Fe3O4@C Nanotubes Grown on Carbon Fabric as a Free-Standing Anode for High-Performance Li-Ion Batteries

Recently, Li-ion batteries (LIBs) have attracted extensive attention owing to their wide applications in portable and flexible electronic devices. Such a huge market for LIBs has caused an ever-increasing demand for excellent mechanical flexibility, outstanding cycling life, and electrodes with superior rate capability. Herein, an anode of self-supported Fe₃O₄@C nanotubes grown on carbon fabric cloth (CFC) is designed rationally and fabricated through an in situ etching and deposition route combined with an annealing process. These carbon-coated nanotube structured Fe₃O₄ arrays with large surface area and enough void space can not only moderate the volume variation during repeated Li⁺ insertion/extraction, but also facilitate Li⁺/electrons transportation and electrolyte penetration. This novel structure endows the Fe₃O₄@C nanotube arrays stable cycle performance (a large reversible capacity of 900 mA h g⁻¹ up to 100 cycles at 0.5 A g⁻¹) and outstanding rate capability (reversible capacities of 1030, 985, 908, and 755 mA h g⁻¹ at 0.15, 0.3, 0.75, and 1.5 A g⁻¹, respectively). Fe₃O₄@C nanotube arrays still achieve a capacity of 665 mA h g⁻¹ after 50 cycles at 0.1 A g⁻¹ in Fe₃O₄@C//LiCoO₂ full cells.     

The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.     

Metal‐Free Reaction of ortho‐Carbonylated Alkynyl‐Substituted Arylaldehydes with Common Amines: Selective Access to Functionalized Isoindolinone and Indenamine Derivatives

Herein we describe a reaction of ortho‐carbonylated alkynyl‐substituted arylaldehydes with common primary amines that can provide functionalized isoindolinone and 3‐hydroxylindenamine products in high yields. Depending on the substituent size of primary amines, two distinct reaction pathways were exploited selectively, that are, an initial aza‐conjugate addition followed by hydrogen transfer to access isoindolinone framework and a unique oxa‐conjugate addition followed by Petasis–Ferrier rearrangement to afford indenamine derivatives. In the presence of Et₃N, the reaction property of small primary amines was changed, proceeding to afford 3‐hydroxylindenamine derivatives efficiently. These products contain interesting substructures that exist in many natural products and bioactive molecules. The reaction features contain the use of transition‐metal‐free catalysts, simple operation, broad substrate scope, and product diversity.     

Rational Design for Rotaxane Synthesis through Intramolecular Slippage: Control of Activation Energy by Rigid Axle Length

We describe a new concept for rotaxane synthesis through intramolecular slippage using π‐conjugated molecules as rigid axles linked with organic soluble and flexible permethylated α‐cyclodextrins (PM α‐CDs) as macrocycles. Through hydrophilic–hydrophobic interactions and flipping of PM α‐CDs, successful quantitative conversion into rotaxanes was achieved without covalent bond formation. The rotaxanes had high activation barrier for their de‐threading, so that they were kinetically isolated and derivatized even under conditions unfavorable for maintaining the rotaxane structures. ¹H NMR spectroscopy experiments clearly revealed that the restricted motion of the linked macrocycle with the rigid axle made it possible to control the kinetic stability by adjusting the length of the rigid axle in the precursor structure rather than the steric bulkiness of the stopper unit.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

Multi-stacked organic light-emitting diodes using zinc oxide nanoparticle interfacial layers

Stacked organic light-emitting diodes (SOLEDs) with 30-nm nanoparticle (NP) interfacial layers were investigated. Zinc oxide (ZnO) was used as an interfacial layer between two green polymer (GP) layers. SOLEDs with NP interfacial layers had higher device efficiency than did a single-unit device due to the high probability of exciton recombination that originated from the Auger electron-assisted energy up-conversion process. Although the current density and luminance of SOLEDs with ZnO NP interfacial layers were smaller than those of the reference device, the efficiency was doubled because of the big band alignment difference and the large band gap between GP and ZnO NP interfacial layers, which induced more radiative-exciton recombination.