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Under and assumption
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 and P
Under Prime Minister P. W.
Under a constant torque of magnitude τ, the gyroscope's speed of precession Ω < sub > P </ sub > is inversely proportional to L, the magnitude of its angular momentum:
Under the leadership of Thomson-Houston's patent attorney, Frederick P. Fish, the company protected its new patent rights.
* C. P. Snow's Death Under Sail ( 1932 ), his first novel, after which he turned to mainstream fiction ; it features unusually complex characters for a mystery of this period
* Harrison, P. ( 1985 ) Inside the Inner City: Life Under the Cutting Edge.
Displaying his influence on rap and hip hop, Clinton also worked with Tupac Shakur on the song " Can't C Me " from the album All Eyez on Me ; Ice Cube on the song and video for " Bop Gun ( One Nation )" on the Lethal Injection album ( which sampled Funkadelic's earlier hit " One Nation Under A Groove "); Outkast on the song " Synthesizer " from the album Aquemini ; Redman on the song " J. U. M. P.
Under the 2002 farm bill ( P. L.
Elephant Story: Jumbo and P. T. Barnum Under the Big Top.
Under the direction of Parley P. Pratt, an exploration of Utah Valley was conducted.
Under Bhonsle served Lt. Col. Shah Nawaz Khan as Chief of General Staff, Major P. K.
Under second president William D. Noon, O. P.
Under President Lorenzo C. McCarthy, O. P.
Under such circumstance P will be a unitary matrix ( resp.
Under orders from Confederate States President Jefferson Davis, troops controlled by the Confederate government under the command of General P. G. T. Beauregard bombarded Fort Sumter on April 12 – 13, 1861, forcing its capitulation on April 14, 1861 before it could be reinforced and resupplied.
Under the assumptions of the preceding section, let P denote the r < sup > th </ sup > derivative of P < sub > n </ sub >.
Under United States law, a " playa lake " may be considered isolated wetlands, and may be eligible to enroll in the new wetlands component of the Conservation Reserve Program, enacted in the 2002 farm bill ( P. L.
* Harrison, P. ( 1985 ) Inside the Inner City: Life Under the Cutting Edge.
Under V. P. Singh, the Janata Dal and the National Front sought to replicate the Janata-style alliance of anti-Congress political parties.
Under the weaker assumption that P NP, the problem is only known to be inapproximable within a constant better than 21 / 22
Under Quintum, the P. R. O. J. E. C. T.
Under the federal P. ramorum quarantine program implemented by USDA APHIS, nurseries in California, Oregon, and Washington are regulated and must participate in an annual inspection regime ; nurseries in the fourteen infested counties in coastal California, plus the limited infested area in Curry County, Oregon, must participate in a more stringent inspection schedule when shipping out of this area.
Under plausible circuit lower bounds ( similar to those implying P =
Under Burger, A & P continued to report record sales and operated with expenses of 12. 6 % of sales when the industry average was 15 %.

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