Let (X\) Yi)',... ,(-Xn, Yny be a sample from a bivariate regular normal distribution with independent components. If r' is the sample correlation coefficient then it is known that Er = 0, varr' = + 0 ( n ~ f ) (1.1) n (see Cramer [4], § 27.8 and § 29.7). If {Xt} and {Yt} are independent time series then the variance of the sample correlation coefficient does not obey the formula (1.1). Let {et...

1. INTRODUCTION Many methodological studies depend on the product of two dependent correlation coefficients. For example, the product of two dependent correlation coefficients is needed in assessing the impact of a confounding variable on a regression coefficient (Frank, 2000). In the literature, there is an extensive research on the distribution of a single correla-but little on the distributi...

We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 ...

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.

In this paper, using vortex blob method (VBM), turbulent flow in a channel is studied and physical concepts of turbulence are obtained and discussed. At first, time-averaged velocities,  and , and then their fluctuations are calculated. To clarify turbulence structures, velocity fluctuations and  are plotted. It is observed that turbulence structures occupy different positions and move with con...