Differential Games of inf-sup Type and Isaacs Equations

Motivated by the work of Fleming, we provide a general framework to associate inf-sup type values with the Isaacs equations. We show that upper and lower bounds for the generators of inf-sup type are upper and lower Hamiltonians, respectively. In particular, the lower (resp. upper) bound corresponds to the progressive (resp. strictly progressive) strategy. By the Dynamic Programming Principle and identification of the generator, we can prove that the inf-sup type game is characterized as the unique viscosity solution of the Isaacs equation. We also discuss the Isaacs equation with a Hamiltonian of a convex combination between the lower and upper Hamiltonians.     

扩张原理的一种新的表现形式

提出一种基于“模糊点”的模糊集合的分解定理，在此分解定理的基础上给出模糊扩张原理的一种新的表现形式。新的扩张原理与以往人们所提出的扩张原理是等价的，而表现形式更为直观、简便。同时，利用该扩张原理得到模糊复合函数以及多元模糊关系合成运算的合理解释。     

以竞赛为抓手,提高化学师范生综合素质

To improve normal university students' comprehensive quality has become a tendency in current innovation of teacher education. Combining with the teaching practice and obtained achievements of students studying in College of Chemistry and Pharmaceutical Science of Guangxi Normal University, this paper discusses the functions of chemistry competitions in cultivating excellent quality, knowledges and skills of normal students, and emphatically introduces principles and implementation strategies.     

从轨道对称守恒原理看Diels-Alder反应区域选择性

根据轨道对称守恒原理(PCOS),推断出决定Diels-Alder反应的区域选择性的轨道相互作用是双烯体与亲双烯体各自最稳定的价轨道之间的相互作用,这种相互作用形成的是反应产物的两根新σ键中能量更低的σ键,即σ1键。在过渡态中具有更稳定的σ1键的那个区域异构体将是反应的优势产物,本文将这个规则称为σ1规则。本文的量子化学计算结果既证实了σ1规则预测Diels-Alder反应区域选择性主产物的正确性,也证实了σ1键的确来自于双烯体与亲双烯体各自最稳定的价轨道之间的相互作用。     

Cognition coming about: Self-organisation and free-energy: Commentary on Wright,J.J. and Bourke,P.D. (2020) “The growth of cognition: Free energy minimization and the embryogenesis of cortical computation”

Wright and Bourke's compelling article rightly points out that existing models of embryogenesis fail to explain the mechanisms and functional significance of the dynamic connections among neurons. We pursue their account of Dynamic Logic by appealing to the Markov blanket formalism that underwrites the Free Energy Principle. We submit that this allows one to model embryogenesis as self-organisation in a dynamical system that minimises free-energy. The ensuing formalism may be extended to also explain the autonomous emergence of cognition, specifically in the brain, as a dynamic self-assembling process.     

Quality assessment of cortex cinnamomi by HPLC chemical fingerprint, principle component analysis and cluster analysis

HPLC fingerprint analysis, principle component analysis (PCA), and cluster analysis were introduced for quality assessment of Cortex cinnamomi (CC). The fingerprint of CC was developed and validated by analyzing 30 samples of CC from different species and geographic locations. Seventeen chromatographic peaks were selected as characteristic peaks and their relative peak areas (RPA) were calculated for quantitative expression of the HPLC fingerprints. The correlation coefficients of similarity in chromatograms were higher than 0.95 for the same species while much lower than 0.6 for different species. Besides, two principal components (PCs) have been extracted by PCA. PC1 separated Cinnamomum cassia from other species, capturing 56.75% of variance while PC2 contributed for their further separation, capturing 19.08% variance. The scores of the samples showed that the samples could be clustered reasonably into different groups corresponding to different species and different regions. The scores and loading plots together revealed different chemical properties of each group clearly. The cluster analysis confirmed the results of PCA analysis. Therefore, HPLC fingerprint in combination with chemometric techniques provide a very flexible and reliable method for quality assessment of traditional Chinese medicines.     

Non-targeted analysis of wastewater treatment plant effluents by high performance liquid chromatography-time slice-solid phase extraction-nuclear magnetic resonance/time-of-flight-mass spectrometry

Extracts of effluents from two different wastewater treatment plants (WWTP) in Switzerland taken during the application period of pesticides were examined by coupling an HPLC-MS system to a nuclear magnetic resonance spectrometer using a post column peak trapping device. By trapping 1 min portions of the chromatogram onto post column solid phase extraction cartridges (time slice-SPE-NMR) a comprehensive overview of proton carrying constituents could be achieved. Non-supervised statistical analysis of the NMR spectra obtained by this approach revealed NMR resonances pointing to contaminants present in decreasing proton concentration in the extracts. Comparison of exact mass data acquired during the trapping process to these NMR resonances enabled the identification of the pesticides Linuron, Metazachlor, Ethofumesate, Isoproturon, Metamitron, Propazine and Chloridazon. Desaminometamitron, a known transformation product of Metamitron could also be identified together with unexpected highly concentrated C8, C10 and C12 fatty acids and their glycerol mono- and di esters. Other compounds identified were a drug metabolite (3-Carboxymefenamic acid), a sun screen agent (Ensulizole: 2-Phenyl-1H-1,3-benzodiazole-6-sulfonic acid) and industrial chemicals (Benzotriazole, N-Benzyl-indole). In addition, a number of well-resolved proton spectra cannot be attributed to a mass response showing the need of further investigations using 2D-NMR and different ionization techniques.     

基于三维荧光特性的汽油聚类分析

应用三维荧光光谱法研究了90#、93#及97#3种汽油纯样品以及它们的相互掺杂样品的荧光特性。选取激发波长(λex)为330nm,发射波长(λem)在340～500nm间的荧光强度数据,用主成分聚类分析法作了研究。结果表明:所得的荧光数据分为三类,属90#汽油样品的数据为一类,处于第Ⅰ象限中;属97#汽油样品为第二类,处于第Ⅲ象限;属93#汽油样品为第三类,处于第Ⅳ象限。在第Ⅰ及第Ⅳ象限中的荧光数据又分为二类,一类为纯品油样,另一类为混杂油样。因此,根据聚类分析结果可方便地对不同标号的汽油加以区别。而且根据纯品汽油样品与混杂油样品的试验点之间的距离可推测油样中混杂组分量的多少。     

基于化学模式识别的大蒜傅里叶变换红外光谱指纹图谱多样性

以不同地理居群的大蒜为研究对象,采用傅里叶变换红外光谱法获取各样品的红外谱图及不同波数下各样品的透过率数据,运用主成分分析及聚类分析等统计学方法对谱图数据进行了比较分析。结果发现,不同地理居群大蒜的红外指纹图谱存在差异,统计学分析结果显示25个品种大致可分为4大类(其中2个样品,4号及25号与这4类间有较大差异),此现象一定程度上反映了大蒜种植地居群环境对大蒜理化性质的影响。     

Stress gradient versus strain gradient constitutive models within elasticity

A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Hellinger–Reissner type variational principle. The main differences between the Eringen stress gradient model and the concomitant Aifantis strain gradient model are pointed out. A rigorous formulation of the stress gradient Euler–Bernoulli beam is provided; the response of this beam model is discussed as for its sensitivity to the stress gradient effects and compared with the analogous strain gradient beam model.