We present a complete set of analytic fits to the non-relativistic photoionization cross sections for the ground states of atoms and ions of elements from H through Si, and S, Ar, Ca, and Fe. Near the ionization thresholds, the fits are based on the Opacity Project theoretical cross sections interpolated and smoothed over resonances. At higher energies, the fits reproduce calculated Hartree-Dir...

We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is rep...

A geometric model for a class of bipartite graphs is introduced, and a type of perfect matching, called an acyclic matching, is defined and through geometric reasoning shown to exist for a subset of the bipartite graphs discussed. These acyclic matchings imply a nonvanishing determinant for a class of weighted biadjacency matrices. This matching theory is applied to address a question raised by...

We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is rep...

We consider the CPT anomaly of two-dimensional chiral U(1) gauge theory on a torus with topologically nontrivial zweibeins corresponding to the presence of torsion. The resulting chiral determinant can be expressed in terms of the standard chiral determinant without torsion, but with modified spinor boundary conditions. This implies that the two-dimensional CPT anomaly can be moved from one spi...

We investigate the validity of the square rooting procedure of the staggered determinant in the context of the Schwinger model. We find some evidence that at fixed physical quark mass the square root of the staggered determinant becomes proportional to the overlap determinant in the continuum limit. We also find that at fixed lattice spacing moderate smearing dramatically improves the chiral be...

Recent advances in analytical methods and exploration of regional diversity patterns in greater depth than simple whole-fauna patterns may change our understanding of the determinants of latitudinal gradients in species richness. Using a comprehensive database on the geographical distributions of the large fauna of endemic shorefishes from the Tropical Eastern Pacific (TEP), we delineated latit...

DFTB is a recent general purpose implementation of density-functional based tight binding. One of the early motivators to develop this code was to investigate lanthanide impurities in nitride semiconductors, leading to a series of successful studies into structure and electrical properties of these systems. Here we describe our general framework to treat the physical effects needed for these pr...

In 1984, Victor Kac [K4] suggested an approach to a description of central elements of a completion of U(g) for any Kac-Moody Lie algebra g. The method is based on a recursive procedure. Each step is reduced to a system of linear equations over a certain subalgebra of meromorphic functions on the Cartan subalgebra. The determinant of the system coincides with the Shapovalov determinant for g. W...

We show that the monopole confinement mechanism in lattice gluo-dynamics is a particular feature of the maximal abelian projection. We give an explicit example of the SU (2) → U (1) projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We perform analytical and numerical study of the loop expansion of the Faddeev–Popov determin...