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However, log-ratios are often used for analysis and visualization of fold changes. The logarithm to base 2 is most commonly used, [ 8 ] [ 9 ] as it is easy to interpret, e.g. a doubling in the original scaling is equal to a log 2 fold change of 1, a quadrupling is equal to a log 2 fold change of 2 and so on.
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
For each integer n > 2, the function n x is defined and increasing for x ≥ 1, and n 1 = 1, so that the n th super-root of x, , exists for x ≥ 1. However, if the linear approximation above is used, then = + if −1 < y ≤ 0, so + cannot exist.
In this article, the following conventions and definitions are to be understood: The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
Specific modulus is a materials property consisting of the elastic modulus per mass density of a material. It is also known as the stiffness to weight ratio or specific stiffness.
The positive square root of the variance is defined to be the standard deviation, and it is a measure of the width of the PDF; there are other measures, but the standard deviation, symbolized by the Greek letter σ "sigma," is by far the most commonly used.