NONCOMMUTATIVE DIFFERENTIALS ON POISSON-LIE GROUPS AND PRE-LIE ALGEBRAS

We show that the quantisation of a connected simply-connected Poisson-Lie group admits a left-covariant noncommutative differential structure at lowest deformation order if and only if the dual of its Lie algebra admits a pre-Lie algebra structure. As an example, we find a pre-Lie algebra structure underlying the standard 3D differential structure on \C_q[SU_2]. At the noncommutative geometry level we show that the enveloping algebra U(\cm) of a Lie algebra \cm, viewed as quantisation of \cm^*, admits a connected differential exterior algebra of classical dimension if and only if \cm admits a pre-Lie algebra. We give an example where \cm is solvable and we extend the construction to the quantisation of tangent and cotangent spaces of Poisson-Lie groups by using bicross-sum and bosonization of Lie bialgebras. As an example, we obtain natural 6D left-covariant differential structures on the bicrossproduct \C[SU_2]\lrbicross U_\lambda(su_2^*).Comment: Expanded result on bicrossproduct construction, added 6D left-covariant differential calculi on \C[SU_2]\lrbicross U_\lambda(su_2^*) as an example, and improved structure of the paper, 40 pages Latex, no figure

Cosmological constant from quantum spacetime

http://dx.doi.org/10.1103/PhysRevD.91.124028© 2015, Physical Review

(E)-2-{3-[4-(Diphenyl­amino)styr­yl]-5,5-dimethyl­cyclo­hex-2-enyl­idene}­malono­nitrile

In the title compound, C31H27N3, the cyclo­hexene ring has an envelope configuration. In the crystal structure, there is an 34 Å3 void around the inversion center, but the low electron density (0.13 e Å−3) in the difference Fourier map suggests no solvent mol­ecule occupying this void. No hydrogen bonding is found in the crystal structure

Superior gas-sensing performance of amorphous CdO nanoflake arrays prepared at room temperature

Highly sensitive and selective detection of volatile organic compounds (VOCs) with fast response time is imperative based on safety requirements, yet often remains a challenge. Herein, we propose an effective solution, preparing a novel gas sensor comprised of amorphous nanoflake arrays (a-NFAs) with specific surface groups. The sensor was produced via an extremely simple process in which a-NFAs of CdO were deposited directly onto an interdigital electrode immersed in a chemical bath under ambient conditions. Upon exposure to a widely used VOC, diethyl ether (DEE), the sensor exhibits excellent performance, more specifically, the quickest response, lowest detection limit and highest selectivity ever reported for DEE as a target gas. The superior gas-sensing properties of the prepared a-NFAs are found to arise from their open trumpet-shaped morphology, defect-rich amorphous nature, and surface CO groups

Exploration and Practice of Blended Teaching Model Based Flipped Classroom and SPOC in higher University

SPOC is characterized by improving teaching effectiveness. Currently open teaching mode is the popular trend, which is mainly related to several aspects: how to carry out teaching practice by using MOOC proprietary, high-quality online teaching resources in open education, that is, deep integration of curriculum resources and teaching design. On the basis of SPOC development, combined with open education analysis of SPOC with instructional design theory and philosophy from flipped classroom as a guide, the present research try to propose instructional design model based on flipped classroom, including design of teaching content system, design of personalized learning strategies, design of teaching activities and teaching evaluation system. Four designs above contribute to the effective implementation of the open teaching activities based on the blended model of flipped classroom and SPOC teaching, so as to enhance the quality of education. Keywords: Teaching design model; SPOC; Teaching methods; Flipped classroo

Manipulation of γ\gamma ray polarization in Compton scattering

High-brilliance high-polarization $\gamma$ rays based on Compton scattering are of great significance in broad areas, such as nuclear, high-energy, astro-physics, etc. However, the transfer mechanism of spin angular momentum in the transition from linear, through weakly into strongly nonlinear processes is still unclear, which severely limits the simultaneous control of brilliance and polarization of high-energy $\gamma$ rays. In this work, we investigate the manipulation mechanism of high-quality polarized $\gamma$ rays in Compton scattering of the ultrarelativistic electron beam colliding with an intense laser pulse. We find that the contradiction lies in the simultaneous achievement of high-brilliance and high-polarization of $\gamma$ rays by increasing laser intensity, since the polarization is predominately contributed by the electron spin via multi-photon absorption channels. For instances, the spin-polarized electrons in high-intensity laser pulse can radiate high-brilliance high-polarization $\gamma$ rays, while, for the spin-nonpolarized electrons, to achieve the similar high-quality $\gamma$ beams with the same laser, the electrons must hold higher energies due to the spin contribution mainly from the laser via the single-photon absorption channel. Moreover, we confirm that the signature of $\gamma$ ray polarization can be applied for observing the nonlinear effects (multi-photon absorption) of Compton scattering with moderate-intensity laser facilities