Bridgman growth and site occupation in LuAG:Ce scintillator crystals

LuAG:Ce single crystals with various activator concentrations were grown by the vertical Bridgman technique. Characterization of crystals was done in terms of actual doping level, macroscopic defects and degree of non-equivalent substitutions by Lu for Al in octahedral lattice sites. Scintillation measurements were performed using 2×2×8 mm³ shaped samples with Ce concentration in the range 0.05–0.55 at%. Essential improvement of performance was demonstrated in samples containing ≥0.2 at% of Ce; the light yield measured in LuAG:Ce (0.55 at%) was about 26000 ph/MeV, or close to that of LSO.     

Comparative asymptotic analysis of coupled and uncoupled thermoelasticity

The asymptotic solution of the three-dimensional dynamic of coupled thermoelasticity problem (with the mutual influence of the strain and temperature fields taken into account) for an isotropic rectangular plate is used to perform a comparative analysis of the results obtained according to this theory and the theory of temperature stresses. The parameters whose values affect the applicability of these theories and of the applied theory used to solve quasistatic problems of thermoelasticity are obtained.     

On HOD-supercompactness

During his Fall 2005 set theory seminar, Woodin asked whether V-supercompactness implies HOD-supercompactness. We show, as he predicted, that that the answer is no.     

Nonlinear approximation of functions from the class L r with respect to the Vilenkin system

In this paper we prove that for any function f from the class L ^r on [0, 1) one can find a function g from the same class (which differs from f on a set of arbitrarily small measure) whose greedy algorithm with respect to the Vilenkin system converges to f.     

Quantum non-Markovian Langevin equations and transport coefficients for an inverted oscillator

Based on the non-Markovian quantum Langevin equations, we obtain time-dependent transport coefficients for an inverted oscillator coupled linearly in the coordinate to a thermostat. We comparatively analyze the diffusion coefficients for harmonic and inverted oscillators and study the role of quantum statistical effects in the passage through a parabolic barrier. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 425–443, September, 2008.     

Almost Everywhere Convergence of Greedy Algorithm with Respect to Vilenkin System

In this paper, we prove that for any ε ∈ (0, 1) there exists ameasurable set E ∈ [0, 1) with measure |E| > 1 ? ε such that for any function f ∈ L¹[0, 1), it is possible to construct a function \(\tilde f \in {L^1}[0,1]\) coinciding with f on E and satisfying \(\int_0^1 {|\tilde f(x) - f(x)|dx < \varepsilon } \), such that both the Fourier series and the greedy algorithm of \(\tilde f\) with respect to a bounded Vilenkin system are almost everywhere convergent on [0, 1).     

Longitudinal waves propagation in plates in the presence of transversal magnetic field

The problem on longitudinal wave propagation in a plate in the presence of a constant transversal magnetic field is studied. The asymptotic behavior of tangential displacement of the points of the plate median surface is found. It is established that the wave of a given initial shape finally turns into a quasiharmonic one. Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 194–196, January–March, 2008.     

The theory of micropolar thin elastic shells

A boundary-value problem of the three-dimensional micropolar, asymmetric, moment theory of elasticity with free rotation is investigated in the case of a thin shell. It is assumed that the general stress-strain state (SSS) is comprised of an internal SSS and boundary layers. An asymptotic method of integrating a three-dimensional boundary-value problem of the micropolar theory of elasticity with free rotation is used for their approximate determination. Three different asymptotics are constructed for this problem, depending on the values of the dimensionless physical parameters. The initial approximation for the first asymptotics leads to the theory of micropolar shells with free rotation, the approximation for the second leads to the theory of micropolar shells with constrained rotation and the approximation for the third asymptotics leads to the so-called theory of micropolar shells “with a small shear stiffness”. Micropolar boundary layers are constructed. The problem of the matching of the internal problem and the boundary-layer solutions is investigated. The two-dimensional boundary conditions for the above-mentioned theories of micropolar shells are determined.     

On the Statistical Calibration of Physical Models

We introduce a novel statistical calibration framework for physical models, relying on probabilistic embedding of model discrepancy error within the model. For clarity of illustration, we take the measurement errors out of consideration, calibrating a chemical model of interest with respect to a more detailed model, considered as “truth” for the present purpose. We employ Bayesian statistical methods for such model‐to‐model calibration and demonstrate their capabilities on simple synthetic models, leading to a well‐defined parameter estimation problem that employs approximate Bayesian computation. The method is then demonstrated on two case studies for calibration of kinetic rate parameters for methane air chemistry, where ignition time information from a detailed elementary‐step kinetic model is used to estimate rate coefficients of a simple chemical mechanism. We show that the calibrated model predictions fit the data and that uncertainty in these predictions is consistent in a mean‐square sense with the discrepancy from the detailed model data.     

Synthesis of 5-substituted furans on the basis of the reactions of 1,3-alkadiynes with Β-dicarbonyl compounds

The reaction of 1,3-hexadiyne, 1,3-heptadiyne, and 1,3-octadiyne with acetylacetone and acetoacetic ester in the presence of manganese(III) and copper(II) acetates proceeds with the participation of both triple bonds and leads to substituted 5-alkynyl- and 5-(5-furyl)furans: in the case of 5-hydroxy-5-methyl-1,3-hexadiyne the terminal triple bond participates selectively in the process as a result of the effective protection of the disubstituted triple bond by the dimethylhydroxymethyl group.Communication 148 in the series Reactions of unsaturated compounds; see [1] for Communication 147.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 738–742, June, 1989.