Solutions to Yang-Mills equations on four-dimensional de Sitter space

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS$_4$ and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS$_4$ as ${\mathbb R}\times S^3$, via an SU(2)-equivariant ansatz we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time $\tau\in{\mathbb R}$ is given by $\tilde{B}_a=-\frac12 I_a/(R^2\cosh^2\!\tau)$, where $I_a$ for $a=1,2,3$ are the SU(2) generators and $R$ is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value $-\frac12j(j{+}1)(2j{+}1)\pi^3$ in a spin-$j$ representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.Comment: 1+7 pages; v2: introduction extended, gauge group representation dependence added, minor clarifications, 3 more references; v3: title change, published versio

Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.Comment: 1+17 pages, 1 figur

The professionalization of journalism in the 20-30-ies of the XIX century

The influence of the process of commercialization in the field of printing of 1820-1830- at the status and the professional quality of journalism is considered.В статье рассматривается влияние процесса коммерциализации в сфере печатного дела периода 1820–1830-х гг. на состояние и профессиональные качества журналистики

К вопросу о дистанционном обучении в аэрокосмической отрасли

Данная статья содержит информацию о возможности применения дистанционного обучения в образовательном процессе для получения степени бакалавра или магистра, либо для получения сертификата о прохождении образовательного курса в области аэрокосмической инженерии. Также рассматриваются преимущества и недостатки электронного обучения в аэрокосмической сфере. Проводится сравнительный анализ различных программ дистанционного обучения в зарубежных странах по основным критериям: стоимость обучения, продолжительность и содержание курса, требования кстуденту и т.д. Кроме того, изучена распростран?нность онлайн обучения в аэрокосмической отрасли в России и выявлены возможные проблемы реализации дистанционного обучения в аэрокосмической инженерии.This article contains an information about the possibilities of applying distance learning in the educational process in order to earn bachelor's degree or master's degree, or to obtain a certificate of passing the educational course in the field of aerospace engineering. The advantages and disadvantages of e-learning in the aerospace field are also mentioned. Comparative analysis of various distance learning programs in foreign countries was made according to the main criteria: tuition fee, duration and course content, student requirements, etc. In addition, the prevalence of online learning in the aerospace industry in Russia and possible problems of implementation ofdistance learning in aerospace engineering are covered

Instantons on sine-cones over Sasakian manifolds

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.Comment: 1+15 pages, 2 figure

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

Dressing Symmetries of Holomorphic BF Theories

We consider holomorphic BF theories, their solutions and symmetries. The equivalence of Cech and Dolbeault descriptions of holomorphic bundles is used to develop a method for calculating hidden (nonlocal) symmetries of holomorphic BF theories. A special cohomological symmetry group and its action on the solution space are described.Comment: 14 pages, LaTeX2

Supernova Ia: a Converging Delayed Detonation Wave

A model of a carbon-oxygen (C--O) presupernova core with an initial mass 1.33 M_\odot, an initial carbon mass fraction 0.27, and with an average mass growth-rate 5 x 10^{-7} M_\odot/yr due to accretion in a binary system was evolved from initial central density 10^9 g/cm^3, and temperature 2.05 x 10^8 K through convective core formation and its subsequent expansion to the carbon runaway at the center. The only thermonuclear reaction contained in the equations of evolution and runaway was the carbon burning reaction 12C + 12C with an energy release corresponding to the full transition of carbon and oxygen (with the same rate as carbon) into 56Ni. As a parameter we take \alpha_c - a ratio of a mixing length to the size of the convective zone. In spite of the crude assumptions, we obtained a pattern of the runaway acceptable for the supernova theory with the strong dependence of its duration on \alpha_c. In the variants with large enough values of \alpha_c=4.0 x 10^{-3} and 3.0 x 10^{-3} the fuel combustion occurred from the very beginning as a prompt detonation. In the range of 2.0 x 10^{-3} >= \alpha_c >= 3.0 x 10^{-4} the burning started as a deflagration with excitation of stellar pulsations with growing amplitude. Eventually, the detonation set in, which was activated near the surface layers of the presupernova (with m about 1.33 M_\odot) and penetrated into the star down to the deflagration front. Excitation of model pulsations and formation of a detonation front are described in detail for the variant with \alpha_c=1.0 x 10^{-3}.Comment: 13 pages, 11 figures, to appear in Astronomy Letter