Assuming that all the particles start from the origin at the initial time t = 0, the diffusion equation has the solution

Assuming that an interaction will occur ( with 100 % probability ) if the projectile hits the solid, and not at all ( 0 % probability ) if it misses, the total interaction probability for the single projectile will be the ratio of the area of the section of the solid ( the cross section, represented by ) to the total targeted area.

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 leadership of the Indian National Congress in 1921, Gandhi led nationwide campaigns for easing poverty, expanding women's rights, building religious and ethnic amity, ending untouchability, increasing economic self-reliance, and above all for achieving Swaraj — the independence of India from British domination.

Assuming that the leaders in the social hierarchy are perfectly conformed to the ruler, who is perfectly submissive to Heaven, conformity in speech and behaviour is expected of all people.

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.

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 that not all possible choices are available to him: How capable is the individual to desire all choices available, in order to choose from among them?

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

* January 1 – Assuming that the copyright laws are not changed further, all works published in 1923 enter the public domain in the U. S., the first works to do so since the passage of the 1998 Sonny Bono Copyright Term Extension Act.

* February 15 – Assuming no further extensions to the term of copyrights become law in the interim, all sound recordings fixed before February 15, 1972 will enter the public domain in the U. S.

* Assuming no further changes in the copyright law, all sound recordings fixed between February 15 and December 31, 1972 will enter public domain in the United States:

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 keys are equally likely, H ( k ) = lg ( 26!

Assuming normalization ( i. e. that all probabilities in the set do total 100 %), the probability density in quantum mechanics is equal to the square of the absolute value of the amplitude of the waveform.

Assuming a vague role as Executive Producer on all their releases is Thomas Fehlmann.

Assuming that the French did not have more than 14, 000 men, he led to the army of La Mancha towards Toledo, reuniting all forces on 10 August in Almonacid.

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

Assuming the foundational premise is correct, the optimal option for all governments would be an agreement to maintain tax harmonization.

Assuming all of the voters vote sincerely ( strategic voting is discussed below ), the results would be as follows, by percentage:

Assuming that the Masters in the city will have killed all their human slaves, thus precluding a second attack by infiltration, the Resistance attempts an aerial bombing using its newly constructed aeroplanes.

Assuming that the image has been pre-smoothed by Gaussian smoothing and a scale space representation at scale has been computed, we can require that the gradient magnitude of the scale space representation, which is equal to the first-order directional derivative in the-direction, should have its first order directional derivative in the-direction equal to zero

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 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 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 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 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 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.

Assuming that two individuals share the same 32 ancestors of n =