Indeed, applications of asymptotic analysis in mathematical modelling often centre around a nondimensional parameter which has been shown, or assumed, to be small through a consideration of the scales of the problem at hand.

Indeed, the energy density of some material involved in the formation of impact craters is many times higher than that generated by high explosives.

Indeed, this integral is strongly suggestive of the notion that the ' density ' of primes around t should be 1 / lnt.

This is a special case of the Chebotarev density theorem for the Nth cyclotomic field K. Indeed, the Galois group of K / Q is abelian and can be canonically identified with the group of invertible residue classes mod N. The splitting invariant of a prime p not dividing N is simply its residue class because the number of distinct primes into which p splits is φ ( N )/ m, where m is multiplicative order of p modulo N ; hence by the Chebotarev density theorem, primes are asymptotically uniformly distributed among different residue classes coprime to N.

Indeed, a very small departure of Ω from 1 in the early universe would have been magnified during billions of years of expansion to create a current density very far from critical.

Indeed, one such clause can be rewritten as, that is, if are all true, then y needs to be true as well.

Indeed, the very first program may very well run for hours without needing access to a peripheral.

Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as TextGraphs, as well as various ' Net ' projects, such as WordNet, VerbNet, and others.

Indeed Homer places Hector as peace-loving, thoughtful as well as bold, a good son, husband and father, and without darker motives.

Indeed, researchers found significant genetic divergence between the two groups, as well as between them and another isolated population of C. a. alleganiensis.

Indeed " he people of Southern Europe, as well as South-East Asia, will be fighting their way into countries such as Canada, Australia and Britain ".

Indeed, a great many of the refugees fleeing to China because of famine still showed significant support for the current government as well as pride in their homeland.

Indeed, as it turned out, all eight electors in Pinckney's home state of South Carolina, as well as at least one elector in Pennsylvania, cast ballots for both Jefferson and Pinckney.

Indeed there were Scots, Germans and Dutch people inhabitating major towns of the area, as well as several Italian artists who had been " imported " to the lands of modern Belarus by the magnates.

Indeed, a unique network of blood vessels is well adapted to provide the photoreceptor layer with copious quantities of blood.

" Indeed, an appearance on The Tonight Show Starring Johnny Carson helped to propel the success of the book, as well as Ehrlich's celebrity.

Indeed, as with the Induction plot, the story of a headstrong woman tamed by a man was a universal and well known one, found in numerous traditions.

) Indeed between 900 BC and AD 100, sacred Delos was a major cult centre, where Dionysus is also in evidence as well as the Titaness Leto, mother of the above mentioned twin deities.

Indeed, he is credited with advocating forced conversions of local Jewry, as well as mob violence against Jews who refused.

Indeed, to Catherine, Diane was an intrusive elder cousin as well as a rival.

Indeed, the unreliability of judicial decisions based on demeanor is well established.

Indeed, the great ships were almost as well known for their ornamental design ( some ships, like the Vasa, were gilded on their stern scrollwork ) as they were for the power they possessed.

Indeed, Dickens knew the area well and was a customer of the Finsbury Savings Bank on Sekforde Street, a street linking Clerkenwell Green to St John Street.

Indeed, evidence suggests that Rosales was very nearly shot as well for helping García Lorca by the Civil Governor Valdes. The Basque Communist poet Gabriel Celaya wrote in his memoirs that he once found García Lorca in the company of Falangist José Maria Aizpurua.

Indeed there are five villages called Hindenburg running in a straight line from Westphalia to Pomerania, as well as three eastern Spiegelbergs and a trail of etymology from Beverungen south of Hamelin to Beveringen northwest of Berlin to Beweringen in modern Poland.

Indeed, so strongly were Powell and Loy identified with the characters of the Charleses in the public mind that many mistakenly assumed the actors were a couple in real life as well.

Indeed, during the second half of the 19th century, when corset wearing was common, there were sport corsets specifically designed to wear while bicycling, playing tennis, or horseback riding, as well as for maternity wear.

Indeed, much awareness of " Ashkenazi Jews " as an ethnic group or category stems from the large number of genetic studies of disease, including many that are well reported in the media, that have been conducted among Jews.

Indeed, all Austrian attempts to frustrate the French crossing by using the tactics that worked so well during the Battle of Aspern-Essling-sending barges or trees downstream to ram the bridges-failed utterly on 5 July, namely because the French flotilla was in full control of the river.

Indeed William may well have been the most learned man in twelfth-century Western Europe.

Indeed, there are some cities where the suburban shopping pulls customers who are geographically much nearer to downtown.

Indeed, in some periods of our history and in some neighborhoods the job opportunities have been so good that undoubtedly a great many boys who were potential members of the professions quit school at an early age and went to work.

Indeed, he rather relished the idea of being of the same rough texture as some of his subjects.

Indeed he seems more or less responsible together with Gasparo da Salò and some Micheli's like Zanetto or Pellegrino for giving the instruments of the modern violin family their definitive profile.

Indeed, some boomerangs were not thrown at all, but were used in hand to hand combat by Indigenous Australians.

Indeed, some Bayesians have argued the prior state of knowledge defines the ( unique ) prior probability-distribution for " regular " statistical problems ; cf.

Indeed, in those cases where no clear consensus exists on a given norm, the drafting of criminal law by the group in power to prohibit the behaviour of another group may seem to some observers an improper limitation of the second group's freedom, and the ordinary members of society have less respect for the law or laws in general — whether the authorities actually enforce the disputed law or not.

Indeed, in the U. S. estimates of the environmental regulation's total costs reach 2 % of GDP, and any new regulation will arguably contribute in some way to that burden.

In a ring all of whose ideals are principal ( a principal ideal domain or PID ), this ideal will be identical with the set of multiples of some ring element d ; then this d is a greatest common divisor of a and b. But the ideal ( a, b ) can be useful even when there is no greatest common divisor of a and b. ( Indeed, Ernst Kummer used this ideal as a replacement for a gcd in his treatment of Fermat's Last Theorem, although he envisioned it as the set of multiples of some hypothetical, or ideal, ring element d, whence the ring-theoretic term.

Indeed earlier, when Babur had become ill, some of the nobles had tried to install Humayun's uncle, Mahdi Khwaja, as ruler.

Indeed, the earliest theories and practices of hypnotism, even those of Braid, resemble the cognitive-behavioural orientation in some respects.

Indeed some, such as consultants and providers of investment services, offer no guarantees of the value for price paid.

Indeed, some experts suggest that Scott deliberately used Ivanhoe to illustrate his own combination of Scottish patriotism and pro-British Unionism.

Indeed, for some programming languages, there is little performance difference between an interpretive-or compiled-based approach to their implementation.

Indeed, his father recognized that Jack was a far better painter than he, and also believed that ' some day I will be remembered as the father of a great poet, and the poet is Jack '.

Indeed, in these countries, a jury trial is seen as a failing of some foreign legal system rather than an advantage ; this is despite the fact that both nations are common law countries.

Indeed, during the Cucuteni-Trypillian Culture, some of the settlements in this area were larger than anywhere on Earth at the time, and they predate even the earliest towns of Sumer in the Mesopotamia.

Indeed, one-size-fits-all programming is no longer seen as tenable by some, as the diversity of musical tastes among the listening public have created a proliferation of radio formats in what some might call a form of narrowcasting.

( Indeed, Pedersen's older contemporary Henry Sweet attributed some of the resistance by Indo-European specialists to hypotheses of wider genetic relationships as " prejudice against dethroning from its proud isolation and affiliating it to the languages of yellow races ".

" Indeed, olive suckers sprout readily from the stump, and the great age of some existing olive trees shows that it was perfectly possible that the olive tree of the Acropolis dated to the Bronze Age.

Indeed, some languages are designed so that the meanings of certain syntactic constructs cannot even be described without referring to the core library.