Flat Complex Vector Bundles,the Beltrami Differential and W-Algebras

Since the appearance of the paper by Bilal et al. in 1991, it has been widely assumed that W-algebras originating from the Hamiltonian reduction of an SL(n,C)-bundle over a Riemann surface give rise to a flat connection, in which the Beltrami differential may be identified. In this Letter, it is shown that the use of the Beltrami parametrization of complex structures on a compact Riemann surface over which flat complex vector bundles are considered, allows the construction of the above mentioned flat connection. It is stressed that the modulus of the Beltrami differential is of necessity less than one, and that solutions of the so-called Beltrami equation give rise to an orientation-preserving smooth change of local complex coordinates. In particular, the latter yields a smooth equivalence between flat complex vector bundles. The role of smooth diffeomorphisms which induce equivalent complex structures is specially emphasized. Furthermore, it is shown that, while the construction given here applies to the special case of the Virasoro algebra, the extension to flat complex vector bundles of arbitrary rank does not provide generalizations of the Beltrami differential usually considered as central objects for such non-linear symmetries.     

Real-time acoustic classification of sperm whale clicks and shipping impulses from deep-sea observatories

The automated real-time detection and classification of cetacean and anthropogenic sounds from deep-sea observatories can play a key role to study cetaceans in the field, to quantify the impact of anthropogenic sounds or to initiate mitigation measures during potentially harmful human activities. In the area of the NEMO-ONDE deep-sea observatory, sperm whales are often present together with heavy shipping. The spatial coincidence of both sound sources allows for the long term monitoring of their interaction. Some ships produce impulsive sounds and the automated separation of these impulses from sperm whale clicks is not a trivial task. As part of a detection, classification and localisation system for acoustic data from marine observatories, we present four modules performing the automated real-time classification of clicks from sperm whales and impulsive sounds produced by ships. First, two modules detect segments that contain impulsive sounds within a specifiable frequency band and return the impulses’ positions. Then, two modules classify the detected impulses as sperm whale clicks or ship impulses. Finally, at the level of 22 s segments, the classification outputs from individual impulses are combined into a decision on the presence of sperm whale clicks or ship impulses. The modules’ reliability was tested on data from the NEMO-ONDE observatory. Training and testing data were separated by more than 2 months, enabling to assess the consistency of the predictions over the long term. The automated separation between segments of the two classes was high with area under the ROC curve (AUC) values between 0.94 and 0.98.     

Classical dynamics of the Bianchi IX model with timelike singularity

We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that differences in the signs of some terms in the set of equations specifying the dynamics of both spacetimes lead to significant differences in their properties.     

Some test statistics for the structural coefficients of the multivariate linear functional relationship model

Summary For the testing problem concerning the coefficients of the multivariate linear functional relationship model, the distribution of a statistic previously proposed by A. P. Basu depends on the unknown covariance matrixV of errors, so limiting its applicability. This article proposes new test statistics with sampling distributions which are independent of the unknown parameters for the cases whereV is either unknown or known only up to a proportionality factor. The exact distributions of the test statistics are also discussed.     

Lanthanide Identity Governs Guest-Induced Dimerization in LnIII[15-MC N(L-pheHA)-5])3+ Metallacrowns

Series of lanthanide-containing metallic coordination complexes are frequently presented as structurally analogous, due to the similar chemical and coordinative properties of the lanthanides. In the case of chiral (Ln^III[15-MC _N(L-pheHA)-5])³⁺ metallacrowns (MCs), which are well established supramolecular hosts, the formation of dimers templated by a dicarboxylate guest (muconate) in solution of neutral pH is herein shown to have a unique dependence on the identity of the MC's central lanthanide. Calorimetric data and nuclear magnetic resonance diffusion studies demonstrate that MCs containing larger or smaller lanthanides as the central metal only form monomeric host-guest complexes whereas analogues with intermediate lanthanides (for example, Eu, Gd, Dy) participate in formation of dimeric host-guest-host compartments. The driving force for the dimerization event across the series is thought to be a competition between formation of highly stable MCs (larger lanthanides) and optimally linked bridging guests (smaller lanthanides).     

Efficient Imine Formation by Oxidative Coupling at Low Temperature Catalyzed by High-Surface-Area Mesoporous CeO2 with Exceptional Redox Property

High-surface-area mesoporous CeO₂ (hsmCeO₂) was prepared by a facile organic-template-induced homogeneous precipitation process and showed excellent catalytic activity in imine synthesis in the absence of base from primary alcohols and amines in air atmosphere at low temperature. For comparison, ordinary CeO₂ and hsmCeO₂ after different thermal treatments were also investigated. XRD, N₂ physisorption, UV-Raman, H₂ temperature-programmed reduction, O₂ temperature-programmed desorption, EPR spectroscopy, and X-ray photoelectron spectroscopy were used to unravel the structural and redox properties. The hsmCeO₂ calcined at 400 °C shows the highest specific surface area (158 m² g⁻¹), the highest fraction of surface coordinatively unsaturated Ce³⁺ ions (18.2 %), and the highest concentration of reactive oxygen vacancies (2.4×10¹⁵ spins g⁻¹). In the model reaction of oxidative coupling of benzyl alcohol and aniline, such an exceptional redox property of the hsmCeO₂ catalyst can boost benzylideneaniline formation (2.75 and 5.55 mmol h⁻¹ based on >99 % yield at 60 and 80 °C, respectively) in air with no base additives. It can also work effectively at a temperature of 30 °C and in gram-scale synthesis. These are among the best results for all benchmark ceria catalysts in the literature. Moreover, the hsmCeO₂ catalyst shows a wide scope towards primary alcohols and amines with good to excellent yield of imines. The influence of reaction parameters, the reusability of the catalyst, and the reaction mechanism were investigated.     

Vertically Grown Few-Layer MoS2 Nanosheets on Hierarchical Carbon Nanocages for Pseudocapacitive Lithium Storage with Ultrahigh-Rate Capability and Long-Term Recyclability

Molybdenum disulfide (MoS₂) is an intensively studied anode material for lithium-ion batteries (LIBs) owing to its high theoretical capacity, but it is still confronted by severe challenges of unsatisfactory rate capability and cycle life. Herein, few-layer MoS₂ nanosheets, vertically grown on hierarchical carbon nanocages (hCNC) by a facile hydrothermal method, introduce pseudocapacitive lithium storage owing to the highly exposed MoS₂ basal planes, enhanced conductivity, and facilitated electrolyte access arising from good hybridization with hCNC. Thus, the optimized MoS₂/hCNC exhibits reversible capacities of 1670 mAh g⁻¹ at 0.1 A g⁻¹ after 50 cycles, 621 mAh g⁻¹ at 5.0 A g⁻¹ after 500 cycles, and 196 mAh g⁻¹ at 50 A g⁻¹ after 2500 cycles, which are among the best for MoS₂-based anode materials. The specific power and specific energy, which can reach 16.1 kW and 252.8 Wh after 3000 cycles, respectively, indicate great potential in high-power and long-life LIBs. These findings suggest a promising strategy for exploring advanced anode materials with high reversible capacity, high-rate capability, and long-term recyclability.