The phrase "also proved that for" is correct and usable in written English.
It can be used when discussing findings or conclusions in a research or analytical context, particularly when building on previous statements or evidence.
Example: "The study also proved that for every action, there is an equal and opposite reaction."
Alternatives: "also demonstrated that for" or "further established that for".
Using the same NSCL, it is also proved that for the ALE extension of the second-order time-accurate trapezoidal rule, the DGCL requirement is a necessary as well as sufficient condition for nonlinear stability on moving grids.
Meanwhile, they also proved that for any continuous function f on (partialmathcal{T}_{n}) there exists a solution of Neumann problem on (mathcal{T}_{n}).
She also proved that, for the case of (1 < q < (3N + 8)/(3N-4)), under an additional technical assumption on (m(t)), the existence of positive periodic classical solutions is also true.
It is also proved that for the frequency β which does not belong to CFs, γ 2r satisfies chi-squared distribution with 2 N degrees of freedom: lim T → ∞ γ 2 r β, τ = χ 2 N 2. (15).
The Hungarian mathematician Csiszar, winner of Shannon prize, had also proved that for a group of information which is not contradictory, there exist unique entropy maximization models and their mathematical forms are exponential functions.
Furthermore, Cao [3] proved that the necessary and sufficient condition of convergence for the operators is lim n → ∞ ( s n / n ) = 0, and he also proved that for n ∈ Q = { n : n ∈ N, and�� 0 < ( s n − 1 ) / n + 1 / n ≤ 1 } the following estimate of approximation degree holds: ∥ L n f − f ∥ ≤ 4 ω ( f, s n − 1 n + 1 n ).
Sequencing of tobacco trichomes cDNA library constructed from cadmium-treated leaves also proved that genes for photosynthesis and primary metabolism were detected with high frequency [ 12].
They also proved that Cesàro α-integrability for appropriate α is also sufficient for the weak law of large numbers to hold for certain special dependent sequences of random variables.
They also proved that if for all and for some, then the sequence converges weakly to a fixed point of.
We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent.
