www.cs.uwaterloo.ca /journals/JIS/VOL3/groups.html (4374 words)

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