ﻻ يوجد ملخص باللغة العربية
For a certain class of partitions, a simple qualitative relation is observed between the shape of the Young diagram and the pattern of zeroes of the Wronskian of the corresponding Hermite polynomials. In the case of two-term Wronskian $W(H_n, H_{n+k})$ we give an explicit formula for the asymptotic shape of the zero set as $n rightarrow infty$. Some empirical asymptotic formulas are given for the zero sets of three and four-term Wronskians.
We investigate the relationship between the semiclassical wave packets of Hagedorn and the Hermite functions by establishing a relationship between their ladder operators. This Hagedorn--Hermite correspondence provides a unified view as well as simpl
A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the simplest mod
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
We compute Haar ensemble averages of ratios of random characteristic polynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that end, we start from the Clifford-Weyl algebera in its canonical realization on the complex of holomorphi
The new complete orthonormal sets of -Laguerre type polynomials (-LTP,) are suggested. Using Schrodinger equation for complete orthonormal sets of -exponential type orbitals (-ETO) introduced by the author, it is shown that the origin of these polyno