Almost overlap-free words and the word problem for the free Burnside semigroup satisfying x^2=x^3

In this paper we investigate the word problem of the free Burnside semigroup satisfying x^2=x^3 and having two generators. Elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a unique "canonical" representative for each equivalence class. We prove that overlap-free words and so-called almost overlap-free words (this notion is some generalization of the notion of overlap-free words) can serve as canonical representatives for corresponding equivalence classes. We show that such a word in a given class, if any, can be efficiently found. As a result, we construct a linear-time algorithm that partially solves the word problem for the semigroup under consideration.Comment: 33 pages, submitted to Internat. J. of Algebra and Compu

Almost Overlap-free Words and the Word Problem for the Free Burnside Semigroup Satisfying x2 = x3

We study the word problem for the free Burnside semigroup satisfying x 2 = x3 and having two generators. The elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a unique "canonical" representative for each equivalence class. We prove that overlap-free words and "almost" overlap-free words can serve as canonical representatives of their equivalence classes. We show that such a word in a given class, if any, can be efficiently found. As a result, we construct a linear-time algorithm that partially solves the word problem for the semigroup under consideration. © 2011 World Scientific Publishing Company

THE EXPERIMENTAL DETERMINATION METHODOLOGY OF THE PARAMETERS IN THE EQUATION OF THE AIR TEMPERATURE DISTRIBUTION ON THE HFS HEIGHT

The research of the HPS effectiveness and the area of their application because of the wide application in the construction of hinged facade systems  (NFS) with a ventilated air interlayer is actual nowadays. The fullscale experimental study of the temperature change in the facade height  in the summer period is carried out. The differential equation for the  distribution of temperature along the interlayer height is used for the process of the experimental data. To simplify the processing of the  experimental data, in this differential equation the variability is made. The  equation contains two parameters, which depend on the temperature of the  outside  solution. The equation is represented in finite differences and by  means of such equation the determination of the parameters of the equation  from the experimental data is obtained. The calculation of the differential equation with the found parameters is presented. The calculations from the  obtained equation are compared with the experimental data. The comparative analysis shows an acceptable error between calculated and experimental data. The developed technique for the equation parameters’  determination makes it possible to find the numerical values of the air gap  characteristics, which would increase the calculations’ accuracy for the operational HFS parameters’ determination in their thermal performance

Fused 1,2-Diboraoxazoles Based on closo-Decaborate Anion–Novel Members of Diboroheterocycle Class

The novel members of the 1,2-diboraoxazoles family have been obtained. In the present work, we have carried out the intramolecular ring-closure reaction of borylated iminols of general type [B10H9N=C(OH)R]− (R = Me, Et, nPr, iPr, tBu, Ph, 4-Cl-Ph). This process is conducted in mild conditions with 83–87% yields. The solid-state structures of two salts of 1,2-diboraoxazoles were additionally investigated by X-ray crystallography. In addition, the phenomena of bonding interactions in the 1,2-diboraoxazole cycles have been theoretically studied by the Quantum Theory of Atoms in Molecules analysis. Several local and integral topological properties of the electron density involved in these interactions have been computed