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

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

* kāma-rūpam: Assuming any form desired

Assuming a function that is defined where, form the definite integral from 0 to x.

Assuming one has a category like that of abelian groups, one can in fact form direct sums of copies of G until the morphism

Assuming that is closed, there is a canonical symplectic form defined as which is compatible with, hence satisfying the first definition.

Assuming smallness of | ψ | and smallness of its gradients, the free energy has the form of a field theory.

Assuming the game can continue as long as the coin toss results in heads, in particular that the casino has unlimited resources, this sum diverges without bound, and so the expected win for the player, at least in this idealized form, is an infinite amount of money.

Assuming these Euclidean vectors are represented in column form, the equation can be equivalently expressed as a matrix-vector multiplication:

Assuming a time-harmonic solution in the form

Assuming the former is stronger than the latter, and the ice driving force is sufficient, a gouge will form in the seabed.

Assuming that the Scandinavian name þurs is the most plausible reflex of the Elder Futhark name, a Common Germanic form can be reconstructed ( c. f.

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 the dielectric properties of the material inside the cable do not vary appreciably over the operating range of the cable, this impedance is frequency independent above about five times the shield cutoff frequency.

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 this is a reference to Mick, this is a slight discontinuity with Skinny Dip, in which he lists his number of ex-wives as six: the five mentioned in Skin Tight, plus Christina.

Assuming the use of strong 1NT openings, the sequence 1-1-1NT would show a balanced 12-14 HCP with five hearts and 1-1-2NT would show 18-19 HCP with five hearts.

Assuming a frequency average of 7 spikes / sec, as few as five randomly firing entorhinal cortical cells would cause a steady level of depolarization in the distal dendrites of CA3b pyramidal cells.

Assuming an adjustment to the July 1 to June 30 fiscal year, the required adjustment of the tax collection years and the towns involved are shown in Table 3.

Assuming that 10 – 15 % of bread is thrown away as stale, if it could be made to stay fresh another 5 – 7 days then perhaps 2 million tons of flour per year would be saved.

Assuming that the use of a 4-digit year field would continue, even in the far future, this would change the time code ambiguity from 100 years to 10 000 years.

Assuming an increase in output of during each year after the start of commercial production, RAND predicts the costs would decline to $ 35 – 48 per barrel ($ 220 – 300 / m < sup > 3 </ sup >) within 12 years.

Assuming a 12 % per year interest rate it follows

Assuming that birthdays are equally likely to happen on each of the 365 days of the year, the probability, P ( 2 ), that Person 2 has a different birthday than Person 1 is 364 / 365.

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 even just the lower estimate of £ 13 trillion hoarded away in offshore accounts, if these assets earned an average 3 % a year in income for their owners taxable at 30 %, then the offshore funds would generate £ 121 billion in tax revenues.

Assuming we know on which day a century starts ( from above ), if we add the number of years elapsed since the start of the century, plus the number of leap years that have elapsed since the start of the century, we get the day of the week on which the year starts.

Assuming non-accession reckoning, as he usually did for coregencies, Thiele determined 54 " actual " years back to 697 / 696 BC, as the year when the Hezekiah / Manasseh coregency began.

Assuming command of a last-place team, Schuerholz went to work and recruited half of a new infield by first signing Sid Bream to a contract, then getting Pendleton to sign a four year, $ 10. 2 million contract with the Atlanta Braves on December 3, 1990.

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 a steady rate of discharge, this alone is sufficient to raise global sea levels by 0. 2 mm per year.

Assuming Winston did not have the irradiation treatment done, it could have taken place any time between 1955 ( when Winston sold it ) and 1971, the year it was offered at auction.

Assuming that each year is 365 days long, the same date on each succeeding year will be offset by a value of.

Assuming no leakage of actinides to the waste stream during reprocessing, a 1GWe IFR-style reactor would consume about 1 ton of fertile material per year and produce about 1 ton of fission products.

Assuming that all goes well, the postulant then begins the period of novitiate, lasting a year, at the beginning of which is received the religious habit.

Assuming that it was not abandoned it would certainly have been closed down in 425 by the Christian emperor Theodosius II when he prohibited the worship of the old Roman and Greek gods.

Assuming Chavez was approximately 10 years old in 1979, that places the events of Debt of Honor to be in or near 2000, although the overall technology presented in the novel and its successive novels Executive Orders and Rainbow Six ( especially in regards to the sophistication of internet technology ) are more consistent with the mid-1990's.

Assuming the old man is dead, Vic rides away.

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

Assuming that the identification of Æthelweard as the brother of Ælfgifu is correct, his mother was the Æthelgifu whose company Eadwig enjoyed along with her daughter whilst escaping his coronation.

Assuming that the inscription on the James ossuary is genuine, the next question is whether " brother of Jesus " refers to Jesus, the founder of Christianity.