The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified.
Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm.
Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud- ).
In addition, Yang gave a matrix trace inequality for products of positive semidefinite matrices in [9]; In [10], Yang et al. established a matrix trace inequality for positive semidefinite matrices, which improved the result given by Yang in [9].
Based on the work in [3 5], Chang established a matrix trace inequality for products of Hermitian matrices in [8], which partly answers a conjecture proposed by Bellman in [4].
Considering the compatibility condition between the girder and diaphragms, solutions for the distortional angle, warping displacements and stresses were derived and further simplified by establishing a matrix equation system.
When a given sample is taken as a point in the space defined by the variables, the distance between this point and all the other points can be calculated, thereby establishing a matrix that describes the proximity between all the samples studied.
In conclusion, we have established a matrix model of 9-mer peptide binding to murine TAP that correlates well with measured affinities in a blinded evaluation.
To establish a matrix adapted for GWAS, markers with a minor allele frequency (MAF) below 5% were discarded.
In our analyses, we established a matrix with six ingroup taxa and one outgroup, and no taxa were removed from the matrix at any time in our analysis regardless of amounts of missing data in the various partitions.
