Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

First-Principles Investigation of β-FeOOH for Hydrogen Evolution: Identifying Reactive Sites and Boosting Surface Reactions

Akaganeite (β-FeOOH) is a widely investigated candidate for photo(electro)catalysis, such as water splitting. Nevertheless, insights into understanding the surface reaction between water and β-FeOOH, in particular, the hydrogen evolution reaction (HER), are still insufficient. Herein, a set of first-principles calculations on pristine β-FeOOH and halogen-substituted β-FeOOH are applied to evaluate the HER performance through the computational hydrogen electrode model. The results show that the HER on β-FeOOH tends to occur at Fe sites on the (010) surface, and palladium and nickel are found to serve as excellent co-catalysts to boost the HER process, due to the remarkably reduced free energy change of hydrogen adsorption upon loading on the surface of β-FeOOH, demonstrating great potential for efficient water splitting.     

Nitrogen Donor Protection for Atomically Precise Metal Nanoclusters

Surface organic ligands are critical in dictating the structures and properties of atomically precise metal nanoclusters. In contrast to the conventionally used thiolate, phosphine and alkynyl ligands, nitrogen donor ligands have not been used in the protection for well-defined metal nanoclusters until recently. This review focuses on recent developments in atomically precise metal nanoclusters stabilized by different types of nitrogen donor ligands, in which the synthesis, total structure determination and various properties are covered. We hope that this review will provide insights into the rational design of N donor-protected metal nanoclusters in terms of structural and functional modulation.     

Fractional-order sliding mode control of uncertain QUAVs with time-varying state constraints

Nonlinear Dynamics - In this paper, a novel robust fractional-order sliding mode (FOSM)-based state constrained control scheme is designed for uncertain quadrotor UAVs (QUAVs). Model uncertainties...     

Small molecule‐mediated glass transition of acrylic copolymers: Effect of hydrogen bonding strength on glass transition temperature

Poly(styrene‐co‐ethyl acrylate) [P(St‐co‐EA)] with different ratios of St/EA was mixed with the small molecule 4,4′‐thio‐bis(6‐tert‐butyl‐m‐methyl phenol) (AO300) to investigate the influence of hydrogen bonding strength on the glass transition behavior. The glass transition temperature (T_g) linearly increased after adding AO300, and the slope value decreased with increased St/EA ratio. All lines could be extended to 62 °C, demonstrating that T_g of the small molecule in situ detected by the polymer chain was much higher than that by small molecule itself (29 °C). Fourier transform infrared spectroscopy analysis showed that the small molecules began to be self‐associated at a concentration where the hydrogen bonded carbonyl ratio of the bulk polymer was approximately 0.5 and irrespective of the St/EA ratio. Above the critical loading, the mixture's T_g negatively deviated from the linearly extended lines because of self‐association of the small molecules. The apparent T_g of AO300 was found to strongly depend on intermolecular hydrogen bonding number and strength. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 400–408     

Automated determination of size and morphology information from soot transmission electron microscope (TEM)-generated images

The thermophoretic sampling of particulates from hot media, coupled with transmission electron microscope (TEM) imaging, is a combined approach that is widely used to derive morphological information. The identification and the measurement of the particulates, however, can be complex when the TEM images are of low contrast, noisy, and have non-uniform background signal level. The image processing method can also be challenging and time consuming, when the samples collected have large variability in shape and size, or have some degree of overlapping. In this work, a three-stage image processing sequence is presented to facilitate time-efficient automated identification and measurement of particulates from the TEM grids. The proposed processing sequence is first applied to soot samples that were thermophoretically sampled from a laminar non-premixed ethylene-air flame. The parameter values that are required to be set to facilitate the automated process are identified, and sensitivity of the results to these parameters is assessed. The same analysis process is also applied to soot samples that were acquired from an externally irradiated laminar non-premixed ethylene-air flame, which have different geometrical characteristics, to assess the morphological dependence of the proposed image processing sequence. Using the optimized parameter values, statistical assessments of the automated results reveal that the largest discrepancies that are associated with the estimated values of primary particle diameter, fractal dimension, and prefactor values of the aggregates for the tested cases, are approximately 3, 1, and 10 %, respectively, when compared with the manual measurements.     

Ultrathin Mn Doped Ni-MOF Nanosheet Array for Highly Capacitive and Stable Asymmetric Supercapacitor

In this study, we demonstrate that an Mn-doped ultrathin Ni-MOF nanosheet array on nickel foam (Mn_0.1-Ni-MOF/NF) serves as a highly capacitive and stable supercapacitor positive electrode. The Mn_0.1-Ni-MOF/NF shows an areal capacity of 6.48 C cm⁻² (specific capacity C: 1178 C g⁻¹) at 2 mA cm⁻² in 6.0 m KOH, outperforming most reported MOF-based materials. More importantly, it possesses excellent cycle stability to maintain 80.6 % capacity after 5000 cycles. An asymmetric supercapacitor device utilizing Mn_0.1-Ni-MOF/NF as the positive electrode and activated carbon as the negative electrode attains a high energy density of 39.6 Wh kg⁻¹ at 143.8 Wkg⁻¹ power density with a capacitance retention of 83.6 % after 5000 cycles.