Assuming that all of an individual's ancestors are otherwise unrelated to each other, that individual has 2 < sup > n </ sup > ancestors in the nth generation before him and a total of about 2 < sup > g + 1 </ sup > ancestors in the g generations before him.

Assuming at least one of the components of w is positive ( otherwise multiply w by-1 ).

Assuming the lower figure for the big blast and one shot estimated by the Japanese at 10 megatons, a conservative computation is that the 24 announced tests produced a total yield of at least 60 megatons.

Assuming the weather is halfway decent that day, hundreds of thousands of persons will mass along this thoroughfare as President John F. Kennedy and retiring President Dwight D. Eisenhower leave Capitol Hill following the oath-taking ceremonies and ride down this historic ceremonial route.

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 that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.

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 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 a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

:< u > The Copenhagen Interpretation </ u >: Assuming wave functions are not real, wave-function collapse is interpreted subjectively.

Assuming the Axiom of choice, is regular for each α.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

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 that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.

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 the above are done one after another, minimum plane turnaround time is:

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 David was the one who repaired the automobile, Dibble promises to bring all of his tractors that need work done to David in the future, and guarantees the forming of other business connections along the way.

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 this is a binary search tree, as stated above, the elements must be interpreted as variables that can be compared to each other.

Assuming the roll didn't botch, the total is ( as above ) compared to the difficulty of the action to determine success or failure ( and the degree of success or failure ).

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 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 that has an inverse in a neighbourhood of and that its derivative at that point is non-zero, its inverse is guaranteed to be differentiable at and have a derivative given by the above formula.

Assuming the sky is clear, the Earth's shadow is visible in the opposite half of the sky to the sunset or sunrise, and is seen right above the horizon as a dark blue band.

Assuming that the height of these layers are about 100km above ground, he estimated that oscillations ( in this case the lowest mode of the Schumann resonances ) would have a period of 0. 1 second.

Assuming that mass is invariant in all inertial frames, the above equation shows Newton's laws of mechanics, if valid in one frame, must hold for all frames.

Assuming the above doStuff is a method, it is being called with zero arguments and as a result, explicit parentheses are not required.

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 the degree of does not exceed, the criterion is correct however, and somewhat stronger than the formulation given above, since if is irreducible modulo, it certainly cannot decompose in into non-constant factors.

Assuming the equivalence of homological and numerical equivalence, i. e. the above standard conjecture D, the functor H is an exact faithful tensor-functor.

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 a nonvanishing mass gap m < sub > 0 </ sub >, the frequency of any state like the above, which is orthogonal to the vacuum, is at least m < sub > 0 </ sub >,

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 that the results of c1 () and c2 () are independent, that means that the function as presented above contains a bug.

Assuming that the transmitting antenna's wavelength, height above average terrain, and effective radiated power is equal, a transmitted signal on 33 centimeters will, generally speaking, usually travel about 3 / 4 of the distance that the same signal would if transmitted on the 70 centimeter band.

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 each atom liberates its 3 valence electrons, this means that there are 40 electrons present, which is one of the magic numbers noted above for sodium, and implies that these numbers are a reflection of the noble gases.

Assuming an outdoor temperature of and an indoor temperature of, the above equation gives ( when temperatures are converted to Kelvin or Rankine ) a COP of 35. 98, or an EER of 122. 69.

NOTE: Assuming a resonance equation of F = 1 /( 2 x Pi x sqrt ( L x C ) ) I believe the above math needs reviewed.