Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory

We present two convergence theorems for Hamilton-Jacobi equations and we apply them to the convergence of approximations and perturbations of optimal control problems and of two-players zero-sum differential games. One of our results is, for instance, the following. LetT andT _h be the minimal time functions to reach the origin of two control systemsy = f(y, a) andy = f _h (y, a), both locally controllable in the origin, and letK be any compact set of points controllable to the origin. If f _h –f Ch, then |T(x) – T _h (x)| C _K h , for all x K, where is the exponent of Hölder continuity ofT(x).     

On the classification problem of free ergodic actions of nonamenable groups

We show that, for any countable discrete nonamenable group Γ, the relations of conjugacy, orbit equivalence, stable orbit equivalence, von Neumann equivalence, and stable von Neumann equivalence of free ergodic pmp actions of Γ on the standard atomless probability space are not Borel. This answers a question of Kechris.     

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.     

On the variety of linear recurrences and numerical semigroups

In this work, we prove the existence of linear recurrences of order M with a non-trivial solution vanishing exactly on the set of gaps (or a subset) of a numerical semigroup S finitely generated by a ₁<a ₂<?<a _N and M=a _N .     

Chemical composition and phytotoxic effects of essential oils from four Teucrium species

The essential oils of four Teucrium species were studied and 131 components, in all, were identified. All oils were rich in sesquiterpenes (50.0-61.9%). Caryophyllene and caryophyllene oxide were the main components of Teucrium arduini; germacrene D, delta-cadinene and gamma-cadinene predominated in Teucrium maghrebinum. Carvacrol and caryophyllene predominated in Teucrium polium ssp. capitatum, while carvacrol, caryophyllene oxide and caryophyllene were the most abundant components in Teucrium montbretii ssp. heliotropiifolium. The germination of radish and garden cress was less sensitive to the four essential oils. The radicle elongation, above all, of radish was significantly inhibited by all oils, in particular by the essential oil of T. arduini, at the highest doses tested. Among the main components of the oils, monoterpenes resulted the more active compounds.     

Magnetic confinement of massless Dirac fermions in graphene

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.