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 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 command of Johnston, the Army immediately entered into the First Battle of Manassas.

* 109 —" Windmill Under The Stars "/" Conchita Lopez " – Johnnie Johnston

* Henry Hamilton Johnston, British Central Africa: An Attempt to Give Some Account of a Portion of the Territories Under British Influence North of the Zambesi ( 1898 )

Under the new state Government, Johnston was elected to the North Carolina Senate in 1783 and 1784.

Under the command of Colonel Peter Stagg, the Michigan Brigade was part of Sheridan's force that rode southward to Petersburg, Virginia, and then proceeded into North Carolina to assist William T. Sherman's army in its quest to defeat another Confederate army under Joseph E. Johnston.

Under Johnston ’ s stewardship, the OECD took the global lead in establishing the Principles of Corporate Governance ( now the world standard ) and revised the Guidelines for Multinational Enterprises, the bedrock of what is now known as corporate social responsibility.

He lent backing vocals to many works, including Chicago's hits " Baby, What a Big Surprise " and " Wishing You Were Here " ( with Al Jardine and brother Dennis Wilson ), Elton John's " Don't Let the Sun Go Down on Me " ( with Bruce Johnston ), David Lee Roth's hit cover of " California Girls ," Warren Zevon's " Desperados Under the Eaves " and the Carnie / Wendy Wilson holiday track " Hey Santa!

Under Johnston ’ s leadership, the school significantly changed.

Under senatorial courtesy, Johnston could have blocked Stagg's confirmation but did not do so.

His literary works include: The Life and Life-Work of Samuel Phelps ( actor and theatre manager ) as well as his own autobiography Johnston Forbes-Robertson: A Player Under Three Reigns ( 1925 ).

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

Under this plan both Cranston and Providence would be on the uniform fiscal year but would still be using the same installment periods.

Under its plan Du Pont would retain its General Motors shares but be required to pass on to its stockholders the right to vote those shares.

Under the circumstances, however, the team considered it would provide the most useful information at this point.

Under Formby's plan, an appointee would be selected by a board composed of the governor, lieutenant governor, speaker of the House, attorney general and chief justice of the Texas Supreme Court.

Under ideal ( adiabatic ) conditions, the exponent would be 1. 4, but a lower value, generally between 1. 2 and 1. 3 is used, since the amount of heat lost will vary among engines based on design, size and materials used, but provides useful results for purposes of comparison.

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 this " Tetrarchy ", or " rule of four ", each emperor would rule over a quarter-division of the Empire.

Under Constantine's rule, Christianity would become the Empire's preferred religion.

Under such a system, a servicemember found to be gay but who had not committed any sexual acts while in service would tend to receive an undesirable discharge.

Under Java or C ++ the visibility of an object is defined in the code itself, meaning that to support a similar change the programmer would be forced to re-write the definitions completely, and could not have two versions at the same time.

Under Java the same methods would be isolated in a particular class.

Under such a system, most people would be able to earn a living without having to rely on the use of the property of others to do so.

Under this policy, Albania would develop its agricultural output in order to supply the Soviet Union and other Warsaw Pact nations while these nations would be developing specific resource outputs of their own, which would in theory strengthen the Warsaw Pact by greatly reducing the lack of certain resources that many of the nations faced.

Under the Constitution of 1791, France would function as a constitutional monarchy.

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 special agreement, also known as the compromise that was signed in December 2008 by Belize and Guatemala it was agreed that if the people of both nations approved, by way of a simultaneous referendum on the same day, that the dispute would proceed to the ICJ.

Under the new structure, the local offices would contribute a percentage of their income to the international organization, which would take responsibility for setting the overall direction of the movement with each regional office having one vote.

Under his tutelage, Sweden and the Protestant cause developed a number of excellent commanders, such as Lennart Torstensson, who would go on to defeat Sweden's enemies and expand the boundaries and the power of the empire long after Gustav Adolph's death in battle.

Under the original estimates ( from 2000 ) this cost would have been € 7. 7 billion, of which only € 2. 6 billion was to be borne by taxpayers and the rest by private investors.