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

Relationship between somatic cell count in goat milk and mature Kashkaval cheese parameters

Received: February 1st, 2021 ; Accepted: March 28th, 2021 ; Published: April 16th, 2021 ; Correspondence: [email protected] is challenging to ensure Kashkaval cheese consistent quality during the production process which is directly correlated to the somatic cell count (SCC) and bacterial presence. This is one of the most popular and widely discussed topic areas in the dairy industry. SCC is used to limit the inflammatory process and to predict the health status of the animal’s mammary glands. The objective of this study was to evaluate the quality characteristics of mature Kashkaval cheese was produced from goat milk with different SCC (below 1,200 thous cells mL-1 - group I (low), above 1,750 thous cells mL-1 - group II (high) and up to 1,600 thous cells mL-1 - group III (medium)) and samples were evaluated on the 1st and 60th day of ripening by chemical, microbiological and sensory profile. The results showed a significant relation (P < 0.05) between the levels of SCC and Kashkaval cheese water content during ripening. For all analysed samples, the total lactic acid bacterial count was the highest between the 15th and 45th day of ripening and reached values up to 6.0 log cfu g -1 . Pathogenic microorganisms (Listeria monocytogenes, Coagulase-positive staphylococci) and coliforms were not detected. The highest number of psychrotrophic microorganisms was observed in Kashkaval samples with high SCC. The sensory evaluation revealed a higher score for cheese samples with low and medium SCC in comparison to the cheese sample with a high SCC

The Formation of Low-Mass Double White Dwarfs through an Initial Phase of Stable Non-Conservative Mass Transfer

Although many double white dwarfs (DWDs) have been observed, the evolutionary channel by which they are formed from low-mass/long-period red-giant-main-sequence (RG-MS) binaries remains uncertain. The canonical explanations involve some variant of double common-envelope (CE) evolution, however it has been found that such a mechanism cannot produce the observed distribution. We present a model for the initial episode of mass transfer (MT) in RG-MS binaries, and demonstrate that their evolution into double white dwarfs need not arise through a double-CE process, as long as the initial primary's core mass (Md,c) does not exceed 0.46M$_{\odot}$. Instead, the first episode of dramatic mass loss may be stable, non-conservative MT. We find a lower bound on the fraction of transferred mass that must be lost from the system in order to provide for MT, and demonstrate the feasibility of this channel in producing observed low-mass (with M$_{d,c}$ < 0.46M$_{\odot}$) DWD systems.Comment: 2 pages, 1 figure, Conference Proceedings for the International Conference on Binaries, Mykonos, Greec

Theoretical basis for composition of economic strategy for industry development

The article deals with the issues related to analysis of domestic engineering problems with the assessment of the current state of the industry as a whole. Considering the prospects of exiting the current crisis, as well as long-term economic growth we expect general welfare within the sector. As the object of the study the authors have selected the engineering industry of the country. The subject of research is the economic relations between producers and consumers of engineering products, as well as issues of strategy formation and development of the engineering industry. The authors analyzed the state of machine-manufacture and highlighted the problems, the solution of which is most relevant given the government policy of increased import substitution and enhanced productivity. Further analysis was carried out in the sphere of sources of financing and attraction of investment resources for all kinds of enterprises of mechanical engineering, on the basis of which economic development strategy for the industry may be constructed. In addition, the authors propose measures and concrete ways of solving the problems identified by the formation of economic strategy of development of the industry, involving plans of achievement of all the defined targets. As a result of the study authors concluded that the need to stop subsidizing loss-making enterprises, creating a favorable climate for the development of venture companies, in order t introduce innovative technology as soon as possible. These technologies could subsequently be exported together with products of greater added value.peer-reviewe

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