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Exact(13)
A ready estimate can be derived from the movie The Day After Tomorrow.
A simple analytic model, validated by rigorous Monte Carlo simulations, reveals that a more accurate error estimate can be derived from the inverse of the bulk modulus.
Since this value is often operator-sensitive, a more quantitative estimate can be derived in terms of fundamental physical quantities, such as plastic viscosity and yield stress.
Finally, a third power level estimate can be derived by forcing a positive definite difference between the data autocorrelation matrix and the candidate matrix, as it was done in [24].
With respect to a representative sample (d_{ell }^=N(t_{ell }),~ell =1,~cdotsots,~L,~L>>2), of the lag and growth phases, a linear least squares estimate can be derived for lnα 2, and hence α 2, and β 2 using the overdetermined system of equations lnleft[ln d_{ell}^-ln N_{0}+a_{1}t_{ell}^{b_{1}}right]=ln alpha_{2}+beta_{2}ln t_{ell}.
The variance of the MMSE estimate can be derived as Var [ Ŝ m i | y i ] = E [ S m i 2 | y i ] - E 2 [ S m i | y i ] = ∑ m i = 0 M S m i 2 p ( y i | c m i ) p ^ ( S m i ) ∑ m i = 0 M p ( y i | c m i ) p ^ ( S m i ) - Ŝ m i 2. (56).
Similar(47)
Since the problem (1.1) is linear, stability estimates can be derived by estimating the size of solutions to the corresponding homogeneous problem.
Remark 3.1 High order implicit Runge-Kutta methods and their discretization error estimates can be derived using order tree methods as described in [1] and [10].
While recent Mars missions have been equipped with capable inertial measurements, attitude measurements for missions to other planetary bodies are rather limited but some angular motion estimates can be derived from accelerometer, Doppler or other data.
As a result, the general form of the REFB-USRD-LS(2) and the REFB-USRD-WLS(2) estimates can be derived in the same way as (44) and (45) by replacing P ˜ i and Q ˜ i with M ˜ j T M ˜ j and Q ˜ i, j, respectively.
Absolute event rates for these lower incidence estimates can be derived similarly.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com