The FWHM values of (1 1 1) Phi-scans and (0 0 2) rocking curves of these tapes were around 9.45°and 5.48°, respectively, measured by X-rays.
The results of the study showed that phosphate removal efficiency and pHf were found to be 97.6% and 10.9 with optimal reaction conditions initial phosphate concentration 25 mg l−1, red mud dosage 1.5 g l−1, pHi 3.0, respectively.
Then we have C_{1}(Phi,infty)neq0.
In view of Lemma 3.1 and Lemma 3.2, we have (C_{1}(Phi,infty)neq0), and according to the Morse equality, the functional Φ has at least one critical point u such that (C_{1}(Phi,u neq0).
The empirical formula is as follows: mu_{text{nf}} = left( { 1- phi } right)^{ 2. 5} mu_{text{f}}.
(phi(t)) is strictly increasing and (phi 2t gelambdaphi(t)) for all (t>0) and some (lambda>1), (phi(t)) satisfies a doubling condition (phi 2t)le c phi(t)) for all (t>0) and some (c>1), (phi'(t ge C_{1}phi(t)/t) for all (t>0) and some (C_{1}).
Assuming that (v_{A}= epsilon+ f 1-phi <1) then (phi_{A} = g(epsilon+ f 1-phi <1 and afthenone firing the system has moved from ((phi_{A}, phi_{B})= (0, phi)) to ((h(phi), 0)) where (h(phi) = g epsilon+ f 1-phi))) is the f 1-phimand(see Fig. 9(c)).
Elevated NSE greater than or equal to 12.5 ng ml-1, PHI greater than or equal to 55 mgl-1 levels were observed in 55% of cases for NSE, 90% for PHI and 49% for CC.
end{aligned} (82 The scale reduction factor (sqrt{left( 1-Phi right) left( 1+Phi ^{2}right) left( 1+Phi right) ^{-3}}) is approximately 0.113 for (Phi =0.95).
Their backshift operator formulas reveal factorizations like others that will be useful: begin{aligned} hat{N}_{t}= & left( 1+Phi right) ^{-2}left{ -Phi B^{q}+left( 1+Phi ^{2}right) -Phi B^{-q}right} Z_{t}nonumber = & left( 1+Phi right) ^{-2}left{ left( 1-Phi B^{q}right) left( 1-Phi B^{-q}right) right} Z_{t}.
Of course, the calendar month subseries of (hat{N }_{t}) are less variable than those of (Z_{t}) in the sense that, from (56), (gamma _{0}^{hat{N}}=left( 1+Phi right) ^{-4}left( 1+Phi ^{2}right) sigma _{a}^{2}=left( 1-Phi right) left( 1+Phi ^{2}right) left( 1+Phi right) ^{-3}gamma _{0}) is less than (gamma _{0}).
