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In this case, the branching ratio is just the ratio of the branching fractions between two states. To use our example from before, if the branching fraction to state |g is p {\displaystyle p} , then the branching ratio comparing the transition rates to |g and |d would be p 1 − p {\displaystyle {\frac {p}{1-p}}} .
A musical interval is a ratio of frequencies and the equal-tempered chromatic scale divides the octave (which has a ratio of 2:1) into twelve equal parts. Each note has a frequency that is 2 1 ⁄ 12 times that of the one below it. [3]
One can then prove that this smoothed sum is asymptotic to − + 1 / 12 + CN 2, where C is a constant that depends on f. The constant term of the asymptotic expansion does not depend on f : it is necessarily the same value given by analytic continuation, − + 1 / 12 .
Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of a ratio between two root-power quantities of √ 10:1. [16] Two signals whose levels differ by one decibel have a power ratio of 10 1/10, which is approximately 1.258 93, and an amplitude (root-power quantity) ratio of 10 1/20 (1.122 ...
In particular, if L n denotes the number of digits of the n-th member of the sequence, then the limit of the ratio + exists and is given by + = where λ = 1.303577269034... (sequence A014715 in the OEIS ) is an algebraic number of degree 71. [ 5 ]
The magnitude of eclipse is the fraction of the angular diameter of a celestial body being eclipsed. [1] This applies to all celestial eclipses. The magnitude of a partial or annular solar eclipse is always between 0.0 and 1.0, while the magnitude of a total solar eclipse is always greater than or equal to 1.0, and has a theoretically maximum ...
Other categorizations have been proposed. For example, Mosteller and Tukey (1977) [1] distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) [2] described continuous counts, continuous ratios, count ratios, and categorical modes
A Hausner ratio greater than 1.25 - 1.4 [9] is considered to be an indication of poor flowability. The Hausner ratio (H) is related to the Carr index (C), another indication of flowability, by the formula = / (). Both the Hausner ratio and the Carr index are sometimes criticized, despite their relationships to flowability being established ...