Fibonacci Numbers and an Area Puzzle: Connecting Geometry and Algebra in the Mathematics Classroom

A mathematical puzzle that asks about “missing” area leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. This article discusses the inquiry, the concepts, the solution, and an extension that deepens all students’ understanding of connections between algebra and geometry.     

Synthesis of Novel Ethyl (substituted)phenyl‐4‐oxothiazolidin‐3‐yl)‐1‐ethyl‐4‐oxo‐1,4‐dihydroquinoline‐3‐Carboxylates as Potential Anticancer Agents

A series of ethyl (substituted)phenyl‐4‐oxothiazolidin‐3‐yl)‐1‐ethyl‐4‐oxo‐1,4‐dihydroquinoline‐3‐carboxylates ( 7a , 7b , 7c , 7d , 7e , 7f , 7g ) has been prepared from reactions between aminoquinolones 6 with arenealdehydes and mercaptoacetic acid. The critical intermediates, 6 a and 6b , were obtained from appropriate amines by a sequence of steps involving (i) reaction with diethylethoxymethylenemalonate, (ii) thermal cyclization in diphenyl ether, (iii) ethylation and (iv) Pd/C catalyzed reduction. New compounds 7a , 7b , 7c , 7d , 7e , 7f , 7g were fully identified and characterized by NMR (¹H and ¹³C) and specifically for 7d by X‐ray crystallography. Compounds 7b , 7c , 7d , 7e , 7f were found not to exhibit activity at 10 uM concentrations against gastric ascitis (AGP‐01), gastric adenocarcinoma kind intestinal (ACP‐02), colon (HCT‐116) and murine melanome (B16F10) cancer cells. However, none exhibited cytotoxicity against normal cells human fibroblast (MRC‐5), murine fibroblast (NIH3T3) and normal human melanocyte (Melan‐A).     

A polymer inclusion membrane based on the ionic liquid trihexyl(tetradecyl)phosphonium chloride and PVC for solid–liquid extraction of Zn(II) from hydrochloric acid solution

Abstract  

Extraction of Zn(II) from aqueous solution using polymer inclusion membranes based on poly(vinyl chloride) containing the phosphonium-based ionic liquid trihexyl(tetradecyl)phosphonium chloride (Cyphos^? IL 101) is described. Zn(II) could efficiently be extracted from 5 M hydrochloric acid solution with membranes containing 30 wt% Cyphos IL 101, whereas back-extraction was successfully achieved with 1 M sulfuric acid. Prepared membranes were evaluated in terms of stability in air as well as in terms of leaching of the ionic liquid from the membranes in aqueous solution.     

Water-soluble peptide-coated nanoparticles: control of the helix structure and enhanced differential binding to immune cells

The stabilizing action of C(α)-tetrasubstituted α-amino acids inserted into a sequence of short peptides allowed for the first time the preparation of water-soluble nanoparticles of different materials coated with a helix-structured undecapeptide. This peptide coating strongly favors nanoparticle uptake by human immune system cells.     

Spectroscopic and electronic structure studies of a dimethyl sulfoxide reductase catalytic intermediate: implications for electron- and atom-transfer reactivity

The electronic structure of a genuine paramagnetic des-oxo Mo(V) catalytic intermediate in the reaction of dimethyl sulfoxide reductase (DMSOR) with (CH(3))(3)NO has been probed by electron paramagnetic resonance (EPR), electronic absorption, and magnetic circular dichroism (MCD) spectroscopies. EPR spectroscopy reveals rhombic g- and A-tensors that indicate a low-symmetry geometry for this intermediate and a singly occupied molecular orbital that is dominantly metal centered. The excited-state spectroscopic data were interpreted in the context of electronic structure calculations, and this has resulted in a full assignment of the observed MCD and electronic absorption bands, a detailed understanding of the metal-ligand bonding scheme, and an evaluation of the Mo(V) coordination geometry and Mo(V)-S(dithiolene) covalency as it pertains to the stability of the intermediate and electron-transfer regeneration. Finally, the relationship between des-oxo Mo(V) and des-oxo Mo(IV) geometric and electronic structures is discussed relative to the reaction coordinate in members of the DMSOR enzyme family.     

In situ microbial fuel cell-based biosensor for organic carbon

The biological oxygen demand (BOD) may be the most used test to assess the amount of pollutant organic matter in water; however, it is time and labor consuming, and is done ex-situ. A BOD biosensor based on the microbial fuel cell principle was tested for online and in situ monitoring of biodegradable organic content of domestic wastewater. A stable current density of 282±23mA/m(2) was obtained with domestic wastewater containing a BOD(5) of 317±15mg O(2)/L at 22±2°C, 1.53±0.04mS/cm and pH 6.9±0.1. The current density showed a linear relationship with BOD(5) concentration ranging from 17±0.5mg O(2)/L to 78±7.6mg O(2)/L. The current generation from the BOD biosensor was dependent on the measurement conditions such as temperature, conductivity, and pH. Thus, a correction factor should be applied to measurements done under different environmental conditions from the ones used in the calibration. These results provide useful information for the development of a biosensor for real-time in situ monitoring of wastewater quality.