Assuming a Levi-Civita connection exists it is uniquely determined.

Assuming this connection is found, the first breakpoint is reached.

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 data is reliable, reasons for falling growth rates and fertility rates probably include late marriage, urbanization, limited housing space, and the expectation that women would participate equally in terms of work hours in the labor force.

Assuming a yield for a 10 year-old tree is a reliable conservative estimate, though some exceptional specimens of that age have yielded.

Assuming that X makes the first move every time:

Assuming that X makes the first move every time:

Assuming the license holder makes the demand for a hearing within the statutory period, a hearing is scheduled.

Assuming that the woman is Shephard's mate, Charlie makes chalk marks which indicate that he likely was a married man with children before he was frozen.

* Assuming that not all possible choices are available to him: How capable is the individual to desire all choices available, in order to choose from among them?

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 an Immirzi parameter on the order of 1, this gives the smallest possible measurable area of ~ 10 < sup >− 66 </ sup > cm < sup > 2 </ sup >.

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

Assuming that load results are bypassed with the same priority as integer results, then it's possible to summarize this recurrence as a load followed by another load — as if the program was following a linked list.

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 proper operation ( no stoppages ) a cook off is possible with this design because a cartridge is kept chambered in the potentially hot chamber, where it can absorb enough heat to cause ignition of its propellant.

Assuming the accuracy of such a guess, Kollikodon would be a contender for the largest Mesozoic mammal known, along with other possible giants such as Repenomamus, Schowalteria, and Bubodens.

Assuming the source to be " rotationally invariant " ( to produce all possible states λ with equal probability ), the probability of a given type of coincidence will clearly be proportional to the corresponding area, and these areas will vary linearly with the angle between a and b. ( To see this, think of an orange and its segments.

Assuming that the four centers of each color in each set are indistinguishable, the number of permutations of each set is reduced to 24 !/( 4 !< sup > 6 </ sup >) arrangements, all of which are possible.

Assuming an impact origin, other possible ways of dating the event include looking for evidence of ejecta material such as tektites, and deposits from the hypothesised tsunami, which might be found anywhere around the North Sea basin.

Assuming that we don ’ t have a commitment to one ' set theory ' ( all toposes are in some sense equally set theories for some intuitionistic logic ) it is possible to state everything relative to some given set theory which acts as a base topos.

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 that man is free to perform or not to perform any act whatever, Molina maintains that this circumstance renders the grace of God neither unnecessary nor impossible: not impossible, for God never fails to bestow grace upon those who ask it with sincerity ; and not unnecessary, for grace, although not an efficient, is still a sufficient cause of salvation ( gratia mere sufficiens ).

Assuming the goal of a system has been articulated and its measurements defined, the steps are: