By the beginning of World War II, many towns and cities had built space, and there were numerous qualified pilots available.

By sweeping this surface through R < sup > 3 </ sup > as a function of the ion sequence input data, such as via ion-ordering, a volume is generated onto which positions the 2D detector positions can be computed and placed three-dimensional space.

* By the definition of addition and scalar multiplication of linear functionals in the dual space,

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

By the same construction, every locally compact Hausdorff space X is a dense subspace of a compact Hausdorff space having at most one point more than X ..

By turning these space to public use, the building got 20 % plot ratio more as bonus.

By the 20th century the novel had come to occupy a canonical space as one of the foundations of modern literature.

By contrast, the Gemini capsule's avionics were designed so the cabin could be exposed to the vacuum of space when one of two large hatches was opened, so no airlock was required, and both the spacewalking astronaut and his companion command pilot were in vacuum during the EVA.

By 2000, the consolidation of grocery store chains, the spread of retailers like Wal-Mart, and growth of private-label brands caused competition for shelf space, and put price pressure on the company's products.

By adding a fourth dimension to the three dimensional space, the self-intersection can be eliminated.

By transferring upper triangularisation of operators of finite-dimensional complex vector space, there is an internal orthonormal Hilbert space basis for where runs from to, such that each of the corresponding-dimensional subspaces is-invariant.

B is the sample space and A is an event. By the ratio of their areas, the probability of A is approximately 0. 4.

By manipulating space in this way, Voidhawks can open wormholes and jump long distances ( many light years ) instantaneously.

By 1990, Keck, Mahin & Cate, a law firm, considered moving out of its space in the Sears Tower and moving into a potential new development, which would become 77 West Wacker Drive.

By the end of its final mission, Atlantis had orbited the Earth 4, 848 times, traveling nearly in space or more than 525 times the distance from the Earth to the Moon.

By Liouville's theorem, Hamiltonian flows preserve the volume form on the phase space.

By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.

By the mid 20th century, humans had achieved a mastery of technology sufficient to leave the atmosphere of the Earth for the first time and space exploration | explore space.

By the time of " The Pirate Planet ," the Doctor had been travelling on board in time and space for 523 years and by the time of " The Doctor's Wife ", he had been travelling in it for 700 years.

By diverse adventures she comes in the space of four years into the hands of nine men in varied places.

By the 1990s, the term was in wide use, even in formal engineering papers such as " Towards unobtainium < nowiki > composite materials for space applications < nowiki ></ nowiki >.

By comparison, in a general topological space, given sets A, B it is meaningful to say that a point x is arbitrarily close to A ( i. e., in the closure of A ), or perhaps that A is a smaller neighborhood of x than B, but notions of closeness of points and relative closeness are not described well by topological structure alone.

By the late 1940s it was known that the properties of atomic nucleus could not be explained by the then-current models ( such as the liquid drop model developed by Niels Bohr amongst others ).

By the 1930s, statisticians and models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.

By making these data available to local public health officials in real time, most models of anthrax epidemics indicate that more than 80 % of an exposed population can receive antibiotic treatment before becoming symptomatic, and thus avoid the moderately high mortality of the disease.

By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries.

By 1981, at the peak of its popularity, CP / M ran on 3, 000 different computer models and DRI had $ 5. 4 million in yearly revenues.

By 2008, most North American minivans had adopted the size and configuration of the long-wheelbase Chrysler vans, with Chrysler dropping their shorter models as well.

By 2001, few lower-end printer models came with support for PostScript, largely due to growing competition from much cheaper non-PostScript ink jet printers, and new software-based methods to render PostScript images on the computer, making them suitable for any printer ; PDF, a descendant of PostScript, provides one such method, and has largely replaced PostScript as de facto standard for electronic document distribution.

By the late 1960s, Khomeini was a marja-e taqlid ( model for imitation ) for " hundreds of thousands " of Shia, one of six or so models in the Shia world.

By the end of the Cold War, many Third World countries had adopted capitalist or communist economic models and continued to receive support from the side they had chosen.

By comparing the spectrum to computed models of stellar evolution, the age, mass, radius and luminosity of Tau Ceti can be estimated.

By the end of World War Two, the US had built eight new wind tunnels, including the largest one in the world at Moffett Field near Sunnyvale, California, which was designed to test full size aircraft at speeds of less than 250 mph and a vertical wind tunnel at Wright Field, Ohio, where the wind stream is upwards for the testing of models in spin situations and the concepts and engineering designs for the first primitive helicopters flown in the US.

By making these data available to local public health officials in real time, most models of anthrax epidemics indicate that more than 80 % of an exposed population can receive antibiotic treatment before becoming symptomatic, and thus avoid the moderately high mortality of the disease.

By the 18th century, following developments by Robert Boyle and Robert Hooke, more easily portable models became available.

By 1968, FM Agency and Models 1 were established and represented models in a similar way they do today.

By the late 1960s, models were treated being treated better and making better wages.

By the 1980s, most models were able to make modeling a full-time profession.

By inputting data on the ratio of stable isotopes < sup > 18 </ sup > O :< sup > 16 </ sup > O into computer models, it has been shown that in conjunction with quick-weathering of volcanic rock, this increased rainfall may have reduced greenhouse gas levels to below the threshold required to trigger the period of extreme glaciation known as Snowball Earth.

By March 1901, the company had a whole line of models ready for mass production.

By 1903, Peugeot produced half of the cars built in France, and they offered the Bébé, a four-seater, and an and resembling contemporary Mercedes models.

By June 1942 the main producer of gas vans, Gaubschat Fahrzeugwerke GmbH, delivered 20 gas vans in two models ( for 30-50 and 70-100 individuals ) to Einsatzgruppen, out of 30 ordered.

By the mid-1890s, he had broken off relations with all of his Jewish friends, publicly disavowed his previous friendships with Jewish artists, and refused to use models who he believed might be Jewish.

By the late 1930s, several radio manufacturers offered remote controls for some of their higher-end models.

By the 1960s, it was clear to Lesney that sales in certain already profitable markets might be increased by providing the markets with models " of their own ".