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This comparison yields relations between the macroscopic continuum parameters and the microscopic lattice parameters.
Furthermore, the description yields relations of "foundation", i.e., one-sided or mutual relative existential dependencies between (1) the experience in question and other experiences and (2) the particular descriptive features of the experience.
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One can show analogously as above that non-negativity of K ij (t, s), i, j = 1,..., n - 1, in the case of negativity of the operators B ni, i = 1,..., n - 1, implies relation (3.10) and in the case of positivity of the operators B ni, i = 1,..., n - 1, yields relation (3.11).
Statistical treatment of the local variations of flow rates yielded relations between the local velocity variations and the bed parameters.
One can then show that the boundaries of these 3-cells yield relations on R / [R, R] which are exactly those of the form ([a,r_j]), for ( a in F). (square ).
Combining (52) and (53) finally yields the relations: (56).
Replacing ∆d from the incremental version of Eq. (3) in the constitutive relation ∆D = k∆d, yields the relation Delta {mathbf{D}}left( x right) = {mathbf{k}}left( x right)Delta {mathbf{d}}left( x right) = {mathbf{k}}left( x right){mathbf{B}}left( x right)Delta {mathbf{q}} (4).
which yields the relation (3.6).
Transitive closure was computed iteratively; it yielded 2154 relations over subsumption and 1,594,896 relations over causality.
The banded matrices yield recursion relations for solving systems of linear equations.
The atomistic studies yield quantitative relations between local stress tensor components and the mobility of dislocations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com