Assuming the stones were used for chiefly houses, it can be argued that Chamorro society was becoming more stratified, either from population growth or the arrival of new people.

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 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 personae were a Greek and Roman tradition that was abandoned during the Medieval period.

Assuming their pneus were originally cylindrical, they were more rigid than worms, jellyfish or logs.

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 that early synapsids had similar features, e. g., as argued by the authors of Palaeos, they were at a disadvantage in a mainly arid world.

Assuming that these trends continued, Russians were likely to lose their status as a majority of the Soviet population around the turn of the 21st century.

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 that Richard A. Locke was the author, his intentions were probably, first, to create a sensational story which would increase sales of the New York Sun, and, second, to ridicule some of the more extravagant astronomical theories that had recently been published.

Assuming that non-members take reasonable precautions and adjusting activities to the association's prohibition of their enforcing their own rights, the association is required to raise the non-member above his actual position by an amount equal to the difference between his position on an indifference curve he would occupy were it not for the prohibition, and his original position.

Assuming there were 501 or 500 jurymen, the prosecution had to gain at least 100 of the judges ' votes.

" Assuming that the boys were pulling a prank, the POWs disregarded the notes.

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 her labor pains were a symptom of nauseous migraine like the ones she suffered as a child, she had simply gone for a walk to clear her head, and this strange thing had happened to her.

" Assuming they were present, these feathers would have been used for insulation, and possibly also for brooding eggs.

Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.

Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this.

Assuming that the matrix W is irreducible, then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate.

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 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 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 that the satellite is in free fall around the primary and that the tidal force is the only relevant term of the gravitational attraction of the primary.

Assuming that the heights are normally ( Gaussian ) distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population.

( Assuming, in this case, that vehicles only have one engine.

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 genetic drift is the only evolutionary force acting on an allele, after t generations in many replicated populations, starting with allele frequencies of p and q, the variance in allele frequency across those populations is

Assuming arrows are produced by labour only, with man-hours per arrow, we have:

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 a court finds no contract, tax-payer is only liable for the fair market value of tax preparation services, which is not inflated up to account for the unusually large refund he enjoyed.

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.

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

Assuming that the brain function is normal or only minimally impaired, ECMO is provided until the patient recovers or receives a long-term ventricular assist device as a bridge to cardiac transplantation.

Using the quasi-stationary equilibrium approximation, that is, Assuming that the system is only slightly non-equilibrium, we have

Assuming the graphics mode is unshifted, PETSCII has only uppercase letters in its powerup state, an up-arrow ( ↑ ) instead of a caret ( ^ ) in position $ 5E and a left-arrow ( ← ) instead of an underscore ( _ ) in position $ 5F.

Assuming a flow is bounded on one side only, and that a rectilinear flow passing over a stationary flat plate which lies parallel to the flow, the flow just upstream of the plate has a uniform velocity.

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 that he is the only one who knows about the money, Ray decides to take it without making it officially part of the estate, and does not tell anyone about it: he knows that if he made it a part of the estate, taxes would take most of the money.

* There are 4 successive shots at the same frame: Assuming the ball is continuously caught, the ball can only be shot at the same frame to a maximum of 3 times, following which the next shot has to be made at the other frame at the opposite end of the playing field.

Assuming that the roots of P ( x ) are distinct ( that is, P ( x ) is separable ), then P ( x ) is additive if and only if the set forms a group with the field addition.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

Assuming that the pixel color is expressed using straight ( non-premultiplied ) RGBA tuples, a pixel value of ( 0. 0, 0. 5, 0. 0, 0. 5 ) implies a pixel which has 50 % of the maximum green intensity and 50 % opacity.

Assuming a specific Nazi usage of the term " Vaterland " ( which in fact never existed ), the direct English translation " fatherland " featured in news reports associated with Nazi Germany and in domestic anti-Nazi propaganda during World War II.

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 both sidebands are symmetric, which is the case for a normal AM signal, no information is lost in the process.

Assuming that it is possible to distinguish an observation corresponding to one of the discrete probability masses from one which corresponds to the density component, the likelihood function for an observation from the continuous component can be dealt with as above by setting the interval length short enough to exclude any of the discrete masses.

Assuming a Unix-style scenario in which one machine ( the client ) requires access to data stored on another machine ( the NFS server ):

Assuming that the Earth is a uniform sphere ( which is not correct, but is close enough to get an order-of-magnitude estimate ) with M

Assuming that the radius of the star does not change over this interval, the long term variation in activity level appears to produce a temperature variation of 15 K, which corresponds to a variation in visual magnitude ( V ) of 0. 014.

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

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.

If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group, which means that if we test all a from a set which generates, one of them must be a witness for the compositeness of n. Assuming the truth of the generalized Riemann hypothesis ( GRH ), it is known that the group is generated by its elements smaller than O (( log n )< sup > 2 </ sup >), which was already noted by Miller.

Assuming that the scene contains objects which reflect all red light, and ( other ) objects which reflect all green light and still others which reflect all blue light, one can then deduce that the illuminating light source is described by ( r < sub > max </ sub >, g < sub > max </ sub >, b < sub > max </ sub >).

Assuming the validity of Bell's theorem, any deterministic hidden-variable theory which is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster-than-light relations ( correlations ) between physically separated entities.

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 the northern part of M82 is nearer to us, which most literature assumes, the observed sense of rotation implies trailing arms.

Assuming you have Verdana version 5. 01 installed, which supports the locl feature for the latn / ROM ( Romanian ) script, a quick demonstration ( on Linux ) is:

Assuming dark energy remains constant ( an unchanging cosmological constant ), so that the expansion rate of the universe continues to accelerate, there is a " future visibility limit " beyond which objects will never enter our observable universe at any time in the infinite future, because light emitted by objects outside that limit can never reach points that expand away from us at less than the speed of light.