举办《应用数学学校》和参加数学应用数学建模竞赛的实践和思考

通过开展应用数学教学活动和开办《应用数学学校》的多年实践 ,我校学生结合实际学习和应用数学知识的意识和能力不断提高 ,在上海市数学知识应用竞赛和美国大学生数学建模竞赛中连续取得好成绩 ,为了争取把这项工作做得更好 ,我们作了进一步思考和打算     

血液净化用吸附剂脱附过程的数学模型研究

对已吸附了低密度脂蛋白（ＬＤＬ）及极低密度脂蛋白（ＶＬＤＬ）达到饱和程度的吸附柱，用１ｍｏｌ／Ｌ的生理盐水进行脱附，采用修正Ｌａｎｇｍｕｉｒ吸附式建立了连续脱附过程的数学模型，计算结果与实验测定值吻合，表明该数学模型适用于描述类似于ＬＤＬ及ＶＬＤＬ这类蛋白质大分子的脱附过程。     

壳聚糖对鞣酸絮凝作用的研究

以壳聚糖为絮凝剂，采用絮凝法除去中药药液中的杂质。以鞣酸为研究对象，从鞣酸浓度，体系温度，ＰＨ絮凝剂用量粘均分子量等方面探讨其絮凝规律，用正交试验优化其絮凝条件，为实施中药药液的絮凝法精制工艺提供参考。     

Comparison of the retention behaviour of phenol derivatives on porous graphitized and octadecylsilica columns

Summary The retention of 22 ring-substituted phenol derivatives on porous graphitized carbon (PGC) (eluents: acetonitrile — water and methanol — water mixtures) and on octadecylsilica (ODS) (eluents: methanol — 0.025 M KH₂PO₄ mixtures) was determined, and the relationship between retention and physicochemical parameters were evaluated by principal component analysis followed by two-dimensional nonlinear mapping and by cluster analysis as well as by canonical correlation analysis. Calculations proved that marked differences can be detected between the retention characteristics of PGC and ODS columns, and the electronic parameters of phenol derivatives have the highest impact on their retention. The comparison of various multivariate mathematical-statistical methods indicated that principal component analysis followed by two dimensional non-linear mapping is the most appropriate method for the evaluation of large data matrices in RP-HPLC.     

Mass distribution in a dynamic sample zone inside a flow injection manifold: modelling integrated conductimetric profiles

A mathematical model for fitting the experimental ICM (integrated conductimetric method) curves developed by the authors in a previous work, is presented for the first time in this study. The proposed model fits the experimental curves with great precision and allows to predict physical dispersion for single-line flow injection system. The correlation of the model’s parameters with typical reactionless FIA peak parameters is also assessed. The IDQ coefficient—a novel dispersion estimator previously reported by the authors—can also be predicted when operational FIA variables are changed. Experimental and modelled profiles are compared as a function of the system’s variables, showing an excellent agreement.     

Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

Dose prediction and process optimization in a gamma sterilization facility using 3-D Monte Carlo code

A model of a gamma sterilizer was built using the ITS/ACCEPT Monte Carlo code and verified through dosimetry. Individual dosimetry measurements in homogeneous material were pooled to represent larger bodies that could be simulated in a reasonable time. With the assumptions and simplifications described, dose predictions were within 2–5% of dosimetry. The model was used to simulate product movement through the sterilizer and to predict information useful for process optimization and facility design.     

Heat transfer in polymer composites filled with inorganic hollow micro-spheres: A theoretical model

The heat transfer mechanisms in inorganic hollow micro-spheres filled polymer composites are analyzed in the present paper. This heat transfer includes mainly three mechanisms: (1) thermal conduction between solid and gas; (2) thermal radiation between the hollow micro-sphere surfaces; and (3) natural thermal convection of the gas in the micro-hollow spheres. A theoretical model of heat transfer in polymer/inorganic hollow micro-sphere composites is established based on the law of minimal thermal resistance and the equal law of the specific equivalent thermal conductivity, and a corresponding equation of effective thermal conductivity is derived. The effective thermal conductivity (k_eff) of hollow glass bead-filled polypropylene composites is estimated by using this equation, and is compared with the numerical simulations by means of a finite element method. The results show that the variation of the theoretical estimations of k_eff are similar to the numerical simulations at lower filler volume fraction (φ_f20%). Moreover, k_eff decreases linearly with increasing φ_f, and reduces somewhat with increase of filler size.