Since the dawn of nuclear physics (d,p) reactions have been the main tool to extract spectroscopic factors (SFs) (we call them phenomenological SFs), which were compared with predictions of the independent-particle shell model (ISPM). Later on electron-induced breakup reactions and nucleon knockout reactions became new tool to determine the SFs. Reduction of the phenomenological SFs deduced fro...

Recently, many q-identities from Slater’s compendium [S] have been interpreted combinatorially by several authors (e.g., see Connor [lo], Subbarao [9], Agarwal [l], and Agarwal and Andrews [2]). In his very recent paper [6], Andrews gave combinatorial interpretations of the Gessel-Stanton q-identities in terms of two-color paritions and expressed the hope that other q-identities such as those i...

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present...

We study the behavior of the fermion determinant at finite temperature and chemical potential, as a function of the Polyakov loop. The phase of the determinant is correlated with the imaginary part of the Polyakov loop. This correlation and its consequences are considered in static QCD, in a toy model of free quarks in a constant A 0 background, and in simulations constraining the imaginary par...

Cyclic division algebra (CDA) has recently become a major technique to construct nonvanishing determinant (NVD) space-time block codes. The CDA based construction method usually consists of two steps. The first step is to construct a degree-n cyclic extension over a base field and the second step is to find a non-norm algebraic integer in the base field. In this paper, we first propose a simple...

Rational solutions for the Painlevé IV equation are investigated by Hirota bilinear formalism. It is shown that the solutions in one hierarchy are expressed by 3-reduced Schur functions, and those in another two hierarchies by Casorati determinant of the Hermite polynomials, or by special case of the Schur polynomials.

Recent developments and applications of approximate actions for full lattice QCD are described. We present first results based on the stochastic estimation of the fermion determinant on 12 3 × 24 configurations at β = 5.2.

The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic N -body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue equations, the MCDF equations. In this paper, we prove the existence of solutions of these equations in the weakly relativistic regime. First, using a new vari...

The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studied for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax functions is that the corresponding bi-Hamiltonian structures are degenerate, i.e. the metric which defines the Hamiltonian structure has va...

In 1992, Goulden and Jackson found a beautiful determinantal expression for the immanant of a matrix. This paper proves the same result combinatorially. We also present a β-extension of the theorem and a simple determinantal expression for the irreducible characters of the symmetric group.