We study a simple nonlinear model defined on the honeycomb and triangular lattices. propose bilinearization scheme for field equations demonstrate that resulting system is closely related to well-studied integrable models, such as Hirota bilinear difference equation Ablowitz-Ladik system. This result used derive two sets of explicit solutions: N-soliton solutions ones constructed Toeplitz deter...

We derive an alternative representation for the f -electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green’s function involves two determinants of continuous matrix op...

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, conver...

A combinatorial proof in terms of Schröder paths and other weighted plane paths is given for a determinant representation of Laurent biorthogonal polynomials (LBPs) and that of coefficients of their three-term recurrence equation. In this process, it is clarified that Toeplitz determinants of the moments of LBPs and their minors can be evaluated by enumerating certain kinds of configurations of...