and the associated line bundles

Let be a compact semi-simple Lie group, and let be a maximal unipotent subgroup of the complexified group . In this paper, we classify all the -invariant Kaehler structures on . For each Kaehler structure , let be the line bundle with connection whose curvature is . We then study the holomorphic sections of , which constitute a -representation space.

     

Method for Visible Light‐Induced Photocatalytic Degradation of Methylparaben in Water Using Nanostructured Ag/AgBr@m‐WO3

An efficient method of photocatalytic degradation of methylparaben in water using Ag nanoparticles (NPs) loaded AgBr‐mesoporous‐WO₃ composite photocatalyst (Ag/AgBr@m‐WO₃), under visible light is presented. In this process, quantification of methylparaben in water was carried out by high‐performance liquid chromatography (HPLC) and the HPLC results showed a significant reduction of methylparaben in water due to the enhanced of photocatalytic degradation efficiency of Ag/AgBr@m‐WO₃. For the material synthesis, highly ordered mesoporous‐WO₃ (m‐WO₃) was initially synthesized by sol–gel method and AgBr nanoparticles (NPs) were subsequently introduced in the pores of m‐WO₃, and finally, the Ag nanoparticles were introduced by light irradiation. The enhanced photocatalytic degradation of methylparaben in water is attributed to the formation of surface plasmonic resonance (SPR) due to the introduction of Ag NPs on the surface of the catalyst. Also, the formation of heterojunction between AgBr and mesoporous‐WO₃ in Ag/AgBr@m‐WO₃ significantly inhibited the recombination of light‐induced electron‐hole pairs in the semiconductor composite. The morphological and optical characterizations of the synthesized photocatalysts (Ag/AgBr@m‐WO₃) were carried out using SEM, TEM, XDR, N₂ adsorption–desorption, UV‐VIS diffuse reflectance spectroscopy (DRS). Also, the photocatalytic studies using radical scavengers were carried out and the results indicated that ${\text{O}}_2^{·-}$ is the main reactive species.     

A facile and green synthetic approach toward fabrication of starch-stabilized magnetite nanoparticles

A facile and green synthetic approach for fabrication of starch-stabilized magnetite nanoparticles was implemented at moderate temperature. This synthesis involved the use of iron salts, potato starch,sodium hydroxide and deionized water as iron precursors, stabilizer, reducing agent and solvent respectively. The nanoparticles(NPs) were characterized by UV-vis, PXRD, HR-TEM, FESEM, EDX, VSM and FT-IR spectroscopy. The ultrasonic assisted co-precipitation technique provides well formation of highly distributed starch/Fe_3O_4-NPs. Based on UV–vis analysis, the sample showed the characteristic of surface plasmon resonance in the presence of Fe_3O_4-NPs. The PXRD pattern depicted the characteristic of the cubic lattice structure of Fe_3O_4-NPs. HR-TEM analysis showed the good dispersion of NPs with a mean diameter and standard deviation of 10.68 4.207 nm. The d spacing measured from the lattice images were found to be around 0.30 nm and 0.52 nm attributed to the Fe3O4 and starch, respectively. FESEM analysis confirmed the formation of spherical starch/Fe_3O_4-NPs with the emission of elements of C, O and Fe by EDX analysis. The magnetic properties illustrated by VSM analysis indicated that the as synthesized sample has a saturation magnetization and coercivity of 5.30 emu/g and 22.898 G respectively.Additionally, the FTIR analysis confirmed the binding of starch with Fe_3O_4-NPs. This method was cost effective, facile and eco-friendly alternative for preparation of NPs.     

Synergy between Brønsted acid sites and Lewis acid sites

Synergy between Br?nsted acid sites and Lewis acid sites in mesoporous Al-Zr-TUD-1 was demonstrated to exist in Br?nsted acid catalysed reactions, but not in Lewis acid catalysed reactions.     

Optical band gap and conductivity measurements of polypyrrole-chitosan composite thin films

Electrical conductivity and optical properties of polypyrrole-chitosan（PPy-CHI） conducting polymer composites have been investigated to determine the optical transition characteristics and energy band gap of composite films.The two electrode method and I-V characteristic technique were used to measure the conductivity of the PPy-CHI thin films,and the optical band gap was obtained from their ultraviolet absorption edges.Depending upon experimental parameter,the optical band gap（E_g） was found within 1.30-2.32 eV as estimated from optical absorption data.The band gap of the composite films decreased as the CHI content increased.The room temperature electrical conductivity of PPy-CHI thin films was found in the range of 5.84×10^-7-15.25×10^-7 S·cm^-1 depending on the chitosan content.The thermogravimetry analysis（TGA） showed that the CHI can improve the thermal stability of PPy-CHI composite films.     

Development and validation of a multiplex real-time PCR method to simultaneously detect 47 targets for the identification of genetically modified organisms

Considering the increase of the total cultivated land area dedicated to genetically modified organisms (GMO), the consumers’ perception toward GMO and the need to comply with various local GMO legislations, efficient and accurate analytical methods are needed for their detection and identification. Considered as the gold standard for GMO analysis, the real-time polymerase chain reaction (RTi-PCR) technology was optimised to produce a high-throughput GMO screening method. Based on simultaneous 24 multiplex RTi-PCR running on a ready-to-use 384-well plate, this new procedure allows the detection and identification of 47 targets on seven samples in duplicate. To comply with GMO analytical quality requirements, a negative and a positive control were analysed in parallel. In addition, an internal positive control was also included in each reaction well for the detection of potential PCR inhibition. Tested on non-GM materials, on different GM events and on proficiency test samples, the method offered high specificity and sensitivity with an absolute limit of detection between 1 and 16 copies depending on the target. Easy to use, fast and cost efficient, this multiplex approach fits the purpose of GMO testing laboratories.

Al-free Zr-zeolite beta as a regioselective catalyst in the Meerwein-Ponndorf-Verley reaction

Al-free Zr-zeolite beta catalyzes the transfer reduction of ketones to the corresponding alcohols in high yield and with exceptional stereocontrol. Notably, the catalyst is very robust and gives good results even with 10% water content in the reaction mixture.     

Kahler Structures and Weighted Actions on the Complex Torus

Let T be the compact real torus, and T_C its complexification.Fix an integral weight , and consider the -weighted T-actionon T_C. If is a T-invariant Kähler form on T_C, it correspondsto a pre-quantum line bundle L over T_C. Let H be the square-integrableholomorphic sections of L. The weighted T-action lifts to aunitary T-representation on the Hilbert space H, and the multiplicityof its irreducible sub-representations is considered. It isshown that this is controlled by the image of the moment map,as well as the principle that ‘quantization commutes withreduction’.     

Kähler structures on complex torus

Consider the complex torus T _C under the natural action of the compact real torus T. In this paper, we study T-invariant Kähler structures ω on T_C. For each ω, we consider the corresponding line bundleL on T _C. Namely, the Chern class ofL is [ω], and L is equipped with a connection ? whose curvature is ω. We construct a canonical T-invariant L ²-structure on the sections ofL,and let H _ω be the square-integrable holomorphic sections ofL.Then the Hilbert space H _ω is a unitary T-representation, and we study the multiplicity of the (l-dimensional) irreducible unitary T-representations in H_ω. We shall see that the multiplicity is controlled by the image of the moment map corresponding to the T-action preserving ω.     

Partially harmonic forms and models of H-series

Let G   be a real reductive Lie group, let H=TA$H=TA$ be the identity component of a Cartan subgroup, and let h$\mathfrak{h}$ be the corresponding Cartan subalgebra. This leads to a parabolic subgroup of G whose identity component is MAN. The unitary G-representations induced by MAN are known as the H  -series. We study symplectic geometry of G×h$G\times \mathfrak{h}$ and apply geometric quantization to construct unitary G-representations by partially harmonic forms. They are direct integrals of the H-series, indexed by the image of the moment map. We also perform symplectic reduction and symplectic induction, and consider their analogues in representation theory via geometric quantization.