We present a method for numerical calculation of two dimensional distributions of the attempt relaxation times and activation energies from the temperature dependence of the experimental dielectric permittivity dispersion. We introduce empirical attempts to account for broad and/or asymmetric dispersions with the idea of using a weighted collection of Debye relaxation times. Then we present a modification of the aforementioned idea including attempt relaxation time and activation energy using the Arrhenius law, which significantly complicates the computation of the aforementioned distribution. Incorporating the activation energy and the attempt relaxation time into the equation transforms the discretized matrix equations into tensor equations. We rework the tensor equations into simpler matrix equations, thus permitting us to solve the presented discretized integral equation by using existing Least Distance Problem solving methods. Also, we present a regularization method and a way to choose the regularization parameter based on a best fit criterion. In the end we discuss the method showing some simulated results and experimental results. We then point out some problems involved in the calculations and propose methods to reduce their significance.

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach.

We classify symmetric backgrounds of eleven-dimensional supergravity up to local isometry. In other words, we classify triples (M, g, F), where (M,g) is an eleven-dimensional lorentzian locally symmetric space and F is an invariant 4-form, satisfying the equations of motion of eleven-dimensional supergravity. The possible (M,g) are given either by (not necessarily nondegenerate) Cahen-Wallach spaces or by products AdS_d × M^11−d for 2 ⩽ d ⩽ 7 and M^11−d a not necessarily irreducible riemannian symmetric space. In most cases we determine the corresponding F-moduli spaces.

Pure and Pr-activated Lu₃Al₅O₁₂ (LuAG) crystals have been grown by the Czochralski method. In order to improve the scintillation properties, several samples have been annealed in air. Various annealing temperatures and periods of time have been tested to determine optimal conditions in the way of scintillation yield and energy resolution enhancement. The largest increase of yield of LuAG:Pr (17%), accompanied by a distinct decrease of resolution, has been observed after annealing at 1100°C for 48 h. On the contrary, in case of undoped LuAG no significant changes following thermal annealing have been noticed.

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superfluid properties and the Mott phase boundary of a Bose-Einstein condensate (BEC) in an optical lattice. The Bloch energy, effective mass, Bogoliubov energy and the superfluid fraction are modified due to the mirror motion. The mirror motion is also found to modify the Mott-superfluid phase boundaries. This study reveals that the mirror emerges as a new handle to coherently control the superfluid properties of the BEC.