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 this time they have undergone metamorphosis, lost their eyes and gills, developed a thicker skin and mouth tentacles, and reabsorbed their teeth.

By piercing their orifices, the nose, the mouth, and ears, they would stop evil entities, “ Khoughkh ”, from entering their bodies ( Osborn, 52 ).

By the 17th century, the Maravi Empire encompassed all the area between Lake Malawi and the mouth of the Zambezi River.

By the time Lewis and Clark arrived at the mouth of the Columbia, at least 14 maritime fur traders had already visited the river's mouth and estuary.

By changing the shape of the mouth, the frequency response of the filter is changed, so removing ( subtracting ) some of the harmonics.

By that time, they had already established settlements around the mouth of the Senegal River and at other points along the coasts of what are now Senegal, Gambia, and Guinea-Bissau.

By 1776 Spanish exploration had reached Bucareli Bay including the mouth of the Columbia River between Oregon and Washington, and Sitka Sound.

By 1663, activists from Virginia persuaded the Virginia Assembly to declare that the Virginia-Maryland border to be 30 miles north of the Pocomoke Sound, at the mouth of the Wicomico River ; and ordered the securing of allegiance of all settlers south of the Wicomico River-including the Annemessex and Manokin settlements-to Virginia.

By suddenly retracting the tongue and distending the gular ( throat ) floor, pressure immediately drops within the mouth sucking the prey in with the water.

By the eleventh round, Rosario's eye was almost completely shut and he was spitting blood from his mouth ; the fight was stopped by his corner, and Rosario lost.

By early October of that year, Lewis ' force had marched downstream to the mouth of the Kanawha River, currently the site of Pt.

By proclamation of the Territorial Secretary and Acting Governor, Winthrop Sargent, on August 15, 1796, the boundaries of Wayne County were declared to begin at the mouth of the Cuyahoga River then west to Fort Wayne, then to the southernmost point of Lake Michigan and along the western shore north to the territorial boundary in Lake Superior and then along the territorial boundary through Lake Huron, Lake St. Clair, and Lake Erie back to the starting point.

By 1913, a hydraulic plant had been installed at Marvel Creek and in 1914 construction of a cat trail began starting south of Aniak on the mouth of the Aniak Slough and proceeding to the diggings at Marvel Creek.

By 1799, French hunters and trappers had built cabins at the mouth of the Cache River.

By 1869 small lumber mills were being built at the mouth of every creek.

By 1850, placer miners settled at the mouth of Gold Canyon, working sand bars deposited over the millennia along the path of the creek.

By the spring of 1944 Rommel had made great progress, but since he believed that the invasion would come somewhere between Dunkirk and the mouth of the Somme, much of his work was directed at strengthening the wrong area.

By 1968 it had become unprofitable to keep dredging a channel from the harbour mouth to the quays in order to accommodate the larger ships of the era, so the port closed.

By contrast, a jar or jug has a relatively large mouth or opening.

By turning the individual on their side into what is known as the recovery position, the stomach contents will often continue past the opening of the lungs and drain out the mouth, thus sparing the victim lung damage or the internal drowning which can be caused by large volumes of stomach material getting into the lungs.

By 1678, the French had driven out the Dutch and established a permanent settlement at Saint Louis at the mouth of the Senegal River, where the French Company of the Senegal River ( Compagnie Française du Sénégal ) had been trading for more than fifty years.

In the " logos " ( speech ) model, God speaks and shapes unresisting dormant matter into effective existence and order ( Psalm 33: " By the word of YHWH the heavens were made, and by the breath of his mouth all their hosts ; he gathers up the waters like a mound, stores the Deep in vaults "); in the second, or " agon " ( struggle ) model, God does battle with the monsters of the sea at the beginning of the world in order to mark his sovereignty and power.

By seizing the port of Chinampo ( modern Nampo, North Korea ) at the mouth of the Taedong River outside of Pyongyang with the spring thaw, the Japanese were able to land the remaining components of the 1st Army by 29 March.

By the time Isabel made landfall, a tropical storm warning existed from Chincoteague, Virginia to Fire Island, New York and from Cape Fear, North Carolina to the mouth of the Santee River in South Carolina, and a hurricane warning existed from Chincoteague, Virginia to Cape Fear.