The momentum transfer from MNPs to the fluid is incorporated by setting the volume force term equal to the magnetic force and the drag force.
The value of is determined by setting the term equal to zero in Eq. (16) and is given by the condition (17).
The first term was an estimate of the prediction error (a standard cost function of the predictive neural net), whereas the second term was a regularization term equal to the weighted sum of the squared norms of the transform matrixes.
Considering the additional effect due to the pressure difference between inlet and outlet, an additional force term equal to the exit area Ae times the exit pressure minus the free stream pressure must be considered.
Under the hypothesis of this proposition, the adversary knows exactly the watermark signal and thus Δ U z)=Δ U ′ z) which makes the third term equal to zero and concludes the proof.
Markov's principle represents an unbounded search: if you have a proof that all terms an being 0 leads to a contradiction, then, by testing the terms a1,…2,a3,… in turn, you are "guaranteed" to come across a term equal to 1; but this guarantee does not extend to an assurance that you will find the desired term before the end of the universe.
To avoid "overfitting" problems, we chose an adequate regularisation method involving the modification of the conventional mean sum of the squares of the network errors by the addition of a term equal to the sum of the squares of the network synaptic weights and bias (Derras et al. 2012, 2014).
To test whether the gender effect varied with age, further terms were added to the model, such as an age by gender interaction term (equal to age for females, zero for males).
To avoid loss of power due to missing values, we used an offset term equal to the log of twice the number of SNPs in the GRS for which each person had genetic data.
A feature of this model is that extrapolation of the binding energy to 1 M salt makes the electrostatic term equal to zero, allowing the nonelectrostatic free energy component to be estimated.
