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

STUDY OF THE NUTRITION OF CHILDREN AGED 6 YEARS IN CONDITIONS OF SEMIBOARDING-SCHOOL OF EDUCATION

No abstrac

Reduction of Some 2-Thiazoline Benzamide and Carbamate Derivatives with Lithium Aluminum Hydride

This paper r eports the reduction with litMum aluminum hydride of 2-benzamido-5-methyl-2-thiazoline (Va) and 2-benzamido- 5,5-dimethyl-2-thiazo1\u27ine (Vb) to give the corresponding 2-benzyfamino-2-thiazolines (Via, b), and of ethyl N-(5-methyl-2- -thiazoline-2-yl)-carbamate (Ila) and ethyl N-(5,5-dimethyl-2-thiazoline- 2-yl)-carbamate (Ilb) to give the corresponding 2-methylamino- 2-thiazolines (Illa, b). No evidence of ring reduction or cleavage was observed either at room temperature or in refluxing ether or tetrahydrofuran. The structure of the products was confirmed by independent syntheses. Characteristic infrared bands ar e described

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

Refraction in a pulsar magnetosphere - the effect of a variable emission height on pulse morphology

The Petrova (2000) model to calculate pulse profiles is extended to a variable emission height model to make it physically self-consistent. In this context variable means that the emission height is no longer considered to be the same for different magnetic field lines. The pulse profiles calculated using this new model seem to be less realistic due to a focusing effect and cannot be used to fit (typical) multifrequency pulsar observations. Apart from the focusing effect the general morphology of pulse profiles is not greatly affected by introducing a variable emission height. Additional extensions of the model will be needed to be able to fit observations, and several suggestions are made.Comment: 7 pages, 5 figures, accepted to A&