We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov’s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville ...

We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov’s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville ...

We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some...

We study the Pöschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms of the Heun function. At particular values there is a interesting interpretation in terms of finite lattice spin2 XXZ quantum chain with ∆ = cos π L (for free...

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract Analytical solutions for the variance, covariance, and spectrum of groundwater level, h(x, t), in an unconfined aquifer described by a linearized Boussinesq equation with random source/sink and initial and boundary cond...

In the analysis of boundary value problems in the theory of plasticity, the general situation arises that different partial differential equations are to be satisfied depending on whether the material is in the plastic or elastic state. The criterion determining the state at any material point depends on the dependent variables and their derivatives with respect to time. Thus the regions of app...

For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained from loop quantum gravity, has shed new light on this question. In this case, boundary conditions are not chosen by hand with some particular physical intuition in mind, but they are part of the dyna...

In this paper we present a comprehensive existence theory for linear and nonlinear reaction random walk systems. The methods are based on semigroup theory for solutions of differential equations on Banach spaces. The solution properties on a bounded domain sensitively depend on the choice of boundary conditions. For Neumann or for periodic boundary conditions, singularities are transported alon...

We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of arbitrary order, posed on the domain {t > 0, 0 < x < L}. We first show that by analysing the so-called global relation, which is an algebraic relation defined in the complex k-plane coupling all boundary values of the solution, it is possible to ident...

Overview and preliminaries. The study of interacting particle systems with conservation laws frequently revolves around hydrodynamic limits, in which the long-time, large-length scale behavior of a system is characterized by the evolution of the local density of the conserved quantity according to a partial differential equation. The typical setup consists of a particle system defined on a clos...