Assuming initially has value, two consecutive evaluations of the expression yield, respectively, and.

Assuming the gamma-ray explosion to be spherical, the energy output of GRB 080319B would be within a factor of two of the rest-mass energy of the Sun ( the energy which would be released were the Sun to be converted entirely into radiation ).

Assuming, the general second-order PDE in two independent variables has the form

Assuming that the second particle is at rest before the collision, the angles of deflection of the two particles, and, are related to the angle of deflection in the system of the center of mass by

Assuming the responsibility of mediator between the two sides, and with Erasmus ' willing participation ( the robot being left as the leader and controlling-force of the thinking machines ), Duncan does something similar to Bene-Gesserit Sharing with the robot ; possibly along with what seems to be a physical-bonding ( similar to what Leto II did with the sandtrout ) into something of a human-machine hybrid.

Assuming a fuel pump had failed, the pilots turned it off, since gravity would still feed fuel to the aircraft's two engines.

Assuming bus commuters do not care about the color of the bus, consumers are expected to choose between bus and car still with equal probability, so the probability of car is still 0. 5, while the probabilities of each of the two bus types is 0. 25.

Assuming both p and q are nonzero, neither of the groups O ( p, q ) or SO ( p, q ) are connected, having four and two components respectively.

Assuming that Jeconiah's reign ended on the day that the Babylonians captured Jerusalem the first time, 2 Adar ( 16 March ) 597 BC, and further assuming that the Jewish calendar in the sixth century BC had the same number of days in the two preceding months as in the modern Jewish calendar, Jehoiachin's reign of three months and ten days () would have started on 21 Heshvan ( 9 December ) 598 BC.

Assuming the dialectical interpretation, it argues that Snow's concept of " two cultures " is not only off the mark, it is a damaging and short-sighted viewpoint ; and that it has perhaps led to decades of unnecessary fence-building.

* By clock: Assuming that the dancer stands at the center of a clock with hands and faces 12, one may say, e. g., " take a step at two o ' clock ".

Assuming the crown, he passed Burgundy to his younger brother, Hugh the Black, after only two years as duke.

Assuming the spacing between two ions is a, the potential in the lattice will look something like this:

Assuming that the prophecy took place after Uzziah became sole regent in 768 / 767, Amos's prophecy can be dated to some time after that and some time before Jeroboam's death in 753 BC, with the earthquake two years after that.

Assuming geostrophic balance, the system is stationary and the first two equations become:

Average growth approximation: Assuming that two stocks have the same earnings growth, the one with a lower P / E is a better value.

Assuming the hidden variable to be polarisation direction ( parallel on the two sides in real applications, not orthogonal ), equation ( 1 ) becomes:

Assuming two competitors per match, if there are competitors, there will be rounds required, or if there are rounds, there will be competitors.

Assuming the route was blocked, he returned to the two cargo ships on one of the expedition's small launches.

Assuming Sharchops still outnumber Ngalops some three to two, the total population is around 212, 500.

Assuming the radius of the first gear wheel is known as a function of z, and using the relationship, the above two equations can be combined to yield the differential equation:

Assuming Sharchops still outnumber Ngalops some three to two, the total Ngalop population is around 141, 700.

Assuming the right amount of current for the right time, this will weld the two pieces of metal together.

Assuming the plain black habit of the institution in 1828, she conducted the affairs of the home while Mother McAuley and two foundress companions were making their novitiate in the Presentation Convent of George's Hill preparatory to the founding of the new congregation.

Assuming the only safe place for power is in many hands, social credit is a distributive philosophy, and its policy is to disperse power to individuals.

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

Assuming the appropriate gravity of the charge, and all other things being equal, a guilty plea to the same charge would cause the reverse effect: An opponent at trial could introduce the plea, over a hearsay objection, as evidence to establish a certain fact.

Assuming that Ictis, Mictis and Corbulo are the same, Diodorus appears to have read Timaeus, who must have read Pytheas, whom Polybius also read.

Assuming all references are to the same person, as some ( but by no means all ) of the Church fathers did, the earliest reference to him is the canonical Acts of the Apostles, this is his only appearance in the New Testament.

Assuming that all atoms in a crystal vibrate with the same frequency ν, the average thermal energy can be estimated using the equipartition theorem as

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 the transcriptions are not intended to be precise, only 11 of the 26 — Bravo, Echo, Hotel, Juliet ( t ), Kilo, Mike, Papa, Quebec, Romeo, Whiskey, and Zulu — are given English pronunciations by all these agencies, though not always the same English pronunciations.

Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

Assuming that the ion and electron saturation current is the same for each probe, then the formulas for current to each of the probe tips take the form

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

Assuming a near free-recoil condition, and neglecting the gases ejected from the barrel, then immediately after firing, conservation of momentum requires that the total momentum of the firearm and projectile is the same as before, namely zero.

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 that bleeding is at a minimum, the other side is castrated in the same manner.

Assuming unprotected intercourse with a man of the same age, women aged 19 – 26 have about a 50 % chance of becoming pregnant during a given menstrual cycle, compared with 40 % in the 27-34 age group and below 30 % for women 35-39.

Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction.

Assuming y ≤ x, the result will always be greater or equal to and dropping the initial ' 1 ' is the same as subtracting, making the result or just, the desired result.

Assuming the legs are recovered with a relative speed between leg and body which amounts to the same as the relative speed between water and body, the legs must be kicked back with five times the mean velocity of the swimmer.

Assuming that the passwords are chosen independently, an adversary who intercepts one challenge – response pair cannot use it to authenticate unless she is lucky enough to get the same challenge.

Assuming that load results are bypassed with the same priority as integer results, then it's possible to summarize this recurrence as a load followed by another load — as if the program was following a linked list.

Assuming most or all group members lean in the same direction, during discussion, items of unshared information supporting that direction are expressed, which provides members previously unaware of them more reason to lean in that direction.

These assumptions can be shown to lead to a " consumer's cost function ", C ( u, p ), the cost of achieving utility level u given a set of prices p. Assuming that the cost function holds across time ( i. e., people get the same amount of utility from one set of purchases in year as they would have buying the same set in a different year ) leads to a " true cost of living index.

Assuming we connect New York with Los Angeles by means of an electronic telecommunication network that operates in strong transmission ranges, as well as with continental satellites, wave guides, bundled coaxial cable, and later also via laser beam fiber optics: the expenditure would be about the same as for a Moon landing, except that the benefits in term of by-products would be greater.