Caption: Figure 17: Magnitude of positional

covariances in each direction (x, y, and z).

The spherical simplex rule and the first-order generalized Gauss-Laguerre quadrature rule are adopted to derive the simplex cubature rule, which is used to approximate the a posteriori mean and

covariance in the nonlinear Kalman filter framework.

Covariances for Subsets of Variables from the Inverse

Covariance Our main contributions in this paper include the following: (i) An improved unscented transformation and the corresponding improved UKF method are proposed to deal with the nonlinear dynamic system with random parameters; (ii) the performance analysis is provided which shows that the approximated mean and

covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion when the nonlinear system function contains random parameters.

Finally, the curved two-headed arrows represent

covariances (i.e., correlations when based on standardized estimates); only those found to be statistically significant are included here.

The means and variances used to generate the

covariance matrices and; therefore, the multivariate random samples for the calculations of the type I error and the power of the LRT for the independence between two groups of variables belong to the groups of adult plants and the production of the hybrid Lyra (Table 1).

Model 4 was the same as Model 3, but allowed for a direct maternal

covariance (Cov (a,m)).

When the

covariance matrices are divided by selected suitable [[mu].sup.2.sub.0] value (for example, variance value of signals), the weight coefficient matrices are obtained by Equation (11).

The risk-free rate of return on the risk-free asset is r, an n x 1 vector of the expected excess rates of return is R - r, and the n x n non-singular

covariance matrix of risky assets' rates of return is [OMEGA].

If the

covariance matrix of the vector meets the alternative assumption (15), the following applies

The Patterns of

Covariances between Growth Parameters and the Corresponding Patterns of Constraints upon the Magnitude of Variation of Functional Parameters

A Negative

Covariance between Growth-Based Parameters [alpha] and [rho] and the Consequences upon the Ranges of Interspecific Variations of the Shell Elongation E and the Ventral Convexity K, in Tellinoidea