When the value of a large quantity of items has a Zipf's law distribution, the total value of the most-valuable items is proportional to the-th harmonic number.
22.
The Euler Mascheroni constant gets a name because it has an intimate connection with the harmonic numbers and the natural logarithm and consequently is quite useful in many applications; that's all.
23.
For the set cover problem, Lov�sz proved that the integrality gap for an instance with " n " elements is " H n ", the " n " th harmonic number.
24.
Like a square wave, the triangle wave contains only odd harmonics, demonstrating roll off much faster than in a square wave ( proportional to the inverse square of the harmonic number as opposed to just the inverse ).
25.
For heterogeneous fork-join queues ( fork-join queues with different service times ), Alomari and Menasce propose an approximation based on harmonic numbers that can be extended to cover more general cases such as probabilistic fork, open and closed fork-join queues.
26.
The previous question elicited a link Wolstenholme _ prime # Definition via harmonic numbers that seems to use the concept of modulo arithmetic applied to rational numbers without defining the concept or providing a suitable link to clarify this ( the cited reference Zhao ( 2007 ) is opaque to me in this regard ).
27.
:I don't know much about harmonic numbers, but what I find interesting is the fact that H " p "-1 being divisible by " p " 3 is equivalent to " p " being a ctb ) 10 : 56, 11 August 2012 ( UTC)
28.
One year later, at the request of the bishop of Meaux, he wrote " The Harmony of Numbers " in which he considers a problem of Philippe de Vitry involving so-called " harmonic numbers ", which have the form 2 " m " ? " n ".
29.
In the paper " Metcalfe's Law is Wrong ", Andrew Odlyzko argues that the incremental value of adding one person to network of " n " people is approximately the " n " th harmonic number, so the total value of the network is approximately " n " log " n ".
30.
If F = h _ 2 / 2 ^ n is the interval ratio in consideration, where n is a positive integer and h _ 2 is the higher harmonic number of the ratio, then its interval can be determined by taking the base-2 logarithm I = 12log _ 2 ( h _ 2 / 2 ^ n ) = 12log _ 2 ( h _ 2 )-12n.
