For the scalar field, the zero-zero (or time-time) component of Equation 27, which has the interpretation of the energy density in flat space, reduces to the following: T 00 = 1 2 ( ∂ 0 ϕ ) 2 + ( ∂ i ϕ ) 2 + m 2 ϕ 2 − h 00 2 + h λ σ ∂ λ ϕ ∂ σ ϕ − h 00 m 2 ϕ 2. Open image in new window (31).
The singular component of equation (17) converges strongly to zero as (krightarrowinfty ), i.e., bigl| A^{dagger}bigl(g^{ ( k ) }bigr)Gamma bigl(G^{ k)}bigr) bigl( i a_{jmath }Phi+mathsf{E}_{11}A bigl(rho^{ ( k ) }bigr)Phi+mathsf {E}_{10}Phi bigr) bigr| _{2}stackrel{krightarrowinfty}{longrightarrow}0, for all Φ in a core domain (mathcal{D}) of H.
From the active component of Equation (5) or (6), we can solve m k = m k ∗ to compute the slow time T k A for which cell k remains active, T k A = 1 ν R ln ( 1 − m k ( 0 ) 1 − m k ∗ ), where ν R ∈ { λ R, μ R } as appropriate.
The weighted average of the voxel coordinates in the first term of Equation (6) arises from maximizing only the image force, i.e. the Gibbs distribution in the first component of Equation (5).
Maximizing the second component of Equation (5) derives the remaining | C j | components that work to shift ψ t, j (s + 1 ) toward the same direction as the other ψ t − 1, k → ψ t, k (s ) for k ∈ C j.
To assess the contribution of the constraints to the solution, we decomposed the gradient component of equation 2 into two parts, one describing the data (A T W d r d ) and one describing the constraints (μ D T W c r c ).
By using the corollary 15 (appendix A) we know that R i - λ i R∞ = O(ν i ) (15) uniformly in i so we finally get for all α uniformly for all n ≥ α and the proposition is then proved by considering the first component of equation (16).
We describe the analytical methods used to estimate the three components of Equation 1 in the following three subsections.
The signal components of Equation 9 form the vector z = [z(1), z(2),..., z(S ]T, where superscript "T" denotes transpose.
