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The inverse A-1 can be explicitly written as a matrix of cofactors.
To begin with, we denote the objective function in problem (30) by, which can be explicitly written as (33).
Note that when the total current is zero, the open circuit voltage (OCV) can be explicitly written as follows: begin{aligned} text{OCV}=A+Blog (S_{I=0}), end{aligned} (9 where (A=B log (K^{mathrm{r}} /K^{mathrm{o}})) and (B=1/2alpha =RT/F) and (S_{I=0}) is the substrate concentration at zero current.
For a single Euler step, the result of the evolution of U can be explicitly written as U^{n+1}_{i} = frac{1}{2} bigl(U^{n}_{i} + 2lambda f_{i-1/2} bigr) +frac{1}{2} bigl(U^{n}_{i} - 2lambda f_{i+1/2} bigr), (14) where the fluxes are defined as in Eq. (12) and λ depends on the maximum propagation speed of the system as well as the CFL factor.
The adapting bump model can be explicitly written as
In particular, recall that in the GBN framework, the likelihood associated to the multivariate Gaussian distribution of the network can be explicitly written as presented in this work.
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The infrared finger vein transmitting model function [3] is explicitly written as left{ {, begin{array}{l} {B_{text{min} } = 0, } {B = f(X),} {B_{text{max} } = 255,} end{array} begin{array}{l} {if} {if} {if} end{array} begin{array}{l} {X le X_{text{min} } } {X_{text{min} } < X < X_{text{max} } } {X_{text{max} } le X } end{array} } right.
Unfortunately, the Riemann functions can be explicitly written only in some simple cases.
and they can be explicitly written in the following form: (10).
Capacity building assessments and agendas should be explicitly written into planning documents.
Homes in Colonial America, on the other hand, did not enjoy the same sanctity as their British counterparts, because legislation had been explicitly written so as to enable enforcement of British revenue-gathering policies on customs; until 1750, in fact, the only type of warrant defined in the handbooks for justices of the peace was the general warrant.
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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