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 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 this authority, Duke Huan intervened in a power struggle in Lu ; protected Yan from encroaching Western Rong nomads ( 664 BC ); drove off Northern Di nomads after they'd invaded Wey ( 660 BC ) and Xing ( 659 BC ), providing the people with provisions and protective garrison units ; and led an alliance of eight states to conquer Cai and thereby block the northward expansion of Chu ( 656 BC ).

Using the president ’ s authority to assassinate people worldwide who pose an “ imminent threat ” if “ capture is not feasible ", the Obama administration routinely calls every victim of extrajudicial killing a militant.

Using his authority, he was also able to convince the communist Romanian government to end the 11-year home imprisonment of Áron Márton, Transylvanian Bishop, in 1967.

Using his authority as Chief Scientific Adviser at the MOD he decided that the subject should not be dismissed without some proper, official investigation.

Using his authority as a religious leader, Shaykh Mahmud called for a jihad against the British in 1919 and thus acquired the support of many Kurds indifferent to the nationalist struggle.

Using thinking similar to that of English philosopher John Locke, the founders of the United States believed in a state built upon the consent of " free and equal " citizens ; a state otherwise conceived would lack legitimacy and legal authority.

Using his knowledge and the legal authority of the Central Bank, Franco imposed heavy losses on the speculators.

Using this Rudd Concession ( so called because Rhodes's business partner, Charles Rudd, was instrumental in securing the signature ) between Rhodes ' British South Africa Company ( allegedly on behalf of Queen Victoria though without any official knowledge or authority ) and Lobengula, he then sought and obtained a charter from the British government allowing him to act, essentially although in a limited way, with the government's consent.

* Using rulesets not sanctioned by a gambling control authority.

Using the costumes and props in Irma's " house of illusions " ( the traditional French name for a brothel ), the patrons ' roles are realised when they pose in public as the figures of authority in a counter-revolutionary effort to restore order and the status quo.

Using ancient authority and divine revelation as the ultimate source of knowledge was replaced by a belief that knowledge of nature could only be obtained through detailed observations or artificial experiments.

Using the authority granted by the ordinance, the City of Honolulu ( the City ) initiated condemnation proceedings to obtain thirty-four leasehold condominium units in the Admiral Thomas condominium complex.

Using Go Nagai's Harenchi Gakuen as a prime example, Bryce notes that Nagai's storylines challenged long-standing social values by ridiculing traditional authority figures.

Using his authority of a foreign force's commander, Berling directly phoned Alexander Vasilevsky-Chief of the Soviet Staff-to inform about this situation.

Using a steering system that controlled the modified rocket's tail surfaces and wings equipped with ailerons, Fiedler was to land the missile on a skid especially bolted under the fuselage.

Using the thoroughbred racing convention of one length equaling one-fifth of a second to calculate Sham ’ s time, he also finished in under two minutes.

Using non-cooperation as a technique, Gandhi initiated a signature campaign where peasants pledged non-payment of revenue even under the threat of confiscation of land.

Using categories, he offers specific examples of both mild and extreme mind control ( both one on one and in groups ), notes the conditions under which each social rule is most easily exploited for false ends, and offers suggestions on how to resist such methods.

Using greases specifically designed for this purpose is also a good idea, as these are often better at sealing under vacuum, thicker and so less likely to flow out of the taper, become fluidic at higher temperatures than Vaseline ( a common substitute ) and are more chemically inert than other substitutes.

Using crop rotation farmers can keep their fields under continuous production, instead of letting them lie fallow, as well as reducing the need for artificial fertilizers, both of which can be expensive.

Using the German press, which was under Allied control, as well as posters and pamphlets, a program was conducted to acquaint ordinary Germans with what had taken place in the concentration camps.

Using contemporary ethnographic and linguistic criteria, these villages have been classed by anthropologists into more than 20 broad ( and widely debated ) ethnic groupings (; ), which were never united under a common polity, kingdom or " tribe ".

Using big-O notation, the performance of the interpolation algorithm on a data set of size N is O ( N ); however under the assumption of a uniform distribution of the data on the linear scale used for interpolation, the performance can be shown to be O ( log log N ).

Using a " hillbilly " accent under the name of " Billy Purl ", he presented a live country music program to the fill dead air on XERF.

Using the traditional “ organ specific ” and “ non-organ specific ” classification scheme, many diseases have been lumped together under the autoimmune disease umbrella.

Using the concepts of modern detective stories ( with Falco as the private investigator, roughly translated into the classical world as a " private informer "), Davis portrays the world of the Roman Empire under Vespasian.

Using Future material, The Human League released a demo tape to record companies under their new name.

Using the school's auditorium, along with professionally made costuming and scenery, a couple of musical plays were staged by the campers during the summer under the guidance of several counselors with drama training.

Using rarely seen photographs from Guderian's private collection, the documentary provides an inside view into the life and career of Guderian and draws a profile of Guderian's character and the moral responsibility of the German general staff under Hitler.

Using the technology and the help of the surviving Arkonides, Rhodan forces the Earth to unite under his leadership, and begins to explore the galaxy while carefully concealing the location of Earth from enemies such as the Arkonide Empire.

Using ancient magic they transformed The Key into a human girl and placed her under the protection of the Slayer Buffy, altering the memories of the Slayer and anyone connected to her into believing the girl was Buffy's younger sister Dawn.

Using this city as their base, the Arabs, led by Qutayba ibn Muslim, brought under subjection large parts of Central Asia, including Balkh, Bokhara, Fergana and Kashgaria, and penetrated into China as far as the province of Gansu early in the 8th century.

Using semi-hardwood cuttings, collected and planted during August and September, low survival rates ( under 30 %) have been achieved.

Using an inflatable raft, Brody gets the shark's attention by pounding the power line with an oar ( thus creating a rhythmic vibration under the water ), and gets the shark to bite the power cable.

Using the transfer roller, the impressions were transferred to the plate under great pressure until the required 240 impressions were completed.

Using active techniques like deauth and ARP re-injection, 40, 000 packets can be captured in less than one minute under good conditions.

; Phase locked loop ( PLL ): Using a varactor-controlled or voltage-controlled oscillator ( VCO ) ( described above in varactor under analog VFO techniques ) and a phase detector, a control-loop can be set up so that the VCO's output is frequency-locked to a crystal controlled reference oscillator.