Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

On cogrowth function of algebras and its logarithmical gap

Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal $I$-reducible word. A {\em cogrowth} function is number of obstructions of length $\le n$. We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.Comment: 5 page

THz Aperture Near-Field Spectroscopy of Dirac Plasmons in Topological Insulator Bi2Se3

We map the dispersion relation in ribbon gratings of topological insulator Bi2Se3 using both far-field and aperture-type near-field THz spectroscopy methods. The results are consistent with theoretical predictions of coupling between the optical phonon and massless Dirac plasmons

Near-field characterization of conductive micro-resonators for terahertz sensing

Near-field (NF) terahertz (THz) time-domain spectroscopy (TDS) is an excellent tool for direct studies of THz electromagnetic resonances occurring on a micrometre scale. Micro-resonators are at the heart of numerous promising THz sensing and detecting solutions. Experimental studies of individual micrometrescale THz resonances are essential, yet extremely challenging for the common far-field spectroscopic methods due to extreme sensitivity requirements. NF THz spectroscopy and microscopy are non-contact techniques for spectroscopic studies of individual micro-resonators and mapping the field patterns of THz resonant modes excited in individual conductive or insulating micro-objects. They give access to essential parameters of micro-resonators, including their resonance frequency, local field enhancement and quality factors. It allows for material and structural characterisation of micro-objects. Using the example of carbon microfibres, we show the advantages of NF THz TDS for non-contact THz conductivity probing and direct observation of the fundamental and the third-order surfaceplasmon resonance modes in conductive THz micro-resonators

Information and communication technologies as the factor of a professional musician training

© Medwell Journals, 2015. The study from the perspective of the current conditions of information considers the issues of a professional musician training improvement from the perspective of the current information system development conditions. According to the researchers, a quick update and the obsolescence of information and communication technologies and computer resources in society is accompanied by a slow adaptation of a musical education system to their use. In order to resolve this situation, the researchers suggest the ways to improve the training of a professional musician which are based on the integration of methodological approaches: a design and technological, a competence-based, a contextual and other ones taking into account the development of computer technologies. The study offers the principles of integration, reflection, subjectivity and productivity. The researchers teaching experience is offered concerning the creation of tutorials that focus on the effectiveness of a professional musician training in terms of information-communicative educational environment

Fast Ray Tracing of Lunar Digital Elevation Models

Ray-tracing (RT) of Lunar Digital Elevation Models (DEM)'s is performed to virtually derive the degree of radiation incident to terrain as a function of time, orbital and ephemeris constraints [I- 4]. This process is an integral modeling process in lunar polar research and exploration due to the present paucity of terrain information at the poles and mission planning activities for the anticipated spring 2009 launch of the Lunar Reconnaissance Orbiter (LRO). As part of the Lunar Exploration Neutron Detector (LEND) and Lunar Crater Observation and Sensing Satellite (LCROSS) preparations RI methods are used to estimate the critical conditions presented by the combined effects of high latitude, terrain and the moons low obliquity [5-7]. These factors yield low incident solar illumination and subsequently extreme thermal, and radiation conditions. The presented research uses RT methods both for radiation transport modeling in space and regolith related research as well as to derive permanently shadowed regions (PSR)'s in high latitude topographic minima, e.g craters. These regions are of scientific and human exploration interest due to the near constant low temperatures in PSRs, inferred to be < 100 K. Hydrogen is thought to have accumulated in PSR's through the combined effects of periodic cometary bombardment and/or solar wind processes, and the extreme cold which minimizes hydrogen sublimation [8-9]. RT methods are also of use in surface position optimization for future illumination dependent on surface resources e.g. power and communications equipment