Symplectic structures associated to Lie-Poisson groups

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Comment: 30 page

Symplectic structure of the moduli space of flat connections on a Riemann surface

We consider canonical symplectic structure on the moduli space of flat {\g}-connections on a Riemann surface of genus $g$ with $n$ marked points. For {\g} being a semisimple Lie algebra we obtain an explicit efficient formula for this symplectic form and prove that it may be represented as a sum of $n$ copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie group $G^{*}$ and $g$ copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group $G$ (the pair ($G,G^{*}$) corresponds to the Lie algebra {\g}).Comment: 20 page

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold

Archaeoastronomical object on Tuzluk Mount in the Elbrus region (Northern Caucasus)

The article presents the results of a study of an object of four megaliths (outcrops) of fairly regular forms on the top of Mount Tuzluk. Outcrops are separated by mutually intersecting passages, forming a shape similar to a cruciform with orientation to the sides of the World. Almost all the sides of the stone-outcrops within the aisles are flat, plumb or slightly inclined, visually artificially aligned and treated. It is assumed that the outcrops were used in ancient times as near-sight sights for observing sunrises and sunsets of the full moon on significant astronomical dates, while the complex of four outcrops was an ancient near-horizon 'observatory'. Field studies using the methodology of archaeoastronomic research and measurements (Potemkina, Yurevich, 1998, pp. 17-35, 46-47), with direct observations in nature from the supposed relative observation center during the solstices, were carried out by a group of enthusiastic experts from 2001 to 2012. In this case, targeted archaeological researches were not conducted. The works were carried out at the exploration level using data from topography and astronomy. The main attention was paid to survey from the top of Mount Tuzluk a circular panorama of the horizon with a mark on it of the calculated and observed directions of rising / setting of the main luminaries on significant astronomical dates. The adjacent territory was also explored, where archaeological monuments were revealed: anthropomorphic stone sculptures (6), plates with molds for casting tools (3), stones with different indentations and traces of strong fire (2), tours of ethnographic modernity, more than 10 in total. There were done photography and mapping of the location of all the artifacts found on the ground and linking them to the object on the top of Mount Tuzluk. Subsequent systematization and analysis of field research results obtained over 10 years allows us to reasonably assume the use of an object at the top of a mountain as an ancient observation point for the annual movement of main luminaries on the surrounding horizon. This conclusion is based primarily on the coincidence of the azimuths calculated and observed relative to the prospective observation center of not only significant astronomical directions, but also with the undercut sides of the outcrops as near viewers and with noticeable sight on the far horizon, which cannot be accidental. The presence in the vicinity of the mountain of these archaeological objects of a cult nature, located on significant astronomical directions, suggests the existence of a cult center on the mountain Tuzluk and the adjacent territory. The beginning of the time of its functioning, if we proceed from the proposed by researchers for the stone sculpture No. 1 located near the Tuzluk mountain, date - VII centuries BC, can be pre-determined by pre-Scythian time. The most similar analogue to the archaeoastronomic object on Mount Tuzluk is the rocky sanctuary Kabile in Bulgaria, reliably functioning in ancient Thrace at the same time and located at the same geographical latitude, in the same Circumpontin region

Influence of Carbon Fibers on Structure and Properties of Polytetrafluoroethylene

In this paper, we studied the effect of carbon fibers on the performance properties of polymer composites based on polytetrafluoroethylene. It was shown that the introduction of PTFE carbon fibers significantly improved tribological and mechanical properties of the composite. The correlation between the performance properties and supramolecular structure was found. Initial lamellar structure of the polymer became less in size without significant changes in morphology when filled. Such process was accompanied by the increase of crystalline regions number and the crystallinity degree of composite. Structural studies have shown that materials with more densely packed and highly crystalline structure have increased mechanical and tribological properties. The developed materials can be used in friction units of machines and devices, where the use of lubricants is not acceptable or restricted

On the SO(N) symmetry of the chiral SU(N) Yang--Mills model

The posibility of quantizing the anomalous $SU(N)$ Yang--Mills model preserving the symmetry under the orthogonal subgroup is indicated. The corresponding Wess--Zumino action (1-cocycle) possesses the additional $SO(N)$ symmetry and can be expressed in terms of chiral fields taking values in the homogeneous space $SU(N)/SO(N)$. The modified anomaly and the constraints commutator (2-cocycle) are calculated.Comment: 9 pages, preprint PAR-LPTHE 92-48 (DECEMBER 1992), Late

МОНИТОРИНГ ДЕФОРМАЦИЙ ЗДАНИЯ ГЕОДЕЗИЧЕСКИМИ МЕТОДАМИ ПРИ РЕКОНСТРУКЦИИ ЕГО ФУНДАМЕНТА

The article analyzes the results of geodetic monitoring of bearing structures of the building during the work on strengthening its foundations. The technique works reasonably required accuracy of geodetic measurements. As a result of geodetic monitoring established quantitative and qualitative characteristics of the strain of bearing structures of the building. It is shown that as a result of works to strengthen the soil deformation processes at the base of the foundations of the building were stabilized.В статье анализируются результаты геодезического мониторинга несущих конструкций здания в период работ по усилению его фундаментов. Рассмотрена методика работ, обоснована требуемая точность геодезических измерений. По результатам геодезического мониторинга установлены количественные и качественные характеристики деформаций несущих конструкций здания. Показано, что в результате проведенных работ по укреплению грунтов деформационные процессы в основании фундаментов здания были стабилизированы

Expanded Strings in the Background of NS5-branes via a M2-brane, a D2-brane and D0-branes

Classical configurations of a M2-brane, a D2-brane and D0-branes are investigated in the background of an infinite array of M5-branes or NS5-branes. On the M2-brane, we discuss three kinds of configurations, such as a sphere, a cylinder and a torus-like one. These are stabilized by virtue of the background fluxes of M5-branes. The torus-like M2-brane configuration has winding and momentum numbers of 11th direction, and in terms of the type IIA superstring theory, this corresponds to a torus-like D2-brane with electric and magnetic fluxes on it. We also reproduce the same configuration from a non-abelian Born-Infeld action for D0-branes. It will be a construction of closed strings from D0-branes. An electric flux quantization condition on the D2-brane is also discussed in terms of D0-branes.Comment: 33 pages, 6 figures, references and footnote added, confusing expressions and introduction are improved, version to appear in JHE

Two dimensional lattice gauge theory based on a quantum group

In this article we analyze a two dimensional lattice gauge theory based on a quantum group.The algebra generated by gauge fields is the lattice algebra introduced recently by A.Yu.Alekseev,H.Grosse and V.Schomerus we define and study wilson loops and compute explicitely the partition function on any Riemann surface. This theory appears to be related to Chern-Simons Theory.Comment: 35 pages LaTex file,CPTH A302-05.94 (we have corrected some misprints and added more material to be complete