The identity exp ( " x " ) exp ( " y " ) } } can fail for Lie algebra elements and that do not commute; the Baker Campbell Hausdorff formula supplies the necessary correction terms.
32.
The correction term of } } corresponds to the difference between the median and mean of the log-normal distribution, or equivalently for this distribution, the geometric mean and arithmetic mean, with the median ( geometric mean ) being lower.
33.
The Christoffel symbols of an affine connection on a manifold can be thought of as the correction terms to the partial derivatives of a coordinate expression of a vector field with respect to the coordinates to renders the vector field's covariant derivative.
34.
The final MP2 calculations use a larger basis set, generally just called G3large, and correlating all the electrons not just the valence electrons as in G2 theory, additionally a spin-orbit correction term and an empirical correction for valence electrons are introduced.
35.
Reduction of the Dirac equation for an electron in a magnetic field to its non-relativistic limit yields the Schr�dinger equation with a correction term which takes account of the interaction of the electron's intrinsic magnetic moment with the magnetic field giving the correct energy.
36.
If-\ operatorname { J } ( x ) is a smooth connection, expanding above quantity to second order in infinitesimal quantities | u |, | v | one obtains for the ordered exponential the identity with a correction term that is proportional to the curvature tensor.
37.
Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error.
38.
Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error.
39.
The cpompressibility is the isothermal compressibility, but the correction term you need to subtract to compute the isentropic compressibility would change it by a few percent and the value for the compressibility isn't that accurate to start with . talk ) 16 : 24, 14 July 2010 ( UTC)
40.
Tiku ( 1971 ) found that " the non-normal theory power of " F " is found to differ from the normal theory power by a correction term which decreases sharply with increasing sample size . " The problem of non-normality, especially in large samples, is far less serious than popular articles would suggest.
