Free subalgebras of Lie algebras close to nilpotent

We prove that for every automata algebra of exponential growth, the associated Lie algebra contains a free subalgebra. For n\geq 1, let L_{n+2} be a Lie algebra with generator set x_1,..., x_{n+2} and the following relations: for k\leq n, any commutator of length $k$ which consists of fewer than k different symbols from {x_1,...,x_{n+2}} is zero. As an application of this result about automata algebras, we prove that for every n\geq 1, L_{n+2} contains a free subalgebra. We also prove the similar result about groups defined by commutator relations

Measurements of vector magnetic field using multiple electromagnetically induced transparency resonances in Rb vapor

We study intensity distribution of transmission resonances under the conditions of electromagnetically induced transparency (EIT) with lin||lin configuration in 87Rb vapor. We demonstrate that for various orientations of the external magnetic field all seven resolved EIT resonances exhibit maxima or minima at certain directions of the linear polarization of the laser field. This effect can be used for development of a high-precision vector EIT magnetometer.Comment: 4 pages, 4 figure

An Ontology for Service Semantic Interoperability in the Smartphone-Based Tourist Trip Planning System

This paper presents an ontology-based approach for semantic interoperability tourist trip planning services. The proposed ontology describes a tourist, an attraction route and context information about tourist and his/her environment. This ontology is developed within the Tourist Trip Planning System, which consists of a set of interacting services. All services work accordingly to the proposed ontology which leads to service semantic interoperability and allows to increase interaction speed between them

M3-Driven smart space creation using a DD-WRT-Based device

The paper describes the process of smart space creation based on integration of Smart-M3 platform with a DD-WRT-based device. Smart-M3 is an open source platform which implements concept of smart space. Wi-Fi router is used as platform hosting which reduces the number of devices participating in smart space-based scenarios. The article covers a process of compilation and installation of Smart-M3 platform on DD-WRT-based Wi-Fi router. Evaluation shows that smart space organized this way can be used for scenarios with few participants. The authors developed “Smart-M3 Control Panel” web-service which allows users to control Smart-M3 platform by a graphical web interface. “Smart-M3 Control Panel” user can view the current status of platform; launch, stop, and reload it; view information storage content and change it; download log files; and change startup options. SocketIO interface was used for the user interaction with web service

Nonlinear optics of graphene in a strong magnetic field

Graphene placed in a magnetic field possesses an extremely high mid/far-infrared optical nonlinearity originating from its unusual band structure and selection rules for the optical transitions near the Dirac point. Here we study the linear and nonlinear optical response of graphene in strong magnetic and optical fields using quantum- mechanical density-matrix formalism. We calculate the power of coherent terahertz radiation generated as a result of four-wave mixing in graphene. We show that even one monolayer of graphene gives rise to appreciable nonlinear frequency conversion efficiency and Raman gain for modest intensities of incident infrared radiation.Comment: 16 pages, 6 figure

Investigation of Optical Properties and Radiation Stability of TiO2 Powders before and after Modification by Nanopowders of Various Oxides

The titanium dioxide powders are widely used as a pigment for coatings and paints, the important characteristics of which are reflectivity and stability to irradiation. The results of investigations of the optical properties and radiation stability of titanium dioxide powders before and after high-temperature modification with nanopowders are presented in this chapter. The diffuse reflection spectra of various titanium dioxide powders in the UV, visible, and near-IR ranges, and their change during irradiation by electrons with 30 keV energy and a different fluence in vacuum in situ were investigated: (1) TiO2 powders with particle size in the range 60–240 nm; (2) Microsized TiO2 powder (240 nm) modified by Al2O3, ZrO2, SiO2, TiO2, ZnO, MgO nanoparticles with grain size from 30 up to 60 nm; (3) Microsized TiO2 powder (260 nm) modified by SiO2 with the grain size of 12–14 nm at the temperature of 150, 400, and 800°C. The reduction in reflectivity in entire spectrum with decrease in grain sizes of TiO2 nanopowders was established. Nanopowder with the grain size of 80 nm possesses the highest stability to irradiation. It was shown that the average grain size and specific surface of introduced nanoparticles effect noticeably on the radiation stability increase of titanium dioxide powders modified with nanoparticles of various oxides. The micro-sized TiO2 powder heating at temperature of 800оС is the factor which positively influences on the radiation stability

Measurements of the magnetic field vector using multiple electromagnetically induced transparency resonances in Rb vapor

We study the dependence of electromagnetically induced transparency (EIT) resonance amplitudes on the external magnetic field direction in a linearly polarized bichromatic light (lin||lin) configuration in (87)Rb vapor. We demonstrate that all seven resolvable EIT resonances exhibit maxima or minima at certain orientations of the laser polarization relative to the wave vector and magnetic field. This effect can be used for the development of a high- precision EIT vector magnetometer

Context-Driven Tour Planning Service: An Approach Based on Synthetic Coordinates Recommendation

The paper presents a hybrid context/model-based tour planning service aimed at recommendation generation by providing the tourists the sequence of attractions that are more interesting for him/her based on previous activity with the service. The service is developed based on SCoR recommender system that is aimed at recommendation generation based on calculating the synthetic coordinate between tourists of the service in according with their ratings. SCoR is a model-based collaborative filtering algorithm, constructing a model based on the user's personal ratings as well as exploiting collaborative information from the ratings of the rest of the users. One of the main advantages of SCoR's model is its ability to incorporate additional training information (new ratings) without having to perform the training process from the beginning. The prototype has been implemented for Android-based smartphone and has been evaluated for St. Petersburg city. For the evaluation the attraction database has been formed that includes attraction location information from OpenStreeMaps platform, location description and media from Wikipedia, and ratings from Google Place