The general theory on exact boundary controllability for general first order quasilinear hyperbolic systems requires that the characteristic speeds of the system do not vanish. This paper deals with exact boundary controllability, when this is not the case. Some important models are also shown as applications of the main result. The strategy uses the return method, which allows one in certain s...

domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The r...

Boundary algebra (BA) is a mathematical alternative to standard algebra. It represents numbers and functions using space and boundaries, which can be manipulated with three simple equivalence rules. In BA, the behavior of large constructions, such as complex numbers and transcendental functions, can be directly deduced from the basic rules of BA, suggesting that it represents a fundamental core...

We give an elementary proof of the Cannon-Thurston Theorem in the case of the Gieseking manifold. We work entirely on the boundary, using ends of trees, and obtain pictures of the regions which are successively filled in by the Peano curve of Cannon and Thurston.

It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope. JEL Classification: C720.

We consider the method of particular solutions for numerically computing eigenvalues and eigenfunctions of the Laplacian on a smooth, bounded domain Ω in Rn with either Dirichlet or Neumann boundary conditions. This method constructs approximate eigenvalues E, and approximate eigenfunctions u that satisfy ∆u = Eu in Ω, but not the exact boundary condition. An inclusion bound is then an estimate...

Given a solid S ⊂ R with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution speed of the so called characteristic...

A simple kinetic model is introduced as an elementary contribution to understanding cooperative relaxation processes in condensed matter. This model involves n hard disks mutually trapped initially just inside an impenetrable circular boundary. Disk invasion of the interior of the system requires one of the disks to discover an exit passageway that only appears when the other disks collectively...

We investigate the validity of an idea that the Bμ problem is solvable via the renormalization effect in the strongly interacting hidden sector within the gauge mediated supersymmetry breaking scenario. Our analysis starts with a naive boundary condition, which is that the squared scalar masses experience 16π suppression. We use softsusy to get the low energy spectra of superparticles with the ...

We argue in the following that the entropy-area law of black-hole physics and the various holographic bounds are the consequences of the microscopic dynamics of elementary degrees of freedom living on or near the Planck scale. We locate them both in the interior and on the boundary of, for example, the black hole with the strange area-behavior of various quantities being the result of a long-ra...