Integrable Systems and Metrics of Constant Curvature

In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature. Kaup-Boussinesq system has three local Hamiltonian structures and one nonlocal Hamiltonian structure associated with metric of constant curvature. Darboux theorem (reducing Hamiltonian structures to canonical form ''d/dx'' by differential substitutions and reciprocal transformations) for these Hamiltonian structures is proved

Hydrodynamic chains and a classification of their Poisson brackets

Necessary and sufficient conditions for an existence of the Poisson brackets significantly simplify in the Liouville coordinates. The corresponding equations can be integrated. Thus, a description of local Hamiltonian structures is a first step in a description of integrable hydrodynamic chains. The concept of $M$ Poisson bracket is introduced. Several new Poisson brackets are presented

Intrinsic defects in silicon carbide LED as a perspective room temperature single photon source in near infrared

Generation of single photons has been demonstrated in several systems. However, none of them satisfies all the conditions, e.g. room temperature functionality, telecom wavelength operation, high efficiency, as required for practical applications. Here, we report the fabrication of light emitting diodes (LEDs) based on intrinsic defects in silicon carbide (SiC). To fabricate our devices we used a standard semiconductor manufacturing technology in combination with high-energy electron irradiation. The room temperature electroluminescence (EL) of our LEDs reveals two strong emission bands in visible and near infrared (NIR), associated with two different intrinsic defects. As these defects can potentially be generated at a low or even single defect level, our approach can be used to realize electrically driven single photon source for quantum telecommunication and information processing

Metric Fourier approximation of set-valued functions of bounded variation

We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.Comment: 26 pages, 1 figur

Muon stopping power and range tables 10 MeV-100 TeV

The mean stopping power for high-energy muons in matter can be described by −dE/dx = a(E) + b(E)E, where a(E) is the electronic stopping power and b(E) is the energy-scaled con-tribution from radiative processes—bremsstrahlung, pair production, and photonuclear interac-tions. a(E) and b(E) are both slowly-varying functions of the muon energy E where radiative effects are important. Tables of these stopping power contributions and continuous-slowing-down-approximation (CSDA) ranges (which neglect multiple scattering and range straggling) are given for a selection of elements, compounds, mixtures, and biological materials for incident kinetic en-ergies in the range 10 MeV to 100 TeV. Tables of the contributions to b(E) are given for the same materials