Calling the quantity; 2ΔAΔB/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises, above unity, the lower bound of the UPR for each member of an infinite collection of pairs of incompatible observables. Conversely, any UPR is subject to lower bounds abo...

The coefficient of correlation evaluates the similarity of two sets of measurements (i.e., two dependent variables) obtained on the sameobservations. The coefficient of correlation indicates the amount of information common to two variables. This coefficient takes values between −1 and +1 (inclusive). A value of 0 indicates that the two series of measurement have nothing in common. A value of +...

We define a set of orthogonal functions on the complex projective space CPN−1, and compute their Clebsch-Gordan coefficients as well as a large class of 6–j symbols. We also provide all the needed formulae for the generation of high-temperature expansions for U(N)-invariant spin models defined on CPN−1.