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 frames for expert systems is an application of object-oriented programming, with inheritance of features described by the " is-a " link.

Using a simple design, it became possible to connect almost any network to the ARPANET, irrespective of their local characteristics, thereby solving Kahn's initial problem.

Using a DBMS that has been specifically designed to store data as objects gives an advantage to those companies that are geared towards multimedia presentation or organizations that utilize computer-aided design ( CAD ).

Using general specifications provided to her, Will created the design sketch for the present medal of the Purple Heart.

Using the same printer as for the Penny Black, Brazil opted for an abstract design instead of a portrait of Emperor Pedro II, so that his image would be not be disfigured by a postmark.

Using a wire frame model allows visualization of the underlying design structure of a 3D model.

Using hydrogen propellant, a solid-core design typically delivers specific impulses ( I < small >< sub > sp </ sub ></ small >) on the order of 850 to 1000 seconds, about twice that of liquid hydrogen-oxygen designs such as the Space Shuttle Main Engine.

can be calculated from the specific impulse, I < sub > sp </ sub >, where ( when I < sub > sp </ sub > is in seconds and g < sub > n </ sub > is the standard, not local, acceleration of gravity ), Using the J-2 on the S-IVB as a baseline design, we have P = ( 1014 kN )( 414 s )( 9. 81 m / s < sup > 2 </ sup >)/ 2

Using transformation optics it is possible to design the optical parameters of a " cloak " so that it guides light around some region, rendering it invisible over a certain band of wavelengths.

Using the same conceptual design, the Fat Man device was detonated over Nagasaki, Japan, on August 9, 1945.

Using a RISC design with a 32-bit CPU, at its launch in June 1987, the Archimedes was stated as running at 4 MIPS, with a claim of 18 MIPS during tests.

Using an oversampling design and a modulation scheme called sigma-delta modulation ( SDM ), analog anti-aliasing filters can effectively be replaced by a digital filter.

* Algorithm design – Using ideas from algorithm theory to creatively design solutions to real tasks.

* Using computational fluid dynamics in the design stage can produce vehicles which take significantly less energy to push through the air, a major consideration at highway speeds.

Using lorem ipsum to focus attention on graphic elements in a webpage design proposal

* Reynolds, John C. Using category theory to design implicit conversions and generic operators.

Using this design, Crewe demonstrated the ability to image atoms using annular dark-field imaging.

Using its inventory of easy-to-service Ford mechanicals built up during World War II and bodywork of Allard's own design, three post-war models were introduced: the J, a competition sports car ; the K, a slightly larger car intended for road use, and the four seater L. Sales were fairly brisk for a low-volume car, and demand was high for cars in general, which led to the introduction of several larger models, the M and N.

Using a hull mounted gun, the M3 design was produced quicker than if a turret mounted gun design had been manufactured.

High platform design ( Using outside steps to avoid having a level entry from the platform ) is troublesome.

Using heuristic evaluation prior to user testing will reduce the number and severity of design errors discovered by users.

Using E-Cash and other modern cryptographic methods, it is possible to design systems that do not know where individuals are, but are still able to enforce fares.

Using much of its old on-screen appearance design features, it went from a basic blue setting to a more orangish-gold setting.

Using previous results to design further decisions and experiments is a central concept of adaptive management.