Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X.

Using this distance and other photographs, more information about the object, including its orbital elements, can be obtained .< ref >

Using this binding mechanism, an antibody can tag a microbe or an infected cell for attack by other parts of the immune system, or can neutralize its target directly ( for example, by blocking a part of a microbe that is essential for its invasion and survival ).

Using as a pretext the insulting behavior of a few Tlatelolcan citizens, Axayacatl invaded his neighbor, killed its ruler, Moquihuix, and replaced him with a military governor.

Using the techniques of modern biotechnology, one or two genes ( Smartstax from Monsanto in collaboration with Dow AgroSciences will use 8, starting in 2010 ) may be transferred to a highly developed crop variety to impart a new character that would increase its yield.

" Freedom of contract is a qualified and not an absolute right ...," Hughes declared in upholding an Iowa law that voided contracts limiting the legal rights of railroad workers: The state may " interfere where the parties do not stand upon an equality ...." Using similar reasoning, the associate justice upheld a California law that mandated a forty-eight-hour work-week for women in various industries and allowed a federal statute to override a contract between an interstate railroad and its employees.

Using its authority under Section 5 of the FTC Act, which prohibits unfair or deceptive practices, the FTC has brought a number of cases to enforce the promises in corporate privacy statements, including promises about the security of consumers ’ personal information.

Using the data collected by Vesto Slipher and his ( Hubble's ) assistant Milton Humason ( a former mule-driver and janitor ), Hubble and Humason found a direct relationship between a galaxy's distance and its relative speed away from the solar system.

Using their E-REV ( Extended-Range Electric Vehicle ) powertrain technology, the Hummer plug-in hybrid would run up to 40 miles per day on its battery alone, then a small 4-cylinder internal combustion engine would start to generate more electricity.

Using a telescope, Rømer observed the motions of Jupiter and one of its moons, Io.

Using its divided upper lip, an adult manatee will commonly eat up to 10 % of its body weight ( about 50 kg ) per day.

Using them its simple to send individually controlled copies of your film to various recipients with different expiry dates.

Using its dichromatic color vision, it can detect predators from a great distance and then alert other prairie dogs to the danger with a special, high-pitched call.

Using the explicit continued fraction expansion of e, one can show that e is not a Liouville number ( although the partial quotients in its continued fraction expansion are unbounded ).

Using methods that would not become common in Biblical scholarship until the nineteenth century, Paine tested the Bible for internal consistency and questioned its historical accuracy, concluding that it was not divinely inspired.

) Using the customary international law principle of a nation's right to protect its natural resources, President Truman in 1945 extended United States control to all the natural resources of its continental shelf.

" Using offshore bank accounts, third-party agents and deceptive pricing practices, these companies AG, its subsidiaries and affiliates saw foreign bribery as a way of doing business ," said Mythili Raman, a principal deputy in the Justice Department ’ s criminal division.

Using overhead wires to feed electricity to the trams, this network continued to expand so greatly & profitably that when the MMTB was established in July 1919 Alex Cameron was appointed its full-time chairman.

Using his experience with explorative travel, Dias helped in the construction of the São Gabriel and its sister ship, the São Rafael that were used by Vasco da Gama to circumnavigate the Cape of Good Hope and continue the route to India.

Using its 0. 30 cal light-gas gun and powder gun, the AVGR can launch projectiles to velocities ranging from.

Using these coefficients gives the Taylor polynomial of f. The Taylor polynomial of degree d is the polynomial of degree d which best approximates f, and its coefficients can be found by a generalization of the above formulas.

Using this technique, each user program can be moved (" relocated ") in main memory by the operating system, as long as the RA register reflects its position in memory.

Using Babur's own text, he translated the Bāburnāma into Persian.

Using Natasha and several other volunteers, Luthor forms his own team of superheroes which are introduced as the new Infinity Inc.

Using reports that the abbot had been lining his own pockets rather than spending it on his monastery, Honorius publicly denounced Oderisio, calling him a soldier and a thief, not a monk.

Using money earned from the Dollars trilogy, accountant and Eastwood advisor Irving Leonard helped establish Eastwood's own production company, Malpaso Productions, named after Malpaso Creek on Eastwood's property in Monterey County, California.

Using her own supporters at court, and the patronage of her French family, Isabella attempted to find a political path through these challenges ; she successfully formed an alliance with Gaveston, but after his death at the hands of the barons her position grew increasingly precarious.

Using the Method, the actor also recalls emotions or reactions from his or her own life and uses them to identify with the character being portrayed.

Using this power to great advantage, the Mule conquers planets simply by visiting them in force, with his own army, instilling the inhabitants with great fear, then again with great loyalty to himself.

Using data he collected from his own observations Gersonides ' refuted Ptolemy's model in what the notable physicist Yuval Ne ' eman has considered as " one of the most important insights in the history of science, generally missed in telling the story of the transition from epicyclic corrections to the geocentric model to Copernicus ' heliocentric model ".

Using, for the most part, his own compositions it exemplifies the types of verse forms used in Old Norse poetry.

Using, for the most part, his own compositions, it exemplifies the types of verse forms used in Old Norse poetry.

Using software to analyze one's own histories is generally accepted, however acquiring histories of hands in which a player did not participate violates the rules of most cardrooms.

Using the pin from a brooch he took off Jocasta's gown, Oedipus stabbed his own eyes out, and was then exiled.

Using his power and wealth, he drove Toki Yorinari out of Mino Province in a coup d ' état in 1542, and claimed the region as his own, becoming a daimyo in his own right.

Using his wife's wealth as a foundation on which to build his own, Ryan launched his business career.

Using the forums as an opportunity to assess the current art scene, Rothko also discussed in detail his own artwork and philosophy of art.

Using computer animation techniques, Monkhouse was seen in a graveyard next to his own grave ( though in reality he was cremated ) talking about the disease seriously, interspersed with humorous asides to another camera (" What killed me kills one man per hour in Britain.

Using analysis of one nDNA and 2 mtDNA sequences, Moyle & Marks ( 2006 ) found one largely Asian lineage and one African group of greenbuls and bristlebills ; the Golden Greenbul seemes to be very distinct and form a group of its own.

Using the road bridge, they would reinforce the perimeter east of Arnhem, linking up with their own artillery who would be flown in by glider to LZ ' L '.

Using this device, the Fleischer brothers got a contract with Bray Studio in 1919 to produce their own series called Out of the Inkwell, which featured their first characters, the as yet unnamed Koko the Clown, and Fitz the Dog, who would evolve into Bimbo in 1930.

Using experimental data from his own research and the work of others, Edelman developed molecular models of antibody proteins.

Using de Vaux's Period 1a findings, his own excavations at Ain el-Ghuweir 15 km south of Qumran, and Mazar's level 2 at ' En-Gedi, Bar-Adon argued, " these fortresses to John Hyrcanus, who needed a strong, comprehensive defence system commanding vital water sources, agricultural fields, flocks, Jordan River crossings, the plains of Jericho and the caravan routes in the Judean desert.

Using theory and methods drawn from such behavioral sciences as industrial / organizational psychology, industrial sociology, communication, cultural anthropology, administrative theory, organizational behavior, economics, and political science, the change agent's main function is to help the organization define and solve its own problems.

Using her own notes and George's journals, Joy wrote Born Free to tell the lions ' tale.

Using his own tuxedo, Jimmy defeats the villain, Banning, and his henchmen.