Given a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given enough time and repeated exposure to the antibiotic, a population of antibiotic-resistant bacteria will emerge.

Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm.

Heterogeneity / Variability: Given the very nature of services, each service offering is unique and cannot be exactly repeated even by the same service provider.

Given the evidence of A. C. Elias about the acrimony of Swift's departure from the Temple household, evidence from Swift's Journal to Stella about how uninvolved in the Temple household Swift had been, and the number of repeated observations about himself by the Tale's author, it seems reasonable to propose that the digressions reflect a single type of man, if not a particular character.

Given the possibility of accumulation of toxins, repeated consumption is not recommended.

Given an action that must be repeated, for instance, five times, different languages ' for loops will be written differently.

Given the hero's repeated laments over his own ageing and mortality, the title can be seen as ironic.

Given the consistent failures in this research literature to disprove the null hypothesis, the burden of empirical proof is on those who argue that the children of sexual minority parents are worse off than the children of heterosexual parents.

Given Zemlya i Volya's failures in its propaganda efforts among the peasants in the movements " to the people " in the early 1870s, Narodnaya Volya turned its energies against the central government.

Given the supposed closeness of war, the FI thought that the Communist Parties and social democratic parties would be the only significant force that could defend the workers of the world against the imperialist camp in those countries where there were mass forces.

Given the fact that the Lakeport area has an economy that is based somewhat on agricultural activities occurring in the Big Valley and Scotts Valley area which involve the growing and harvesting of food and nut crops as well as the increasing wine industry, there are a significant number of transient and seasonal farm workers.

Given racial discrimination, more established white workers had an easier time gaining jobs in other localities, and the city demographics became increasingly black.

Given this lack of semantic transparency, researchers, outreach workers, critical theorists and LGBT activists have proposed and use terms such as institutionalized homophobia, state (- sponsored ) homophobia, sexual prejudice, anti-gay bigotry, straight privilege, The Straight Mind ( a collection of essays by French writer Monique Wittig ), heterosexual bias, compulsory heterosexuality or the much lesser known terms heterocentrism, homonegativity, and from gender theory and queer theory, heteronormativity.

Labor Party News quoted Leonard Riley, President of the Charleston International Longshoremen's Association Local 1422 as saying, " Given the results of the past few elections, I think the workers of South Carolina would jump at the opportunity to consider a Labor Party which would guarantee an uncompromising voice for working people on their issues.

Given the shortage of workers and consequent price rises the Ordinance of Labourers 1349 and the Statute of Labourers 1351 attempted to suppress sources of wage inflation by banning workers organisation, creating offences for any able-bodied person that did not work, and fixing wages at pre-plague levels.

Given that menudo is time and labor intensive to prepare — the tripe takes hours to cook ( or else it is extremely tough ), and many ingredients and side dishes ( such as salsa ) need to be cut and cooked — the dish is often prepared communally and eaten at a feast ; documents from the Works Progress Administration indicate that in the 1930s, among ( migrant ) workers in Arizona, menudo parties were held regularly to celebrate births, Christmas, and other occasions.

Given that it was one of the few remaining structures, the authorities expressed the desire to see it rebuilt in part to cancel traumatic events from memory however rebuilding the tower would have required its total demolition and removing the fallen parts would have meant an unacceptable risk for the workers.

Given their initial lack of experience, workers ' earnings start out low.

Given that the company's workers had become more mobile and that the majority of them now lived in these suburban areas, Brown & Sharpe saw an easy opportunity to relocate into a more practical facility.

Given its historical underpinnings, we should not be surprised that the revolution in warfare that has been brought about both by the confluence of the aerospace and the electronic revolutions, and by the off-shoot of both — the precision guided munition — is one that has been a long-time coming, back to the Second World War, back, even, to the experimenters of the First World War who attempted, however crudely, to develop " smart " weapons to launch from airships and other craft.

Given their known departure time and movements, had they not made the summit, it is unlikely that they would have still been out by nightfall.

Given the absolute necessity of a complete text for liturgical use, it is likely that Mozart spliced in movements from his earlier Masses for the premiere.

Given the level of surveillance, and consistent with the conspiratorial traditions of Irish political movements, the union proceeded clandestinely, forming small groups of trusted friends in order to keep informers at bay, meeting in isolated locations and in subway tunnels.

Given a target optimal product mix, an independent oil refiner can attempt to hedge itself against adverse price movements by buying oil futures and selling futures for its primary refined products according to the proportions of its optimal mix.

Given the simplicity of the strategy, as well as the fact that it is difficult to stamp out, leaderless resistance has been employed by a wide-range of movements, from terrorist and hate groups, to the animal-liberation movement, radical environmental movement, as well as anti-corporate and anti-abortion activists.

" Given the elimination of these pernicious influences, Marx allowed that " normal conditions of spontaneous development " of the rural commune could exist.

Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

Given the absolute magnitude, you can also compute apparent magnitude from its parallax:

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given Chrétien's known tendency to create new stories and characters, being the first to mention the hero Lancelot and his love affair with Queen Guinevere for example, the name might also be entirely invented.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given Pauling's recent success in discovering the Alpha helix, they feared that Pauling might also be the first to determine the structure of DNA.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

He also made some good long-term signings like Gary Speed and Shay Given.

Given the above commonalities there appear to be only two string theories: the heterotic string theory ( which is also the type I string theory ) and the type II theory.

* Sentence breaking ( also known as sentence boundary disambiguation ): Given a chunk of text, find the sentence boundaries.

Given the use of similar symbols on the Roman standard, this depiction also conveyed another victory, namely that of the Christian faith: the Roman soldiers who had once arrested Jesus and marched him to Calvary now walked under the banner of a resurrected Christ.

# Composition operator ( also called the substitution operator ): Given an m-ary function and m k-ary functions:

Given current trends in the UMC — with overseas churches growing, especially in Africa, and U. S. churches collectively losing about 1, 000 members a week — it has been estimated that Africans will make up at least 30 % of the delegates at the 2012 General Conference, and it is also possible that 40 % of the delegates will be from outside the U. S. One Congolese bishop has estimated that typical Sunday attendance of the UMC is higher in his country than in the entire United States.

Given the questioning of Antisemitism in the speech and also the Nazi use of the play for antisemitic propaganda purposes, the quote is seen as particularly poignant and symbolic.

Given a sample of wood, the variation of the tree ring growths provides not only a match by year, it can also match location because the climate across a continent is not consistent.

Given the closeness shared by the countries bordering the Mediterranean basin, and very topical interest to the consolidation of the European Union's enlargement policy, he also intended to establish trade relations with the Republic of Malta aimed at encouraging mutual knowledge and awareness in a profitable way their local communities on European issues of common interest and current.

** Closure axiom for addition: Given two integers a and b, their sum, a + b is also an integer.

** Closure axiom for multiplication: Given two integers a and b, their product, a · b is also an integer.

Given as a series of linked short stories, the book is also interspersed with brief commentaries on contemporary British politics.

Given the shared nature of the Canadian monarch, most members of the Canadian Royal Family are also members of the British Royal Family, and thus the House of Windsor.

Pope Saint Adeodatus I or Deodatus I ( which is Given by God in Latin, also called Deusdedit, which is God Has Given ; both are now considered variants of the same name ) ( died 8 November 618 ) was Pope from 13 November 615 to his death.