The quantum dilogarithm and representations quantum cluster varieties

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the cluster modular groups. The examples of the latter include the classical mapping class groups of punctured surfaces. One of applications is quantization of higher Teichmuller spaces. The constructed unitary representations can be viewed as analogs of the Weil representation. In both cases representations are given by integral operators. Their kernels in our case are the quantum dilogarithms. We introduce the symplectic/quantum double of cluster varieties and related them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version. To appear in Inventiones Math. The last Section of the previous versions was removed, and will become a separate pape

Feasibility of a Small, Rapid Optical-to-IR Response, Next Generation Gamma Ray Burst Mission

We present motivations for and study feasibility of a small, rapid optical to IR response gamma ray burst (GRB) space observatory. By analyzing existing GRB data, we give realistic detection rates for X-ray and optical/IR instruments of modest size under actual flight conditions. Given new capabilities of fast optical/IR response (about 1 s to target) and simultaneous multi-band imaging, such an observatory can have a reasonable event rate, likely leading to new science. Requiring a Swift-like orbit, duty cycle, and observing constraints, a Swift-BAT scaled down to 190 square cm of detector area would still detect and locate about 27 GRB per yr. for a trigger threshold of 6.5 sigma. About 23 percent of X-ray located GRB would be detected optically for a 10 cm diameter instrument (about 6 per yr. for the 6.5 sigma X-ray trigger).Comment: Elaborated text version of a poster presented at 2012 Malaga/Marbella symposiu

Renormalization group equations in curved space-time with non-trivial Topology

Renormalization group equations for massless GUT's in curved space-time with non-trivial topology are formulated. The asymptotics of the effective action both at high and low energies are obtained. It is shown that the Casimir energy contribution at high curvature (early Universe) becomes non-essential in the effective action.Comment: 7 Page

Use of Physicochemical Method for Evaluation of Mucilage Producing Ability of the Linum Usitatissimum L. Seeds

Abstract In the modern medicine of many European countries flax is used as a medicament with a wide range of use. Wholesome effect of flax seeds is determined by the large amount of enveloping substances. This property is connected with content of mucilage up to 10% and glycoside linamarin. Flaxseed polysaccharides also possess antiinflammatory effect. Furthermore, mucilage production can be a chemosystematic characteric of intraspecific taxons. In literature intervarietal variability data is limited. Therefore, comparative evaluation of mucilage producing ability of flax seeds with different morphotypes is of interest. The research of micromorphological characteristics of seed coat and mucilage production dynamics was carried out and it was established that mucilage-producing cells are localized predominantly in the external layer of seed coat. It was established that Bahmalskiy, Nebesnyj, Kustanayskiy yantar varieties possess the highest level of mucilage production. Morphotype and varietal specificity of mucilage production are determined, consequently it can be used as a marker feature of L. usitatissimum new forms. The proposed technique is based on the determination of seed physicochemical characteristics and can be used for express analysis of the vegetal samples and their differentiation by the directions of use: as a fatty oil or mucilage-containing raw material. Keywords: Linum usitatissimum L. varieties, seeds, mucilage production, hydration dynamics, physicochemical method

Helium Measurements using the Pellet Charge Exchange in Large Helical Device

In Large Helical Device (LHD), it is possible to perform the simulation experiment of the α particle heating by using the ion cyclotron resonance heating (ICH) because high-energy particle generated by ICH is well confined in the plasma. The neutral particles (mainly hydrogen), which are generated by the charge exchange between the high-energy ion and the background neutrals, can be observed by using them. However a few neutral helium particles can be observed since fully ionized helium like α particle can emit only by double charge exchange process. Therefore we also introduce the pellet charge exchange system (PCX). The diagnostic pellet is injected to the plasma in order to obtain the charge exchange neutral particle, which is produced by the charge exchange reaction between the ablated pellet cloud and high-energetic particle. The helium distribution measurement in helium plasma is also demonstrated

Temperature Inversion Symmetry in Gauge-Higgs Unification Models

The temperature inversion symmetry $R\to \frac{1}{T}$ is studied for the finite temperature effective potential of the N=1, $d=5$, supersymmetric $SU(3)_{c}{\times}SU(3)_{w}$ model, on the orbifold $S^{1}/Z_{2}$. For the value of the Wilson line parameter $\alpha=1$ ($SU(2)_{L}$ breaks to a $U'(1)$), it is found that the effective potential contains a symmetric part and an anti-symmetric part under $\xi\to \frac{1}{\xi}$, with, $\xi=RT$. When $\alpha=0$ (for which, $SU(2)_{L}$ remains unbroken) it is found that the only contribution to the effective potential that spoils the temperature inversion symmetry comes from the fermions in the fundamental representation of the gauge group, with $(+,+)$ or $(-,-)$, $Z_{2}$ parities. This is interesting since it implies that the bulk effective potential corresponding to models with orbifold fixed point localized fundamental fermions (and with no bulk fundamental fermions) has the temperature inversion symmetry.Comment: 21 pages, version accepted for publication in Theoretical and Mathematical Physic

p Si n SiC NANOLAYER PHOTOVOLTAIC CELL

Thin films of amorphous SiC were prepared by non reactive magnetron sputtering in an Ar atmosphere. A previously synthesized SiC was used as a solid state target. Deposition was carried out on a cold substrate of p Si 100 with a resistivity of 2 Ohm amp; 61655;cm. The Raman spectrum shows a dominant band at 982 cm 1, i.e. in the spectral region characteristic for SiC. The film thickness determined from atomic force microscopy measurements was about 8 40 nm, the height of the structural units of the film was 1 2 nm, while the linear dimensions were of the order of tens of nanometers. The amorphous nature of SiC grown on the Si substrate is confirmed by the presence of the diffraction rings which indicate the absence of the dominant orientation of the prepared films. A heterostructure consisting of a p type Si 100 and a layer of amorphous n type SiC was fabricated and studied. The investigation of its electrical and photoelectric properties shows that the entire space charge region is located in Si. This is in addition confirmed by the spectral dependence of the p Si n SiC photo sensitivity. The barrier height at the p Si n SiC interface estimated from dark I V characteristics is of the order of 0.9 1.0 eV. Load I V characteristics of p Si n SiC amorphous nanolayer solar cells demonstrate under standard AM1.5 illumination conditions a conversion efficiency of 7.2