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2.4 × 10 3 W geo: average power consumption per person worldwide in 2008 (21,283 kWh/year) 3.3–6.6 × 10 3 W eco: average photosynthetic power output per square kilometer of ocean [23] 3.6 × 10 3 W tech: synchrotron radiation power lost per ring in the Large Hadron Collider at 7000 GeV [6] 10 4: 1–5 × 10 4 W tech: nominal power of clear ...
n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n tesseracted, hypercubed, zenzizenzic, biquadrate or supercubed instead of “to the power of 4”. The sequence of fourth powers of integers, known as biquadrates or tesseractic ...
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If the fractional part of x is 0.5, choose y randomly between x + 0.5 and x − 0.5, with equal probability. All others are rounded to the closest integer. Like round-half-to-even and round-half-to-odd, this rule is essentially free of overall bias, but it is also fair among even and odd y values. An advantage over alternate tie-breaking is ...
Let k be an algebraic number field with ring of integers that contains a primitive n-th root of unity.. Let be a prime ideal and assume that n and are coprime (i.e. .). The norm of is defined as the cardinality of the residue class ring (note that since is prime the residue class ring is a finite field):
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
Where a power of ten has different names in the two conventions, the long scale name is shown in parentheses. The positive 10 power related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10 [(prefix-number + 1) × 3] Examples: billion = 10 [(2 + 1) × 3] = 10 9; octillion = 10 [(8 + 1) × 3 ...
If x is the distribution function of a random variable on the real line, then the n th convolution power of x gives the distribution function of the sum of n independent random variables with identical distribution x. The central limit theorem states that if x is in L 1 and L 2 with mean zero and variance σ 2, then