Object and Mathematical Simulation of Ammonium Hexafluorosilicate Sublimation

An integration of different modelling methods including object and mathematical simulation are suggested for sublimation processes of inorganic fluorides to optimally simulate the real technological conditions. The paper presents the results of testing this methodology on ammonium hexafluorosilicate sublimation.     

The Effect of Temperature and Standings Can Cause Deviations in Prostate Specific Antigen (PSA) Assays

Abstract

Blood samples were assayed for PSA values immediately after sampled or by standing for an assigned period. Variation of the free‐ (f), total‐ (t) values, and the free to total (f/t) ratios were determined. Mathematical models were used to interpret the phenomena of deviation. Smaller values of PSA values changed randomly with time and temperature of standings, resulting in varying f/t ratios, while larger initial PSA values were relatively unaffected to any significant extent.

Model interpreted that the changes of PSA values might be caused by higher temperature and time of standings, and conformational participation was also possible.     

数学建模思想渗入大学数学课堂教学的试验研究

以高等数学课堂教学为例,通过科学试验的方法分析数学建模思想渗入大学数学课堂教学对学生学习的影响力。通过精心设计教学试验,采集大量试验数据进行建模分析,结果表明,数学建模思想渗入高等数学课堂教学会对学生的学习产生积极影响,值得推广并长期坚持。     

Percolation Thresholds in Ternary Polymer Melt Blends with Separate Dispersions of the Inner Phases: Mathematical Model

A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work.     

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.     

Mechanistic Simulation Studies on Viscous-Elastic Polymer Flooding in Petroleum Reservoirs

Based on the theory and application developments of polymer flooding on enhancing oil recovery, an improved mathematical model has been developed to simulate the mechanism of viscous-elastic polymer flooding. IMPES method has been presented to solve the polymer flooding model considering the viscosifying effect of elasticity, the effect of decreasing residual oil and the degradation of polymer molecules. The validation of the model is approved by an experiment. A simulation example was carried out using the developed numerical simulator. The enhanced oil recovery mechanism was discussed for viscous-elastic polymer flooding, and corresponding influencing factors were also studied.     

计算富勒烯结构的新方法:曲率定理*

介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。     

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.     

An efficient strategy based on two-stage chromatography and in vitro evaluation for rapid screening and isolation of acetylcholinesterase inhibitors from Scutellaria baicalensis Georgi

The extraction of Scutellaria baicalensis Georgi was investigated using the response surface methodology-genetic algorithm mathematical regression model, and the extraction variables were optimized to maximize the flavonoid yield. Furthermore, a simple and efficient ultrafiltration–liquid chromatography–mass spectrometry and molecular docking methods were developed for the rapid screening and identification of acetylcholinesterase inhibitors present in Scutellaria baicalensis Georgi. Subsequently, four major chemical constituents, namely baicalein, norwogonin, wogonin, and oroxylin A, were identified as potent acetylcholinesterase inhibitors. This novel approach, involving the use of ultrafiltration–liquid chromatography–mass spectrometry and molecular docking methods combined with stepwise flow rate counter-current chromatography and semi-preparative high-performance liquid chromatography, could potentially provide a powerful tool for the screening and extraction of acetylcholinesterase inhibitors from complex matrices and be a useful platform for the production of bioactive and nutraceutical ingredients.     

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.