Statistical approach to estimation Examine the multivariate Gaussian distribution: (x-)\v-(x-) Multivariant f(x)= Minimize (x-u)'v(x-u) gives largest probability density By minimizing the argument of the exponential in the probability density function, we maximize the likelihood of the estimates(MLE)
2.7 Some Important Crystallographic Formulas 1. Zone and zone equation All Planes parellel to common axis [uvw] constitute a (crystal) zone, the [u v w] zone. If (h k l) belongs to zone [u v w], then hukv+=0 2.ifhuk+hw=0,then[uvw] lies in(hk) 3. For cubic crystals, [h (h k)
National Motto of the United States In God We Trust The phrase derives from the line \And this be our motto. 'In God is our trust, \in the battle song that later became the U.S. national anthem, \The Star-Spangled Banner. \The phrase first appeared on U. S. coins in 1864 and became