We therefore substitute the time-dependent kernel K(t − t′) in the second term of Equation 13 with an effective space-dependent one, K, using the average speed of the animal to fix the relationship between the two: (14) H = H K + H A = = 1 V ∫ Γ d χ d 2 + γ 1 V ∫ Γ d χ Ψ ∫ Γ d χ ′ Ψ K, where we have also made explicit the normalization by the area V of the d-dimensional environment Γ.
By substituting the time integration of gene expression, i.e. k i ⋅ ∫ 0 t q τ ⋅ dτ, for δE, and assuming the proportional and derivative actions a part of the metabolic process (14), (16) δ X ˙ = N ⋅ E ss ⋅ f ′ X ⋅ δX + N ⋅ f X ss ⋅ k i ⋅ ∫ 0 δφ X ⋅ dt + γ ⋅ δp This describes the overall dynamics of a closed-loop metabolic system under perturbation as a sum of three terms.
Column (ii) shows the results when substituting the time-specific effects with a time trend variable.
Maybe it is time to substitute the sentence "sequence determines structure" with the sentence "unfolded structure determines folded structure".
After substituting the stress time history data, relevant load time history data, and optimized coefficient of D46 into the above equation, the following can be obtained.
Partial derivative terms of several time-point variables substitute for the time derivatives of the converted general ordinary differential equation.
You may wish to substitute the most recent New York Times article on this event for the article included below.
Yankey made the 125th international appearance of a career dating back to 1997, although she had been substituted by the time England made the breakthrough in the 92nd minute when Fara Williams' cross was nodded home by White.
In the starting eleven for the final against his boyhood heroes Liverpool, Horsfield had been substituted by the time Birmingham lost in a penalty shootout.
In a more recent study of MTX omission, mycophenolate mofetil was substituted at the time of omission resulting in similar outcomes, although grade 2 4 acute GVHD was higher in the mycophenolate mofetil/omission arm.
