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 Bayesian interpretation of probability, Bayes ' rule may be thought of as Bayes ' theorem in odds form.

* " Under some conditions, all admissible procedures are either Bayes procedures or limits of Bayes procedures ( in various senses ).

Under the frequentist interpretation of probability, Bayes ' rule is a general relationship between and, for any events, and in the same event space.

Under the Bayesian interpretation of probability, Bayes ' rule relates the odds on probability models and before and after evidence is observed.

Under these assumptions the Tikhonov-regularized solution is the most probable solution given the data and the a priori distribution of, according to Bayes ' theorem.

Under optimal conditions, celery can be stored for up to seven weeks between.

Under optimal conditions bacteria can grow extremely rapidly and can double as quickly as every 10 minutes.

Under optimal conditions, northern red oak is fast growing and a 10-year-old tree can be 5 – 6 m ( 15 – 20 ft ) tall.

Under Kaldor – Hicks efficiency, an outcome is considered more efficient if a Pareto optimal outcome can be reached by arranging sufficient compensation from those that are made better off to those that are made worse off so that all would end up no worse off than before.

Under optimal conditions there may be eight to 10 generations per season.

Under optimal conditions, it can destroy an entire orchard in a single growing season.

Under the theory of the second best, for example, if the fulfillment of a subset of optimal conditions cannot be met under any circumstances, it is incorrect to conclude that the fulfillment of any subset of optimal conditions will necessarily result in an increase in allocative efficiency.

Under local anesthesia, a hole about 14 mm in diameter is drilled in the skull and the electrode is inserted, with feedback from the patient for optimal placement.

Under certain common conditions, optimality requires the use of bang – bang control ; hence, sliding mode control describes the optimal controller for a broad set of dynamic systems.

Under optimal conditions, well-trained animals produce a high percentage of CRs (> 90 %).

Under optimal conditions, it may produce 450 kg of seed per hectare with about 330, 000 seeds / kg.

Under optimal conditions GAMBIT would thus have been able to record ground features as small as 0. 28 m to 0. 56 m ( 1 ft to 2 ft ) using the Eastman Kodak Type 3404 film.

Under optimal conditions ( approximately ), the two-spotted spider mite can hatch in as little as 3 days, and become sexually mature in as little as 5 days.

Under differentiability and constraint qualifications, the Karush – Kuhn – Tucker ( KKT ) conditions provide necessary conditions for a solution to be optimal.

Under such a mechanism the agents of course find it optimal to reveal type since the mechanism plays the strategies they found optimal anyway.

Under optimal conditions, a duckweed farm can produce 10 to 30 tons of dried duckweed per hectare per year .< ref >

* Under low-speed, high load, MIVEC ensures optimal torque delivery with the intake valve closing timing advanced to ensure sufficient air volume.

Under optimal ecological and climatic conditions, several successive generations can occur, causing swarms to form and invade countries on all sides of the recession area, as far north as Spain and Russia, as far south as Nigeria and Kenya, and as far east as India and southwest Asia.

Under it, the interviewer rejects the first r − 1 applicants ( let applicant M be the best applicant among these r − 1 applicants ), and then selects the first subsequent applicant that is better than applicant M. It can be shown that the optimal strategy lies in this class of strategies.