A note on the limiting weak-type behavior for maximal operators

We study the following open question raised by Janakiraman in (2006): for and , what is the limiting behavior of

as ? In this note, we give a complete answer to this question.

     

Dynamically Resettable Electrode-Electrolyte Interface through Supramolecular Sol-Gel Transition Electrolyte for Flexible Zinc Batteries

Flexible batteries based on gel electrolytes with high safety are promising power solutions for wearable electronics but suffer from vulnerable electrode-electrolyte interfaces especially upon complex deformations, leading to irreversible capacity loss or even battery collapse. Here, a supramolecular sol-gel transition electrolyte (SGTE) that can dynamically accommodate deformations and repair electrode-electrolyte interfaces through its controllable rewetting at low temperatures is designed. Mediated by the micellization of polypropylene oxide blocks in Pluronic and host-guest interactions between α-cyclodextrin (α-CD) and polyethylene oxide blocks, the high ionic conductivity and compatibility with various salts of SGTE afford resettable electrode-electrolyte interfaces and thus constructions of a series of highly durable, flexible aqueous zinc batteries. The design of this novel gel electrolyte provides new insights for the development of flexible batteries.     

Braided Fiber Current Collectors for High-Energy-Density Fiber Lithium-Ion Batteries

Fiber lithium-ion batteries represent a promising power strategy for the rising wearable electronics. However, most fiber current collectors are solid with vastly increased weights of inactive materials and sluggish charge transport, thus resulting in low energy densities which have hindered the development of fiber lithium-ion batteries in the past decade. Here, a braided fiber current collector with multiple channels was prepared by multi-axial winding method to not only increase the mass fraction of active materials, but also to promote ion transport along fiber electrodes. In comparison to typical solid copper wires, the braided fiber current collector hosted 139 % graphite with only 1/3 mass. The fiber graphite anode with braided current collector delivered high specific capacity of 170 mAh g⁻¹ based on the overall electrode weight, which was 2 times higher than that of its counterpart solid copper wire. The resulting fiber battery showed high energy density of 62 Wh kg⁻¹.     

Characterization of Column Hold-Up Volume with Static and Dynamic Methods on an Immobilized Polysaccharide-Based Chiral Stationary Phase

Polysaccharide-based chiral stationary phases (CSPs) are efficient for enantioseparation of many chiral compounds. Immobilized polysaccharide CSP, as used in the Chiralpak IA column, is a new configuration that was recently introduced for application in chiral separation. As shown in several previous studies, the characteristics of Chiralpak IA columns cannot be simply extrapolated from the coated version. In this study, hold-up volume of a Chiralpak IA column was evaluated by static and dynamic methods. The static pyconometry method gave similar hold-up volumes either as an average value from a range of solvents or a direct measurement from the carbon tetrachloride-isopropanol (IPA) solvent pair. The dynamic method with 1,3,5-tri-tert-butylbenzene (TTBB) was influenced by the ratio of n-hexane and 2-propanol in the mobile phase but not by the dissolving solvent of TTBB. The two methods resulted in the same hold-up volume of ∼3.0 mL. TTBB showed weaker retention on the IA column after correction of isobaric thermal expansion of the mobile phase. During temperature variations in the range of 15–50 °C, the hold-up volume of TTBB was highly reproducible. Results of this study improve our understanding of the chromatographic features of the immobilized polysaccharide IA column.     

Dimensional and Optoelectronic Tuning of Lead-free Perovskite Cs3Bi2I9−nBrn Single Crystals for Enhanced Hard X-ray Detection

Inorganic Bi-based perovskites have shown great potential in X-ray detection for their large absorption to X-rays, diverse low-dimensional structures, and eco-friendliness without toxic metals. However, they suffer from poor carrier transport properties compared to Pb-based perovskites. Here, we propose a mixed-halogen strategy to tune the structural dimensions and optoelectronic properties of Cs₃Bi₂I_9−nBr_n (0≤n≤9). Ten centimeter-sized single crystals are successfully grown by the Bridgman technique. Upon doping bromine to zero-dimensional Cs₃Bi₂I₉, the crystal transforms into a two-dimensional structure as the bromine content reaches Cs₃Bi₂I₈Br. Correspondingly, the optoelectronic properties are adjusted. Among these crystals, Cs₃Bi₂I₈Br exhibits negligible ion migration, moderate resistivity, and the best carrier transport capability. The sensitivities in 100 keV hard X-ray detection are 1.33×10⁴ and 1.74×10⁴ μC Gy_air⁻¹ cm⁻² at room temperature and 75 °C, respectively, which are the highest among all reported bismuth perovskites. Moreover, the lowest detection limit of 28.6 nGy_air s⁻¹ and ultralow dark current drift of 9.12×10⁻⁹ nA cm⁻¹ s⁻¹ V⁻¹ are obtained owing to the high ionic activation energy. Our work demonstrates that Br incorporation is an effective strategy to enhance the X-ray detection performance by tuning the dimensional and optoelectronic properties.     

Photoenolization of o‐Methylvalerophenone Ester Derivative

Photolysis of ester 1 in argon‐saturated methanol and acetonitrile does not produce any product, whereas irradiation of 1 in oxygen‐saturated methanol yields peroxide 2 . Laser flash photolysis studies demonstrate that 1 undergoes intramolecular H atom abstraction to form biradical 3 (λ _max ~ 340   nm), which intersystem crosses to form photoenols Z ‐ 4 and E ‐ 4 (λ _max ~ 380   nm). Photoenols 4 decay by regenerating ester 1 . With the aid of density functional theory calculations, it was concluded the photoenol E ‐ 4 does not undergo spontaneous lactonization or electrocyclic ring closure because the transition state barriers for these reactions are too large to compete with reketonization of E ‐ 4 to form 1 .     

Modification of microcrystalline cellulose with pyridone derivatives for removal of cationic dyes from aqueous solutions

Microcrystalline cellulose (MCC) was modified with pyridone derivatives such as pyridone diester (PDE) and pyridone diacid (PDA) by using succinic acid anhydride as a linker. The modified MCCs were characterized by the fourier transform infrared spectroscopy, scanning electron microscopy, thermal gravimetric analysis, elemental analysis and solid state ¹³C NMR. The adsorption capacities of the modified MCCs to cationic dyes were examined by using methylene blue (MB) as a model dye. It was found that the kinetic adsorption data followed the pseudo-second-order kinetic model, and the adsorption equilibriums were reached less than 10 min. The isothermal adsorption data were fitted with the Langmuir isotherm model very well, from which the maximum adsorption capacities of the MCCs modified with PDE and PDA were determined to be 101.01 and 142.86 mg/g, respectively. Further investigation showed that the modified MCCs were pH-dependent for adsorption of MB in aqueous solutions. The modified MCCs could be used for removal of MB from an aqueous solution at pH 8, and reused by regeneration in an acidic solution. It was tested that the modified MCCs had a high reusability for removal of MB from aqueous solutions, and still maintained high adsorption capacities even after multiple cycles of desorption–adsorption processes. Hence, the MCCs modified with PDE and PDA could be an effective and efficient approach to removal of cationic dyes from aqueous solutions.     

Elastin-calmodulin scaffold for protein microarray fabrication

In this work, we report a new method to reversibly immobilize proteins to a surface in a functionally active orientation directly from cell lysate by employing a fusion protein consisting of a thermal-responsive elastin (ELP) domain as the surface anchor and a calcium-responsive calmodulin (CalM) domain for protein capturing. Incorporation of an M13 tag into recombinant proteins enables not only easy surface immobilization but also direct purification from cell lysates. The feasibility of concept was demonstrated using the M13-tagged yellow fluorescent protein (M13-YFP). The ELP-CalM functionalized surfaces were shown to capture M13-YFP directly from cell lysate through the specific calmodulin-M13 association in a calcium-dependent manner. We also demonstrated that immobilization is reversible; the bound proteins were released from the surface in the presence of EDTA.     

具有泛函解的二维非线性双曲型守恒律组

本文考虑初值是分片常数且间断线经过原点的一类二维非线性双曲型守恒律组．解包含一类新的波──称之为Dirac-接触波．本文给出了这种Dirac-接触波的熵条件,方程组的解可以视为上有界线性泛函.     

Synthesis of Low‐Viscosity Ionic Liquids for Application in Dye‐Sensitized Solar Cells

Two types of ionic liquids (ILs), 1‐(3‐hexenyl)‐3‐methyl imidazolium iodide and 1‐(3‐butenyl)‐3‐methyl imidazolium iodide, are synthesized by introducing an unsaturated bond into the side alkyl chain of the imidazolium cation. These new ionic liquids exhibit high thermal stability and low viscosity (104 cP and 80 cP, respectively). The molecular dynamics simulation shows that the double bond introduced in the alkane chain greatly changes the molecular system space arrangement and diminishes the packing efficiency, leading to low viscosity. The low viscosity of the synthesized ionic liquids would enhance the diffusion of redox couples. This enhancement is detected by fabricating dye‐sensitized solar cells (DSSCs) with electrolytes containing the two ILs and I₂. The highest efficiency of DSSCs is 6.85 % for 1‐(3‐hexenyl)‐3‐methyl imidazolium iodide and 5.93 % for 1‐(3‐butenyl)‐3‐methyl imidazolium iodide electrolyte, which is much higher than that of 5.17 % with the counterpart 1‐hexyl‐3‐methyl imidazolium iodide electrolyte.