An analogue of the Magnus problem for associative algebras

We prove an analogue of the Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by n+k generators and k relations and has an n-element system of generators, then this algebra is a free algebra of rank n

OPO-laser system for atmospheric sounding in the MID-IR range

A laser system is designed that provides for tunable generation of nanosecond radiation pulses in the 3–4 μm range. Optical block-diagram and specifications of the system are presented. The laser system as a part of a differential absorption lidar designed can be used for remote control of pollutant concentrations along surface atmospheric path

Non-contact infrared temperature measurements in dry permafrost boreholes

While planning the COAST Expedition to the Siberian Laptev Sea in 2005, the question of how to make a short equilibrium temperature measurement in a dry borehole arose. As a result, an infrared borehole tool was developed and used in three dry boreholes (up to 60.2 m deep) in the coastal transition zone from terrestrial to sub-sea permafrost near Mamontovy Klyk in the western Laptev Sea. A depth versus temperature profile was acquired with equilibration times of 50 × 10−3 s at each depth interval. Comparison with a common resistor string revealed an offset due to limitations of accuracy of the infrared technique and the influence of the probe's massive steel housing. Therefore it was necessary to calibrate the infrared sensor with a high precision temperature logger in each borehole. The results of the temperature measurements show a highly dynamic transition zone with temperature gradients up to −0.092°C/m and heat flow of −218 mW/m. A period of submergence of only 600 years the drilled sub-sea permafrost is approaching the overlying seawater temperature at −1.61°C with a temperature gradient of 0.021°C/m and heat flow of 49 mW/m. Further offshore, 11 km from the coastline, a temperature gradient of 0.006°C/m and heat flow of 14 mW/m occur. Thus the sub-sea permafrost in the Mamontovy Klyk region has reached a critical temperature for the presence of interstitial ice. The aim of this article is to give a brief feasibility study of infrared downhole temperature measurements and to present experiences and results of its successful application

Class preserving automorphisms of unitriangular groups

Let $\textrm{UT}_n (K)$ be a unitriangular group over a field $K$ and $\Gamma_{n,k} := \textrm{UT}_n (K)/ \gamma_k(\textrm{UT}_n (K))$, where $\gamma_k (\mathrm{UT}_n(K))$ denotes the $k$-th term of the lower central series of $\mathrm{UT}_n (K)$, $2 \le k \le n$. We prove that the group of all class preserving automorphisms of $\Gamma_{n,k}$ is equal to \Inn(\Gamma_{n,k}) if and only if $K$ is a prime field. Let $G_n^{(m)} := \mathrm{UT}_n (\mathbb{F}_{p^m}) / \gamma_3 (\mathrm{UT}_n(\mathbb{F}_{p^m}))$. We calculate the group of all class preserving automorphisms and class preserving outer automorphisms of $G_n^{(m)}$.Comment: 19 pages, accepted for publication in International Journal of Algebra and Computatio

Electron correlation effects in electron-hole recombination in organic light-emitting diodes

We develop a general theory of electron--hole recombination in organic light emitting diodes that leads to formation of emissive singlet excitons and nonemissive triplet excitons. We briefly review other existing theories and show how our approach is substantively different from these theories. Using an exact time-dependent approach to the interchain/intermolecular charge-transfer within a long-range interacting model we find that, (i) the relative yield of the singlet exciton in polymers is considerably larger than the 25% predicted from statistical considerations, (ii) the singlet exciton yield increases with chain length in oligomers, and, (iii) in small molecules containing nitrogen heteroatoms, the relative yield of the singlet exciton is considerably smaller and may be even close to 25%. The above results are independent of whether or not the bond-charge repulsion, X_perp, is included in the interchain part of the Hamiltonian for the two-chain system. The larger (smaller) yield of the singlet (triplet) exciton in carbon-based long-chain polymers is a consequence of both its ionic (covalent) nature and smaller (larger) binding energy. In nitrogen containing monomers, wavefunctions are closer to the noninteracting limit, and this decreases (increases) the relative yield of the singlet (triplet) exciton. Our results are in qualitative agreement with electroluminescence experiments involving both molecular and polymeric light emitters. The time-dependent approach developed here for describing intermolecular charge-transfer processes is completely general and may be applied to many other such processes.Comment: 19 pages, 11 figure

The First Director: Academician A. M. Rumiantsev

Romanovskii N. V. The First Director: Academician A. M. Rumiantsev [Электронный ресурс] / N. V. Romanovskii// Sociological Research. - 2009. - Vol. 48, № 5 : The History of Sociology in Russia and the Soviet Union (I). - P. 55-64

The First Director: Academician A. M. Rumiantsev

Romanovskii N. V. The First Director: Academician A. M. Rumiantsev [Электронный ресурс] / N. V. Romanovskii// Sociological Research. - 2009. - Vol. 48, № 5 : The History of Sociology in Russia and the Soviet Union (I). - P. 55-64