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By differentiating the quadratic equation and equating the derivative to zero, a maximum or minimum dose can be determined.
Around 1636, Descartes and Fermat founded analytic geometry by equating solutions to an equation of two variables with points on a plane curve.
In order to find an optimized point at which delay is minimized (and consequently throughput maximized), it is necessary to find the maximal point of above equation by taking first derivative and equating it to zero.
By maximizing the likelihood L y, m) with respect to β, m and equating it to zero, we obtain a set of linear equations [known as Henderson's mixed model equations (MME ]: (X ′ R − 1 X X ′ R − 1 Z Z ′ R − 1 X Z ′ R − 1 Z + G − 1 ) (β ^ m ^ ) = (X ′ R − 1 y Z ′ R − 1 y ), where R = Var e) and G = Var(m).
The frequency equation is a 2 x 2 determinant equated to zero.
Σ a l, and equate to zero.
Then, Equations 13 and 14 equate to zero naturally.
Equations 13 and 14 equate to zero naturally.
For a truncated beam any combinations of the four boundary conditions is possible and the frequency equations are the determinant of a 4 × 4 matrix equated to zero.
The frequency equations for a "complete" beam is the determinant of a 2 × 2 matrix equated to zero.
The frequency equation for truncated beam is the determinant of a 4 × 4 matrix equated to zero.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com