In this work we analyze a class of diminishing 2 × 2 Pólya-Eggenberger urn models with ball replacement matrix M given by M = ` −a 0 c −d´, a, d ∈ N and c ∈ N0. We obtain limit laws for this class of 2 × 2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which correspond...

To overcome the space limit of orifice-type and capillary restrictors in hybrid bearings, a kind of atypical long orifice-type restrictor is proposed and its experimental model is established. Through the analysis of the structure and flow rate of orifice-type restrictor and capillary restrictor, a long orifice-type restrictor and a feasible experimental modeling method are presented by use of ...

Zamolodchikov found an integrable field theory related to the Lie algebra E8, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E8 in the universality class of the Ising model in a field. The dilute A3 model is a solvable lattice model with a critical point in the Ising universality class. The paramete...

The problem of limit cycles for Kolmogorov model is interesting and significant both in theory and applications. Our work is concerned with limit cycles bifurcations problem for a class of quartic Kolmogorov model with two positive singular points (i.e. (1, 2) and (2, 1)). The investigated model is symmetrical with regard to y = x. We show that each one of points (1, 2) and (2, 1) can bifurcate...