We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary c...

We discuss the influence of boundary conditions on the continuum limit of the sixvertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences using the known phase diagram of the six-vertex model. In some particular cases we compute explicitly the corresponding partial differential equations by means of...

We present a domain theoretic framework for obtaining exact solutions of linear boundary value problems. Based on the domain of compact real intervals, we show how to approximate both a fundamental system and a particular solution up to an arbitrary degree of accuracy. The boundary conditions are then satisfied by solving a system of imprecisely given linear equations at every step of the appro...

Three-dimensional deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions at its edges are analyzed by the generalized Eshelby-Stroh formalism. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. Perfect bonding is assumed between the adjoining laminae in the sense that both surface t...

We apply the counterterm subtraction technique to calculate the action and other quantities for the Kerr–AdS black hole in five dimensions using two boundary metrics; the Einstein universe and rotating Einstein universe with arbitrary angular velocity. In both cases, the resulting thermodynamic quantities satisfy the first law of thermodynamics. We point out that the reason for the violation of...

We show a superconvergence property for the Semi-Lagrangian Discontinuous Galerkin scheme of arbitrary degree in the case of constant linear advection equation with periodic boundary conditions.

We determine the set of Busemann points of an arbitrary finite– dimensional normed space. These are the points of the horofunction boundary that are the limits of “almost-geodesics”. We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is closed in the Painlevé–Kuratowski topology.

We derive a closed form expression for the Green function of linear evolution equation with the Dirichlet boundary condition for an arbitrary region, based on singular perturbation approach to boundary problems. PACS numbers: 03.65.-w, 03.65.Ge, 02.90.+p Published in Journal of Physics A: Mathematical and General Vol. 32 (1999) 1261-1267 e–mails: [email protected], [email protected] 1

We outline the structure of boundary conditions in conformal field theory. A boundary condition is specified by a consistent collection of reflection coefficients for bulk fields on the disk together with a choice of an automorphism ω of the fusion rules that preserves conformal weights. Non-trivial automorphisms ω correspond to D-brane configurations for arbitrary conformal field theories.

For the Lamé system, we prove in the three-dimensional case that both Lamé coefficients are uniquely recovered from partial Cauchy data on an arbitrary open subset of the boundary provided that the coefficient μ is a constant. In a bounded domain ⊂ R3 with smooth boundary, we consider the Lamé system