The separation of the variables of the pseudo-second-order in the differential form and integration are given in the following equation (Sun et al. 2014); frac{t}{{q_{t} }} = frac{1}{{K^{prime} q_{text{e}}^{2} }} + left( {frac{1}{{q_{text{e}} }}} right)t, (1 where q e and q t are the amounts of metal ion adsorbed (mg g−1) at equilibrium and at time t, respectively.
The separation of the most predictive variables (WOMAC and EQ-5D preoperatively) to support individual patient information and decision making showed that, for all groups, a significant improvement in WOMAC and HRQoL scores can be reached.
This approach made it possible to control the effects of the design variables on the separation of the target compounds.
For this, an F value and eta2 for each cluster solution is calculated that indicate the contribution of the classification variables to the separation of the clusters.
The analytical formula of the unsteady temperature distribution is derived by using the separation-of-variables method and hence the maximum thermal stress attained at the surface of the FGM solid cylinder as well as its time of occurrence can be calculated.
The quasi-static part is obtained in an explicit form by the state space method and the dynamic part is obtained by the separation of variable method.
Using the separation of variable, the eigenfunction of Ĥ 0 is written as ψ ( ρ, ϕ, z ) = f h ( z ) e imϕ m = 0, ± 1,.. (5)The radial wave function of the ground state can be expressed as f = C w J 0 ω 1 ρ ρ ≤ R C b K 0 ω 2 ρ ρ > R (6).
By virtue of the introduction of new dependent variable and the separation of variables technique, the transient responses of a special non-homogeneous magneto-electro-elastic hollow cylinder are transformed to two Volterra integral equations of the second kind of about two functions with respect to time.
If the responses of the practitioners do not provide good fit, or the separation of persons along the variable is poor, it suggests that the assessment does not adequately represent the ability and understanding of the sample.
