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.     

工业催化:选择性提升策略

工业催化直接或间接贡献了世界GDP的20%-30%,推动了产业变革和社会进步.对于工业催化,开发高活性、高选择性和高稳定性的多相催化剂至关重要,而选择性是最主要的挑战.因为实现催化选择性的精确控制是绿色化学的重要概念之一,更是工业催化可持续发展的重要驱动力;而且,选择性不仅决定了催化过程的原子经济性,也影响到后续分离过程的能耗.针对多数工业催化反应存在'活性越高、选择性越低'的相互制约与矛盾问题,本文以若干能源化工催化反应为例,试图总结催化选择性提升的一般策略,以期为有关工业应用的催化新过程提供科学参考.多相催化一般经历与反应物有关的步骤(反应物的外扩散、内扩散和化学吸附)、与反应有关的步骤(活化和表面反应)、以及与产物相关的步骤(产物脱附、内扩散和外扩散).本文依此归纳并举例说明提高选择性的一般策略.在汽油催化吸附脱硫中,主要利用了催化剂中零价镍-氧化锌耦合活性中心的选择吸附策略,使零价镍优先吸附含硫化合物,从而实现选择性脱硫而不饱和烯烃.在甲苯和甲醇侧链烷基化反应中,主要利用了特定空间分布的酸碱吸附位,实现吸附甲苯和稳定甲醛中间体的协同匹配.在乙苯脱乙基型二甲苯异构化反应中,主要利用了双床层对催化剂功能的分离策略,在不同的择形催化剂床层中分别进行乙苯脱乙基反应和二甲苯异构化反应,从而提高对二甲苯的产量.在苯选择加氢制环己烯反应中,主要利用强化产品脱附的策略,促进环己烯产品从亲水改性的催化剂表面脱附,实现环己烯选择性的提升.这些炼油与化工研究案例中同时存在多个连串-平行反应,主要是利用吸附中心、反应中心在时间或空间上的耦合、解耦或限域策略,调控不同途径的扩散能垒、反应能垒,实现了催化剂选择性的提升.多相催化多是复杂过程,基于提高选择性的初步认识,还要结合具体复杂催化过程,系统研究单策略以及多策略组合作用下的选择催化过程,实现在合理时间尺度、空间尺度上设计高选择性的催化剂,而这本质上是一种介尺度催化.     

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.