The interactions between valence electrons and the atom centers were approximated using generalized norm-conserving Hamann pseudopotentials [49, 50] for O, and H and a norm-conserving Troullier Martin pseudopotential [51], which contained 4s, 4p, and 3d projectors and a semi-core correction was used for Fe.
And again, the generalized normativity of truth appears to make trouble for pluralists, insofar as the thesis that there are several ways of being true apparently implies a proliferation of doxastic truth norms.
This allows a generalized p-norm.
A generalized H∞-norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived.
The last term is a generalized L2-norm penalty using the graph Laplacian matrix, which encourages smoothness on coefficients of genes that are connected in the biological network.
The chapter includes convolution, correlation, window functions, and a generalized category of norms, Lp-norm, which is used for scaling of data as well as for noise and error estimation.
To be more general, researchers considered the weighted generalized ℓ 2,1 norm (|z|_{w,2,1} = sum _{i=1}^{n} |w_{g}circ (z_{i})_{g}|_{2}) (we only consider that each group has the same weight, which means translation invariant) instead of the former generalized ℓ 2,1 norm.
In particular, the weighted generalized ℓ 2,1 norm degenerates into the generalized ℓ 2,1 norm if each entry of w g equals to 1.
In particular, if s=1, the generalized ℓ 2,1 norm degenerates into the original ℓ 1 norm, and the relevant regularization problem (3) degenerates to (1).
The generalized ℓ 2,1 norm ∥z∥2,1 can be treated as the generalized ℓ 1 norm of generalized points, whose entry (z i ) g is also a vector, and the absolute value of each entry is treated as the ℓ 2 norm of (z i ) g. See Fig. 1 a intuitively, where the top line is the vector z, the rectangles with dashed line are original (z i ) g, and the rectangles with solid line are the generalized points.
