Integrable boundary conditions are studied for critical A–D–E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley-Lieb algebra and fusion, a set of boundary Boltzmann weights which satisfies the boundary Yang-Baxter equation is obtained for each boundary condition. When appropriately specialized, these boundary weights, ...

Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of nonnegative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a...

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under the assumption of the product structure near boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dir...

Many numerical models of magnetospheric dynamics treat the ionosphere as an inner boundary condition. These models have traditionally used the current continuity condition, treating the ionosphere as a sheet current in which the electric field is electrostatic. A more general boundary condition is suggested that not only is more complete, but also straightforward to implement. Results from a mo...

Knowledge base completion is a method for extending both the terminological and assertional part of a Description Logic knowledge base by using information provided by a domain expert. It ensures that the extended knowledge base is complete w.r.t. a fixed interpretation in a certain, well-defined sense. Here we consider the problem of explaining user errors in knowledge base completion. We show...

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

Let M be a complete finite-volume hyperbolic 3–manifold with compact non-empty geodesic boundary and k toric cusps, and let T be a geometric partially truncated triangulation of M . We show that the variety of solutions of consistency equations for T is a smooth manifold or real dimension 2k near the point representing the unique complete structure on M . As a consequence, the relation between ...

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of...

in this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. the conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. this study evaluates the advantages of using the integral form of the equations in the...