Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

Dynamic Modeling of the Feed Drive System of a CNC Metal Cutting Machine

Studying the vibrational behavior of feed drive systems is important for enhancing the structural performance of computer numerical control (CNC) machines. The preload on the screw and nut position have a great influence on the vibration characteristics of the feed drive as two very important operational conditions. Rotational acceleration of the screw also affects the performance of the CNC feed drive when machining small parts. This paper investigates the influence of preload and nut position on the vibration characteristics of the feed drive system of a CNC metal cutting machine in order to be able to eliminate an observed resonance occurred at high rotational speeds of the screw, corresponding to high feed rates. Additionally, rational structural parameters of the feed drive system are selected in order to increase the rotational acceleration for improving the performance of the CNC machine. Experiments and analyses showed that by selecting specific parameters of feed drive system and simultaneously applying a certain value of preload, a 97% increase in rotational acceleration and 30% time reduction considering the vibration resistance at high rotational speeds can be achieved.     

Kinetics Study of the Thermal Decomposition of Post-consumer Poly(Ethylene Terephthalate) in an Argon Atmosphere

The thermal decomposition of post-consumer samples of a carbonated water bottle made of poly(ethylene terephthalate), PC-PET, was examined by linear temperature programing under an argon atmosphere to determine its mass loss kinetics. A simple kinetic model, called the first order pseudo single-component model, was used. The total weight-loss of each sample assumed to be in two periods, with each period corresponding to a one step decomposition of the PC-PET to volatiles. Three methods for determining the kinetic parameters by thermal gravimetric analysis were examined: differential analysis at a constant heating rate (differential), temperatures of a given conversion at a number of heating rates (isoconversional), and the maximum rate at multiple heating rates (peak temperature). The latter two multiple heating rates methods results were comparable to each other but they were not in agreement with the results from the differential method. The results of the differential method were insensitive to the heating rate and consistent with kinetics data reported in the literature for PET.     

Modeling of Anionic Polymerization of Isoprene in an Industrial Reactor

One of the most important reasons for modeling polymerization processes is to provide a tool for estimating the risks of runaway reactions in polymer industry. This is especially important for batch processes, such as anionic polymerization of isoprene or butadiene. This work presents a theoretical and experimental research of the anionic polymerization of isoprene using cyclohexane as solvent and n‐butyllithium as initiator. In the first part, a phenomenological kinetic expression is obtained that describes the anionic polymerization of isoprene initiated by n‐butyllithium in cyclohexane. In the second, the mass and energy balance equations are solved to model the anionic polymerization of isoprene in a quasi‐adiabatic batch reactor. Adjustment of reactor parameters is made using the data obtained from a laboratory reactor. The proposed model predicts adequately the obtained temperature, pressure, and conversion profiles from this set of experiments. Finally, a mathematical model is developed to predict the behavior for the anionic polymerization of isoprene in an industrial reactor.     

Controlled-advancement rigid-body optimization of nanosystems

In this study, we propose a novel optimization algorithm, with application to the refinement of molecular complexes. Particularly, we consider optimization problem as the calculation of quasi-static trajectories of rigid bodies influenced by the inverse-inertia-weighted energy gradient and introduce the concept of advancement region that guarantees displacement of a molecule strictly within a relevant region of conformational space. The advancement region helps to avoid typical energy minimization pitfalls, thus, the algorithm is suitable to work with arbitrary energy functions and arbitrary types of molecular complexes without necessary tuning of its hyper-parameters. Our method, called controlled-advancement rigid-body optimization of nanosystems (Carbon), is particularly useful for the large-scale molecular refinement, as for example, the putative binding candidates obtained with protein–protein docking pipelines. Implementation of Carbon with user-friendly interface is available in the SAMSON platform for molecular modeling at https://www.samson-connect.net . © 2019 Wiley Periodicals, Inc.     

Characterization of new Pt(IV)–thiazole complexes: Analytical,spectral, molecular modeling and molecular docking studies and applications in two opposing pathways

New thiazole derivatives were synthesized and fully characterized, then coordinated with PtCl₄ salt. Also, the newly synthesized Pt(IV) complexes were investigated analytically (elemental and thermogravimetric analyses), spectrally (infrared, UV–visible, mass, ¹H NMR, ¹³C NMR, X‐ray diffraction) as well as theoretically (kinetics, modeling and docking). The data extracted led to the establishment of the best chemical and structural forms. Octahedral geometry was the only formula proposed for all complexes, which is favorable for d⁶ systems. The molecular ion peaks from mass spectral analysis coincide with all analytical data, confirming the molecular formula proposed. X‐ray diffraction (XRD) and scanning electron microscopy (SEM) allowed discrimination of features between crystalline particles and other amorphous morphology. By applying Gaussian09 as well as HyperChem 8.2 programs, the best structural forms were obtained, as well as computed significant parameters. Computed parameters such as softness, hardness, surface area and reactivity led us towards application in two opposing pathways: tumor inhibition and oxidation activation. The catalytic oxidation for CO was conducted over PtO₂, which was yielded from calcination of the most reactive complex. The success of catalytic role for synthesized PtO₂ was due to its particulate size and surface morphology, which were estimated from XRD patterns and SEM images, respectively. The antitumor activity was tested versus HCT‐116 and HepG‐2 cell lines. Mild toxicity was recorded for two of the derivatives and their corresponding complexes. This degree of toxicity is more favorable in most cases, due to exclusion of serious side effects, which is coherently attached with known antitumor drugs.     

Automated chemical resonance generation and structure filtration for kinetic modeling

This work discusses efficient and automated methods for constructing a set of representative resonance structures for arbitrary chemical species, including radicals and biradicals, consisting of the elements H, C, O, N, and S. Determining the representative reactive structures of chemical species is crucial for identification of reactive sites and consequently applying the correct reaction templates to generate the set of important reactions during automated chemical kinetic model generation. We describe a fundamental set of resonance pathway types, accounting for simple resonating structures, as well as global approaches for polycyclic aromatic species. Automatically discovering potential localized structures along with filtration to identify the representative structures was shown to be robust and relatively fast. The algorithms discussed here were recently implemented in the Reaction Mechanism Generator (RMG) software. The final structures proposed by this method were found to be in reasonable agreement with quantum chemical computation results of localized structure contributions to the resonance hybrid.     

The Special “Morse Code” between Solvent Polarity and Morphology Flexibility in a POSS–Dendrimer Supramolecular System

An amazing phenomenon of the relative magnitude of modulus of two liquid-crystal (LC) gels is found inverted under/above their phase transition temperature T_LC-iso, which is further proved to be caused by their diverse morphology flexibility. By testing the polarity of two LCs, gelator POSS-G1-Boc (POSS=polyhedral oligomeric silsesquioxane) was discovered to self-assemble into more flexible structures in a relatively low polar LC, whereas more rigid ones are formed in higher polar LC. Hence, a fitting function to connect morphology flexibility with solvent polarity was established, which can even be generalized to a number of common solvents. Experimental observations and coarse-grained molecular dynamics simulations revealed that solvent polarity mirrors a “Morse code”, with each “code” corresponding to a specific morphology flexibility.     

Solubility of aminotriethylene glycol functionalized single wall carbon nanotubes: A density functional based tight binding molecular dynamics study

Pristine CNTs are exemplary hydrophobic solutes; properly functionalized CNTs can be seen as hydrophilic ones. The solubility of aminotriethylene glycol (ATG) functionalized single walled carbon nanotubes (fSWCNTs) were examined using density functional based tight binding method. According to the dynamics study, the ATG-fSWCNTs interaction energies (IE) and diffusion coefficients (D) are diameter dependent. As the diameter of the (n,0) tube is incrementally increased, a distinguishable pattern is observed, specifically the IE of the ATG-fSWCNT in water is quite higher for n that is an integral multiple of three (n = 9,12,15) while the D is lower due to its π bonding structures. In general, the metallic ATG functionalized nanotube possess a higher IE and a much lower D in aqueous media. © 2019 Wiley Periodicals, Inc.