Assuming that the warrior is dead, Drago and Empress Zara are free to conquer the Earth using their army of biomechanical beasts.

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 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 a uniform distribution does well, and it is possible to calculate inferences about unseen tiles that marginally improves on that assumption.

Assuming for simplicity a uniform distribution of branch targets, 0. 5, 1. 5, and 3. 5 instructions fetched are discarded, respectively.

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 parallel plate capacitor with uniform electric field, and neglecting fringing effects around the edges of the plates, differentiation provides:

Assuming this radius represents a sphere of uniform density we can further determine the particle's volume and density.

Assuming both the hydraulic conductivity and the horizontal components of flow are uniform along the entire saturated thickness of the aquifer ( i. e., and ), we can express Darcy's law in terms of integrated discharges, Q < sub > x </ sub > and Q < sub > y </ sub >:

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 the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius < var > r </ var >, which intercepts some of the power which is spread over the surface of a sphere of radius < var > D </ var >.

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

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.

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.