Given that spinning a Dyson Sphere would result in the atmosphere pooling around the equator, the Ringworld removes all the extraneous parts of the structure, leaving a spinning band landscaped on the sun-facing side, with the atmosphere and inhabitants kept in place through centrifugal force and 1000 mile high perimeter walls ( rim walls ).

Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even in glasses with an amorphous structure.

Given the high thermal design power of high-speed computer CPUs and components, modern motherboards nearly always include heat sinks and mounting points for fans to dissipate excess heat.

Given high fixed costs, the new price was below average total cost, resulting in a loss.

Given the currently keen interest in biotechnology and the high levels of funding in that field, attempts to exploit the replicative ability of existing cells are timely, and may easily lead to significant insights and advances.

Given its high concentration of morphine, opium tincture is useful for treating moderate to severe pain.

Given their long range, high survivability and ability to carry many medium-and long-range nuclear missiles, submarines were credible and effective means for full-scale retaliation even after a massive first strike.

Given the choice, who wouldn't rather believe their children are special and chosen for some high mission rather than that they have a brain disorder?

Given initial speed u, one can calculate how high the ball will travel before it begins to fall.

Given this high percentage, it seeks to diversify and expand trade opportunities with non-EU countries.

Given the simpleness of the design, and high usability with some people ( e. g. those owning an orchard ), some people have started building their own do-it-yourself ( DIY ) fruit press and have uploaded detailed instructions on how to do so.

Given its high charge-to-size ratio nearly all compounds of boron are covalent, barring some complexed anionic and cationic species.

Given the size of Merchant's capital outlay — including construction in Boswell of the world's largest tipple, a central business district and a high school — the company planned big things for Boswell.

Given the high value of these areas for wildlife species, close to 70 % of this big-tree old growth forest is protected in reserves, and will never be eligible for harvest.

Given the guaranteed low prices during contract days and the continued high cost of logging in Southeast Alaska today, one analysis concludes that, since 1980, the forest service has lost over a billion dollars in Tongass timber sales.

Given the high level of support within the party for her leadership, MacPhail surprised many by choosing not to seek the party leadership in 2003.

Given the very rapid technological changes underway in propulsion ( from coal to oil, from boilers to turbines ), ordnance ( with better fire directors, and new high explosives ) and armor and emergence of new craft such as destroyers and submarines, Mahan's emphasis on the capital ship and the command of the sea came at an opportune moment.

Given their high rotational speed of up to 4000 rpm ( 67 Hz ) and tight clearances, they are not very tolerant of solids such as sand.

Given that the problem of high textbook prices is linked to the " broken " economics of the market, requiring publishers to disclose textbook prices to faculty is a solution pursued by a number of legislatures.

Given the high premium placed by Novo Ecijanos on education, a legislator from Nueva Ecija took the crucial step to compel the American colonial government to allot funding for public education via a legislative act.

Given this and high public expectations of quality, the budget in developing the car reportedly exceeded A $ 1 billion.

Given a black tuxedo by his father, he started doing gigs when in high school.

Given the high death rate, many servants did not live to the end of their terms.

Given that the high latitudes in this period were warm and tropical, it is hypothesized that the deciduous habit evolved in response to the unusual light availability patterns, not to major seasonal variations in temperature.

Given a sufficiently high and well known amount of electric current and voltage, the timing of the bridgewire vaporization is both extremely short ( a few microseconds ) and extremely precise and predictable ( standard deviation of time to detonate as low as a few tens of nanoseconds ).

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required.

Given the same bullet and cartridge, a faster burning powder will generally use a smaller charge of powder than required with a slower powder.

Given the extraordinary competition and technological craftsmanship required for top search engine placement, the implication of the term " search engine optimization " has deteriorated over the last decade.

" Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce.

Given typical workloads, Cray felt that the small cost incurred by being required to break large sequential memory accesses into segments was a cost well worth paying.

Given the requirements of weight, and fragment density required this dictated using approximately 700 fragments, and being able to aim the mine with an accuracy of around two feet ( 0. 6 m ) at the center of the target zone.

) Given that the telephone system nominal voiceband ( including guardband ) is 4, 000 Hz, the required digital sampling rate is 8, 000 Hz ( see Nyquist rate ).

Given its " grandfathered " status, opium tincture has never been required to undergo the strict FDA drug review and approval process.

Given the elevations of those three places, at least a 3 % grade would have been required.

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 Reagan National Airport's proximity to the city and high-security facilities, Reagan National has extra security precautions required by the Washington Air Defense Identification Zone that were in place since the airport began operations.

Given a more realistic yield of 36 tonnes / hectare ( 3834 US gal / acre ) the area required is about 152, 000 square kilometers, or roughly equal to that of the state of Georgia or of England and Wales.

Given that virtually all illegal CB radios were contraband, this concession required the licensed amateur to pay outstanding import duty and VAT.

Although the German Command expected another Allied landing in the Mediterranean, the advancing Red Army and the Allied Landing at the Normandy required all German resources, so little was done to improve the condition of Army Group G. Given the advancing Allied forces in northern France, the German Command deemed a realistic defense in the South impossible.

Given the technical limitations of daguerreotype photography which required long exposure times, this was one situation where the portrait subject remained quite still.

Given the city's central position in both Israeli nationalism ( Zionism ) and Palestinian nationalism, the selectivity required to summarise more than 5, 000 years of inhabited history is often influenced by ideological bias or background ( see Historiography and nationalism ).

Given the New York Central's axle load limits, the Pacific type could not be made any larger ; a new locomotive type would be required to carry the larger boiler that Kiefer's research indicated was needed.

Given the large volume of records and limited resources, the amendment also extended the agencies ' required response time to FOIA requests.

Given the extensive renovations that would have been required to bring the station up to modern standards, the city decided to close it instead.

Given n equally probable choices, the average reaction time T required to choose among them is approximately

Given a good model, it is best to make as many observations as practicable, depending of the expected reliability of prior knowledge, cost of observations, time and resources available, and accuracy required.

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 the scope of modern regulation, however, legislatures frequently find areas where it is impractical for lawmakers to apply the level of detail or expertise required to establish complete standards.

Given M doctors and N patients, the minimum number of gloves G ( M, N ) required for all the doctors to examine all the patients is given by: