This technique involves linear transformation of the equations such that the slope of the line represents the V T. Logan images were used for visual interpretation and quantitative evaluation of the effect of IDM.
After construction of the C-DVH's and BED-DVH's, it was clear that the general shape of the two were slightly different, as would be expected by the non-linear transformation in Equation (1) above.
Because GMR involves a non-linear transformation of equation (1) parameters, whose estimators are t-distributed, the sampling distribution of the GMR estimator exp μ ^ bs - μ ^ br is not known.
Since the approximate MSE, ε2 τ0,γ,ψ), is a linear transformation of ψ (see Equation (43)), it is straightforward to calculate its mean μ ε 2 = E { ε 2 ( τ 0, γ, ψ ) } = D + C e σ dB 2 ( 10 log 10 e ) 2, (50).
To study the local stability of the interior equilibrium (hat{E}=(hat{P}, hat{M}, hat{I})) for the delay system, first we use linear transformation in the system equations (1 - 3) as (P=P_{1}+hat{P}), (M=M_{1}+hat{M}), and (I=I_{1}+hat{I}), where (P_{1}ll 1), (M_{1}ll 1), (I_{1}ll 1}ll
If one assumes that the reaction is diffusion-limited and all chemical species have the same diffusion coefficient, one can employ a linear transformation to rewrite the governing equations in terms of invariants, which are unaffected by the reaction.
Equation (2) shows the linear transformation that describes both processes.
The linear transformation in this paper is similar to equation 8 of Karigl's approach [ 4].
Consider the model x=A·s; we need a linear transformation that applies to both sides of the equation to yield a new sparse source vector.
Boole submitted a stream of original papers to the new Cambridge Mathematical Journal, beginning in 1839 with his "Researches on the Theory of Analytical Transformations". These papers were on differential equations and the algebraic problem of linear transformation, emphasizing the concept of invariance.
The solution process successively employ Laplace transformation and linear transformation steps to uncouple the governing set of coupled differential equations.
