Assuming A is true is therefore enough to guarantee that B is true regardless of the truth of statement B.

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

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 block of various sizes are transmitted on the LAN, software overhead is computed on average and novel time evaluation is used to estimate the bandwidth ( capacity ) of covert channels are also presented.

Assuming even just the lower estimate of £ 13 trillion hoarded away in offshore accounts, if these assets earned an average 3 % a year in income for their owners taxable at 30 %, then the offshore funds would generate £ 121 billion in tax revenues.

Assuming an accurate CBA, changing the status quo by implementing the alternative with the lowest cost-benefit ratio can improve pareto efficiency .. An analyst using CBA should recognize that perfect evaluation of all present and future costs and benefits is difficult, and while CBA can offer a well-educated estimate of the best alternative, perfection in terms of economic efficiency and social welfare are not guaranteed.

Assuming that the diameter of a choking pulley is twice the diameter of its shaft, which is a generous estimate, then the frictional resistance force at the outer diameter of a choking pulley is half the frictional resistance force at the shaft of a choking pulley.

Assuming the missing data are missing at random this results in an estimate for the covariance matrix which is unbiased.

Assuming ( the maximum likelihood estimate of ) is non-singular, the first order condition for the estimate of the mean vector is

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 purely random distribution of wars between states, regardless of their democratic character, the predicted number of conflicts between democracies would be around ten.

Assuming the game can continue as long as the coin toss results in heads, in particular that the casino has unlimited resources, this sum diverges without bound, and so the expected win for the player, at least in this idealized form, is an infinite amount of money.

Assuming that L denotes radiance, we have that at each particular position and direction, the outgoing light ( L < sub > o </ sub >) is the sum of the emitted light ( L < sub > e </ sub >) and the reflected light.

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.

), the total human biomass is the average weight multiplied by the current human population of approximately 6. 5 billion ( see, e. g., ): Assuming 60 – 70 kg to be the average human mass ( approximately 130 – 150 lb on the average ), an approximation of total global human mass of between 390 billion ( 390 × 10 < sup > 9 </ sup >) and 455 billion kg ( between 845 billion and 975 billion lb, or about 423 million – 488 million short tons ).

Assuming an increase in output of during each year after the start of commercial production, RAND predicts the costs would decline to $ 35 – 48 per barrel ($ 220 – 300 / m < sup > 3 </ sup >) within 12 years.

* January 1 – Assuming that the copyright laws are not changed further, all works published in 1923 enter the public domain in the U. S., the first works to do so since the passage of the 1998 Sonny Bono Copyright Term Extension Act.

* February 15 – Assuming no further extensions to the term of copyrights become law in the interim, all sound recordings fixed before February 15, 1972 will enter the public domain in the U. S.

Assuming unprotected intercourse with a man of the same age, women aged 19 – 26 have about a 50 % chance of becoming pregnant during a given menstrual cycle, compared with 40 % in the 27-34 age group and below 30 % for women 35-39.

Assuming a ceiling insulated to R – 2 ( R

Assuming an FLC with levels, the Rate – Distortion minimization problem can be reduced to distortion minimization alone.

Assuming that the passwords are chosen independently, an adversary who intercepts one challenge – response pair cannot use it to authenticate unless she is lucky enough to get the same challenge.

Assuming can be decided by a TM using cells, and following from the Immerman – Szelepcsényi theorem follows that can also be determined by a TM ( which we will call ) using cells.

Assuming that her relationship with Edward and her marriage to John are over, Florence takes prussic acid – which she has carried for years in a vial that John thought held her heart medicine – and dies.

→ Assuming non-zero rates of labor growth complicates matters somewhat, but the basic logic still applies – in the short-run the rate of growth slows as diminishing returns take effect and the economy converges to a constant " steady-state " rate of growth ( that is, no economic growth per-capita ).

Assuming an application used by a hospital needs to map the data element concepts to the UDEF, the last name and first name ( within UDEF you will find Family Name and Given Name under the UDEF property Name ) of several people that are likely to appear on a medical record that could include the following example data element concepts –

Assuming no loss of time when moving a car from one station to another, the longest stage on the assembly line determines the throughput ( 20 minutes for the engine installation ) so a car can be produced every 20 minutes, once the first car taking 35 minutes has been produced.

Assuming that the solution of this equation can be written as

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

Assuming perfect combustion conditions, such as complete combustion under adiabatic conditions ( i. e., no heat loss or gain ), the adiabatic combustion temperature can be determined.

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 the diffusion coefficient D to be a constant we can exchange the orders of the differentiation and multiply by the constant:

Assuming the stones were used for chiefly houses, it can be argued that Chamorro society was becoming more stratified, either from population growth or the arrival of new people.

Assuming that the six factors are present and Miranda applies, the statement will be subject to suppression unless the prosecution can demonstrate

Assuming that the six factors are present, the Miranda rule would apply unless the prosecution can establish that the statement falls within an exception to the Miranda rule.

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 machine executing the program itself continues to function, it can detect this failure and abort.

Assuming no high-grade obstruction or associated infection is found in the urinary tract, and symptoms are relatively mild, various nonsurgical measures can be used to encourage the passage of a stone.

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 that one knows the signal propagation speed in the particular cable-under-test, then in this way, the distance to the short can be measured.

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

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 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 zeroes of f are discrete, we can say gT < sup > 2 </ sup >/ L

Assuming an ideal solution, the dependence can be quantified as:

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.