Assuming a perfect sphere with no terrain irregularity, the distance to horizon from a high altitude transmitter ( i. e., line of sight ) can readily be calculated.

Assuming perfect information, p < sub > e </ sub > is the same for all participants in the market, and this is identical to:

Assuming perfect competition and α + β = 1, α and β can be shown to be labor and capital's share of output.

Assuming an accurate CBA, changing the status quo by implementing the alternative with the lowest cost-benefit ratio can improve pareto efficiency .. An analyst using CBA should recognize that perfect evaluation of all present and future costs and benefits is difficult, and while CBA can offer a well-educated estimate of the best alternative, perfection in terms of economic efficiency and social welfare are not guaranteed.

Assuming that the factor costs are constant ( that is, that the firm is a perfect competitor in all input markets ), a firm experiencing constant returns will have constant long-run average costs, a firm experiencing decreasing returns will have increasing long-run average costs, and a firm experiencing increasing returns will have decreasing long-run average costs.

Assuming that perfect wetting of the plate occurs ( θ

Assuming standard conditions ( T =

Assuming these conditions the first law is rewritten as:

Assuming they form a set, the definable numbers form a field containing all the familiar real numbers such as 0, 1, π, e, et cetera.

Assuming we restrict our measurements to the z-and x-axes, such a hidden variable theory is experimentally indistinguishable from quantum mechanics.

For instance, raising the note B to B is equal to the note C. Assuming all such equivalences, the complete chromatic scale adds five additional pitch classes to the original seven lettered notes for a total of 12 ( the 13th note completing the octave ), each separated by a half-step.

Assuming a full-scale sine wave signal ( that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal ), the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level and uniform distribution.

Assuming that decision-makers make cost-benefit analyses when deciding to use force, China's doctrine calls for acquiring a nuclear arsenal only large enough to destroy an adversary ’ s " strategic points " in such a way that the expected costs of a first strike outweigh the anticipated benefits.

Assuming the radiation levels are not too high and the area does not need to be abandoned such as the town of Pripyat near the Chernobyl reactor, an expensive and time consuming cleanup procedure will begin.

Assuming each character equals one byte, there are about 2 < sup > 320 </ sup > such passwords, which is about 2 × 10 < sup > 96 </ sup >.

Assuming the fulfillment of certain technical criteria ( such as the sentencing of the accused whose punishment was not yet executed ), wherever it is possible to punish the conspirators with exactly the same punishment through which they had planned to harm their fellow, the court carries out this direct reciprocal justice ( including when the punishment constitutes the death penalty ).

Assuming q > 1 / 2 ( it is a real casino ) and he may only place bets at even odds, his best strategy is bold play: at each spin, he should bet the smallest amount such that if he wins he reaches his target immediately, and if he doesn't have enough for this, he should simply bet everything.

Assuming such a state were to exist at some point, any departure of the diver from its current depth, however small, will alter the pressure exerted on the bubble in the diver due to the change in the weight of the water above it in the vessel.

Assuming there is no future question as to the status of such a species, the absence of a type specimen does not invalidate the name, but it may be necessary in the future to designate a neotype for such a taxon, should any questions arise.

Assuming Volkov signed a standard contract, he would have no say whatsoever in whether an edition in this or that language appears ; such decisions would be made by his publisher.

Assuming that all rocks and minerals had once been fluid, Nicolas Steno reasoned that rock strata were formed when particles in a fluid such as water fell to the bottom.

Assuming T * is arithmetically definable, there is a natural number n such that T * is definable by a formula at level of the arithmetical hierarchy.

Assuming the pieces are the remnants of a flying saucer, the military " reconstructs " Bender's body as such.

Assuming the accuracy of such a guess, Kollikodon would be a contender for the largest Mesozoic mammal known, along with other possible giants such as Repenomamus, Schowalteria, and Bubodens.

Assuming that the natural median prey would be a small rodent such as a mouse, the bite would elicit a fear response quickening heart rate and increasing blood pressure.

Assuming a civilian disguise in order to travel incognito, Cobra Commander was shown unmasked for the first time in the comic series, though only after he had donned obscuring accessories such as sunglasses and a false mustache.

Assuming such a statistical ensemble consists of an overall collection of N microscopic states, the ensemble is constructed so that the proportion p < sub > i </ sub >/ N of members of the ensemble which are in microscopic state i is proportional to the probability, over time, of finding the real-world system in that microscopic state i. Thus the ensemble is an imaginary static collection of microscopic states created to mirror the statistics of the successive fluctuations of the macroscopic physical system which is being modeled.

Assuming an impact origin, other possible ways of dating the event include looking for evidence of ejecta material such as tektites, and deposits from the hypothesised tsunami, which might be found anywhere around the North Sea basin.

Assuming there exists an eigenpair ( λ, y ) for A, such that vector y is positive, and given ( r, x ), where x-is the right Perron-Frobenius eigenvector for A ( i. e. eigenvector for A < sup > t </ sup >), then

Assuming that a router administrator on such a metanet knows only information about the adjacent routers, standard routing protocols can take care of finding the proper path for a packet to take to reach its destination.

Assuming a modern PC could output 1 billion strings per second, it would take one billionth of 2 × 10 < sup > 96 </ sup > seconds, or 2 × 10 < sup > 87 </ sup > seconds to complete its task, which is about 6 × 10 < sup > 79 </ sup > years.

Assuming that this site, identified as KV54, was Tutankhamun's complete tomb, Davis concluded the dig.

Assuming that one had taken the necessary prerequisite courses, one could complete an OAC course before the OAC year, and so in many schools it was common for Grade 11 or Grade 12 students to have taken some OAC courses.

Assuming that the series converges to a value n, the Turing machine would complete an infinite execution in n time units.

Assuming substitution of genes to take place slowly, one gene at a time over n generations, the fitness of the species will fall below the optimum ( achieved when the substitution is complete ) by a factor of about 30 / n, so long as this is small-small enough to prevent extinction.

Assuming the player successfully memorizes the majority of the FMV sequences, then the game takes about 10 minutes to complete.

Assuming that a Miranda violation occurred — the six factors are present and no exception applies — the statement will be subject to suppression under the Miranda exclusionary rule.

Assuming office in 1770, he had a controversial career during which land title disputes and factional conflict slowed the initial attempts to populate and develop the island under a feudal system.

Assuming that the Hunnic forces were roughly the same size as the Romano-Gothic, the number involved in battle is just under 100, 000 combatants in total.

Assuming the subject has been under guard, the screener often can get valuable information about the subject's behavior from the guards.

Assuming that these documents are authentic, the attachment of these obligations to the King of England to ownership of land in Cornwall suggests that the area was under his direct rule and implies that the legal and administrative relationship between the king and his subjects was the same there as elsewhere in his kingdom.

Assuming this crate was the common type, its size would appear to support de Loys ’ measurement of the creature, although others say the crate is only 15 inches tall and the ape would measure under 4 feet-smaller than de Loys ' claims.

* Assuming there is a signalling equilibrium under which the sender signals honestly and the receiver trusts that information, under what circumstances will that equilibrium break down?

Assuming an application used by a hospital needs to map the data element concepts to the UDEF, the last name and first name ( within UDEF you will find Family Name and Given Name under the UDEF property Name ) of several people that are likely to appear on a medical record that could include the following example data element concepts –