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In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. [1] [2] It is denoted by π(x) (unrelated to the number π). A symmetric variant seen sometimes is π 0 (x), which is equal to π(x) − 1 ⁄ 2 if x is exactly a prime number, and equal to π(x) otherwise.
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
In some simplified expositions, the monetary multiplier is presented as simply the reciprocal of the reserve ratio, if any, required by the central bank. More generally, the multiplier will depend on the preferences of households , the legal regulation and the business policies of commercial banks - factors which the central bank can influence ...
With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [56] As a result, 8 and 144 (F 6 and F 12) are the only Fibonacci numbers that are the product of other Fibonacci numbers. [57]
The university received 1.8 million shares of Google in exchange for use of the patent; it sold the shares in 2005 for $336 million. [ 29 ] [ 30 ] PageRank was influenced by citation analysis , early developed by Eugene Garfield in the 1950s at the University of Pennsylvania, and by Hyper Search , developed by Massimo Marchiori at the ...
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time.In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates: [p 1] [1] [2]
The CGS unit is the poise (P, or g·cm −1 ·s −1 = 0.1 Pa·s), [28] named after Jean Léonard Marie Poiseuille. It is commonly expressed, particularly in ASTM standards, as centipoise (cP). The centipoise is convenient because the viscosity of water at 20 °C is about 1 cP, and one centipoise is equal to the SI millipascal second (mPa·s).
A high ROC AUC, such as 0.9 for example, might correspond to low values of precision and negative predictive value, such as 0.2 and 0.1 in the [0, 1] range. If one performed a binary classification, obtained an ROC AUC of 0.9 and decided to focus only on this metric, they might overoptimistically believe their binary test was excellent.