Under this assumption the space group must be Af and the following are the positions of the atoms in the unit cell.

Under the assumption of the axiom of choice, this transfinite sequence includes every cardinal number.

Under the decentralization plan, regulatory responsibilities were transferred from the central government to mayors and other municipal officials on the assumption that local officials would provide better oversight.

Under the monopsonistic assumption, an appropriately set minimum wage could increase both wages and employment, with the optimal level being equal to the marginal productivity of labor.

Under the assumption of the generalized Riemann hypothesis, it can be shown to take time

Under the assumption of perfect competition, supply is determined by marginal cost.

Under this assumption, half the round-trip delay is the propagation delay to be compensated.

Under an assumption of constant gravity, Newton's law of universal gravitation simplifies to F = mg, where m is the mass of the body and g is a constant vector with an average magnitude of 9. 81 m / s < sup > 2 </ sup >.

Under the assumption that the universe is homogeneous and isotropic, the curvature of the observable universe, or the local geometry, is described by one of the three " primitive " geometries ( in mathematics these are called the model geometries ):

Under the assumption of replica symmetry, the free energy is given by the expression:

Under this assumption, some American groups created programs which aimed to increase the self-esteem of students.

Under assumption, when U equals U * and λ equals unity, expected real wages would increase with labor productivity.

Under this assumption, the doctor, who is given n and m, wishes to estimate k, the number of children where both parents have agreed to participate.

Under the assumption that the Earth was composed of concentric ellipsoidal shells of uniform density, Clairaut's theorem could be applied to it, and allowed the ellipticity of the Earth to be calculated from surface measurements of gravity.

Under the assumption of economic rationality, it is the utility of its least urgent possible use from the best feasible combination of actions in which its use is included.

Under the open world assumption, if a statement cannot be proven to be true with current knowledge, we cannot draw the conclusion that the statement is false.

Under the assumption that the Ottoman viceroy wanted a Catholic Patriarch for the Coptic Catholics in 1824, the Pope erected the Patriarchate of Alexandria from the Apostolic Vicariate of Syria, Egypt, Arabia and Cyprus but it was basically titular.

Under this assumption, the reflected particles in the two-body case will not fully compensate the shadowing effect, because the reflected flux is weaker than the incident flux.

Under this assumption strings behave as one-dimensional objects and obey the Nambu-Goto action, which is classically equivalent to the Polyakov action that defines the bosonic sector of superstring theory.

Under such an assumption, the Declaration of Independence would declare that government existed primarily for the reasons Locke gave, and some have extended that line of thinking to support a conception of limited government.

Under the assumption of logistic growth, resource limitation does not constrain individuals ’ reproductive rates when populations are small, but because there are few individuals, the overall yield is small.

Under this assumption the equation above can be rearranged into:

Under the assumption V = L, not all projective sets have the perfect set property or the property of Baire.

Under this assumption of " generic intersection ", the number of regions can also be determined in a non-inductive way, using the formula for the Euler characteristic of a connected planar graph ( viewed here as a graph embedded in the 2-sphere S < sup > 2 </ sup >).

Under the heading of " places ," his class explores where texts were made, read, and listened to, including monasteries, schools and universities, offices of the state, the shops of merchants and booksellers, printing houses, theaters, libraries, studies, and closets.

Under the action of gravity, a particle acquires a downward speed of, where is the mass of the particle, is the acceleration due to gravity, and is the particle's mobility in the fluid.

Under the flag is the high table where the professors and college administration lunch.

Under the administration of Félix Éboué, France's first black colonial governor, a military column, commanded by Colonel Philippe Leclerc de Hauteclocque, and including two battalions of Sara troops, moved north from N ' Djamena ( then Fort Lamy ) to engage Axis forces in Libya, where, in partnership with the British Army's Long Range Desert Group, they captured Kufra.

Under § 1332 ( d ) ( 2 ) the federal district courts have original jurisdiction over any civil action where the amount in controversy exceeds $ 5, 000, 000 and

Under King Agaja ( ruled 1708 – 1732 ), the kingdom conquered Allada, where the ruling family originated.

Under Italian law franchise is defined as an arrangement between two financially independent parties where a franchisee is granted, in exchange for a consideration, the right to market goods and services under particular trademarks.

Under the Hallstein Doctrine, the FRG did not have any diplomatic relations with countries in Eastern Europe until the early 1970s, when Willy Brandt's Ostpolitik led to increased dialogue and treaties like the Treaty of Warsaw, where West Germany accepted the Oder-Neisse line as German-Polish border, and the Basic Treaty, where West and East Germany accepted each other as sovereign entities.

Under such conditions every formula of the form, where ( T ) is a string of quantifiers containing all quantifiers in ( S ) and ( S ') interleaved among themselves in any fashion, but maintaining the relative order inside ( S ) and ( S '), will be equivalent to the original formula Φ '( this is yet another basic result in first-order predicate calculus that we rely on ).

Under Dodd-Frank, hedge fund managers who have less than US $ 100 million in assets under management will be overseen by the state where the manager is domiciled and become subject to state regulation.

Under their auspices, she gained a second meeting, where she made a remarkable prediction about a military reversal near Orléans.

Under Frey, the Royals rebounded in 1980 and advanced to the ALCS, where they again faced the Yankees.

Under the plan of the US Constitution the Congress was delegated the power to declare or define the Law of Nations in cases where its terms might be vague or indefinite.

Under this interpretation, there may be cases where the mentally ill know that their conduct is legally prohibited, but it is arguable that their mental condition prevents them making the connection between an act being legally prohibited and the societal requirement to conform their conduct to the requirements of the criminal law.

Under gadaa, every eight years, the Oromo would hold a popular assembly called the Gumi Gayo, where laws were established for the following eight years.

Under the guise of a reporter, Bulero travels to Eldritch's estate on the Moon, where Eldritch holds a press conference.

Under the Covenant of the League of Nations, all League members agreed that where there was a dispute between states which they " recognize to be suitable for submission to arbitration and which cannot be satisfactorily settled by diplomacy ", the matter would be submitted to the Court for arbitration, with suitable disputes being over the interpretation of an international treaty, a question on international law, the validity of facts which, if true, would breach international obligations and the nature of any reparations to be made for breaching international obligations.

Under command of Potsanaquahip ( Buffalo Hump ), 500-700 Comanche cavalry warriors swept down the Guadalupe River valley, killing and plundering all the way to the shore of the Gulf of Mexico, where they sacked the towns of Victoria and Linnville.

Under the influence of romantic nationalism, among economic and political forces, both Germany and Italy found political unity, and movements to create nations similarly based upon ethnic groups would flower in the Balkans ( see for example, the Carinthian Plebiscite, 1920 ), along the Baltic Sea, and in the interior of Central Europe, where in the eventual outcome, the Habsburgs succumbed to the surge of Romantic nationalism.

Under the command of Commodore Richard Dale the squadron sailed into the Mediterranean on July 1 where it stopped at Gibraltar for supplies and information.

Under the Countryside and Rights of Way Act 2000, many public rights of way in England and Wales that authorities had not explicitly classified as Bridleway or Byway defaulted to the classification " Restricted Byway " which precludes the use of motor vehicles at all times, except authorised vehicles and where required for access.

Under IOC rules, the lighting of the Olympic cauldron must be witnessed by those attending the opening ceremony, implying that it must be lit at the location where the ceremony is taking place.

* December 1 – Under the County and Borough Police Act, in any county or area of England and Wales where a police force has not already been established, the Justices of the Peace must from this date take steps to create one according to nationally defined standards.

Under the Broadcasting Act, a network is defined as " any operation where control over all or any part of the programs or program schedules of one or more broadcasting undertakings is delegated to another undertaking or person " and must be licensed by the Canadian Radio-television and Telecommunications Commission ( CRTC ).