The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

An AIE-Active probe for detection and bioimaging of pH values based on lactone hydrolysis reaction

Cellular pH homeostasis is essential for many physiological and pathological processes. pH monitoring is helpful for the diagnosis, treatment and prevention of disorders and diseases. Herein, we developed a ratiometric fluorescent pH probe (TCC) based on a coumarin derivative containing a highly active lactone ring. TCC exhibited a typical AIE effect and emitted blue fluorescence under weak acidic condition. When under weak basic condition, the active lactone moiety underwent a hydrolysis reaction to afford a water-soluble product, which gave red-shifted emission. The emission color change from blue through cyan and then to yellow within pH 6.5–9.0 which is approximate to the biological pH range. And the fluorescence color change along with pH value is reversible. Furthermore, TCC was successfully utilized in the detection of the intracellular pH change of live HeLa cells, which indicated that TCC had practical potential in biomedical research.

     

石墨烯负载的氧配位钴单原子稳定金属锂负极

Lithium (Li)-based batteries are the dominant energy source for consumer electronics, grid storage, and electrified transportation. However, the development of batteries based on graphite anodes is hindered by their limited energy density. With its ultrahigh theoretical capacity (3860 mAh∙g⁻¹), low redox potential (−3.04 V), and satisfactorily low density (0.54 g∙cm⁻³), Li metal is the most promising anode for next-generation high-energy-density batteries. Unfortunately, the limited cycling life and safety issues raised by dendrite growth, unstable solid electrolyte interphase, and "dead Li" have inhibited their practical use. An effective strategy is to develop a suitable lithiophilic matrix for regulating initial Li nucleation behavior and controlling subsequent Li growth. Herein, single-atom cobalt coordinated to oxygen sites on graphene (Co-O-G SA) is demonstrated as a Li plating substrate to efficiently regulate Li metal nucleation and growth. Owing to its dense and more uniform lithiophilic sites than single-atom cobalt coordinated to nitrogen sites on graphene (Co-N-G SA), high electronic conductivity, and high specific surface area (519 m²∙g⁻¹), Co-O-G SA could significantly reduce the local current density and promote the reversibility of Li plating and stripping. As a result, the Co-O-G SA based Li anodes exhibited a high Coulombic efficiency of 99.9% at a current density of 1 mA∙cm⁻² with a capacity of 1 mAh∙cm⁻², and excellent rate capability (high current density of 8 mA∙cm⁻²). Even at a high plating capacity of 6 mAh∙cm⁻², the Co-O-G SA electrode could stably cycle for an ultralong lifespan of 1300 h. In the symmetric battery, the Co-O-G SA based Li anode (Co-O-G SA/Li) possessed a stable voltage profile of 18 mV for 780 h at 1 mA∙cm⁻², and even at a high current density of 3 mA∙cm⁻², its overpotential maintained a small hysteresis of approximately 24 mV for > 550 h. Density functional theory calculations showed that the surface of Co-O-G SA had a stronger interaction with Li atoms with a larger binding energy, −3.1 eV, than that of Co-N-G SA (−2.5 eV), leading to a uniform distribution of metallic Li on the Co-O-G SA surface. More importantly, when matched with a sulfur cathode, the resulting Co-O-G SA/lithium sulfur full batteries exhibited a high capacity of 1002 mAh∙g⁻¹, improved kinetics with a small polarization of 191 mV, and an ultralow capacity decay rate of 0.036% per cycle for 1000 cycles at 0.5C (1C = 1675 mA∙g⁻¹) with a steady Coulombic efficiency of nearly 100%. Therefore, this work provides novel insights into the coordination environment of single atoms for the chemistry of Li metal anodes for high-energy-density batteries.     

Manage Pension Deficit with Heterogeneous Insurance

This paper considers a positive and increasing pension deficit of a certain pay-as-you-go (PAYG) pension system, and tries to make up for this deficit by using heterogeneous insurance. The positive pension deficit is formulated as a mathematical function in continuous time. The surplus of an appropriate heterogeneous insurance is described by diffusion approximation of a Cramér-Lundberg process. The system of extended Hamilton-Jacobi-Bellman equations under mean-variance criterion is established. The closed-form solution and optimal surplus-multiplier of heterogenous insurance are obtained. Some interpretations further explain the theoretical values of the results.

     

Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Enhanced Power Density of Alcohol Biofuel Cell by Polymer-assisted Crosslinks of 3D Graphene on Carbon Paper as the Bioanode

Herein, we successfully construct the 3D biocompatible graphene through crosslinking 2D graphene nanosheet onto carbon fiber paper with poly(diallyldimethylammonium chloride) (PDDA) as anode of the alcohol biofuel cell. Compared with the bioanode without 3D graphene, the current density and output power of PDDA-graphene-ADH bioanode is increased by 23 % and 41 % at a high concentration of ethanol at pH 8.9, suggesting the stabilization role of graphene in enzyme loading. The study provides us a deep analysis on structures and performances of the bioanode incl. electrochemistry, X-ray photoelectron spectra, and atomic force microscopy images, which is significant to develop the new methods to construct 3D porous electrodes in energy conversion device.     

Multi-scale Fractured Coal Gas–Solid Coupling Model and Its Applications in Engineering Projects

With coal mining entering the geological environment of “high stress, rich gas, strong adsorption and low permeability,” the difficulty of joint coal and gas extraction clearly augments, the risk of solid–gas coupling dynamic disasters greatly increases, and the underlying mechanisms become more complex. In this paper, based on the characteristics of coal’s multi-scale structure and spatiotemporal variation, the multi-scale fractured coal gas–solid coupling model (MSFM) was built. In this model, the interaction between coal matrix and its fractures and the mechanical characteristics of gas-bearing coal were considered, as well as their coupling relationship. By MATLAB software, the stress–damage–seepage numerical computation programs were developed, which were applied into Comsol Multiphysics to simulate gas flow caused by coal mining. The simulation results showed the spatial variability of coal elastic modulus and cross-flow behaviors of coal seam gas, which were superior to the results of traditional gas–solid coupling model. And the numerical results obtained from MSFM were closer to the measured results in field, while the computation results of traditional model were slightly higher than the measured results. Furthermore, the MSFM in a large scale was verified by field engineering project.     

Semiconducting Polymer Dots with Dual-Enhanced NIR-IIa Fluorescence for Through-Skull Mouse-Brain Imaging

Fluorescence probes in the NIR-IIa region show drastically improved imaging owing to the reduced photon scattering and autofluorescence in biological tissues. Now, NIR-IIa polymer dots (Pdots) are developed with a dual fluorescence enhancement mechanism. First, the aggregation induced emission of phenothiazine was used to reduce the nonradiative decay pathways of the polymers in condensed states. Second, fluorescence quenching was minimized by different levels of steric hindrance to further boost the fluorescence. The resulting Pdots displayed a fluorescence QY of ca. 1.7 % in aqueous solution, suggesting an enhancement of ca. 21 times in comparison with the original polymer in tetrahydrofuran (THF) solution. Small-animal imaging by using the NIR-IIa Pdots exhibited a remarkable improvement in penetration depth and signal to background ratio, as confirmed by through-skull and through-scalp fluorescent imaging of the cerebral vasculature of live mice.