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

Constraints on Ho\v{r}ava-Lifshitz gravity from GRB 170817A

In this work we focus on a toy model: (3+1)-dimensional Ho\v{r}ava-Lifshitz gravity coupling with an anisotropic electromagnetic (EM) field which is generated through a Kaluza-Klein reduction of a (4+1)-dimensional Ho\v{r}ava-Lifshitz gravity. This model exhibits a remarkable feature that it has the same velocity for both gravitational and electromagnetic waves. This feature makes it possible to restrict the parameters of the theory from GRB 170817A. In this work we use this feature to discuss possible constraints on the parameter $\beta$ in the theory, by analyzing the possible Lorentz invariance violation effect of the GRB 170817A. This is achieved by analyzing potential time delay of gamma-ray photons in this event. It turns out that it places a stringent constraint on this parameter. In the most ideal case, it gives $|1-\sqrt{\beta}|<(10^{-19}-10^{-18})$.Comment: 21 pages, 2 tables. Accepted for publication in EPJ

(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

Determining layer number of two dimensional flakes of transition-metal dichalcogenides by the Raman intensity from substrate

Transition-metal dichalcogenide (TMD) semiconductors have been widely studied due to their distinctive electronic and optical properties. The property of TMD flakes is a function of its thickness, or layer number (N). How to determine N of ultrathin TMDs materials is of primary importance for fundamental study and practical applications. Raman mode intensity from substrates has been used to identify N of intrinsic and defective multilayer graphenes up to N=100. However, such analysis is not applicable for ultrathin TMD flakes due to the lack of a unified complex refractive index ($\tilde{n}$) from monolayer to bulk TMDs. Here, we discuss the N identification of TMD flakes on the SiO$_2$/Si substrate by the intensity ratio between the Si peak from 100-nm (or 89-nm) SiO$_2$/Si substrates underneath TMD flakes and that from bare SiO$_2$/Si substrates. We assume the real part of $\tilde{n}$ of TMD flakes as that of monolayer TMD and treat the imaginary part of $\tilde{n}$ as a fitting parameter to fit the experimental intensity ratio. An empirical $\tilde{n}$, namely, $\tilde{n}_{eff}$, of ultrathin MoS$_{2}$, WS$_{2}$ and WSe$_{2}$ flakes from monolayer to multilayer is obtained for typical laser excitations (2.54 eV, 2.34 eV, or 2.09 eV). The fitted $\tilde{n}_{eff}$ of MoS$_{2}$ has been used to identify N of MoS$_{2}$ flakes deposited on 302-nm SiO$_2$/Si substrate, which agrees well with that determined from their shear and layer-breathing modes. This technique by measuring Raman intensity from the substrate can be extended to identify N of ultrathin 2D flakes with N-dependent $\tilde{n}$ . For the application purpose, the intensity ratio excited by specific laser excitations has been provided for MoS$_{2}$, WS$_{2}$ and WSe$_{2}$ flakes and multilayer graphene flakes deposited on Si substrates covered by 80-110 nm or 280-310 nm SiO$_2$ layer.Comment: 10 pages, 4 figures. Accepted by Nanotechnolog

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