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

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15We consider the nonlinear hyperbolic equation with delays uxy + λuxy(x - σ, у - τ) + c(x, у, u, ux, uy) = f(x, у) . We obtain sufficient conditions for oscillation of the solutions of problems of Goursat in the case, where λ>0.This work was partly supported by Grant MM-437 and Grant MM-516

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

On the Nature of Precursors in the Radio Pulsar Profiles

In the average profiles of several radio pulsars, the main pulse is accompanied by the preceding component. This so called precursor is known for its distinctive polarization, spectral, and fluctuation properties. Recent single-pulse observations hint that the sporadic activity at the extreme leading edge of the pulse may be prevalent in pulsars. We for the first time propose a physical mechanism of this phenomenon. It is based on the induced scattering of the main pulse radiation into the background. We show that the scattered component is directed approximately along the ambient magnetic field and, because of rotational aberration in the scattering region, appears in the pulse profile as a precursor to the main pulse. Our model naturally explains high linear polarization of the precursor emission, its spectral and fluctuation peculiarities as well as suggests a specific connection between the precursor and the main pulse at widely spaced frequencies. This is believed to stimulate multifrequency single-pulse studies of intensity modulation in different pulsars.Comment: 5 pages, no figures. Accepted for publication in MNRAS Letter

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

Elastic properties of FeSi

Measurements of the sound velocities in a single crystal of FeSi were performed in the temperature range 4-300 K. Elastic constants $C_{12}$ and $C_{44}$ deviate from a quasiharmonic behavior at high temperature; whereas, $C_{12}$ increases anomalously in the entire range of temperature, indicating a change in the electron structure of this materia