We present a corrected proof of Proposition 2.3 in the article “Boundary integral formula for harmonic functions on Riemann surfaces” [2].

An improved correspondence formula is proposed for the calculation of correlation functions of a conformal field theory perturbed by multi-trace operators from the analysis of the dynamics of the dual field theory in Anti-de Sitter space. The formula reduces to the usual AdS/CFT correspondence formula in the case of single-trace perturbations. In a recent paper [1] Witten proposed an improved b...

We construct integrable boundary conditions for ŝl(2) coset models with central charges c = 32 − 12 m(m+2) and m = 3, 4, . . . The associated cylinder partition functions are generating functions for the branching functions but these boundary conditions manifestly break the superconformal symmetry. We show that there are additional integrable boundary conditions, satisfying the boundary Yang-Ba...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

The extraction problem of information about the location and shape of the cavity from a single set of the temperature and heat flux on the boundary of the conductor and finite time interval is a typical and important inverse problem. Its one space dimensional version is considered. It is shown that the enclosure method developed by the author for elliptic equations yields the extraction formula...

We study the eta-invariants of links and show that in many cases they form link concordance invariants, in particular that many eta-invariants vanish for slice links. This result contains and generalizes previous invariants by Smolinsky and Cha–Ko. We give a formula for the eta-invariant for boundary links. In several intersting cases this allows us to show that a given link is not slice. We sh...

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general formula for the ground-state degeneracy for abelian Fractional Quantum Hall phases, including the cases when connected components of the boundary are subdivided in...