Sentence examples for expression of equation from inspiring English sources

The simpler expression of Equation (28) can be expressed as ∂ ln p Y, H ∂ H = 1 σ 2 A ̄ H Y − A ̄ H A ̄ H. (31).

The received signal after HPA and channel filtering can be expressed, after substituting u(t) in Equation 10 by the expression of Equation 15, as z ( t ) = i ( t ) ⊗ [ K h c ( t ) ] + d ( t ) ⊗ h c ( t ) + w ( t ).

The expression of Equation 21 is equivalent to the one for beamspace manifold in [8].

The integral expression of Equation (5) is shown by Equation (6).

When γ≠γ0, the approximate MSE ε2 τ0,γ,ψ) is given by the general expression of Equation (38).

The generic expression of Equation (18) was derived by assuming fully orthogonal SFBCs for any value of N R.

It is hard to find the exact expression of Equations 25 and 26, so we approximate the result of message multiplication as a Gaussian distribution: h x m → Δ m, n ≈ 1 z exp - 1 2 x m ( k ) - μ x m → n ( k ) × Σ x m → n ( k ) - 1 x m ( k ) - μ x m → n ( k ) T (27).

Integration limits in expressions of Equation 8 are from 0 to α for depth of crack and the limits for width are not specified (Figure 1b).

The principles used in the preceding derivation are still valid, and we can deduce that the magnetic field is now given by Equation (9): 1 (9) and the evolution of the magnetization, still considering independent spins 1/2, is obtained by inserting the new expression of into Equation (8), to yield Equations (10) and (11): (10) (11) where straightforward extensions of the notations were used.

The optimization criterion of Equation 20 includes the expressions of Equations 21 and 23 with unknown h k and α k, k=0 … K−1.

If Equation (3) is amended with the residual correlation factor or its complement to yield the observed-to-QSAR activity proportionality or if the averaged activity in Equation (8) is replaced with expressions of Equations (9) and (10), then the results are systematically the same or very close to those reported in Table 3.