Sentence examples for a function evaluated at from inspiring English sources

The classical Ostrowski integral inequality ([2] see also [[1], p.468]) in one dimension stipulates a bound between a function evaluated at an interior point x and the average of the function f over an interval.

We then have: Since q ij / q ji can be written as a function evaluated at s j divided by the same function evaluated at s i, evolution is time reversible according to this model with: Here, c and c' are constants with c' = -l/4 N e log c, which will be chosen to make the equilibrium frequencies sum to one.

Modeling the test probabilities as those delivering event probabilities bounded above by a concave distribution function evaluated at the physical event probability, leads to upper and lower prices as distorted expectations.

Population balance equations for microbial or cell cultures contain a state-dependent fission intensity function which is such that the product of this function, evaluated at a given state, and a differential increment of time is the fraction of cells of the given state that divide in that increment of time.

They are computed as the discrete differences of the logistic function evaluated at a 10%% increase in the variables' values with respect to the logistic function evaluated at the observed variables' values.

The covariance between two r.v.s equals a minus mixed second order log-derivative of their characteristic function evaluated at zero.

We combined these weights with the baseline survivor function evaluated at 1 and 2 years to derive a risk equation which could be applied for each time period.

We also give a new representation for Euler's constant in terms of the Riemann zeta function evaluated at positive odd integers.

Approximately, we have (23) E r g, g ^ ≈ E s g, g ^ E s g 2 E s g ^ 2. Note that the correlation involves a function of three correlated random variables (s g ^, g, s g 2, s g ^ 2 ) and we must acknowledge that the expected value of a function of random variables is not usually exactly equal to the same function evaluated at the expected values of the random variables [ 19].

The steepest descent direction is the negative gradient of the loss function evaluated at the current model Fm−1, where the step length is chosen using line search.

The total energy can also be given by the characteristic function evaluated at zero.