Given a natural number x, h outputs the index of the partial computable function that performs the following computation:

The general scenario is the following: Given a class S of computable functions, is there a learner ( that is, recursive functional ) which for any input of the form ( f ( 0 ), f ( 1 ),..., f ( n )) outputs a hypothesis ( an index e with respect to a previously agreed on acceptable numbering of all computable functions ; the indexed function should be consistent with the given values of f ).

Given a basis with n-dimensional integer coordinates, for a lattice L in R < sup > n </ sup > with, the LLL algorithm outputs an LLL-reduced ( short, nearly orthogonal ) lattice basis in time

Given a specific input ( token ) history for a process, the process must be deterministic so that it always produces the same outputs ( tokens ).

The cylindrification operation takes a relation as input of arity k and outputs a relation of arity k + 1 as follows: Given a relation R of arity K, its cylindrification denoted by c ( R ), is the following set

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given its dimensions ( 10, 000 kilometers in diameter ) it is more like Banks ' Culture Orbitals ( though much smaller ) than Niven's behemoth.

Given the above, the 39 melakhot are not so much activities as " categories of activity.

Given the exclusivity of the criteria needed to become a magician, much magic is performed by specialists.

Given that Papua New Guinean anglophones almost invariably refer to Tok Pisin as Pidgin when speaking English, it may be considered something of an affectation to call it Tok Pisin, much like referring to German and French as Deutsch and français in English.

Given the presence of the KULeuven, an important European institution for academic research and education, much of the local economy is concentrated on spin-offs from academic research.

Given a core geometry, the B field needed for a given force can be calculated from ( 2 ); if it comes out to much more than 1. 6 T, a larger core must be used.

Given the flat nature of most of the river this was not easily addressed and nothing much was done till the twentieth century.

Given the nature of the book, the room is full of precautions ; not so much for the protection of the book as much as for the protection of its visitors.

Given that no Interstate, US or New Jersey State Highway runs very near to Mendham Township, the township has not become so much of a New York City suburb as nearby communities with more accessible highway and commuter rail access.

Given the parallels between visual and musical arts, it is possible that general acceptance of the value of digital art will progress in much the same way as the increased acceptance of electronically produced music over the last three decades.

Given the choice between an AdLib card or a fully compatible Sound Blaster card that came with a game port, saved a slot, and included the " DSP " for not much more in price, many consumers opted for the Sound Blaster.

Given key responsibilities for the country's diplomacy in the Napoleonic Wars, he was responsible for planning the attack on Copenhagen in September 1807, much of which he undertook at his country estate, South Hill Park at Easthampstead in Berkshire.

Given the frequency of GC two-nucleotide sequences, the number of CpG dinucleotides is much lower than would be expected.

Given Juwayni's polemical aims, and the fact that he burned the Ismaili libraries which may have offered much more reliable testimony about the history, scholars have been dubious about his narrative but are forced to rely on it given the absence of alternative sources.

Given Ely's wealth and ease, this promotion was clearly as much to do with status and consolidating the conspirators ' control in the north as with remuneration.

Given that much of the first half of the novel focuses on the initial encounter, blossoming friendship and eventual estrangement of these central characters, this issue continues to pique the curiosity of readers.

" Given that Edison, as much a businessman as an inventor, spent approximately $ 24, 000 on the system's development and went so far as to build a facility expressly for moviemaking before his U. S. patent was awarded, Rausch's interpretation is not widely shared by present-day scholars.

Given Klein's aggressive spending cuts, which shaped the political climate of Alberta for much of the 1990s, Getty's legacy with respect to public finances has been criticized.

Given that the landing package of NASA's Spirit rover mission rebounded off the surface in Gusev crater numerous times before coming to a standstill-taking much more time than anticipated-Beagle's timer may have been set to a too short time ( see Section 5. 4. 8 of the Inquiry Report );

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.

Given that this scale is much smaller than any cosmological scale these strings are often studied in the zero width, or Nambu-Goto approximation.

Given its much higher density, a CPU designer may be inclined to use MRAM to offer a much larger but somewhat slower cache, rather than a smaller but faster one.

Given sufficient travel time and engineering work, both unmanned and generational interstellar travel seem possible, though present considerable technological and economic challenges are unlikely to be met in the near future, particularly for manned probes.

" Given a memex, a scholar could create her own knowledge tools as connections within reams of information, share these tools, and use complexes of tools to create yet more sophisticated knowledge that could in turn be deployed toward this work.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given these issues, Microsoft started to work in parallel on a version of Windows which was more future-oriented and more portable.

Given the date of his publication and the widespread, permanent distribution of his work, it appears that he should be regarded as the originator of the concept of space sailing by light pressure, although he did not develop the concept further.

Given a normalized light vector l ( pointing from the light source toward the surface ) and a normalized plane normal vector n, one can work out the normalized reflected and refracted rays:

Given the circumstances, the Ghent Altarpiece is a difficult work to use for comparison when assessing other attributions, especially as several other artists from the brothers ' workshops probably worked on it as well.

Given Zelazny's academic interest in the Medieval European period, it is not a stretch to see a possible influence in Henry Adams ' 1905 work Mont Saint-Michel and Chartres, wherein he discusses the building of Chartres Cathedral, and the tidal-islet of Mont Saint-Michel, on the Normandy coast of France.

Given Bull's work schedule they were rarely able to see each other, but they became engaged in February 1954, and married on July 15.

Given a closed system in an initial state, if work is done on the system in an adiabatic ( i. e. no heat transfer ) way, and given the final state after a process, the amount of work required to be transferred to the system is the same, irrespective of how this work is performed.

Given that the success of any organization is founded on the knowledge of the people who work for it, these activities will and, indeed, must continue.

Given typesetters of sufficient skill, experienced proofreaders familiar with their typesetters ' work can accurately scan their pages without reading the text for errors that neither they nor their typesetters are responsible for.

# Given an artifact whose performance has been evaluated, it is important to determine why and how the artifact worked or did not work within its environment.

Given that salamanders are not prone to taking orders, this didn't work out, and most were slain by Belial's servants and vassals.

A review by Richard Kuipers in Variety praised it as " a pleasant gambol through the backwoods of Quebec ... Given plenty of room to work off each other, the members of this fine ensemble keep pic on track ... Big plus is the music and heartfelt songs by Philippe Katerine ".

Given that in Brazil all private and public sector employees and civil servants receive an additional compensation equivalent to one monthly salary after a year of work ( this compensation is known as the thirtheenth salary ), the President receives thirteen payments of R $ 26. 723, 13 per year, resulting in an annual salary of R $ 347. 400, 69.

Given at the discretion of the Council of the Academy on the recommendation of a nominating committee, the prize is awarded to a person for his or her total literary achievement rather than for a specific work.

Given the relative invisibility of references to AIDS in mainstream Hollywood filmmaking, the work of New Queer Cinema was hailed by the gay community as a welcome correction to a history of under-representation and stereotyping of gay and lesbian people.

Given Earl and Otto Binder ceased to co-author stories in 1955, and that Earl died in 1965 and Otto in 1974, it seems unlikely any of these stories was a commissioned work.

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 both companies have a work force of approximately 100, 000 employees, and a U. S. employment base of roughly 20, 000 H-1B holders, this indicates that roughly 1 / 5 of the Indian workforce of Infosys & Wipro applied for a visa in 2006.