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The velocity components are given by u = U ∞ x f ′ and v = − ( U ∞ ν f ) 1 2 f.

The velocity components are given by u = ( α m x ) Ra x f ′ and v = ( α m 2 x ) Ra x 1 2 [ y x Ra x 1 2 f ′ − f ]. (8).

According to Eq. (10), the velocity components are given by the equations: u = 2 K ( y − g ( z, t ) ), v = − 2 K ( x − f ( z, t ) ). (15) Let c be any constant and let π be the plane z = c.

In each experimental trial, a length-n, s-sparse signal (a signal having exactly s nonzero components), is generated in such a way that non-zero components are given by eta_{1} 10^{thetaeta_{2}}, (17).

The non-dimensional velocity components are given by begin{array}{cc}hfill u=xfrac{d{e}^{-beta eta }}{left(1+beta gamma -delta {beta}^2right)},hfill & hfill v=-left(s+frac{dleft 1-{e}^{-beta eta}right)}{beta left(1+beta gamma -delta {beta}^2right)}right).hfill end{array} (18).

As shown by Shapley [11], its components are given by (9). and it is the unique vector satisfying the following axioms: (a) lies in the efficiency hyperplane, (b) it is invariant under permutation of players, and (c) if and are two games, then.

The relationship between different disturbance components is given by formulas, and.

An alternative in the area of unobserved components is given by Kitagawa (1987).

An outer bound on the secrecy capacity of the relay eavesdropper channel with orthogonal components is given by the following.

Without any loss of generality, Eq. (5) can be rewritten as (7) The final solution for the weight components is given by (8) where * defines the Hadamard product of matrices with equal size.

The concept of seemingly unrelated models is used for multivariate observations when the components of the multivariate dependent variable are governed by mutually different sets of explanatory variables and the only relation between the components is given by a fixed covariance within the observational units.