Chalk it up to experience: using chalkboard paint to create mathematical manipulatives

In this article, we give two examples of creating portable chalkboards using chalkboard paint for students to use during cooperative learning. This provides a creative method for professors to facilitate active learning in the undergraduate mathematics classroom.     

Cubic Bridgeless Graphs and Braces

There are many long-standing open problems on cubic bridgeless graphs, for instance, Jaeger’s directed cycle double cover conjecture. On the other hand, many structural properties of braces have been recently discovered. In this work, we bijectively map the cubic bridgeless graphs to braces which we call the hexagon graphs, and explore the structure of hexagon graphs. We show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig’s augmentations. In addition, we present a reformulation of Jaeger’s directed cycle double cover conjecture in the class of hexagon graphs.     

The swap graph of the finite soluble groups

A graph is reflexive if the second largest eigenvalue of its adjacency matrix is less than or equal to 2. In this paper, we characterize trees whose line graphs are reflexive. It turns out that these trees can be of arbitrary order—they can have either a unique vertex of arbitrary degree or pendant paths of arbitrary lengths, or both. Since the reflexive line graphs are Salem graphs, we also relate some of our results to the Salem (graph) numbers.     

The influence of a beta-electron withdrawing substituent in aldol reactions of methylketone boron enolates

We wish to describe here that good levels of substrate-based, 1,5-syn-stereocontrol could be achieved in the boron-mediated aldol reactions of beta-trichloromethyl methylketones with achiral aldehydes, independent of the nature of the beta-alkoxy protecting group.     

Catalytic oxidation of imines based on methyltrioxorhenium/urea hydrogen peroxide: a mild and easy chemo- and regioselective entry to nitrones

[reaction: see text] The first successful catalytic oxidation procedure for the chemoselective conversion of imines to nitrones is reported. The reaction is general, high yielding, and user and environmentally friendly, and furnishes a solution to the yet unanswered issue of regioselective access to nitrones by oxidation of nitrogen derivatives.     

Simultaneous detection of L-glutamate and nitric oxide from adherently growing cells at known distance using disk shaped dual electrodes

An ex vivo system for simultaneous detection of nitric oxide (NO) and L-glutamate using integrated dual 250 microm platinum disk electrodes modified individually with suitable sensing chemistries has been developed. One of the sensors was coated with an electrocatalytic layer of Ni tetrasulfonate phthalocyanine tetrasodium salt (Ni-TSPc) covered by second layer of Nafion, which stabilises on the one hand the primary oxidation product NO(+) and prevents interferences from negatively charged compounds such as NO(2)(-). For glutamate determination, the second electrode was modified with a crosslinked redox hydrogel consisting of Os complex modified poly(vinylimidazol), glutamate oxidase and peroxidase. A manual x-y-z micromanipulator on top of an inverted optical microscope was used to position the dual electrode sensor at a defined distance of 5 microm from a cell population under visual control. C6 glioma cells were stimulated simultaneously with bradykinin or VEGF to release NO while KCl was used to invoke glutamate release. For evaluation of the glutamate sensors, in some experiments HN10 cells were used. To investigate the sensitivity and reliability of the system, several drugs were applied to the cells, e.g. Ca(2+)-channel inhibitors for testing Ca(2+)-dependence of the release of NO and glutamate, rotenone for inducing oxidative stress and glutamate antagonists for analysing glutamate release. With these drugs the NO and glutamate release was modulated in a similar way then expected from previously described systems or even in-vivo measurements. We therefore conclude that our system is suitable to analyse stress-induced mechanisms in cell lines.     

Reproducible SERRS from structured gold surfaces

Metallic substrates with ordered spherical cavities have been shown to be very effective for surface-enhanced Raman scattering (SERS) and can be fabricated reproducibly using electrodeposition. The sensitivity of detection is increased by several orders of magnitude by using surface-enhanced resonance Raman scattering (SERRS). In this report we demonstrate SERRS for the first time on electrodeposited gold films templated with colloidal spheres and demonstrate the reproducibility of the response. We also obtain a direct comparison between SERRS and SERS by choosing two dyes, Cy5 and Cy3, which are similar in structure but differ in their excitation maxima, such that one is resonant and the other non-resonant with our laser excitation. As expected, the resonant enhancement is found to be of the order of 10(3) over and above that for SERS. The net SERRS enhancements are shown to be of the order of 10(9). We also find that the resonant enhancement profile of the different peaks for the chromophore follows the plasmonic resonance absorption spectrum obtained for the structured surface.     

cis-trans photoisomerization in [Ru(DIP)2(MeOH)2][OTf]2: synthesis, NMR, X-ray structure of the trans-isomer and photophysical properties

The first trans-ruthenium complex trans-[Ru(DIP)2(MeOH)2][OTf]2 (1b, where DIP = 4,7-diphenyl-1,10-phenanthroline) incorporating a pi-extended ligand was prepared via two methods: either photolysis of cis-[Ru(DIP)2(OTf)2] in MeOH-Et(2)O or via crystallization from MeOH-Et(2)O in direct sunlight. The X-ray molecular structure of is reported and confirmed the trans geometry of the title compound. The cis-trans isomerization process was monitored by 1H-NMR and showed that 1b reverts back to cis-[Ru(DIP)2(MeOH)2][OTf]2 (1a) in methanol-d4 after 15 h at 55 degrees C or several days at room temperature. The absorption spectra recorded in MeOH showed a bathochromic shift of the MLCT band of the trans-isomer 1b relative to that of the cis complex 1a. Interestingly at 77 K the emission spectrum of 1b is red shifted compared to the cis analog 1a. A rational explanation in terms of the energy of the excited states in the cis- and trans-isomers is proposed to explain this behavior.     

The bioinorganic and medicinal chemistry of carboranes: from new drug discovery to molecular imaging and therapy

The role of carboranes in medicinal chemistry has diversified in recent years and now extends into areas of drug discovery, molecular imaging, and targeted radionuclide therapy. An introduction to carborane chemistry is provided to familiarize the non-expert with some key properties of these molecules, followed by an overview of current medicinally-orientated research involving carboranes. The broad-ranging nature of this research is illustrated, with emphasis placed on recent highlights and advances in this field.