Shadowing is Generic on Various One-Dimensional Continua with a Special Geometric Structure

Continua with spin structure

A continuum Lagrangian-Hamiltonian description of alloys with spin glass structure in magnetic saturation conditions is presented here, paying attention to the interaction between gross deformation and spin substructures. A version of Noether theorem accounting for gyroscopic inertia of spins is proven so that the covariance of the balance of spin interactions and, as a special case, the one of...

Special Unions of Unicoherent Continua

It is proved that a Hausdorff continuum is unicoherent if it is the union of two unicoherent continua whose intersection is connected and locally connected.

Dimensional reduction via dimensional shadowing

1. Uni ed eld theories suggest a N dimensional conguration space with N̄ = N−4 > 0 extra dimensions not perceived in nature. The common heuristic reasons for this proposition are: (i) the volume [Hausdor measure] does not scale like μH(δ,R ) = δ μH(1,R ), where δ is some length scale and 1 stands for its unity. Instead, experience tells us that increasing (or decreasing) the spacial size of an o...

On the One Dimensional Poisson Random Geometric Graph

Some examples in one-dimensional \geometric" scattering on manifolds

We consider \geometric" scattering for a Laplace-Beltrami operator on a compact Riemannian manifold inserted between two half-lines. We discuss applicability and correctness of this model. With an example, we show that such scattering problem may exhibit unusual properties: the transition coeecient has a sequence of sharp peaks which become more and more distant at high energy and otherwise tur...