航空器供油问题中完全逆序类中的多项式时间可解类

航空器供油问题是一类非线性组合优化问题,其目标函数为分式形式,该问题目前不存在多项式时间算法,也未被证明是NP完全问题。一般可以用置换来刻画n架飞机的一个供油顺序。该问题中有一类实例被称为“完全逆序类”,“完全逆序类”用动态规划算法求解计算时间为O(n2ⁿ),具有指数时间复杂度。本文通过对该“完全逆序类”问题做进一步分析,发现在“完全逆序类”中也存在着多项式时间可解的情况。定理1研究一类一次可解的情况,若问题满足定理1的条件,则求解一次即可找到其最优解;定理2研究一类多项式时间可解的情况,当问题满足定理2的条件时,其最优解可在多项式时间内获得。     

考虑溯源系统应用的优质农产品双渠道供应链决策研究

优质农产品溯源系统的引入,既能提升有效供给、缩短流通时间,又能降低流通中的数量损耗和价值损失,由此带来了双渠道供应链系统在投资、销售、定价等方面的系列决策问题。考虑制造商开辟电子渠道、从溯源系统降低流通损耗和提高质量出发,分别构建制造商主导型的双渠道供应链决策模型。通过对比分析应用前后各成员在投资、定价及销售方面的最优策略,得到相关的核心边界值。数值仿真结果表明:核心边界值主要与双重损耗的改善程度及其他参数相关,各成员及系统接受溯源系统的应用成本不同,应用成本对各渠道销量的影响程度亦不相同,但各成员调整定价的应用成本边界值是一致的。     

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.     

理想弹塑性固体Riemann问题的解结构与初值条件

针对理想弹塑性固体材料的一维Riemann问题，在不考虑真空的情况下，讨论其所有可能存在的解结构，给出每一种解结构下对应的初值条件且证明该系列初值条件的完备性，即任意给定的物理量初值均有且只有一种解结构与之对应.基于该理论，在设计精确或近似理想弹塑性Riemann问题求解器时，可以依据初值条件对任意物理量初值直接判断其对应的解结构，从而提高求解器的精度和效率.数值试验验证了该系列初值条件的正确性和有效性.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

Catalytic cross-coupling of aniline by pyrite and dissolved oxygen under alkaline conditions

Pyrite catalyzes oxidation of various organic contaminants by dissolved oxygen (DO) under acidic conditions; however, the catalytic mechanism under alkaline conditions is still not clear. In this study, we observe increased oxidation rates of aniline with increasing pHs (7.0–11.0). Electron paramagnetic resonance (EPR) analysis and quenching experiments rule out contributions of •OH, O₂^•−, ¹O₂ and Fe (IV) to aniline oxidation and suggest that the Fe (III)–OOH peroxo and/or H₂O₂ are the primary oxidative species in the oxidation of aniline at pH 11.0. In addition, 200 mg L⁻¹ H₂O₂ does not apparently increase the oxidation rate of aniline, which also rules out the predominant contribution of the produced H₂O₂ to aniline oxidation. We therefore suggest that the Fe (III)–OOH peroxo is indeed the primary oxidative species in the pyrite–DO system under alkaline conditions. Analyses of solid total organic carbon (TOC), gas chromatography–mass spectrometry and Fourier-transform infrared spectroscopy further reveal that more than 83.3% aniline has been polymerized to polyaniline, instead of being mineralized into CO₂ and H₂O, indicating that H-abstraction from aniline by the Fe (III)–OOH peroxo is an important step in the oxidation of aniline under alkaline conditions. This study provides new insight into the oxidative species in the pyrite–DO system, and opens a new door for organic degradations under alkaline conditions.     

On the Effect of the Various Assumptions and Approximations used in Molecular Simulations on the Properties of Bio-Molecular Systems: Overview and Perspective on Issues

Computer simulations of molecular systems enable structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic or supra-molecular level and plays an increasingly important role in chemistry, biology and physics. To interpret the results of such simulations appropriately, the degree of uncertainty and potential errors affecting the calculated properties must be considered. Uncertainty and errors arise from (1) assumptions underlying the molecular model, force field and simulation algorithms, (2) approximations implicit in the interatomic interaction function (force field), or when integrating the equations of motion, (3) the chosen values of the parameters that determine the accuracy of the approximations used, and (4) the nature of the system and the property of interest. In this overview, advantages and shortcomings of assumptions and approximations commonly used when simulating bio-molecular systems are considered. What the developers of bio-molecular force fields and simulation software can do to facilitate and broaden research involving bio-molecular simulations is also discussed.     

不同退火条件对PEALD制备的Ga2O3薄膜特性的影响

利用等离子增强原子层沉积技术(PEALD)在c面蓝宝石衬底上制备了氧化镓(Ga₂O₃)薄膜,研究了退火气氛(v(N₂)∶v(O₂)=1∶1(体积比)、空气和N₂)及退火时间对Ga₂O₃薄膜晶体结构、表面形貌和光学性质的影响。研究结果表明,退火前的氧化镓处于亚稳态,不同退火气氛下退火后晶体结构发生明显改变,而且退火气氛中N₂比例增加有利于Ga₂O₃重结晶。在N₂气氛下退火达到30 min,薄膜结构已由亚稳态转变成择优取向的β-Ga₂O₃。而且表面形貌分析表明,退火30 min后表面形貌开始趋于稳定,表面晶粒密度不再增加。另外实验样品在 400~800 nm的平均透射率几乎是100%,且光吸收边陡峭。采用N₂气氛退火,对于富氧环境下沉积的Ga₂O₃更利于薄膜表面原子迁移,以及择优取向Ga₂O₃重结晶。