Hence, ideally, we would obtain the multivariate Gaussian solution of the two linear FPEs, compare and then decide upon the validity of the heuristic CME.
It is shown in [4] that a multivariate Nash bargaining solution always exists for the three-player/three-cake problem and that it is unique.
For the global game ((mathcal V_{{ij}}, mathcal V_{{ik}}, mathcal V_{{jk}}, d)) where d=(d i,d j,d k ), the multivariate Nash bargaining solution is defined by the set (x = (x_{{ij}}, x_{{jk}}, x_{{ik}})in mathbb R^{2times 3}) where (x_{{ij}} = tilde v(mathcal V_{{ij}},d, m_{{ij}}(x))).
The Cholesky decomposition, represented as a multivariate correlated factors solution (Fig. 1a), was used to examine the genetic and environmental relationship between mindfulness, depressive symptoms, and anxiety sensitivity.
The coefficients obtained from quaternary-solution multivariate analysis are in good agreement with separate binary and ternary measurements reported in the literature.
In addition, multivariate curve resolution (MCR) of the Raman spectra has been applied to obtain information on the molecular structure and speciation of the different complexes present in solution.
Our results illustrate that the multi-objective optimization provides a balanced solution for multivariate responses and gives better representation of streamflow and LAI dynamics.
Generalized radial basis function (GRBF) networks which are kernel based ANNs, have the best approximation property since they represent the optimal solution of multivariate linear regularization theory.
6, 7 Another mathematical solution are multivariate methods, which are based on least-square minimization of the global diffusion coefficient data set, followed by an optimization of the amplitudes of different components.
