A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation

A bijective map $r: X^2 \longrightarrow X^2$, where $X = \{x_1, ..., x_n \}$ is a finite set, is called a \emph{set-theoretic solution of the Yang-Baxter equation} (YBE) if the braid relation $r_{12}r_{23}r_{12} = r_{23}r_{12}r_{23}$ holds in $X^3.$ A non-degenerate involutive solution $(X,r)$ satisfying $r(xx)=xx$, for all $x \in X$, is called \emph{square-free solution}. There exist close relations between the square-free set-theoretic solutions of YBE, the semigroups of I-type, the semigroups of skew polynomial type, and the Bieberbach groups, as it was first shown in a joint paper with Michel Van den Bergh. In this paper we continue the study of square-free solutions $(X,r)$ and the associated Yang-Baxter algebraic structures -- the semigroup $S(X,r)$, the group $G(X,r)$ and the $k$- algebra $A(k, X,r)$ over a field $k$, generated by $X$ and with quadratic defining relations naturally arising and uniquely determined by $r$. We study the properties of the associated Yang-Baxter structures and prove a conjecture of the present author that the three notions: a square-free solution of (set-theoretic) YBE, a semigroup of I type, and a semigroup of skew-polynomial type, are equivalent. This implies that the Yang-Baxter algebra $A(k, X,r)$ is Poincar\'{e}-Birkhoff-Witt type algebra, with respect to some appropriate ordering of $X$. We conjecture that every square-free solution of YBE is retractable, in the sense of Etingof-Schedler.Comment: 34 page

Time dependent correlations in marine stratocumulus cloud base height records

The scaling ranges of time correlations in the cloud base height records of marine boundary layer stratocumulus are studied applying the Detrended Fluctuation Analysis statistical method. We have found that time dependent variations in the evolution of the $\alpha$ exponent reflect the diurnal dynamics of cloud base height fluctuations in the marine boundary layer. In general, a more stable structure of the boundary layer corresponds to a lower value of the $\alpha$ - indicator, i.e. larger anti-persistence, thus a set of fluctuations tending to induce a greater stability of the stratocumulus. In contrast, during periods of higher instability in the marine boundary, less anti-persistent (more persistent like) behavior of the system drags it out of equilibrium, corresponding to larger $\alpha$ values. From an analysis of the frequency spectrum, the stratocumulus base height evolution is found to be a non-stationary process with stationary increments. The occurrence of these statistics in cloud base height fluctuations suggests the usefulness of similar studies for the radiation transfer dynamics modeling.Comment: 12 pages, 6 figures; to appear in Int. J. Mod. Phys. C, Vol. 13, No. 2 (2002

Influence of raw material properties on the quality of solid biofuel and energy consumption in briquetting process

ArticleThe present paper is related to a pressing process research of raw materials with different density in order to investigate impact of biomass density on a formation of monolithic structure and the briquette’s strength. Another focus of the study is an influence of raw materials particles’ size on agglomeration process and quality of final product. Different biomass materials like two varieties of miscanthus, industrial hemp and apple wood were selected for experimental purposes of this research. Mechanical durability which represents one the main indicator of briquettes’ mechanical quality (strength) was determined. The research was conducted using hydraulic piston briquetting press. For assessment of briquetting efficiency during the whole process energy consumption was measured. One of the most important factors that can affect briquetting process is the temperature of pressing chamber which was registered as well. The main goal of the research was practical study of possibilities for increasing production efficiency and quality of briquettes on hydraulic piston briquetting press with respect to optimization of particles’ size of raw materials and use of raw materials the most appropriate density

Using of high-speed mills for biomass disintegration

ArticleThe need for mechanical disintegration of biomass is very current topic with regard to the requirements of an agrarian sector, beside the importance of a material’s moisture content reduction to be used in further applications. The drawbacks of commonly applied devices are the limited use of moist biomass and high energy consumption for disintegration. In collaboration with LAVARIS company, there were tested two high-speed mills LAV 400/1R with single rotor (used for a first milling) and LAV 300/2R with double rotors (used for a second milling), which were primarily designed for crushing of concrete, rubber and construction waste. The goal of the new technical solution was a disintegration of biomass on example of pine sawdust and miscanthus together with examination of simultaneous drying in order to achieve a desired fraction (particle size) and moisture content of biomass material. Experimental tests on highspeed mills have shown the following results: in case of pine sawdust about 98% of output particle size after passing through the first and second milling was smaller than 1.5 mm, and smaller than 1 mm for miscanthus (sieve analysis method was used for determination), i.e. significant reduction was achieved comparing to initial particle size. Moisture content of the materials after disintegration (first and second) decreased from 37.08% to 8.55% for pine sawdust and from 24.43% to 7.19% for miscanthus. Based on the results, it can be concluded that the mechanical disintegration of biomass by high-speed mills has a great potential to become an effective part of raw materials’ pre-treatment technology, not only in agriculture, but also in production of different types of biofuels

КОНЦЕПТУАЛЬНІ ПІДХОДИ ДО СИСТЕМАТИЗАЦІЇ МЕТОДІВ ОЦІНКИ ЯКОСТІ МЕДИЧНОЇ ДОПОМОГИ

Methodology of estimating the quality of medical care is offered. On the basis of generalization of world experience and new authorial developments on original quadrupole model of process of estimating the quality of medical care is offered. A model consists of four clusters which contain four criteria for estimating the quality of medical care and corresponding indeces for the analysis of these criteria. Clusters have been presented as an integral estimation of quality of medical care, technological, methodological and estimation of quality of medical care on separate additional criteria. The detailed description of clusters and indeces has been accordingly given. A particular attention has been paid to the mathematical design of processes of estimating the quality of medical care. Indisputable advantages of the worked out quadrupole model are simplicity of its introduction and availability for understanding by medical personnel.Предлагается методология оценки качества медицинской помощи. На основании обобщения мирового опыта и на основе авторских разработок предлагается оригинальная квадрупольная модель процесса оценки качества медицинской помощи. Модель состоит из четырех кластеров, включающих по четыре критерия оценки качества медицинской помощи и соответствующие показатели для анализа этих критериев. Кластеры представлены как интегральная оценка качества медицинской помощи, технологическая, методологическая и оценка качества медицинской помощи по отдельным дополнительным критериям. Представлена детальная характеристика кластеров и показателей. Отдельно освещено математическое моделирование процессов оценки качества медицинской помощи. К бесспорным преимуществам разработанной квадрупольной модели отнесены простота ее внедрения и доступность для понимания медицинским персоналом.Пропонується методологія оцінки якості медичної допомоги. На підставі узагальнення світового досвіду та на основі авторських розробок пропонується оригінальна квадрупольна модель процесу оцінки якості медичної допомоги. Модель складається з чотирьох кластерів, що містять по чотири критерії оцінки якості медичної допомоги та відповідні показники для аналізу цих критеріїв. Кластери представлені як інтегральна оцінка якості медичної допомоги, технологічна, методологічна та оцінка якості медичної допомоги за окремими додатковими критеріями. Представлена детальна характеристика кластерів та показників.Окремим розділом висвітлено математичне моделювання процесів оцінювання якості медичної допомоги. До безперечних переваг розробленої квадрупольної моделі віднесено простоту її впровадження та доступність для розуміння медичним персоналом.

Results of investigation of muon fluxes of superhigh energy cosmic rays with X-ray emulsion chambers

The overall data from the investigation of the cosmic ray muon flux in the range of zenith angles (0-90) deg within the energy range (3.5 to 5.0) TeV is presented. The exposure of large X-ray emulsion chambers underground was 1200 tons. year. The data were processe using the method which was applied in the experiment Pamir and differred from the earlier applied one. The obtained value of a slope power index of the differential energy spectrum of the global muon flux is =3.7 that corresponds to the slope of the pion generation differential spectrum, gamma sub PI = 2.75 + or - .04. The analysis of the muon zenith-angular distribution showed that the contribution of rapid generation muons in the total muon flux agree the best with the value .2% and less with .7% at a 90% reliability level

Mercaptophosphonic acids as efficient linkers in quantum dot sensitized solar cells

Control over the deposition of quantum dots (QDs) on nanostructured semiconductors is very important for the photovoltaic performance of QD sensitized solar cells. The best control is typically achieved using bifunctional molecular linkers, such as mercaptopropionic acid (MPA), to attach the QDs to metal oxides in a specific manner; however some materials, such as ZnO, are not compatible with these molecules due to their pH sensitivity. We have developed new linkers, mercaptophosphonic acids of different length, which allow efficient functionalization of ZnO nanowires and also mesoporous TiO2 without damaging their surface. Detailed XPS and contact angle studies of the mechanism of self-assembly of these acids show that their strong chelation of the oxide surface prevents protonic attack and etching. Using these linkers, we show that colloidal ternary quantum dots, CuInS2, can be conformally and homogeneously deposited on the functionalized metal oxides. Photophysical studies by means of time-resolved photoluminescence spectroscopy confirm efficient electron transfer from the QDs to the metal oxides with the rate and efficiency scaling with respect to the linker length and nature. The efficiency of the QD sensitized solar cells fabricated with such assemblies also strongly depends on the linkers used and follows the trends observed for the charge transfer