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The correct branch of the multiple valued function arctan x to use is the one that makes ν a continuous function of E(M) starting from ν E=0 = 0. Thus for 0 ≤ E < π use arctan x = arctan x, and for π < E ≤ 2π use arctan x = arctan x + π. At the specific value E = π for which the argument of tan is infinite, use ν = E.
Modern activation functions include the logistic function used in the 2012 speech recognition model developed by Hinton et al; [2] the ReLU used in the 2012 AlexNet computer vision model [3] [4] and in the 2015 ResNet model; and the smooth version of the ReLU, the GELU, which was used in the 2018 BERT model.
Explicitly state the number of significant figures (the abbreviation s.f. is sometimes used): For example "20 000 to 2 s.f." or "20 000 (2 sf)". State the expected variability (precision) explicitly with a plus–minus sign, as in 20 000 ± 1%. This also allows specifying a range of precision in-between powers of ten.
In mathematical formulas, the ± symbol may be used to indicate a symbol that may be replaced by either of the plus and minus signs, + or −, allowing the formula to represent two values or two equations. [2] If x 2 = 9, one may give the solution as x = ±3. This indicates that the equation has two solutions: x = +3 and x = −3.
In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc.
In air, which has a kinematic viscosity around 0.15 cm 2 /s, this means that the product of object speed and diameter must be more than about 0.015 m 2 /s. Unfortunately, the equations of motion can not be easily solved analytically for this case. Therefore, a numerical solution will be examined. The following assumptions are made:
Vibration (from Latin vibrāre 'to shake') is a mechanical phenomenon whereby oscillations occur about an equilibrium point.Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).
GJ 3929 is a red dwarf of spectral type M3.5V, having a radius of 0.32 ± 0.01 R ☉, a mass of 0.313 +0.027 −0.022 M ☉ and a temperature of 3384 ± 88 K. [6] With an apparent magnitude of 12.7, [2] it cannot be visible with the naked eye, neither with a small telescope. [5]