By 1219, the empire had fallen to the Mongols, led by Genghis Khan.

By 1219 however Donnchadh and his nephew appear to have lost all or most of his Irish land ; a document of that year related that the Justiciar of Ireland, Geoffrey de Marisco, had dispossessed (" disseised ") them believing they had conspired against the king in the rebellion of 1215 – 6.

By 1975 signatories to the 1974 Declaration of Ayacucho, of which Colombia was one, had decided on limitations to nuclear, biological, and chemical weapons.

By about 1900 one finds managers trying to place their theories on what they regarded as a thoroughly scientific basis ( see scientism for perceived limitations of this belief ).

By the early 1920s, however, the inherent limitations of this type of engine had rendered it obsolete, with the power output increasingly going into overcoming the air-resistance of the spinning engine itself.

By way of custom of international law, genocide, crimes against humanity, and war crimes are usually not subject to statute of limitations, nor to prescription.

By this time his bulk had made him a liability in the field and, afterwards, realising his limitations all too clearly, he decided to stand down and surrendered both his place and the captaincy to Archie MacLaren.

By 2000, theorizing " democracy to come ," and thinking the limitations of existing democracies, had become important concerns.

By enacting ( relating to limitations on deductions for passive activity losses and limitations on passive activity credits ) to remove many tax shelters, especially for real estate investments, the Act significantly decreased the value of many such investments which had been held more for their tax-advantaged status than for their inherent profitability.

By contrast, Yahtzee needs only one cup and set of dice regardless of the number of players ( the basic Yahtzee game does have other practical limitations ).

By 1935, recognizing the limitations of her " lovely red Vega " in long, transoceanic flights, Earhart contemplated, in her own words, a new " prize ... one flight which I most wanted to attempt – a circumnavigation of the globe as near its waistline as could be.

By 1967, Touvier's death sentence was barred based on a 20-year statute of limitations.

By this order, critics assert that the CPA drastically altered Iraq's economy, allowing virtually unlimited and unrestricted foreign investment and placing no limitations on the expatriation of profit.

By 1992, Harris had converted his barn into a proper studio, and the new album, Fear of the Dark, was recorded there, resulting in a better overall sound than No Prayer for the Dying, although Dickinson still claims it had limitations due to its size.

By contrast, the U. S. allows as a deduction “ all the ordinary and necessary expenses paid or incurred during the taxable year in carrying on any trade or business ...” subject to qualifications, enhancements, and limitations.

By extension, " Fog of War " is also used to describe the limited view distance of many first person shooters, where unlimited view is considered either bad for gameplay or, more often, because of technical limitations, in that a Fog of War allows for the rendering of a smaller part of the game area.

By this time, however, admirals and captains had become very experienced with the limitations of fire ship attacks and had learned how to avoid them during battle.

By 1950 the enrollment had climbed to 1, 270, this same year the college joined the M. I. A. A .. During this period, the college experienced severe space limitations at the land-locked Franklin Campus as enrollment continued to climb.

By the early 18th century, nearly all of the proprietary colonies had either surrendered their charters to the crown to become royal colonies, or else had significant limitations placed on them by the crown.

By the mid 1990s most of the sanctioning bodies of road racing had placed severe limitations if not outright bans on the use all-wheel drive systems, due in part to Audi's earlier success in campaigning their various 4WD sedans in touring car races around the globe, to Porsche's 959 and its racing version the Porsche 961, and in part to the Nissan Skyline.

By utilizing the doctrine of ' Socialist realism ', all art forms in Soviet occupied nations were forced to adhere to strict guidelines and limitations that subordinated the arts to the needs and demands of the State.

By enacting ( relating to limitations on deductions for passive activity losses and limitations on passive activity credits ) to remove many tax shelters, especially for real estate investments, the Tax Reform Act of 1986 significantly decreased the value of many such investments which had been held more for their tax-advantaged status than for their inherent profitability.

By sidestepping social barriers ( anonymity ) and overcoming limitations of process ( parallelization ) more ideas are generated and shared with less conformity than in a traditional brainstorming or brainwriting session.

By the dawn of the computer age in the 1950s, software became the means to surmount the limitations inherent in the punched card machines of the past.

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.