The best results were obtained using the basic properties of soil as predictors, as well as with the parameters of the Dexter model obtained by its fitting to the CCC data.
Using the basic properties of the partial order of (L_{rho}), we get (lambda h_{0} + (1-lambda) F leqlambda h_{0} + (1-lambda) G) ρ-a.e.
In this paper, the above said limitation has been resolved by simplifying the obtained characteristic equation using the basic properties of block matrices.
Using the basic properties of ω, we get omega_{N} x,y) leqomega^ x,y), for any (x,y in M) with ((x,y in E(G_{omega})).
Our assumptions imply that ω ∗ ( x, y ) < ∞, for any x, y ∈ M. Using the basic properties of ω, we get ω N ( x, y ) ≤ ω ∗ ( x, y ), for any x, y ∈ M.
Obtained characteristic equation is further analytically simplified using the basic properties of block matrices, and in order to solve the problem numerically, it is sufficient to consider the determinant of the 6 × 6 matrix instead of taking the determinant 12 × 12 matrix, which reduces the numerical work considerably.
Obtained characteristic equation is further simplified using the basic properties of block matrices, and in order to solve the problem numerically, it is sufficient to consider the determinant of the 6 × 6 matrix instead of taking the determinant 12 × 12 matrix.
Using the basic properties of G-metric together with (5) and (8), we have G ( x n + 1, T u, x n + 2 ) ≤ G ( T x n, T u, T 2 x n ) ≤ β ( x n, u, x n + 1 ) G ( T x n, T u, T 2 x n ) ≤ ψ ( G ( x n, u, x n + 1 ) ). Letting n → ∞, using Proposition 11 and since ψ is continuous at t = 0, it follows that G ( u, T u, u ) = 0.
Then, using the basic property (mathbb {E}(mathbb {E}(X|Y))=mathbb {E}(X)), where X and Y are random variables, we obtain (28).
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