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Diffusion within the perfect lattice is described with a diffusion-coefficient matrix determined by kinetic Monte Carlo simulations for a binary, thermodynamically ideal alloy in which the components have different vacancy-exchange frequencies.
The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3×3 matrix determined by a geometric distribution of the points.
A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos procedure applied to A with initial vector u, and then evaluating pairs of Gauss and Gauss Radau quadrature rules associated with the tridiagonal matrix determined by the Lanczos procedure.
Paired comparison matrix determined by imposing judgments.
Let Q ̄ 1 be an m dimension transition matrix determined by Q1.
Then Q ̄ 1 is called an m-dimensional stochastic matrix determined by the m th-order transition matrix.Q1.Q1
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where is the identity matrix, and are the time-varying weighted matrices determined by the mean square criterion.
Orthogonal matrices, determined by the condition MTM = I, form the orthogonal group.
A guild-lumped web was established for each site by taking the sub-predation-matrix determined by the trophic guilds that were present (binary matrix published online in Mulder et al. [11], their sub-predation-worksheet).
Accurate cell parameters and orientation matrix were determined by the full-matrix least-squares fit of 25 reflections.
The matrix D is a Vandermonde matrix and determined by the choice of the N points.
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