Thus by defining a product of two variables that gives rise to a quadratic term as one unknown variable, we increase the number of unknowns but make the equations linear in nature.
22.
This is because a quadratic term is present in the low energy effective action of heterotic string theory, and it also appears in six-dimensional Calabi Yau compactifications of M-theory.
23.
That means you can create a quadratic polynomial that passes through all your points by adding up the nine quadratic terms you fit that way . talk ) 20 : 18, 25 April 2012 ( UTC)
24.
At low frequencies near the lowest pole of this amplifier, ordinarily the linear term in ? is more important than the quadratic term, so the low frequency behavior of " D ? " is:
25.
Assuming the above result for \ tau _ 1 is valid, the second time constant, the position of the high frequency pole, is found from the quadratic term in " D ? " as
26.
If neglecting the quadratic terms is valid already for, it is all the more valid for of the order or greater than unity : it gives a reason to consider Eq . 1 to be valid for arbitrary.
27.
The kinetic term \ mathcal { L } _ K contains all the quadratic terms of the Lagrangian, which include the dynamic terms ( the partial derivatives ) and the mass terms ( conspicuously absent from the Lagrangian before symmetry breaking)
28.
To justify that \ boldsymbol \ mu _ n is indeed the posterior mean, the quadratic terms in the exponential can be re-arranged as a quadratic form in \ boldsymbol \ beta-\ boldsymbol \ mu _ n.
29.
Using a Taylor series expansion for the second integral around the mean free-surface elevation z = 0, and only retaining quadratic terms in \ Phi and \ zeta, the Lagrangian density L _ 0 for linear wave motion becomes
30.
More generally, the term "'Riccati equation "'is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control.
