Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

Theoretical and experimental study of high-pressure synthesized B20-type compounds Mn1−x_{1-x}(Co,Rh)x_xGe

The search and exploration of new materials not found in nature is one of modern trends in pure and applied chemistry. In the present work, we report on experimental and \textit{ab initio} density-functional study of the high-pressure-synthesized series of compounds Mn$_{1-x}$(Co,Rh)$_x$Ge. These high-pressure phases remain metastable at normal conditions, therewith they preserve their inherent noncentrosymmetric B20-type structure and chiral magnetism. Of particular interest in these two isovalent systems is the comparative analysis of the effect of $3d$ (Co) and $4d$ (Rh) substitution for Mn, since the $3d$ orbitals are characterized by higher localization and electron interaction than the $4d$ orbitals. The behavior of Mn$_{1-x}$(Co,Rh)$_x$Ge systems is traced as the concentration changes in the range $0 \leq x \leq 1$. We applied a sensitive experimental and theoretical technique which allowed to refine the shape of the temperature dependencies of magnetic susceptibility $\chi(T)$ and thereby provide a new and detailed magnetic phase diagram of Mn$_{1-x}$Co$_x$Ge. It is shown that both systems exhibit a helical magnetic ordering that very strongly depends on the composition $x$. However, the phase diagram of Mn$_{1-x}$Co$_x$Ge differs from that of Mn$_{1-x}$Rh$_x$Ge in that it is characterized by coexistence of two helices in particular regions of concentrations and temperatures.Comment: 12 pages, 11 figure

Peculiar behavior of the electrical resistivity of MnSi at the ferromagnetic phase transition

The electrical resistivity of a single crystal of MnSi was measured across its ferromagnetic phase transition line at ambient and high pressures. Sharp peaks of the temperature coefficient of resistivity characterize the transition line. Analysis of these data shows that at pressures to ~0.35 GPa these peaks have fine structure, revealing a shoulder at ~ 0.5 K above the peak. It is symptomatic that this structure disappears at pressures higher than ~0.35 GPa, which was identified earlier as a tricritical poin

High Pressure studies of the magnetic phase transition in MnSi: revisited

New measurements of AC magnetic susceptibility and DC resistivity of a high quality single crystal MnSi were carried out at high pressure making use of helium as a pressure medium. The form of the AC magnetic susceptibility curves at the magnetic phase transition suddenly changes upon helium solidification. This implies strong sensitivity of magnetic properties of MnSi to non hydrostatic stresses and suggests that the early claims on the existence of a tricritical point at the phase transition line are probably a result of misinterpretation of the experimental data. At the same time resistivity behavior at the phase transition does not show such a significant influence of helium solidification. The sharp peak at the temperature derivative of resistivity, signifying the first order nature of the phase transition in MnSi successfully survived helium crystallization and continued the same way to the highest pressure.Comment: 4 pages, 6 figure

THE MISSION OF THE REGIONAL UNIVERSITY AND ITS FOCUS ON THE DEVELOPMENT OF HUMAN CAPITAL IN THE REGION

The purpose of the article: The article clarifies and justifies the mission of a modern regional university, which focuses on the activities of a university on the development of human capital in the region.Materials and methods: Based on the data of scientific literature, strategic documents of the state, materials of regional statistics, surveys of respondents, the strategic direction of the formation of a regional university is justified - orientation of its mission, research and educational activities on the development of human capital. A range of directions for improving the functioning of a regional university has been proposed and justified in order to bring the content of its activities in line with the regional focus and the new mission.Results of the research: Regional universities are presented in the article as high-tech educational organizations of higher education, the vector of strategic development of which should be focused on maximum integration into the economy and social sphere of the regions. Structural components of human capital are proposed - education capital, health capital, labor, cultural and moral capital, intellectual capital, entrepreneurial capital, social capital, cyclically interacting with each other in the process of personal and professional development of a teacher. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of The mission of the regional university and its focus on the development of human capital in the region is presented in a comprehensive and complete manner

Strength properties and structure of a submicrocrystalline Al–Mg–Mn alloy under shock compression

The results of studying the strength of a submicrocrystalline aluminum A5083 alloy (chemical composition was 4.4Mg–0.6Mn–0.11Si–0.23Fe–0.03Cr–0.02Cu–0.06Ti wt % and Al base) under shockwave compression are presented. The submicrocrystalline structure of the alloy was produced in the process of dynamic channel-angular pressing at a strain rate of 104 s–1. The average size of crystallites in the alloy was 180–460 nm. Hugoniot elastic limit σHEL, dynamic yield stress σy, and the spall strength σSP of the submicrocrystalline alloy were determined based on the free-surface velocity profiles of samples during shock compression. It has been established that upon shock compression, the σHEL and σy of the submicrocrystalline alloy are higher than those of the coarse-grained alloy and σsp does not depend on the grain size. The maximum value of σHEL reached for the submicrocrystalline alloy is 0.66 GPa, which is greater than that in the coarse-crystalline alloy by 78%. The dynamic yield stress is σy = 0.31 GPa, which is higher than that of the coarse-crystalline alloy by 63%. The spall strength is σsp = 1.49 GPa. The evolution of the submicrocrystalline structure of the alloy during shock compression was studied. It has been established that a mixed nonequilibrium grain-subgrain structure with a fragment size of about 400 nm is retained after shock compression, and the dislocation density and the hardness of the alloy are increased

Project "The Moon - 2012+": Spin-orbital evolution, geophysics and selenodesy of the Moon

The Russian scientific project "The Moon - 2012+" is directed at solving fundamental problems of celestial mechanics, selenodesy and geophysics of the Moon through the pursuance of theoretical research and computer simulations of the following fields. 1. Spin-orbital longtime evolution and physical librations of the multilayered Moon: (a) development of the analytical theory of rotation of the two- /three-layer Moon and construction of the physical libration's tables for processing accurate observations and for constructing a lunar annual book; and (b) analysis of the spin-orbital evolution of the early Moon, an estimation of internal energy dissipation, and modeling of the long-term mechanism maintaining the free librations of the Moon. 2. Geodynamics of a lunar core: analysis of differentiation of a lunar core, detailed elaboration of plume-tectonics of mantle and a core of the early Moon, evolution of a boundary layer of a core-mantle boundary, reconstruction of the gravitational and viscous-mechanical interactions of a lunar core and mantle, research on resonant dissipation of internal energy, and calculation of free and forced nutations of a lunar core and of free fluctuations of a core-mantle system. 3. Selenodesy of lunar far-side: solution of an inverse problem in lunar gravimetry, construction of a geodynamic model of the lunar crust and of a Moho's boundary, reconstruction of initial mascons on the far-side of the Moon, and creation of accurate topographical and gravitational models of the Moon on the basis of modern observations. © 2008

Interplay between lattice, orbital, and magnetic degrees of freedom in the chain-polymer Cu(II) breathing crystals

The chain-polymer Cu(II) breathing crystals C21H19CuF12N4O6 were studied using the x-ray diffraction and ab initio band structure calculations. We show that the crystal structure modification at T=146 K, associated with the spin crossover transition, induces the changes of the orbital order in half of the Cu sites. This in turn results in the switch of the magnetic interaction sign in accordance with the Goodenough-Kanamori-Andersen theory of the coupling between the orbital and spin degrees of freedom.Comment: 6 pages, 7 figure

Optimising the management of vaginal discharge syndrome in Bulgaria: cost effectiveness of four clinical algorithms with risk assessment

OBJECTIVES: To evaluate the performance and cost effectiveness of the WHO recommendations of incorporating risk-assessment scores and population prevalence of Neisseria gonorrhoeae (NG) and Chlamydia trachomatis (CT) into vaginal discharge syndrome (VDS) algorithms. METHODS: Non-pregnant women presenting with VDS were recruited at a non-governmental sexual health clinic in Sofia, Bulgaria. NG and CT were diagnosed by PCR and vaginal infections by microscopy. Risk factors for NG/CT were identified in multivariable analysis. Four algorithms based on different combinations of behavioural factors, clinical findings and vaginal microscopy were developed. Performance of each algorithm was evaluated for detecting vaginal and cervical infections separately. Cost effectiveness was based on cost per patient treated and cost per case correctly treated. Sensitivity analysis explored the influence of NG/CT prevalence on cost effectiveness. RESULTS: 60% (252/420) of women had genital infections, with 9.5% (40/423) having NG/CT. Factors associated with NG/CT included new and multiple sexual partners in the past 3 months, symptomatic partner, childlessness and >or=10 polymorphonuclear cells per field on vaginal microscopy. For NG/CT detection, the algorithm that relied solely on behavioural risk factors was less sensitive but more specific than those that included speculum examination or microscopy but had higher correct-treatment rate and lower over-treatment rates. The cost per true case treated using a combination of risk factors, speculum examination and microscopy was euro 24.08. A halving and tripling of NG/CT prevalence would have approximately the inverse impact on the cost-effectiveness estimates. CONCLUSIONS: Management of NG/CT in Bulgaria was improved by the use of a syndromic approach that included risk scores. Approaches that did not rely on microscopy lost sensitivity but were more cost effective