Assuming the truth of the GRH, the estimate of the character sum in the Pólya – Vinogradov inequality can be improved to, q being the modulus of the character.

Assuming genetic drift is the only evolutionary force acting on an allele, after t generations in many replicated populations, starting with allele frequencies of p and q, the variance in allele frequency across those populations is

Assuming both p and q are nonzero, neither of the groups O ( p, q ) or SO ( p, q ) are connected, having four and two components respectively.

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

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.

), 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 now that light travels along the x < sub > 3 </ sub > axis, the path of a light ray may be parametrized as and

Assuming that the tankage mass triples, we have a m < sub > 1 </ sub > of 31, 500 + 6, 800 = 38, 300 kg, and since we have fixed at 119, 900 kg, we get

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 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.

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

Assuming zero empirical mean ( the empirical mean of the distribution has been subtracted from the data set ), the principal component w < sub > 1 </ sub > of a data set X can be defined as:

Assuming the columns of A ( and hence R ) are independent, the projection solution is found from A < sup > T </ sup > Ax = A < sup > T </ sup > b. Now A < sup > T </ sup > A is square ( n × n ) and invertible, and also equal to R < sup > T </ sup > R.

Assuming perfect information, p < sub > e </ sub > is the same for all participants in the market, and this is identical to:

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 an adjustment to the July 1 to June 30 fiscal year, the required adjustment of the tax collection years and the towns involved are shown in Table 3.

Assuming they form a set, the definable numbers form a field containing all the familiar real numbers such as 0, 1, π, e, et cetera.

Assuming that a TNT explosion releases 1, 000 small ( thermochemical ) calories per gram ( 4. 2 kJ / g ), one tonne of TNT is equivalent to 4. 2 gigajoules.

Assuming opener bids 1 and partner responds 2 ; opener will know from this bid that partner has 9 losers ( using basic LTC ), if opener has 5 losers rather than the systemically assumed 7, then the calculation changes to ( 5 + 9

* 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.

Assuming a 100 % conversion of antiprotons to antihydrogen, it would take 100 billion years to produce 1 gram or 1 mole of antihydrogen (

Assuming that birthdays are equally likely to happen on each of the 365 days of the year, the probability, P ( 2 ), that Person 2 has a different birthday than Person 1 is 364 / 365.

Assuming that the cost of traversing any network segment is 1, the least cost path from bridge 4 to the root bridge goes through network segment c. Therefore, the root port for bridge 4 is the one on network segment c.

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.

Assuming no absorption, conservation of energy requires T + R = 1.

Assuming the probability of the insured risk is 1 %, the potential loss is $ 1, 000 and the premium is $ 15.

Assuming the segments all are oriented left-to-right ( in increasing order from A < sub > k </ sub > to A < sub > k + 1 </ sub >), the boundary is A < sub > 6 </ sub > − A < sub > 1 </ sub >.

* June 1: Assuming of functions of the Iraqi Interim Government led by Prime minister Iyad Allawi ; Ghazi al-Yawer is designed head of the Iraqi state.

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 the magma that formed Tharsis contained carbon dioxide ( CO < sub > 2 </ sub >) and water vapor in percentages comparable to that observed in Hawaiian basaltic lava, then the total amount of gases released from Tharsis magmas could have produced a 1. 5-bar CO < sub > 2 </ sub > atmosphere and a global layer of water 120 m thick.

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 20 / 20 vision, the resolution of the eyes is about one minute of arc.

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 that the prophecy took place after Uzziah became sole regent in 768 / 767, Amos's prophecy can be dated to some time after that and some time before Jeroboam's death in 753 BC, with the earthquake two years after that.

Assuming non-accession reckoning, as he usually did for coregencies, Thiele determined 54 " actual " years back to 697 / 696 BC, as the year when the Hezekiah / Manasseh coregency began.

Average growth approximation: Assuming that two stocks have the same earnings growth, the one with a lower P / E is a better value.

* Connor, Rachel and Crofts, Charlotte ( 1998 ), ' Assuming White Identities: Racial and Gendered Looking Across the Literature / Media Divide ', in Heloise Brown, Madi Gilkes, Ann Kaloski-Naylor ( eds ), White? Women, York: Raw Nerve Books.

Assuming substitution of genes to take place slowly, one gene at a time over n generations, the fitness of the species will fall below the optimum ( achieved when the substitution is complete ) by a factor of about 30 / n, so long as this is small-small enough to prevent extinction.

Assuming your data cannot be compressed, the 8. 192 seconds to transmit a 64 kilobyte file over a 64 kilobit / s communications link is a theoretical minimum time which will not be achieved in practice.

Assuming that carfentanil and remifentanil were the only active constituents ( which has not been verified by the Russian military ), the primary acute toxic effect to the theatre victims would have been opioid-induced apnea ; in this case mechanical ventilation and / or treatment with opioid antagonists would have been life-saving for many or all victims.

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 a hemoglobin concentration of 15g / dl and an oxygen saturation of 99 %, the oxygen concentration of arterial blood is approximately 200ml of O < sub > 2 </ sub > per litre.

Assuming you have downloaded a NetBSD / pmax 5. 0 CD-ROM ISO image ( pmaxcd-5. 0. iso ),

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

Assuming f is continuously differentiable and f, f ' drop to zero faster than 1 / r, we can set and.

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

Assuming that Developers have no organizational skills or time to spend attention to this topic, this can present a problem: the goal of the Business Owner is to get what they want very quickly, and the goal of the Developer is to give the Business Owner what they want as quickly as he / she can give it to him / her.

Assuming that seasons run from equinox to solstice or vice versa, the season L < sub > s </ sub > 0 to L < sub > s </ sub > 90 ( northern-hemisphere spring / southern-hemisphere autumn ) is the longest season lasting 194 Martian sols, and L < sub > s </ sub > 180 to L < sub > s </ sub > 270 ( northern hemisphere autumn / southern-hemisphere spring ) is the shortest season, lasting only 142 Martian sols.