Inspired by Remark 3.2 and the technique used in [14] to prove (1.7), we formulate the following estimate of the same type as that in Proposition A.
We can formulate the pure tangential derivative estimates as follows.
We formulate the forward problem: given estimates of the fringe visibility and phase { A, ϕ} and { B, θ}, predict the measured values m and γ.
Out of the 90 points, 60 points were used to formulate the model used for estimating the volume of the hydrated products and the remaining 30 points were used to validate the predictions from the proposed model.
First, we have formulated the channel estimate MSE minimization problem for a determined subcarrier set as an SDP, then we have employed convex optimization techniques to obtain near optimal power distribution to a given subcarrier set.
Then the bounded operator DW φ, ψ : A α Φ p → Y is compact if and only if for every bounded sequence { f n } n ∈ N in A α Φ p such that f n → 0 uniformly on every compact subset of D as n → ∞, it follows that lim n → ∞ ‖ DW φ, ψ f n ‖ Y = 0. Now we formulate the following two useful point estimates.
We formulate the analysis in terms of estimating the full h until explicit equalization is performed.
Then, from the developed iterative technique, the sequences converging uniformly to the unique solution are formulated, and the estimates of the error and the convergence rate are derived.
3, we introduce a double iterative technique and establish the condition for which Eq. (1.2) has a unique positive solution, then from the developed iterative technique, the sequences converging uniformly to the unique positive solution are formulated, and the estimates of the approximation error and the convergence rate are derived.
In my field, we formulate the computer algorithms used for this and provide estimates for the reliability of the answer.
