Combining the rates of grain size growth (8) and reduction (11) additively [ Austin and Evans, 2007] along trajectories of mantle flow gives the full equation for grain size evolution as (12) Equation (12) is put into nondimensional form using the following characteristic scales:, and.
The system of equations is put into an equivalent form by solving for the nonzero variables x0, x2, x3, x5 in terms of those variables now at zero; i.e., x1 and x4.
The estimation equations, once put into the recursive form are then easily generalized to the prediction problem.
After construction, these structures can be put into mathematical form and then be solved numerically.
To be more precise, although the equation (82) can be put into Hirota bilinear form (83), in both cases Hirota perturbation fails to produce further solutions.
By processing the data by blocks of L time samples, the signal model given in Equation 90 can be put into a vector form as: y m ( t ) = x m ( t ) + v m ( t ), m = 1, 2, …, M, (91).
Then equations of the thermal wave put into a dimensionless form are proposed and discussed.
Fermat indicated that any quadratic equation in x and y can be put into the standard form of one of the conic sections.
In this paper, the classical model of marine craft is put into a PHS form.
This generalizes Schur's lemma, which guarantees that any complex n × n matrix may be put into upper triangular form.
However, can any set be put into well-ordered form?
