Again we waited for Montero.

Again omitting recent developments, E.T. Leeds' dictum of 1913 has stood unchallenged: `` So far as archaeology is concerned, there is not the least warrant for the second ( shore occupied by ) of these theories ''.

Again among those jubilantly reunited bunkmates, I was shy with Jessie and acted as I had during those early Saturday mornings when we all seemed to be playing for effect, to be detached and unconcerned with the girls who were properly our dates but about whom, later, in the privacy of our bunks, we would think in terms of the most elaborate romance.

Again, be sure your tripod is handy for those sometimes-necessary time exposures.

Again Reverend Corder saved the bridge when Union soldiers planned to destroy it, after filling its two lanes with hay and straw -- but for what reason is not recorded nor remembered, certainly not because of pressure from an opposing Confederate force.

Again, I at first misconstrued this disconcertingly intense communication, and I quickly cast through my mind to account for her being able to speak, with such utter conviction, of an opinion held by my father, now several years deceased.

Again, in deciding on the content and method of his teaching, does he favor a curriculum which will make his students stronger competitors in the race for higher economic status, or does he favor a curriculum which strengthens students in other ways??

Again it was used as the title for the hoss wrangler, and when the order was given to go out and `` rustle the hosses '', it meant for 'im to go out and herd 'em in.

Again the plan was for me to go alone, but they wouldn't let me.

Again he groped for the light switch.

Again, India has imposed formidable barriers against the entrance of additional missionaries, and fanatical Hindu parties are expected to seek further action against Christians once the influence making for tolerance due to Nehru and his followers is gone.

Again, a force too strong for unfrozen bodies to endure would be applied.

Again, this difference is much more obvious to a Turkish speaker, for whom and are separate phonemes, than to an English speaker, for whom they are allophones of a single phoneme.

*" When Johnny Comes Marching Home " ( sometimes " When Johnny Comes Marching Home Again ") is a popular song of the American Civil War that expressed people's longing for the return of their friends and relatives who were fighting in the war.

Again, due primarily to the VFL recruiting the best players, Victoria dominated interstate matches for three quarters of a century.

Again the massive amounts and new types of data generate new opportunities for bioinformaticians.

A rough acoustic version of " Never Go Hungry Again ", recorded during an interview for The Times in November, was also released.

Again by assumption, a similar function also exists for f at g ( a ).

Again, a liquid receives its shape from the vessel in which it is contained ; but were the pressure of the containing sides withdrawn, it would not retain its form for an instant.

" Again, the Cubs ' unusually high number of day games is often pointed to as one reason for the team's inconsistent late season play.

( Again, the line blurs with high-end calculators, which use processor chips associated with computer and embedded systems design, particularly the Z80, MC68000, and ARM architectures, as well as some custom designs specifically made for the calculator market.

Again the track, owned by the municipality of Zandvoort, was in danger of being permanently lost for motorsports.

In 1996, Destry Rides Again was selected for preservation in the United States National Film Registry by the Library of Congress as being " culturally, historically, or aesthetically significant ".

Again, by spreading one's purchases over several wine dealers, one becomes familiar with the names and specialties of reputable wine dealers and shippers abroad.

Again, since P ( A ∩ B ) usually becomes a very small error term, the exclusive OR gate has limited value in a fault tree.

Again involved with Lila Cheney, the team becomes trapped in a confrontation between her and the alien race, the K ' Lanti.

The sixth season episode " Normal Again " posits Buffy's world of Sunnydale as a manifestation of psychopathology: after being stabbed by a demon, Buffy becomes convinced that the world in which she is a hero is an illusion.

Again by coincidence, Xuzhu becomes the prince consort of Western Xia due to a previous affair with Princess Yinchuan, to whom he is happily married.

Again, that further subsidiary body corporate becomes a member of the principal body corporate.

* Charmed Again ( Part 2 ) ( season four, as a ghost, she then becomes corporeal to meet and hug Paige for the first time )

Again, Egypt becomes the mystified cradle of civilization.

* January 25 — At age 84, octogenerian comedian George Burns becomes by far the oldest performer ( to that time ) to have a single in the top 40 of Billboards Hot Country Singles chart with " I Wish I Was 18 Again.

Again this becomes clear if the visitors are viewed as individuals on a small scale, but still causes a large number of complaints that analytics software cannot be working because of a failure to understand the metrics.

Again, whenever a waste pile becomes empty, no matter how many cards it previously had, it is filled with a card from the wastepile.

Another polynomial viewpoint is exploited by the Winograd algorithm, which factorizes into cyclotomic polynomials — these often have coefficients of 1, 0, or − 1, and therefore require few ( if any ) multiplications, so Winograd can be used to obtain minimal-multiplication FFTs and is often used to find efficient algorithms for small factors.

In 1847 Gabriel Lamé announced a solution of Fermat's Last Theorem for all -- i. e., that the Fermat equation has no solutions in nonzero integers, but it turned out that his solution hinged on the assumption that the cyclotomic ring is a UFD.

This geometric fact accounts for the term " cyclotomic " in such phrases as cyclotomic field and cyclotomic polynomial ; it is from the Greek roots " cyclo " ( circle ) plus " tomos " ( cut, divide ).

In algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique polynomial with integer coefficients, which is a divisor of X < sup > n </ sup >- 1 and is not a divisor of X < sup > k </ sup >- 1 for any k < n.

Any cyclotomic extension ( for either definition ) is abelian.

Then there is a cyclic cubic field inside the cyclotomic field of pth roots of unity, and a normal integral basis of periods for the integers of this field ( an instance of the Hilbert – Speiser theorem ).

The cyclotomic polynomials, taken over all sphenic numbers n, may contain arbitrarily large coefficients ( for n a product of two primes the coefficients are or 0 ).

the conjugacy class is called a Frobenius element of p. If we take for K the mth cyclotomic field, whose Galois group over Q is the units modulo m ( and thus

23 is the first prime P for which unique factorization of cyclotomic integers based on the Pth root of unity breaks down.

A significant case in the theory of cyclotomic fields is that for the nth roots of unity, for n a composite number, the subfields generated by the p < sup > k </ sup > th roots of unity for prime powers dividing n are linearly disjoint for distinct p.

An important class of polynomials whose irreducibility can be established using Eisenstein's criterion is that of the cyclotomic polynomials for prime numbers p. Such a polynomial is obtained by dividing the polynomial by the linear factor corresponding to its obvious root 1 ( in fact its only rational root if ):

Remarkably Schönemann and Eisenstein, once having formulated their respective criteria for irreducibility, both immediately apply it to give an elementary proof of the irreducibility of the cyclotomic polynomials for prime numbers, a result that Gauss had obtained in his Disquisitiones Arithmeticae with a much more complicated proof.

The left hand side of the cyclotomic identity is the generating function for the free associative algebra on α generators, and the right hand side is the generating function for the universal enveloping algebra of the free Lie algebra on α generators.

In Mémoire sur la résolution des équations ( 1771 ) he reported on symmetric functions and solution of cyclotomic polynomials ; this paper anticipated later Galois theory ( see also abstract algebra for the role of Vandermonde in the genesis of group theory ).

* Ideal Numbers, Proof that the theory of ideal numbers saves unique factorization for cyclotomic integers at Fermat's Last Theorem Blog.

Similar statistical laws also hold for splitting of primes in the cyclotomic extensions, obtained from the field of rational numbers by adjoining a primitive root of unity of a given order.