Sentence examples for using the basic properties from inspiring English sources

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.

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})).

In this paper, the above said limitation has been resolved by simplifying the obtained characteristic equation using the basic properties of block matrices.

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.

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.

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.

Then, using the basic property (mathbb {E}(mathbb {E}(X|Y))=mathbb {E}(X)), where X and Y are random variables, we obtain (28).

In this research, we use the basic properties of Kronecker product operation and low-dimensional orthogonal basis to get higher dimensional column vector, Kronecker product, and construct the Kronecker product measurement matrix based on orthogonal basis.

This implies that implant shapes designed using the basic structural property maps for the L3 L5 endplates are appropriate for use in patients with a wide range of pathologies, even though overall failure loads are generally lower in patients with reduced bone density and greater degrees of disc degeneration.

We derived it using two the basic properties illustrated in Fig. 8 and as described in [32].

By using these basic properties of the optimal nodes a numerical procedure based on a nonlinear Remez search and exchange algorithm is given to compute the optimal nodes for polynomial interpolation on ([-1, 1] ) [31].