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( For generalizations, see the next subsection.
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For and generalizations
For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations.
For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest.
For this reason, generalizations of vector operations to matrices ( e. g. in matrix calculus and statistics ) often involve a trace of matrix products.
For example, a handful of people might promote hateful racial generalizations which spread to the rest of a culture through the bandwagon effect, leading to discrimination against members of that race.
* For generalizations to infinite dimensions.
* For generalizations to infinite dimensions.
For generalizations to Grassmannians, see also tautological bundle.
For a review as well as generalizations to weighted networks, see Opsahl et al.
For and see
( For details see inset, fig. 5.
For some significant new items see the pictures.
( For instance, see Example 2 of Section 5-5, on red cards in hands of 5.
For A good many seasons I've been looking at the naughty stuff on television, so the other night I thought I ought to see how immorality is doing on the other side of the fence in movies.
Last season, the Comedie's two principal experiments came to grief, and, in consequence, we can expect fairly soon to see still newer productions of Racine's `` Phedre '' and Moliere's `` School For Wives ''.
For all he saw or cared to see, this could have been a town in Italy, not the outskirts of Philadelphia.
: For a detailed presentation of the various points of view around the definition of " algorithm " see Algorithm characterizations.
For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming.
: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.
( For an example, see Proto-Uralic language.
For the Hungarian clothing, see Atilla ( clothing ).
For other uses, see Attila ( disambiguation ).
* For a utilitarian analysis of religion, see The ( F ) Utility of Religion: Who Needs God ( s )?– A Prospective Bible for Non-Believers at http :// bradmusil. kramernet. org
For a table of accented Greek characters, see Greek diacritics: Computer encoding.
For Soviet transportation, see Transport in the Soviet Union.
* For Ibn Sina's life, see Ibn Khallikan's Biographical Dictionary, translated by de Slane ( 1842 ); F. Wüstenfeld's Geschichte der arabischen Aerzte und Naturforscher ( Göttingen, 1840 ).
* For a new understanding of his early career, based on a newly discovered text, see also: Michot, Yahya, Ibn Sînâ: Lettre au vizir Abû Sa'd.
* For relations, see relation-preserving automorphism.
For other uses, see Athena ( disambiguation ), Athene ( disambiguation ), Athina ( disambiguation ) and Pallas Athena ( disambiguation )
For cryptographers, a cryptographic " break " is anything faster than a brute force — performing one trial decryption for each key ( see Cryptanalysis ).
For more details of this early work, see Alpha particle # History of discovery and use.
For all ice shelfs see List of Antarctic ice shelves.
For a list of all Antarctic islands see List of Antarctic and sub-Antarctic islands.
For all ice shelfs see List of Antarctic ice shelves.
For and next
For instance, a site adjoining other publicly owned lands, such as a national forest or a public road, may be desirable, whereas a site next to an industrial plant might not.
For four of the six ( the anaconda and the amethystine python cannot be included for lack of data ) there is also a correlation between size at maturity and maximum length, the boa constrictor being the smallest and the Indian python the next in size at the former stage.
For the next hour he scrambled happily up and down the ladder, sharing the excitement of reporters who had seen McKinley's assassination, the Iroquois Theater fire in Chicago, and the Hall-Mills trial.
For example, three isomers exist for cresol because the methyl group and the hydroxyl group can be placed next to each other ( ortho ), one position removed from each other ( meta ), or two positions removed from each other ( para ).
For the next 100 years the Anadyr was the main route from the Arctic to the Pacific and Kamchatka.
For the next few years, Newton was raised by his emotionally distant stepmother while his father was at sea, and spent some time at a boarding school where he was mistreated.
For the next twelve months Alexei was kept constantly on the move.
For the next five years, the Danes occupied other parts of England.
For the next five years, they were educated at home, largely by their father and aunt.
For the next five years, Anne spent no more than five or six weeks a year with her family, during holidays at Christmas and in June.
For example, cold weather crops like rye, oats, wheat, and apples are expected to decline by about 15 % in the next fifty years and strawberries will drop as much as 32 % simply because of projected climate changes of a few degrees.
For the next two years he taught alongside his father.
For the next half-century, Fuller developed many ideas, designs and inventions, particularly regarding practical, inexpensive shelter and transportation.
For the next thirty years Gladstone and Liberalism were synonymous.
For the next several years, the BPCA made slow progress.
For the next five years he and the Northern Alliance were busy fighting the Taliban until the 2001 US-led Operation Enduring Freedom in which the Taliban government was toppled.
For the next ten years, the team would winter at NAS Key West, Florida.
For example, if the black pawn has just advanced two squares from g7 ( initial starting position ) to g5, then the white pawn on f5 may take it via en passant on g6 ( but only on white's next move ).
For his next film Chaplin returned to comedy.
For the next decade, this was the name the nation was listed under.
For almost the next 1, 000 years, these states, their relations with each other, and their effects on the peoples who lived in stateless societies along their peripheries dominated Chad's political history.
For the next forty years, Chile's armed forces would be distracted from meddling in politics by skirmishes and defensive operations on the southern frontier, although some units got embroiled in domestic conflicts in 1851 and 1859.
For the next four centuries, the Kingdom of Croatia was ruled by the Sabor ( parliament ) and a Ban ( viceroy ) appointed by the king.
For the next half-century, Constantinople was the seat of the Latin Empire.
For example, if you bet on " 5 and 1 " on the hop, you are betting that the next roll will have a 5 on one die and a 1 on the other die.
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