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 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 the assumption of naturalism and indeterminism, where there only exists the natural world and that the natural world is indeterministic — events are not predetermined ( e. g., for quantum mechanical reasons ) and any event has a probability assigned to it — no event can be determined by a physical organism's perceived free will, and nor can any event be strictly determined by anything at all.

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 capable direction of the choir's founder, Geroge Bragg, the twenty-six boys made some lovely sounds in an opening group of Renaissance and Baroque madrigals and motets, excerpts from Pergolesi's `` Stabat Mater '' and all of the Britten `` Ceremonial Of Carols ''.

Under instructions from the emperor, he undertook an invasion of southern Scotland, winning some significant victories, and constructing the Antonine Wall from the Firth of Forth to the Firth of Clyde, although it was soon abandoned for reasons that are still not quite clear.

Under his lead, some good results were achieved and European football was secured.

* A name used for a tank ( an armoured fighting vehicle ) in some works of speculative fiction, such as Harry Turtledove's books, and Victoria: An Empire Under the Sun.

Under cover of darkness some 19 legions and 12, 000 cavalry fled before Antony was able to engage Octavian in a land battle.

Under the latest such decree, president Turbay had implemented security policies that, though of some military value against the M-19 in particular, were considered highly questionable both inside and outside Colombian circles due to numerous accusations of military human rights abuses against suspects and captured guerrillas.

Under some conditions, forests and peat bogs may become sources of CO < sub > 2 </ sub >, such as when a forest is flooded by the construction of a hydroelectric dam.

Under some circumstances, the signal radiated from the electron guns, scanning circuitry, and associated wiring of a CRT can be captured remotely and used to reconstruct what is shown on the CRT using a process called Van Eck phreaking.

Under some circumstances, some creditors, otherwise the United States Trustee can request for the court converting the case into a demolition under chapter 7, or appointing a trustee to manage the debtor's business.

Under the APG II definition some well-known members of Dipsacales are honeysuckle, elder, viburnum, and valerian.

Under exceptional circumstances, a redive may be granted, but these are exceedingly rare ( usually for very young divers just learning how to compete, or if some event outside the diver's control has caused them to be unable to perform ).

Under the Cronquist system and some other plant classification systems, the order Fabales contains only the family Fabaceae.

Under the disputed Nostratic theory and similar theories such as that of monogenesis, some of these examples would indeed be distantly related cognates, but the evidence for reclassifying them as such is insufficient.

Under the erroneous impression that he needed papers from some left-wing organisation to cross the frontier, on John Strachey's recommendation he applied unsuccessfully to Harry Pollitt, leader of the British Communist Party.

Under President Shevardnadze's leadership, the government had nonetheless made some progress on basic market reforms: all prices and most trade have been liberalized, a stable national currency ( the lari ) was introduced, and massive government downsizing took place.

Under his command, they besieged Cologne and, after some weeks, the defenders of the city opened the gates and handed Saloninus and Silvanus to Postumus who had them killed.

Under Franco, Spain actively sought the return of Gibraltar by the UK, and gained some support for its cause at the United Nations.

Under Jean-Claude Duvalier, Haiti's economic and political condition continued to decline, although some of the more fearsome elements of his father's regime were abolished.

Under some circumstances, and in some technical contexts, transcluded sections of text may not require strict adherence to the " context neutrality " principle, because the transcluded sections are capable of parameterization.

Under their rule, Mysore fought a series of wars sometimes against the combined forces of the British and Marathas, but mostly against the British, with Mysore receiving some aid or promise of aid from the French.

) Under this legal definition, the Irish diaspora is considerably smaller — some 3 million persons, of whom 1. 2 million are Irish-born emigrants.

Under some conventions – e. g. the European Convention on Human Rights – individuals or states are permitted, subject to certain conditions, to take individual cases to the enforcement mechanisms ; under most, however ( e. g. the UN conventions ), individual access is contingent on the acceptance of that right by the relevant state party, either by a declaration at the time of ratification or accession, or through ratification of or accession to an optional protocol to the convention.

Under Ravalomanana these investments produced substantial economic growth but the benefits were not evenly spread throughout the population, producing tensions over the increasing cost of living and declining living standards among the poor and some segments of the middle class.