The top-order zonal polynomials Ck(A),and top-order invariant polynomials Ck1,...,kr(A1,...,Ar)in which each of the partitions of ki,i = 1,..., r,has only one part, occur frequently in multivariate distribution theory, and econometrics - see, for example Phillips (1980, 1984, 1985, 1986),...

<p>Using generating functions, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other symmetric functions (power-sum and elementary symmetric functions, Ruben, Hillier, Kan, and Wang). Typically, in a recursion of this type the...</p>

Sample autocorrelation coefficients are widely used to test the randomness of a time series. Despite its unsatisfactory performance, the asymptotic normal distribution is often used to approximate the distribution of the sample autocorrelation coefficients. This is mainly due to the lack of an...

The top-order zonal polynomials <italic>C</italic>(<italic>A</italic>), and top-order invariant polynomials <italic>C</italic>_null_,…,<italic>null</italic> (<italic>A</italic>₁, …, <italic>A</italic>) in which each of the partitions of <italic>k</italic>, <italic>i</italic> = 1, …, <italic>r</italic>, has only one part, occur frequently in multivariate distribution theory, and econometrics — see, for example, Phillips (1980, <italic>Econometrica</italic>...

In the dynamic floor field model, the bosons are homogeneous. This causes a problem that the pedestrians are confused by their own traces. The model has been modified by the heterogeneous bosons. Compared with the dynamic floor field model based on the homogeneous bosons, the modified model...