Sentence examples for functions log from inspiring English sources

In general, finer intervals are required for calculating logarithmic functions of smaller numbers for example, in the calculation of the functions log sin x and log tan x.

Obviously, χ ( U ) ⊆ f ∗ ( U ) and the two functions log Φ ∘ χ and z ↦ log | χ ′ ( z ) z n − α | are continuous on U ¯, harmonic on U and coincide on ∂U.

In this case, it is sufficient to consider the potential at time n = 0. Thanks to the bounds (53), one can make a series expansion of the functions log and log ( 1 − π ) and rewrite the potential under the form of the expansion: (57).

(c) Since the functions log P k ( f t ) are convex for k = 1,..., 8, and D i 's associated with them, therefore for t ≤ u, r ≤ v, t ≠ r, u ≠ v, we have [[4], p.2], log P k ( f t ) - log P k ( f r ) t - r ≤ log P k ( f u ) - log P k ( f v ) u - v, concluding B k, i ( t, r ; f t ) ≤ B k, i ( u, v ; f t ).

To accelerate the calculation of the math functions (log, sincos), we leveraged a free math library, SSEMath by Julien Pommier [ 20].

As is standard in regression, to raw phenotype values y ˜ i we applied suitable normalizing transformations y i = f (y ˜ i ), using common monotonic functions (log, x1/2, …) that improved Gaussianity of the noise.

A particular solution log Y p of the above complex equation is the function log Y p = ( γ − 1 2 − i α ) log a : = P γ ( a ).

In contrast, also shown is a picture of the natural logarithm function log(1 + x) and some of its Taylor polynomials around a = 0.

This model is the only empirically derived model that predicts flight distances across bee species and is based on a log-log linear regression model between body size (i.e. intertegular span, [38]) and foraging distance according to the function log y = log a+b * log x (where y =  foraging distance, a =  constant, b =  power parameter, x =  body size of the bee).

For the longevity assay, we used the survdiff function (log rank test) of the R package « survival » as to test the effect of the treatment.

The statistical analyses used binomial (logit link function), Poisson (log link function), and gamma (log link function) error terms for the outcome of encounters (oviposition vs. rejection), frequencies of behaviours, and handling times, respectively.