Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

X‐ray Raman spectroscopy of lithium‐ion battery electrolyte solutions in a flow cell

The effects of varying LiPF₆ salt concentration and the presence of lithium bis(oxalate)borate additive on the electronic structure of commonly used lithium‐ion battery electrolyte solvents (ethylene carbonate–dimethyl carbonate and propylene carbonate) have been investigated. X‐ray Raman scattering spectroscopy (a non‐resonant inelastic X‐ray scattering method) was utilized together with a closed‐circle flow cell. Carbon and oxygen K‐edges provide characteristic information on the electronic structure of the electrolyte solutions, which are sensitive to local chemistry. Higher Li⁺ ion concentration in the solvent manifests itself as a blue‐shift of both the π* feature in the carbon edge and the carbonyl π* feature in the oxygen edge. While these oxygen K‐edge results agree with previous soft X‐ray absorption studies on LiBF₄ salt concentration in propylene carbonate, carbon K‐edge spectra reveal a shift in energy, which can be explained with differing ionic conductivities of the electrolyte solutions.     

Supramolecular inclusion complexes of a star polymer containing cholesterol end‐capped poly(ε‐caprolactone) arms with β‐cyclodextrin

A novel hexa‐armed and star‐shaped polymer containing cholesterol end‐capped poly(ε‐caprolactone) arms emanating from a phosphazene core (N₃P₃‐(PCL‐Chol)₆) was synthesized by a combination of ring‐opening polymerization and “click” chemistry techniques. For this purpose, the terminal ? OH groups of the synthesized precursor (N₃P₃‐(PCL‐OH)₆) were converted into –Chol through a series of reaction. Both N₃P₃‐(PCL‐OH)₆ and N₃P₃‐(PCL‐Chol)₆ were then employed in the preparation of supramolecular inclusion complexes (ICs) with β‐cyclodextrin (β‐CD). The latter formed ICs with β‐CD in higher yield. The host–guest stoichiometry (ε‐CL:β‐CD, mol:mol) in the ICs of N₃P₃‐(PCL‐Chol)₆ was found to be 1.2. The formation of supramolecular ICs of N₃P₃‐(PCL‐Chol)₆ with β‐CD was confirmed by using Fourier transform infrared (FTIR) and ¹H nuclear magnetic resonance (NMR) spectroscopic methods, wide‐angle X‐ray diffraction (WAXD), and thermal analysis techniques. WAXD data showed that the obtained ICs with N₃P₃‐(PCL‐Chol)₆ had a channel‐type crystalline structure, indicating the suppression of the original crystallization of N₃P₃‐(PCL‐Chol)₆ in β‐CD cavities. Moreover, the thermal stabilities of ICs were found to be higher than those of the free star polymer and β‐CD. Furthermore, the surface properties of N₃P₃‐(PCL‐Chol)₆ and its ICs with β‐CD were investigated by static contact angle measurements. The obtained results proved that the wettability of N₃P₃‐(PCL‐Chol)₆ successfully increased with the formation of its ICs with β‐CD. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3406–3420     

L2-CONVERGENCE AND L2-CAUCHY DOUBLE SEQUENCES

Abstract In this article, we prove a decomposition theorem for L2-convergent double sequences and introduce the notions of L2-Cauchy and L2＊-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly （L2,L）- convergence and （L2, L）-Cauchy double sequence.     

Surface Propensity of Anions in a Binary Ionic-Liquid Mixture Assessed by Full-Range Angle-Resolved X-ray Photoelectron Spectroscopy and Surface-Tension Measurements

Angle-resolved X-ray photoelectron spectroscopy and contact-angle measurements guided by a signal attenuation model are utilized to extract molar composition and anion enrichment in the vacuum interface of a binary ionic liquid mixture, having a common quaternary ammonium cation and two different anions. By using the intensity ratio of the F1s peaks belonging to the two different anions recorded at the full electron take-off angle range, from 0° to 80°, we have determined that only a fractionally covered and anion enriched surface layer can predict the AR-XPS data, which is also consistent with surface tension measurements. Moreover, the more bulky and non-spherical anion enrichment is evident even at the conventional and the so assumed bulk sensitive take-off angle of 0°. This methodology provides a surface enrichment factor of the molecular ions and clearly serves as an experimental evidence for recently debated surface layering and/or island structure in ionic liquid systems.     

I2-convergence and I2-cauchy double sequences

In this article, we prove a decomposition theorem for I₂-convergent double sequences and introduce the notions of I₂-Cauchy and I^*₂)-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I₂,I)-convergence and (I₂,I)-Cauchy double sequence.     

Effects of solvent casted poly (lactic acid)/poly(ethylene glycol)/paraben derivative triazine films on antibacterial performance and cytotoxicity

A series of poly(lactic acid) (PLA) films that including fully paraben substituted triazine derivatives having anti-bacterial properties have been prepared by utilizing the solvent-casting method. PLA as biodegradable polymer, poly(ethylene glycol) (PEG) as a plasticizing agent and s-triazine molecules (TA01, TA02, TA03, TA04, and TA05) behaving as an anti-bacterial component have been utilized in the experiments. The influence of TA compounds on the antibacterial performance of PLA/PEG films was investigated for the first time against Gram-negative Escherichia coli (E. coli) and Gram-positive Staphylococcus aureus (S. aureus) bacteria via the contact active method. TA01-03-05 incorporated PLA/PEG films gave the best results against E.coli bacteria and log10 reductions of these films were 0.78, 0.64, and 0.65 respectively. The effect of TA compounds on the cell viability was investigated against cancer and non-cancerous cell lines using an MTS assay. The results showed that TA compounds had a positive effect on cell growth in non-cancerous cells, while they had a negative effect on cell growth in cancer cells. Furthermore, the addition of TA considerably increased the decomposition temperatures from 349° to 361° and char yield from 0.65 for PLA/PEG film to 2.3 for PLA/PEG/TA05. All of the films had good transparency and low opacity which was 7.2 for pure PLA used for control and the maximum opacity value was 11.2 observed for PLA/PEG/01. TA03 and TA04 caused a decrement of water vapor permission when compared to PLA/PEG films from 1439 to 749 and 664. It was also observed that pure PLA/PEG film lost weight rapidly over time during degradation tests. On the other hand, weight loss wasn't observed in PLA/PEG/TA films. This study focused on demonstrating the use of our new, flexible PLA/PEG derivatives in food and medical packaging.     

Synthesis of AB3‐type miktoarm star polymers with steroid core via a combination of “Click” chemistry and ring opening polymerization techniques

Well‐defined AB₃‐type miktoarm star‐shaped polymers with cholic acid (CA) core were fabricated with a combination of “click” chemistry and ring opening polymerization (ROP) methods. Firstly, azide end‐functional poly(ethylene glycol) (mPEG), poly(methyl methacrylate) (PMMA), polystyrene (PS), and poly(ε‐caprolactone) (PCL) polymers were prepared via controlled polymerization and chemical modification methods. Then, CA moieties containing three OH groups were introduced to these polymers as the end groups via Cu(I)‐catalyzed click reaction between azide end‐functional groups of the polymers ( mPEG‐N₃ , PMMA‐N₃ , PS‐N₃ , and PCL‐N₃ ) and ethynyl‐functional CA under ambient conditions, yielding CA end‐functional polymers ( mPEG‐Cholic , PMMA‐Cholic , PS‐Cholic , and PCL‐Cholic ). Finally, the obtained CA end‐capped polymers were employed as the macroinitiators in the ROP of ε‐caprolactone (ε‐CL) yielding AB₃‐type miktoarm star polymers ( mPEG‐Cholic‐PCL₃ , PMMA‐Cholic‐PCL₃ , and PS‐Cholic‐PCL₃ ) and asymmetric star polymer [ Cholic‐(PCL)₄ ]. The chemical structures of the obtained intermediates and polymers were confirmed via Fourier transform infrared and ¹H nuclear magnetic resonance spectroscopic techniques. Thermal decomposition behaviors and phase transitions were studied in detail using thermogravimetric analysis and differential scanning calorimetry experiments. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3390–3399