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 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 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 influence of English, which uses the preposition " to " for both indirect objects ( give to ) and directions of movement ( go to ), the term " dative " has sometimes been used to describe cases that in other languages would more appropriately be called lative.

Under scientific management people would be directed by reason and the problems of industrial unrest would be appropriately ( i. e., scientifically ) addressed.

Under this method, it is fairly common that a drummer get appropriately sized bass drum hoops to complete the conversion process.

Under the current terminology, adiponectin, leptin ( Ob ligand ), and resistin are not appropriately considered adipokines ( cytokines ) as they do not act on the immune system.

Under the Constitution of Finland, everyone is entitled to have their case heard by a court or an authority appropriately and without undue delay.

Under Lincoln's leadership, the Union set up a naval blockade that shut down the South's normal trade, took control of the border slave states at the start of the war, gained control of communications with gunboats on the southern river systems, and tried repeatedly to capture the Confederate capital at Richmond, Virginia.

Under this point of view, often attributed to James McClelland and David Rumelhart, the mind could be characterized as a set of complex associations, represented as a layered network.

Under the plan which starts within 90 days, Bell will be able to charge wholesale service providers a flat monthly fee to connect to its network, and for a set monthly usage limit per each ISP customer the ISP has.

Under Fan Noli, the government set up a special tribunal that passed death sentences, in absentia, on Zogu, Verlaci, and others and confiscated their property.

Under the tutelage of actor-manager Nigel Playfair, Whale worked as an actor, set designer and builder, " stage director " ( akin to a stage manager ) and director.

Under a standard set of conditions, the melting point of a substance is a characteristic property.

Under this system, Norwegian is grouped together with the neighbouring languages Danish and Swedish, because the last millennium has seen all three undergo important changes, especially in grammar and lexis, which have set them apart from Faroese and Icelandic.

Under the U. S. legal system, courts are set up in a hierarchy.

Under United States law the principal limitations on whether and the extent to which the State may interfere with property rights are set by the Constitution.

Under this circumstance, the parties agree to temporarily set aside their political differences and unite to face the national crisis.

Under code pleading, the required elements of each action are supposed to be set out in carefully codified statutes.

Under the law, the meaning of racketeering activity is set out at.

Under meteorological definitions, all seasons are arbitrarily set to start at the beginning of a calendar month and end at the end of a month.

Under a cloud of his affair, Hughes and Plath separated in the autumn of 1962 and she set up life in a new flat with the children.

Under heavy fire from the public, the Graham government eventually announced that it would set aside the possibility of UNB Saint John losing its status as a university and would refer the report to a working group for further study.

Under the Greeks, and Ptolemy in particular, the planets, Houses, and signs of the zodiac were rationalized and their function set down in a way that has changed little to the present day.

Under a parliamentary ruling in favour of free trade, these private newcomers are able to set up a new company, called the New Company or English Company.

Under propositions A and AA, a new water reclamation facility is also being planned, and the new facilities will meet rigorous Silver-level guidelines set by the U. S. Green Building Council for Leadership in Energy and Environmental Design.

The film set a pattern for a host of imitators, like Under Siege ( 1992 ), Sudden Death ( 1995 ) or Air Force One ( 1997 ), which used the same formula in a different setting.

Under strict orders to clear the Square by dawn, the People's Liberation Army pushed through makeshift blockades set up by demonstrators in western Beijing on their way to Tiananmen Square.

Under third edition rules, unless a Dungeon Master specifically chose to use a different campaign setting, his or her D & D game would be set in the world of Greyhawk.

Some have even theorized that Hagbard Celine is, in fact, Captain Nemo, but that seems physically impossible, or at least very unlikely, as Verne's Twenty Thousand Leagues Under the Sea is set in the second half of the nineteenth century, which would make Hagbard Celine, if the same character and person as Nemo, over a hundred years old.

Under Von Hertzen's leadership, the Housing Foundation bought 660 acres of forest land, six miles from the centre of Helsinki, and set out to create an ideal garden city.

The set consisted of " Sunshine of Your Love ", " Crossroads ", and " Born Under a Bad Sign ", a song they had not previously played live.