Inclusion complexation of 4,4′-dihydroxybenzophenone and 4-hydroxybenzophenone with α- and β-cyclodextrins

The inclusion complexation behaviours of 4,4′-dihydroxybenzophenone (DHBP) and 4-hydroxybenzophenone (HBP) with α-cyclodextrin (α-CD) and β-cyclodextrin (β-CD) were investigated using UV–visible fluorescence, time-resolved fluorescence, molecular modelling, scanning electron microscopy (SEM), FTIR, differential scanning calorimeter, X-ray diffraction, ¹H NMR and molecular modelling techniques. In both molecules, biexponential decay was observed in water, whereas triexponential decay was observed in the CD medium. The DSC thermogram of the DHBP/α-CD and DHBP/β-CD inclusion complex nanomaterials shows the endothermic peak at 60.8, 101.9, 119.6 and 112.8°C. The upfield chemical shift observed for HBP protons reveal that the phenyl ring (without hydroxyl substitution) entered the CD cavity and the hydroxyl group of HBP is exposed outside the CD cavity. The SEM image of DHBP appears as needle-shaped crystals on the micrometre scale, whereas the irregular bar shape was observed for HBP. Transmission electron microscopy images show that both guest molecules formed nano vesicles with α-CD and formed nano rods with β-CD.     

Parameter Selection and Estimation Techniques in a Styrene Polymerization Model

Styrene polymerization literature is reviewed and a model with dicumyl peroxide and benzoyl peroxide initiators is developed. Nine parameters are selected for estimation using statistical methods that account for the influence of parameters on model predictions, correlated effects of parameters and uncertainties of initial literature values. Updated parameters result in improved fits to conversion and molecular weight data from three research groups, reducing the least‐squares objective function by 73%. Use of industrial data from 19 batch reactor runs increases the number of estimable parameters to 16. Good predictions are obtained for validation runs with temperature ramps using both initiators.

     

高光谱定量反演火龙果茎枝叶绿素含量的研究

火龙果是近年来引进我国的营养价值高、经济效益好的新型水果,肉质茎枝是其主要光合器官,与常见果树具有较大差异。为探索以茎枝为光合作用器官的植被的光谱特征及其生化组分的估测方法,以火龙果为研究对象,在贵州省典型种植区罗甸县开展了4个氮肥梯度田间试验,同步测定不同养分丰缺程度下的火龙果茎枝高光谱和相应叶绿素含量数据;然后分析火龙果茎枝光谱数据的演化规律,并采用数学变换、连续小波变换算法并结合相关性分析算法处理分析火龙果茎枝光谱数据,提取并筛选特征波段;最后利用偏最小二乘算法构建火龙果茎枝叶绿素含量估测模型。研究结果表明：（1）火龙果肉质茎枝的原始光谱曲线整体趋势与常见绿叶植物相似,但随施氮量的增加,火龙果近红外处的光谱反射率逐渐降低,变化趋势与常见绿叶植物相反,茎枝光谱的吸收峰（谷）随施氮量的增加呈升高（加深）的趋势。（2）数学变换中的一阶微分与在L₁-L₅尺度内的连续小波变换能有效提升光谱对叶绿素含量的敏感性,火龙果茎枝原始光谱与叶绿素含量的敏感区域主要位于730～1 400 nm,数学变换与连续小波变换均能提升光谱对叶绿素含量的敏感性。与常见绿叶植物相比,火龙果茎枝敏感波段分布相对分散,且多位于730 nm附近与近红外区域（1 100～1 600 nm）。（3）数学变换和连续小波变换能明显提升光谱对火龙果茎枝叶绿素含量的估测能力,其中基于一阶微分的估测模型与基于连续小波变换L₁与L₄的估测模型分别为数学变换与连续小波变换的最优模型,其验证精度分别为R2_验证=0.625,RMSE=0.048,RPD=1.238（一阶微分）;R2_验证=0.678,RMSE=0.037,RPD=1.652（连续小波变换）;表明高光谱技术可以作为火龙果茎枝叶绿素含量和营养诊断的无损监测手段。该研究为完善不同植被类型基于高光谱指数的叶绿素反演提供了补充。     

牛顿是如何站在巨人肩膀上的?

将以现今的微积分学符号,对开普勒(Kepler)行星运行定律进行三步简单的数理分析,推出著名的牛顿(Newton)万有引力定律,以此显示微积分学的巨大威力.在微积分学的教学中,不仅可以让学生知道微积分有用,而且可以让学生知道如何应用.对现代数学建模的教学与学习也具有一定的启发意义.     

Polyesters by a Radical Pathway: Rationalization of the Cyclic Ketene Acetal Efficiency

Radical ring‐opening polymerization (rROP) of cyclic ketene acetals (CKAs) combines the advantages of both ring‐opening polymerization and radical polymerization thereby allowing the robust production of polyesters coupled with the mild polymerization conditions of a radical process. rROP was recently rejuvenated by the possibility to copolymerize CKAs with classic vinyl monomers leading to the insertion of cleavable functionality into a vinyl‐based copolymer backbone and thus imparting (bio)degradability. Such materials are suitable for a large scope of applications, particularly within the biomedical field. The competition between the ring‐opening and ring‐retaining propagation routes is a major complication in the development of efficient CKA monomers, ultimately leading to the use of only four monomers that are known to completely ring‐open under all experimental conditions. In this article we investigate the radical ring‐opening polymerization of model CKA monomers and demonstrate by the combination of DFT calculations and kinetic modeling using PREDICI software that we are now able to predict in silico the ring‐opening ability of CKA monomers.     

Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group

We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the visual areas V1/V2 whose functional architecture have been modeled in previous works by Citti and Sarti as a Lie group equipped with a sub-Riemannian (SR) metric. Here we extend their model proposing that the metric responsible for the cortical connectivity is modulated by the modeled neuro-physiological response of simple cells to the visual stimulus, hence providing a more biologically plausible model that takes into account a presence of visual stimulus. Illusory contours in our model are described as geodesics in the new metric. The model is confirmed by numerical simulations, where we compute the geodesics via SR-Fast Marching.     

Psychological aspects of equation-based modelling

Psychological aspects of equation-based modelling languages like Modelica are under-represented in literature. This does not reflect the growth of the corresponding userbase. In this paper we try to close this gap by tackling the problem from three sides: we conduct expert interviews, we conduct an experiment based on self-reported timings to analyse the effects of inheritance on understandability, and we conduct an online experiment to analyse the effects of model representations on the performance at modelling tasks. The expert interviews suggest that experienced modelling experts tend to develop their models from the top-down, while novices do the opposite. Results from the second experiment indicate that the effect of inheritance on the time to understand a model is both significant and large. The results of the last experiment imply that graphical representations outperform block-diagrams for several metrics. These results open a broad research field on the theory of good modelling practice.     

An integro-PDE model with variable motility

This paper is concerned with a nonlocal reaction–diffusion–mutation model. It involves the spatial variable and a trait variable which govern the spatial diffusion of species. By establishing comparison principle and constructing monotone iterative sequence, we have proved the existence of solution to Cauchy problem. Then, based on the quasi-elementary solution, auxiliary equation and method of successive improvement of upper and lower solutions, the solutions are shown to be unique, bounded and globally stable.     

Computer-assisted Modelling and Analysis of Linear Programming Problems: Towards a Unified Framework

A framework for model formulation and analysis to support operationsand management of large-scale linear programs is developed fromthe combined capabilities of CAMPS and ANALYZE. Both the systemsare reviewed briefly and the interface which integrates thetwo systems is then described. The model formulation, matrixgeneration, and model management capability of CAMPS and thecomplementary model and solution analysis capability of ANALYZEare presented within a unified framework. Relevant generic functionsare highlighted, and an example is presented in detail to illustratethe level of integration achieved in the current prototype system.Some new results on discourse models and model management supportare given in a framework designed to move toward an ‘intelligent’system for linear programming modelling and analysis.