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.     

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     

Highly efficient synthesis of polysubstituted 1,2-dihydroquinolines via cascade reaction of α-ketoesters with arylamines mediated by iodine

An efficient strategy enabling the construction of polysubstituted 1,2-dihydroquinoline derivatives mediated by the commercially available, economical, and environmentally benign iodine (3 mol %) under mild conditions was developed. Various arylamines and α-ketoesters could participate in this cascade reaction, and the desired products were obtained in excellent yields up to 98%.     

Efficient One‐Pot Synthesis of Hydroxyflavanones by Cyclization and O‐Demethylation of Methoxychalcones

An efficient one‐pot method for the synthesis of hydroxyflavanones is described. Methoxychalcones are treated with 36% HBr to afford cyclization and regioselective O‐demethylation products (2a–i) while cyclization and complete O‐demethylation products (3a–e) are obtained in the presence of 45% HI.     

Diffusion Mechanism of As‐spun Polyacrylonitrile Fiber in a Dimethyl Sulfoxide‐Water Coagulation Bath

In this paper, the diffusion mechanism of as‐spun PAN fiber was investigated in dimethyl sulfoxide‐water by determining the dynamic compositions of the fibers and the diffusion coefficients of solvent and nonsolvent during coagulation. The diffusion process could be divided into two stages. Results showed that the first stage of the diffusion process was the most important during the whole process, which was fundamental to further study on the formation mechanism. Also, compared with wet spinning, the dry‐jet wet spinning method had the advantage of mild coagulating at a high jet‐stretch. At high concentrations, the diffusion coefficients increased and the ratio of solvent diffusion coefficient to nonsolvent diffusion coefficient decreased; an increasing temperature resulted in the increase of both diffusion coefficients with a decrease in their ratios. To some extent, for the PAN‐DMSO‐water system, the more the ratios D_s*/D_n* tended to 1, the more the cross‐section shapes of as‐spun PAN fiber tended to be circular.     

Further Studies on the Anionic Copolymerization of Styrene and Glycidyl Methacrylate in Toluene

Sequential anionic copolymerization of styrene and glycidyl methacrylate (GMA) was performed with the protection of argon under normal pressure, where styrene, GMA, toluene, THF, n-butyllithium and a small amount of lithium chloride (LiCl) were used as first monomer, second monomer, solvent, polar reagent, initiator and additive, respectively. Polystyrene-b-poly(glycidyl methacrylate) diblock copolymers (PS-b-PGMA) with well-defined structure and narrow molecular weight distribution were prepared by the copolymerization reaction of poly(styryl)lithium with GMA under certain temperatures. The copolymers were characterized using gel permeation chromatography (GPC), ¹H-NMR, ¹³C-NMR, thin layer chromatography (TLC) and hydrochloric acid-dioxane argentimetric methods. The effects of additives, copolymerization temperature and THF dosage on the copolymerization were studied. No chain transfer reaction of anionic polymerization of styrene in toluene was observed. Slightly broader molecular weight distribution of PS-b-PGMA was observed with the increase the GMA repeat units. Using THF/toluene blend solvent could reduce the polydispersity index (M _w /M _n ) and dissolve the copolymer better than toluene alone. Lower temperature (< -40°C) and LiCl are required to prepare PS-b-PGMA with narrower molecular weight distribution.