We study the known solution of mean spherical approximation (MSA) for primitive model an electrolyte consisting charged hard spheres with unequal diameters. Especially, details non-trivial evaluation chemical potentials are given. They can be obtained in various independent ways from MSA solution. The different utilised to show that consistent results obtained. Details other thermodynamic quant...

using a generalized spherical mean operator, we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the (&apos;; p)-dunkl lipschitz condition in the space lp(rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

Abstract: When it is necessary to approximate a small permutation pvalue p, then simulation is very costly. For linear statistics, a Gaussian approximation p̂1 reduces to the volume of a spherical cap. Using Stolarsky’s (1973) invariance principle from discrepancy theory, we get a formula for the mean of (p̂1− p)2 over all spherical caps. From a theorem of Brauchart and Dick (2013) we get such a ...

Using a liquid-state approach based on Ornstein-Zernike equations, we study the behavior of a fluid inside a porous disordered matrix near the liquid-gas critical point. The results obtained within various standard approximation schemes such as lowest-order γ-ordering and the mean-spherical approximation suggest that the critical behavior is closely related to that of the random-field Ising mod...