On the value distribution properties of the Smarandache double-factorial function

The main purpose of this paper is using the elementary and analytic methods to study the value distribution properties of SDF(n), and give an interesting mean value formula for it

Analytical solution for the lattice Boltzmann model beyond Naviers-Stokes

To understand lattice Boltzmann model capability for capturing nonequilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer