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Up to now the coating elasticity and plasticity properties were approached with the aid of simplified considerations of the nanoindentation procedure and a consequent evaluation of the obtained nanohardness measurement results, depending, however, on the indentation load.
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Approximately 195 comparisons have been made across the 68 studies (simplifying considerations of the sequence of tests and excluding the interval of screening and follow-up strategies) (Figure 2).
In the present paper, we study some small distribution of matter to simplify our considerations.
where p is a positive continuous function on [ a, ∞ ) and F, G are continuous functions on ℝ with u F ( u ) > 0, u G ( u ) > 0 for u ≠ 0. To simplify our considerations we suppose that F and G are increasing and odd.
To simplify our considerations we pass to the homogeneous boundary conditions at (S^{pm}), mathbb{P}_{i}cdotmathbf{e}_{1}=0,quad mathbf{x}in S_{i}^{pm}, i=f,s, 0< t< T, (6) by introducing a new pressure p_{f}rightarrow p_{f}-p^{0}( mathbf{x}), qquad p_{s}rightarrow p_{s}-p^{0}( mathbf{x}),qquad p^{0}(mathbf{x})=frac{1}{2} p^( mathbf{x}) (1-x_{1}).
The model makes use of a decomposition method to simplify the consideration of the multidimensional conditional covariance.
To simplify this consideration, we organized the classes of the interactions with the solar wind or the magnetospheric plasmas by considering only two parameters, the magnetic field at the body and the total neutral gas mass.
Note that the viscosity of the system is taken into account by introducing into the balance of forces a dissipative linear vector function [16], which, to simplify the consideration of the problem, we do not consider in our article.
To simplify our consideration in the following, we shall assume that if (ngeq3), then Ω is a (C^{2,alpha} -domain ((0<alpha<1)) on (mathbf{S}^{n-1}) surrounded by a finite number of mutually disjoint closed hypersurfaces (e.g. see [5],alpha} -domain the definition of (C^{2,alpha})-domain).
It should also be mentioned that this representation is highly simplified as no consideration has been taken to the position of the Fermi-level in relation to the energy level distribution.
For ease of use in engineering applications, the stress expressions are modified and simplified with the consideration of several engineering factors, such as the stress limit that the ground can bear, the overburden, and the topological structure of the cutterhead.
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