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 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 marijuana the beatnik comes alive within and experiences a wonderfully enhanced sense of self as if he had discovered the open sesame to the universe of being.

Under Davros ' guidance, the Daleks steal 27 planets, including Earth, and hide them in the Medusa Cascade, one second out of sync with the rest of the universe.

Under the guise of humbly " serving " the Empire, the Sisterhood is in fact a major power in the universe, using its many areas of influence to subtly guide mankind along the path of their own plan for humanity's future.

Under the physics definition, a " vector " is required to have components that " transform " in a certain way under a proper rotation: In particular, if everything in the universe were rotated, the vector would rotate in exactly the same way.

Under the names of magnitude come what is continuous and unified and divisible into divisibles, all cases of non-collective nouns: the universe, matter, mass, energy, liquid, material, animal, plant, tree.

Under Davis, the Phoenix Force's nature was revealed to be that of the embodiment of all life in the universe, and the Phoenix Force's appearance as a flaming bird was based on visions of the magician Feron, ally of Merlyn and Necrom.

Under present models, the structure of the visible universe was formed in the following stages:

Under this kind of pressure, it is not surprising that Wright would make sweeping statements to the newspapers.

Under modern conditions, this is especially true of the ready reserve.

Under the auspices of the Women's Recreation Association, interclass competition is organized in badminton, basketball, field hockey, golf, tennis, and swimming.

Under the new rules, testimony is taken orally in open court in all cases except those of an extraordinary character.

Under the circumstances, the only protection for the relatively small manufacturers is to engage in exactly the kind of conspiracy with the giants for which the latter were convicted.

Under the surface of the wide range of folk movements is apparent a sound technical ballet training, and an equally professional sense of performing.

Under Parthian and Sassanian Iranian empires, scholars concentrated on exchanging knowledge and inventions by the countries around them – India, China, and the Roman Empire, when it is thought to be expanded over the other countries.

Under this definition, Anatolia is bounded to the East by the Armenian Highland, and the Euphrates before that river bends to the southeast to enter Mesopotamia.

Under the strictest definition, an argot is a proper language, with its own grammar and style.

Under certain conditions, it may result in preferential growth of resistant bacteria, while growth of susceptible bacteria is inhibited by the drug.

Under unfavourable conditions, the organism will form a cyst, which is multi-walled and covered in spikes.

Under the Act of Settlement, male-preference primogeniture succession of an Anglican legitimate descendant of the Electress Sophia is automatic and immediate, neither depending on, nor waiting for, any proclamation.

Under the null hypothesis of no autocorrelation, this statistic is

Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance ( As a result, angular momentum is not conserved for general curved spacetimes, unless it happens to be asymptotically rotationally invariant ).

Under 28 USC 3, when the Chief Justice is unable to discharge his functions, or that office is vacant, his duties are carried out by the most senior Associate Justice until the disability or the vacancy ends.

Under Adoptionism Jesus is currently divine and has been since his adoption, although he is not equal to the Father, per " my Father is greater than I " ().

Under the new rule, when any runner is thrown out, and the other ( s ) are successful, the successful runners will not be credited with a stolen base.

Under modern canon law, a man who is appointed a cardinal must accept ordination as a bishop, unless he already is one, or seek special permission from the pope to decline such ordination.

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.