Bellman最优性原理——论动态规划(Ⅰ)

对于Bellman最优性原理,本文举出实例表明:(1)策略不一定有(合理的)子策略;(2)子策略不一定存在最优子策略;(3)最优策略不一定有最优子策略;(4)用最短路与反证法来论述最优性原理的正确性,不能肯定成立;(5)Bellman最优性原理与其递推公式并不等价。 讨论四类最优策略之后,给出最优性原理与递推公式等价的一个充分性定理。     

拓扑线性空间中的Drop定理和Phelps引理以及Ekeland变分原理

将Phelps引理, Ekeland变分原理, Pareto有效性定理推广到拓扑线性空间,同时证明了这三个定理与郑喜印证明的拓扑线性空间中的Drop定理彼此等价．     

直键与弯键的对称性判据

一穹键的提出人们认为,杂化轨道(HAO)角函数的最大值方向(亦即HAO的方向)指向与之键合的原子,这样形成的化学键称为“直键”。但环丙烷分子中的三个碳原子构成三元环,有60°的键角。而任意两个正交的S-P杂化轨道之间的夹角θ都不可能小于90°,因而形成C-C键的HAO,不可能指向键合原子,环上的C-C键不可能是直键,而是“弯键”(BentBond)。通常,人们认为张力分子环上的键是弯键,其他的键为直键。     

Overwriting information: Correlations,physical costs,and environment models

In this sequel to our previous study of the entropic and energetic costs of information erasure [N.G. Anderson, Phys. Lett. A 372 (2008) 5552], we consider direct overwriting of classical information encoded in a quantum-mechanical memory system interacting with a heat bath. Lower bounds on physical costs of overwriting – in both “single-shot” and “sequential” overwriting scenarios – are obtained from globally unitary quantum dynamics and entropic inequalities alone, all within a referential approach that grounds information content in correlations between physical system states. A heterogeneous environment model, required for consistent treatment of sequential overwriting, is introduced and used to establish and relate bounds for various cases.     

Use of the Bell–Evans–Polanyi Principle to predict regioselectivity of nucleophilic aromatic photosubstitution reactions

Regioselectivity of nucleophilic aromatic photosubstitution has been shown experimentally to depend upon activation energies of the competing transition states. Computational means of determining relative activation energies were sought, therefore, in order to predict regioselectivity. Optimization of the three triplet transition states of 2-chloro-4-nitroanisole with hydroxide ion gave energies of insufficient accuracy to predict regioselectivity. Computed enthalpy changes from the first triplet transition state to the triplet σ-complexes correlated precisely with the experimental activation energies. This exemplifies the Bell–Evans–Polanyi Principle, and it provides an accurate means of assessing regioselectivity.     

Escape from the quantum pigeon conundrum

It has recently been argued in Aharonov et al. (2016) that quantum mechanics violates the Pigeon Counting Principle (PCP) which states that if one distributes three pigeons among two boxes there must be at least two pigeons in one of the boxes. However, this conclusion cannot be justified by rigorous theoretical arguments. The issue is further complicated by experimental confirmation of the transition amplitudes predicted in this paper that nevertheless do not support the conclusion of PCP violation. Here we prove via a set of operator identities that the PCP is not violated within quantum mechanics, regardless of interpretation.     

直观推导式演进特征投影法在拖尾重叠色谱峰解析中的应用

直观推导式演进特征投影法(HELP)已成功应用于复杂体系的重叠色谱峰解析.当色谱峰拖尾时,演进特征投影图(ELPG)显示的直线段对应的区域中可能含有前面拖尾组分的信息,据此进行HELP解析可能得不到满意结果.选择ELPG上直线段的一部分,即拖尾组分末端,前面组分的信息已基本消失的区域作为选择性区域进行HELP解析.同时,提出一种新的定量方法:用主成分分析法(PCA)分解待测组分标准样品的二维数据,将得到的“标准”色谱引入HELP的定量过程,在色谱峰拖尾或解得谱峰不平滑时,得到更准确的结果.用HELP方法解析了依诺沙星、诺氟沙星和环丙沙星三组分实验体系,结果表明,加入上述措施的HELP可有效改善拖尾重叠色谱峰的解析结果.     

Improving the neural network method for finite element model updating using homogenous distribution of design points

In developing a neural network technique for a finite element model updating, researchers have been shown that the number of training samples and their quality, significantly affect the accuracy of the NN predication. In this study, based on the genetic algorithm (GA) method, we reduce the number of analyses required to develop the training pairs and reduce the amount of time for training the NN. In the other words, a uniform distribution of design points inside the design space will be obtained by means of this approach. To validate the efficiency of GA sample selection, random generation (RG) method is used for comparison. Two comparisons are made based on a numerical and experimental example. One is updated from 10 degrees of freedom lumped parameters system and the other is updated from a free–free beam using test data. The results indicate that the GA sample selection can reduce the number of training samples without affecting the accuracy of the NN predication. In our present study, also, the advantages of using frequency response function (FRF) data as input to the NN are kept and the drawback of having too many frequency points is overcome by the application of principal component analyses (PCA).     

Positive Reachability for Diffusion Equations

Counterexamples are constructed for some plausible conjectures. Typical of these: as the Maximum Principle ensures that positive boundary data give a positive state at time T from 0 initial data, one might (plausibly, but falsely) conjecture that all positive terminal states should be approximately reachable in this way, i.e., subject to the requirement that the boundary data stays nonnegative.     

PbTe纳米晶高压热电性能的研究

 利用自建的400 t四柱双缸液压机,研究了PbTe纳米晶在0~0.8 GPa压力范围内热电性能随压力的变化。实验结果表明：PbTe纳米晶电导率随压力的增加而增加,而热电动势随压力的增加而减小,两者随压力的变化具有可逆性;PbTe纳米晶具有极高的热电动势,在常压下达到565 μV/K,在0.8 GPa压力下,材料的电导率为常压下的4倍,热电动势仅降低20%,功率因子则达到常压下的3倍。研究表明,高压能显著提高PbTe纳米晶的热电性能。利用第一性原理计算了0.4~4.0 GPa压力范围内材料的简约费米能级,计算结果与实验结果相吻合。