Firstly the mathematical relation between the interconnection matrix and the library pattern matrix, and the stability of the EAPNN with infinite precision data have been studied, strictly mathematical proofs for them have been given.
Considering matrix W representing the coefficients that link the c, Δc, and Δ2c as expressed in Equations (2) and (3), the relation between the observation matrix O and the static parameter matrix C is: O = W C. (4).
It is employed to learn the relation between the parameter matrix and the individual core tensor.
We also obtain the explicit relation between the shape matrix of E-inclusion and remote applied strain which will be convenient for engineering applications of these new geometries.
The simple rule <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0011187.e247.PNG" class= inline-graphic"/> reveals such a relation between the payoff matrix and the parameters of the linking dynamics.
R ij (t) is the response curve, as a function of t, for the ith species to an impulse of the jth species at time 0. The relation between the correlation matrix and the fundamental solution is expected for a linear system.
This article investigates the minimaxity of matrix linear estimators of regression coefficient matrix in a general multivariate linear model with a nonnegative definite covariance matrix allowing for relations between the covariance matrix and the design matrix under a balanced loss function.
The required modification, however, does not lend itself to a convenient relation between the original matrices and the modified ones that can be used in mathematical derivations.
In addition, we set up a relation between the gain matrices in the protocol and the convergence time and consensus accuracy of the agents, and then design the gain matrices with respect to a pre-specified convergence time and a required consensus accuracy.
Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements.
Consequently, given the relation between the normalized Laplacian matrix and the adjacency matrix eigenvalues, we provide some new bounds for the HL-index.
