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

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

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

Black Hole Formation in X-Ray Binaries: The Case of XTE J1118+480

In recent years, an increasing number of proper motions have been measured for Galactic X-ray binaries. When supplemented with accurate determinations of the component masses, orbital period, and donor luminosity and effective temperature, these kinematical constraints harbor a wealth of information on the systems' past evolution. The constraints on compact object progenitors and kicks derived from this are of immense value for understanding compact object formation and exposing common threads and fundamental differences between black hole and neutron star formation. Here, we present the results of such an analysis for the black hole X-ray binary XTE J1118+480. We present results from modeling the mass transfer phase, following the motion in the Galaxy back to the birth site of the black hole, and examining the dynamics of symmetric and asymmetric core-collapses of the black hole progenitor

Modification of epoxy resin by oligomaleimidohydroxyphenylene

The article is devoted to development and research of new film materials on the basis of epoxy pitches with the improved properties. The assessment of protective properties is defined by electrochemical methods of research, and also with physic-mechanical that gives the most complete idea of the corrosion processes proceeding under a paint and varnish film. Data of researches allowed to correct covering structure for separate scopes for the purpose of achievement of high extent of protection of metal surfaces

Protective properties of modified epoxy coatings

Article is devoted to the development and research of new film materials based on epoxy resins with improved properties. Evaluation of protective properties is determined by electrochemical and physico-mechanical methods of research that provides the most complete picture of the corrosion processes occurring under the paint film . These studies allowed to adjust the coating composition to the individual applications in order to achieve a high degree of protection of metal surfaces

Theoretical and practical aspects of quality of life in the economic security system

© Medwell Journals, 2017. The study analyzes theoretical approaches to studying quality of life parameters in the system of economic security. The essence of the main economic categories is generalized, the components structure of quality of life is shown and the factors of internal destabilization of the Russian economy are identified. Calculation of the main socio-economic indicators of quality of life in Russia over the past 5 years served the basis for the researchers conclusions on improving quality of life and economic security