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.     

A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters

In a fairly recent paper (2008 American Control Conference, June 11‐13, 1035‐1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal‐value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution. Copyright © 2014 JohnWiley & Sons, Ltd.     

Enhanced mechanical properties of AZ31 magnesium alloy sheets by continuous bending process after V-bending

The effects of V-bending process, continuous bending process and combination process on the microstructure and mechanical properties and formability of an AZ31 magnesium alloy sheet were investigated. The experimental results showed that no twins were found in the microstructure of all samples after processes due to the fine grain. The V-bending and continuous bending processes were proved to be an effective approach to modify the mechanical properties and formability. While the samples after the combination process exhibited better mechanical properties and formability than the single processed sample. The yield strength significantly decreased with the value of 100 MPa and the fracture elongation enhanced to 18.3% at room temperature. The Erichsen value was 5.0 mm which was significantly increased by 117% compared with as-received sample. The superior formability of combination processed samples was mainly attributed to the smaller r-value and n-value.     

Corrosion behavior of AZ91D magnesium alloy in distilled water

The corrosion of AZ91D magnesium alloy has received extensive attention due to the continuous expansion of its application field in recent years. However, the corrosion of AZ91D magnesium alloy in distilled water is relatively few. In this paper, the corrosion behavior of AZ91D magnesium alloy was studied in distilled water by electrochemical tests in combination with weight loss and surface analysis methods. The results indicated that the corrosion rate of AZ91D magnesium alloy increased with the increase of temperature and immersion time. The increase of the corrosion rate of AZ91D magnesium alloy with the increase of immersion time might be attributed to the damage of the structure of corrosion product film by hydrogen evolution, significantly accelerating the anodic process of AZ91D magnesium alloy. It was interesting that, in distilled water, the EIS of AZ91D magnesium alloy excluded an inductive arc in the low frequency region, which indicated that there was no the adsorption and desorption of aggressive ions or the damage and repair of film. The corrosion product film of AZ91D magnesium alloy in distilled water was composed of a compact inner corrosion product film and a loose outer corrosion product film.     

热处理工艺对触变成形AZ91D镁合金组织的影响

对触变成形AZ91D镁合金在不同热处理条件下的时效组织进行了研究,结果表明:随着固溶温度的增加,第二相具有较大的时效析出速度,并且析出数量较多.经415 ℃、24 h固溶处理后的试样在时效处理过程中,第二相有两种析出方式:连续与不连续析出.在180 ℃没有连续析出,温度高于200 ℃后两种方式交替进行.时效处理温度越高,第二相析出的速度越快.同时也使得连续析出在很短时间内就开始发生,并且在晶粒内部与不连续析出互相交织在一起进行.     

AuCl_3催化2-丙炔基-苯胺和丙炔反应机理的研究

采用密度泛函理论方法B3PW91研究了AuCl3催化剂作用下2-丙炔基-苯胺和丙炔环加成生成吲哚衍生物的反应机理。研究结果表明,吲哚衍生物的生成需要经过六个步骤,其中氢迁移过程具有最高的活化自由能为214.22 kJ/mol,是反应的速率控制步骤。整个反应是强放热的,AuCl3催化下反应能够顺利进行,而且AuCl3易于从产物上离去,所以,对于该反应AuCl3是一种有效的催化剂。     

Microstructure evolution of T91 heat-resistant steels after long-time aging

To investigate the evolution of microstructure damage degree and the precipitated phases of heat-resistant metal in power plant under high temperature and stress environment, the high-temperature aging tests were conducted to investigate the aging behavior of T91 steel at different temperatures and stress. The optical microscopy, scanning electron microscopy, and transmission electron microscopy were used to investigate the structure and precipitated phases, the results showed that the orientation characteristics of tempered martensite was dispersed, and the grain size is obviously increased. The density of dislocation decreased with increasing temperature and stress. The important strengthening phase of M23C6 (M=Fe, Cr) was coarsened by the diffusion of main alloying elements Cr, while the smaller size MX (M=Nb,V; X=C, N) phase distributed in the grain is relatively stable in the aging.     

Resolution,absolute configuration and antifilarial activity of coumarinyl amino alcohols

The resolution of racemic coumarinyl amino alcohols 5–10 was achieved by using the inexpensive and readily accessible chiral resolving agent N-carbethoxy-l-proline (S)-11. Direct esterification of rac-5–10 with (S)-11 furnished diastereomeric esters, which were easily separated by column chromatography. The obtained diastereomers yielded the desired enantiopure coumarinyl amino alcohols (S)-(+)-5–10 and (R)-(?)-5–10 in good yields with high enantiomeric excess on saponification. The absolute configurations were determined by X-ray crystal analysis and/or by comparison of the specific rotations. Furthermore, in in vitro antifilarial motility inhibition assays, enantiopure coumarins (S)-(+)-9, (R)-(?)-9 and (S)-(+)-10, (R)-(?)-10 were found to be less efficient in affecting the viability of macrofilariae of Brugia malayi than their racemic forms 9 and 10, respectively, indicating the synergistic effect of the enantiomers in evoking antifilarial action.     

AZ91镁合金热扩渗涂层的研究

采用固体粉末法对AZ91镁合金实施了渗Al、Al-Ce共渗．通过扫描电子显微镜、X射线衍射、能谱和腐蚀测量系统对渗层组织进行了分析．结果表明，该方法能使镁合金表面得到良好的渗层组织，有一定的工程意义．经检验渗Al、Al-Ce渗层均能提高镁合金的耐腐蚀性能，渗Al-ce的耐蚀性更是明显高于渗纯铝．