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 a receiver is nearly tuned to the desired frequency, the AFC circuit in the receiver develops an error voltage proportional to the degree to which the receiver is mistuned.

Assuming it does, a full demand schedule can be deduced as the price of one good fluctuates.

Assuming the radiation levels are not too high and the area does not need to be abandoned such as the town of Pripyat near the Chernobyl reactor, an expensive and time consuming cleanup procedure will begin.

Assuming the plate boundary does not change as hypothesized, projected motion indicates that the landmass west of the San Andreas Fault, including Los Angeles, will eventually slide past San Francisco, then continue northwestward toward the Aleutian Trench, over a period of perhaps twenty million years.

Assuming the responsibility of mediator between the two sides, and with Erasmus ' willing participation ( the robot being left as the leader and controlling-force of the thinking machines ), Duncan does something similar to Bene-Gesserit Sharing with the robot ; possibly along with what seems to be a physical-bonding ( similar to what Leto II did with the sandtrout ) into something of a human-machine hybrid.

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 that the original statement is actually identified by, it should be clear by comparing the original statement with the reification that the reification actually does describe it.

Assuming the player's optical pickup is in proper working order, crosstalk distortion normally does not occur during playback of CAV format Laser discs, as the rotational speed never varies.

Assuming the cube does not have a fixed orientation in space, and that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced by a factor of 24.

Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area ( Pappus's second centroid Theorem ).

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

Assuming that they are continuous, the order of differentiation does not matter ( Clairaut's theorem ).

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 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.

Assuming the wheel and axle does not dissipate or store energy, the power generated by forces applied to the wheel must equal the power out at the axle.

Assuming that the marginal cost of extracting the resource does not depend on the rate of extraction and doest not vary over time, then the market price of the asset over time would be

Assuming energy demand does not change, this reduces the carbon dioxide emitted.

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 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 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 the foundational premise is correct, the optimal option for all governments would be an agreement to maintain tax harmonization.

Assuming this theory is correct, many scholars consider the possibility that one " chronicler " wrote this book.

Assuming the date of death of Cossa is correct, this one must have been completed prior to the others.

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 f ( r ) drops to zero more quickly than 1 / r, the inverse Abel transform is however given by