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 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 his watch, the Browns won the AAFC championship in all four years of its existence, including the AAFC's only perfect season in 1948, and continued to succeed after moving to the NFL in 1950.

Under Belichick, the team won three Super Bowls in four years, and finished the 2007 regular season with a perfect 16 – 0 record, becoming only the fourth team in league history to go undefeated in the regular season, and the only one since the league expanded its regular season schedule to 16 games.

Under perfect division of labor, you would do job A and somebody else would do job B.

Under his reign were the golden ages men tell of: in such perfect peace he ruled the nations.

Under the direction of Sefton Delmer, a British journalist who spoke perfect Berliner German, Soldatensender Calais and its associated shortwave station, Kurzwellensender Atlantik, broadcast music, up-to-date sports scores, speeches of Adolf Hitler for " cover " and subtle propaganda.

Under perfect dark sky conditions where all light pollution is absent, stars as faint as + 8 < sup > m </ sup > might be visible.

Under perfect competition, marginal revenue product is equal to marginal physical product ( extra unit produced as a result of a new employment ) multiplied by price.

* Moon Under Water, George Orwell's essay describing his perfect pub, has inspired a number of real pubs.

Under Keefer's leadership, the events tabulated a perfect safety record with nearly 600, 000 miles raced, over 3, 200 safe landings at 81 different airports in 43 states and two countries in 25 events.

The near perfect first side also has the Cramps-like " Skull Baby ", the lightning fast " Plate in My Head ", sung from the point of view of a Vietnam vet, the heavy " Under the Christmas Fish ", a frequent concert opener with its pounding bass and drum rhythm and Sims hooky lead guitar line, and the closer, a wobbly version of Little Richard's " Lucille ".

# Under the conditions that a is not a perfect power and that a < sub > 0 </ sub > is not congruent to 1 modulo 4, this density is independent of a and equals Artin's constant which can be expressed as an infinite product

Under less than perfect capital mobility, the depreciated exchange rate shifts the BoP curve somewhat back down.

Under perfect capital mobility, the BoP curve is always horizontal at the level of the world interest rate.

Under perfect capital mobility, the new BoP curve will be horizontal at the new world interest rate, so the equilibrium domestic interest rate will equal the world interest rate.

Under the Mundell – Fleming framework of a small economy facing perfect capital mobility, the domestic interest rate is fixed and equilibrium in both markets can only be maintained by adjustments of the nominal exchange rate or the money supply ( by international funds flows ).

Under hypothetically perfect preservation and no fragmentation, these estimates should be the same.

Under NFL practices at the time, tied games were discounted when the win percentage was calculated ; so, these four teams were recorded with perfect win percentages of 1. 000.

Under the guidance of head coach Howard Buck, the freshman team posted a perfect 8 – 0 record in its inaugural season.