Thermally Crosslinkable and Chemically Modifiable Aromatic Polyesters Possessing Pendant Propargyloxy Groups

New aromatic (co)polyesters containing pendant propargyloxy groups were synthesized by phase transfer‐catalyzed interfacial polycondensation of 5‐(propargyloxy)isophthaloyl chloride (P‐IPC) and various compositions of P‐IPC and isophthaloyl chloride with bisphenol A. FTIR and NMR spectroscopic data, respectively, revealed successful incorporation of pendant propargyloxy groups into (co)polyesters and formation of (co)polyesters with desired compositions. (Co)polyesters exhibited good solubility in common organic solvents such as chloroform, dichloromethane, and tetrahydrofuran and could be cast into transparent, flexible, and tough films from chloroform solution. Inherent viscosities and number average molecular weights of (co)polyesters were in the range 0.77–1.33 dL/g and 43,600–118,000 g/mol, respectively, indicating the achievement of reasonably high‐molecular weights. The 10% weight loss temperatures of (co)polyesters were in the range 390–420 °C, demonstrating their good thermal stability. (Co)polyesters exhibited T_g in the range 146–170 °C and T_g values decreased with increase in mol % incorporation of P‐IPC. The study of non‐isothermal curing by DSC indicated thermal crosslinking of (co)polyesters via propargyloxy groups. The utility of pendant propargyloxy group was demonstrated by post‐modification of the selected copolyester with 1‐(4‐azidobutyl)pyrene, 9‐(azidomethyl)anthracene, and azido‐terminated poly(ethyleneglycol) monomethyl ether via copper(I)‐catalyzed Huisgen 1,3‐dipolar cycloaddition reaction. FTIR and ¹H NMR spectra confirmed that click reaction was quantitative. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 588–597     

双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

Scanning tunnelling microscope studies of growth of RuO2（110） thin layer on Ru（0001）

This paper reports that the growth of RuO_x(110) thin layer growth on Ru(0001) has been investigated by means of scanning tunnelling microscope (STM). The STM images showed a domain structure with three rotational domains of RuO_x(110) rotated by an angle of 120℃. The as-grown RuO_x(110) thin layer is expanded from the bulk-truncated RuO_x(110) due to the large mismatch between RuO_x(110) and the Ru(0001) substrate. The results also indicate that growth of RuO_x(110) thin layer on the Ru(0001) substrate by oxidation tends first to formation of the Ru-O (oxygen) chains in the [001] direction of RuO_x(110).     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

Sensitivity analysis for discrete optimal control problems

We present local sensitivity analysis for discrete optimal control problems with varying endpoints in the case when the customary regularity of boundary conditions can be violated. We study the behavior of the optimal solutions subject to parametric perturbations of the problem.     

线性分式规划最优解集的求法

本文使用多面集的表示定理，导出了线性分式规划最优解集的结构，并给出确定全部最优解的计算步骤。     

OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.