Using dynamic geometry to explore non-traditional theorems

The purpose of this article is to provide examples of ‘non-traditional’ theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The Appendix contains proof outlines for each theorem.     

1,2,5-Oxadiazolo[3,4-g]indoles via annelation of 6,7-dihydrobenzo[c][1,2,5]oxadiazol-4(5H)-one oxime with acetylene

1. Download high-res image (95KB)
2. Download full-size image

     

Design,Synthesis, and Application of a Water-soluble Photocage for Aqueous Cyclopentadiene-based Diels-Alder Photoclick Chemistry in Hydrogels

Spatiotemporally functionalized hydrogels have exciting applications in tissue engineering, but their preparation often relies on radical-based strategies that can be deleterious in biological settings. Herein, the computationally guided design, synthesis, and application of a water-soluble cyclopentadienone-norbornadiene (CPD-NBD) adduct is disclosed as a diene photocage for radical-free Diels-Alder photopatterning. We show that this scalable CPD-NBD derivative is readily incorporated into hydrogel formulations, providing gels that can be patterned with dienophiles upon 365 nm uncaging of cyclopentadiene. Patterning is first visualized through conjugation of cyanine dyes, then biological utility is highlighted by patterning peptides to direct cellular adhesion. Finally, the ease of use and versatility of this CPD-NBD derivative is demonstrated by direct incorporation into a commercial 3D printing resin to enable the photopatterning of structurally complex, printed hydrogels.     

12-Tungstophosphoric acid supported on inorganic oxides as heterogeneous and reusable catalysts for the selective preparation of alkoxymethyl ethers and their deprotections under different reaction conditions

A wide variety of primary and secondary alcohols were efficiently converted to their corresponding methoxymethyl (MOM) and ethoxymethyl (EOM) ethers in the presence of catalytic amounts of supported H₃PW₁₂O₄₀ on silica gel and zirconia at room temperature and under microwave irradiation at solvent-free conditions, whereas, phenols and tertiary alcohols remained intact under the same reaction conditions. Deprotection of these ethers to their parent alcohols was also achieved using these heterogeneous catalysts in ethanol, as a green solvent, under reflux conditions and microwave irradiation. Selective deprotection of primary and secondary MOM- and EOM-ethers in the presence of phenolic and tertiary ones, methyl and benzyl ethers, esters and trimethylsilyl ethers was achieved by these reagent systems. The present methodology offers several advantages such as short reaction times, high yields, simple procedure, heterogeneous reaction conditions, selectivity, non-toxicity and reusability of the catalysts.     

Microwave-promoted one-pot conversion of alcohols to oximes using 1-methylimidazolium nitrate, [Hmim][NO3], as a green promoter and medium

A wide variety of oximes were prepared from different types of alcohols with hydroxylamine hydrochloride using 1-methylimidaziloum nitrate, [Hmim][NO₃], ionic liquid as a reaction medium and promoter under microwave irradiation. This protocol provides a one-pot oxime synthesis with high yields that is facile, eco-friendly and the ionic liquid can be recovered and reused.     

Liquid–gas–liquid technique for microextraction and preconcentration of short chain fatty acids from aqueous samples

In this study, an organic solvent‐free microextraction technique termed liquid–gas–liquid microextraction (LGLME) was applied for cleanup and preconcentration of volatile short chain fatty acids in beverages and dairy products. Various parameters affecting the extraction efficiency such as extraction time, stirring speed, sodium chloride content, concentration and volume of donor and acceptor phases, and extraction temperature were studied. Repeatability (RSD, 4.2–8.5%), correlation coefficients (0.998–0.999), LODs (10–20 μg/L) and enrichment factors (152–249) were also investigated. Recoveries were achieved in the range of 90–102% in different matrices. The presented method was applied for the analysis of target analytes in some samples such as grape juice, vinegar and dairy products.     

Structure-based tuning of T(m) in lipid-like ionic liquids. Insights from Tf2N- salts of gene transfection agents

Ionic liquids of cations bearing two lipid-like aliphatic tails are shown to have values of T(m) that can be very low, and that can be tuned up or down by the addition, deletion, or combination of dipolar modules and side-chain double bonds.     

Proposed method of partial discharge allocation with acoustic emission sensors within power transformers

Employing acoustic emission sensors for detection of partial discharge, PD, introduces many advantages. Besides easy installation and replacement, they are non-invasive and immune to electromagnetic noise and interference and their sensitivity does not vary with object capacitance. For PD allocating utilizing AE sensors, distance calculations are based on the arrival time of acoustic waves to the sensors. Considering structure-borne waves of higher speed, the peaks of some of indirect path AE signals with significant contribution are mistakenly considered as peaks of direct path AE signals. Furthermore, the acoustic signals are propagating through certain parts of the transformer, such as the windings, and this complicates the partial discharge detection and allocation. These would imply an incorrect distance between the source and sensor. A method based on a heuristic algorithm has been proposed which considering all possible indirect paths with the relevant propagation times and all the barriers on the travel path of acoustic signal, calculates the more precise arrival times to sensors. A test chamber has been utilized and artificial PD signals are produced at various points. Output results of algorithm have been compared with results of classic method. It has been shown that proposed method significantly reduces the positioning errors.