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For the second definition, P ( X ) is separable if all of its irreducible factors in K have distinct roots in the splitting field of P ( X ), or equivalently in an algebraic closure of K. For this definition, separability depends explicitly on the field K, as an irreducible polynomial P which is not separable becomes separable over the splitting field of K. Also, for this definition every polynomial over a perfect field is separable, which includes in particular all fields of characteristic 0, and all finite fields.
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For and second
For a second, engages, cooks, voyageurs appeared struck dumb.
For men who had left cattle alone after getting their first notices had received no second.
The second specific comment was the report of Eisenhower's Commission on National Goals, titled Goals For Americans.
For the second we might have to choose the volume of reactor or amount of cooling to be supplied ; ;
For another second or two he gave in to the annoyance that was directed at himself ; ;
For a split second, Nick relaxed his grip and Poet's slippery body spun completely around before Nick could stop him, holding him now from the rear.
-- For a second month in a row, Multnomah County may be short of general assistance money in its budget to handle an unusually high summer month's need, the state public welfare commission was told Friday.
In chapter four of the second Inspector Hanaud novel, The House of the Arrow ( 1924 ), Hanaud declares sanctimoniously to the heroine, " You are wise, Mademoiselle … For, after all, I am Hanaud.
For a 256-bit block, the first row is unchanged and the shifting for the second, third and fourth row is 1 byte, 3 bytes and 4 bytes respectively — this change only applies for the Rijndael cipher when used with a 256-bit block, as AES does not use 256-bit blocks.
Grant followed the album with her second Christmas album, Home For Christmas in 1992, which included the song " Breath of Heaven ( Mary's Song )", written by Chris Eaton and Grant, and would later be covered by many artists, including Donna Summer, Jessica Simpson ( who acknowledged Grant as one of her favorite artists ), Vince Gill, Sara Groves, Point of Grace, and Broadway star Barbara Cook.
For Canadian use and as a second source for US missiles, Canadair was selected to build the missiles in Quebec.
For the third movement, Beethoven used variation techniques ; he also did this in the second movement of his Quartet op.
For example, a runner on first base advances to second on a passed ball.
For example, a 500 gigabyte hard drive holds bytes, and a 100 megabit per second Ethernet connection transfers data at bit / s.
For a binomial involving subtraction, the theorem can be applied as long as the opposite of the second term is used.
For example, the second edition of the popular introductory textbook, An Outline of Money, devoted the last three of its ten chapters to questions of foreign exchange management and in particular the ' problem of balance '.
For the second exam, called the Principles and Practices, Part 2, or the Professional Engineering exam, candidates may select a particular engineering discipline's content to be tested on ; there is currently not an option for BME with this, meaning that any biomedical engineers seeking a license must prepare to take this examination in another category ( which does not affect the actual license, since most jurisdictions do not recognize discipline specialties anyway ).
" For his second appearance in front of cameras, Chaplin selected the costume with which he became identified.
For Irenaeus the imitation of Christ is based on God's plan of salvation, which involved Christ as the second Adam.
For example the President for the second half of 2007, Portugal, was the second in a trio of states alongside Germany and Slovenia with whom Portugal had been co-operating.
For example, in a copper wire of cross-section 0. 5 mm < sup > 2 </ sup >, carrying a current of 5 A, the drift velocity of the electrons is on the order of a millimetre per second.
For the 1999 season, Cleveland added relief pitcher Ricardo Rincón and second baseman Roberto Alomar, brother of catcher Sandy Alomar, Jr, and won the Central Division title for the fifth consecutive year.
For instance, in any group second powers behave well
For example, if the first approach is taken then " car park " will come after " carbon " and " carp " ( as it would if it were written " carpark "), whereas in the second approach " car park " will come before those two words.
For and definition
: For a detailed presentation of the various points of view around the definition of " algorithm " see Algorithm characterizations.
For Lie algebras the definition is slightly different.
For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects.
For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero.
For a rigorous treatment of the Dirac inner product of non-normalizable states see the definition given by D. Carfì in and.
For a rigorous definition of basis with a continuous set of indices and consequently for a rigorous definition of position and momentum basis see.
For example, they might interpret a tomato as a vegetable — according to the English definition of tomato — even though the ideal Blissymbol of vegetable was restricted by Bliss to just vegetables growing underground.
For example, in Virginia, the definition of the conduct that constitutes the crime of robbery exists only in the common law, and the robbery statute only sets the punishment.
For example, jīngjì ( 经济 ／ 經濟, keizai ), which in the original Chinese meant " the workings of the state ", was narrowed to " economy " in Japanese ; this narrowed definition was then re-imported into Chinese.
For alternative ( equivalent ) formulations of the definition in terms of a bijective function or a surjective function, see the section Formal definition and properties below.
In his preface to Jürgen Osterhammel's Colonialism: A Theoretical Overview, Roger Tignor says, " For Osterhammel, the essence of colonialism is the existence of colonies, which are by definition governed differently from other territories such as protectorates or informal spheres of influence.
For example, in formal languages like mathematics, a ' stipulative ' definition guides a specific discussion.
For this reason, Locking adds that a definition of a term must not comprise of terms which are synonymous with it.
For terms such as these it is not possible and indeed not necessary to state a definition ; rather, one simply comes to understand the use of the term.
For the mathematical definition, see Decimal representation.
For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.
For example, should animal experimentation become illegal in a society, it will no longer be an ethical issue on Hoy's definition.
For example, the statement " A society is free if and only if liberty is maximized and people are required to take responsibility for their actions " is true or paradoxical, depending on the individual's definition of liberty.
For a long time this definition was used with a derogatory intention.
For all intents and purposes, the 1947 ICC definition confirmed the 1895 MCC definition and gave it international recognition and usage.
For a planar graph, the crossing number is zero by definition.
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