Case Studies With Mathematical Modeling of Free-Radical Multi-Component Bulk/Solution Polymerizations: Part 1

In part 1 of this series of two extensive overviews of multi-component polymerization case studies, we present mathematical modelling results with experimental confirmations. The case studies are from free-radical, bulk and/or solution polymerizations, covering the range from homo- to hexa-polymerization at both regular and elevated temperature levels, i.e., without and with possible depropagation steps. The model eventually tackles complex polymerization features, ranging from conversion-time histories to more esoteric multi-component composition and/or sequence length profiles. Part 2 of the series will describe more complicated situations with depropagation and composition control policies, all relying solely on a unique monomer/polymer database of physico-chemical properties and other characteristics, with no further parameter adjustment. These database items will be cited in tables in part 2 of the series.     

Modeling of the Simultaneous Hydrogen Evolution and Cobalt Electrodeposition

A mathematical model of simultaneous cobalt deposition and hydrogen evolution was developed and applied to the electroreduction process of 5 mM Co²⁺ ions investigated by cyclic voltammetry (CV) technique at different hydrogen ion concentrations (pH=2, 3, 4). The kinetic parameters of such a complex process were determined, and the validity of the model and its sensitivity to changes in individual parameters were verified. The relative value of the approximate standard deviation (ASD_%) was used to determine the degree of fit of the model to the experimental data. The catalytic effect of cobalt on the hydrogen evolution process was comprehensively confirmed.     

复杂边界条件下渗流场流线分布研究

流线分布研究已受到油藏工程师们的普遍关注。本文从无限大油藏稳态渗流场基本解出发,结合边界元方法求解出复杂边界条件下稳态渗流场的势分布,以此为基础提出了流线场的生成办法,并给出了应用实例。本文方法的优点在于求解过程中将问题的维数降低了一维,减少了计算量;计算精度较高且具有一定的普遍应用性;适应于求解任意形状的包括定压、定流量或混合边界在内的组合边界问题。实例表明,利用本文方法产生的流线分布因能够较为直观地反映出油藏流体在注采井间的运动轨迹,为优化井网和注入方案提供了重要依据。     

数学建模活动对培养人才的作用

文章论述建模活动对培养人才的作用 ,对专科院校高等数学教学改革具有启发性 .     

从对比中更好地把握微积分的教学改革

美国微积分教学改革的许多方面值得借鉴.从对比的角度反思微积分教改的不足和差距,以便更好地把握今后的教改工作,明确在点点滴滴的教学过程中,应当实实在在地做些什么、怎么做.     

数学建模思维方法论

数学建模过程是一个复杂的思维过程,全国大学生数学建模竞赛又加以竞赛的形式,有其特殊性,其中如何研究问题、如何做出成果、如何争取获奖,本文探讨其思维规律、方法技巧.     

基于光纤布拉格光栅的智能服装人体测温模型研究

根据热量传递机理建立了智能服装中光纤布拉格光栅人体测温的热传递物理模型,对人体、空气层和服装之间的热传递进行了有限元建模和稳态热分析,确定了智能服装中光纤布拉格光栅温度场的数学模型,利用该数学模型对光纤布拉格光栅测量温度值进行了修正.在多点加权皮肤平均温度的基础上,提出了由左右胸、左右腋和后背五处皮肤温度构成的智能服装...     

基于形态学4子带分解金字塔的图像融合

提出了一种基于数学形态学滤波的多分辨力图像融合。这种融合方法使用了形态学开闭运算构造了低通与高通滤波器,将原始图像分解为4子带图像金字塔和4子带方向衬比度图像金字塔。然后利用方向衬比度和区域标准差进行图像融合得到融合的4子带图像金字塔,最后应用子带图像重构得到融合图像。融合实验表明,该方法优于传统的形态学金字塔图像融合,衬比度金字塔图像融合和小波分解图像融合。     

“穿越沙漠”赛题评述

对2020年"高教社杯"全国大学生数学建模竞赛"穿越沙漠"一题作简要评述,介绍赛题的数学基础和求解思路,探讨答卷所用的方法和存在的问题.     

Sufficient conditions for duality in homogeneous programming

A symmetric duality theory for programming problems with homogeneous objective functions was published in 1961 by Eisenberg and has been used by a number of authors since in establishing duality theorems for specific problems. In this paper, we study a generalization of Eisenberg's problem from the viewpoint of Rockafellar's very general perturbation theory of duality. The extension of Eisenberg's sufficient conditions appears as a special case of a much more general criterion for the existence of optimal vectors and lack of a duality gap. We give examples where Eisenberg's sufficient condition is not satisfied, yet optimal vectors exist, and primal and dual problems have the same value.