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 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 average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.

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 that the rule is known, one can derive the function that is used above in the classical heat calculation with respect to pressure.

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 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 the mark in question meets certain other standards of protectibility, it is protected from infringement on the grounds that other uses might confuse consumers as to the origin or nature of the goods once the mark has been associated with a particular supplier.

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 a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.

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 quality ( diffraction limited ) optics, lenses with larger numerical apertures collect more light and will generally provide a brighter image, but will provide shallower depth of field.

Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2 < sup > n </ sup >/ 1.

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 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 linear variation of glaze and decoration with time, and that these variables are independent,

) Assuming the student has read the case and can articulate the court's argument, the professor then asks whether the student agrees with the argument.

Assuming the butt is gripped with the left hand, moving the staff slightly to the right to defend blows is called the outside guard.

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 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 that they should be destroyed, he made to smite the seven Fathers of the Dwarves with a great hammer, weeping as he did so.

Assuming colocation with the biblical Mount Zion, its southern section would have been walled at the beginning of the 2nd millennium BCE, in around 1850 BCE, by Canaanites who established a settlement there ( or in the vicinity ) named Jebus.

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 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 there are no complications, the remaining portion of the first day's dose is then given.

Assuming that there are seven players on the field, and that a cup is in effect, this leaves four players to cover the rest of the field.

Assuming Odo commissioned the tapestry, it was probably designed and constructed in England by Anglo-Saxon artists ( Odo's main power base being by then in Kent ); the Latin text contains hints of Anglo-Saxon ; other embroideries originate from England at this time ; and the vegetable dyes can be found in cloth traditionally woven there.

Assuming that in the context cheese means some type of dairy product, the Euler diagram has the cheese zone entirely contained within the dairy-product zone — there is no zone for ( non-existent ) non-dairy cheese.

Assuming that capture of the Chinese capital would be the decisive turning point in the war, there was an eagerness to be among the first to claim the honor of victory.

Assuming that a certain percentage of these representations are in fact Tages, there appears to be no standard way to depict him.

Assuming the worst, the miners of the 7: 30 raced up the trail to the entrance, and there they found Clifford Griffin, shot through the heart, in a grave he'd dug himself.

Assuming there is no bookmaker fee or built-in profit margin, the actual probability of winning is 50 %.

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

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.

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

Assuming that there are not multiple non-trivial roots of we have the " exact formula " by the residue theorem:

Assuming that the fluid is at rest at infinity and that the pressure is defined to be zero there, this constant is zero, and thus

Assuming there are no side entries, on the distribution shown East must duck once to prevent declarer from running the suit.

Assuming proper operation ( no stoppages ) a cook off is not possible with this design because a cartridge is not chambered until the moment the trigger is pulled and the weapon is fired, thus there is nothing in the chamber.

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 that there is at least 1 free electron near A, that electron will begin to accelerate to the right toward electrode B.

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 there are no mistakes, the game will continue in sequence up to 21.

Assuming for simplicity that a and b are positive, one can say that a ruler, marked off in units of length c, could be used to measure out both a line segment of length a, and one of length b. That is, there is a common unit of length in terms of which a and b can both be measured ; this is the origin of the term.

Assuming the opponents have an eight-card spade fit, there are 17 total tricks.

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

Assuming that f '( x ) < 0, there are no distinct roots.

** Assuming infant surgery is successful, there is no barrier to engaging in normal sexual activities, and less distortion of psychosexual identity.