Nonobtuse triangulation of polygons

We show how to triangulate a polygon without using any obtuse triangles. Such triangulations can be used to discretize partial differential equations in a way that guarantees that the resulting matrix is Stieltjes, a desirable property both for computation and for theoretical analysis.A simple divide-and-conquer approach would fail because adjacent subproblems cannot be solved independently, but this can be overcome by careful subdivision. Overlay a square grid on the polygon, preferably with the polygon vertices at grid points. Choose boundary cells so they can be triangulated without propagating irregular points to adjacent cells. The remaining interior is rectangular and easily triangulated. Small angles can also be avoided in these constructions.     

What you thought you already knew about the bending motion of triatomic molecules

The bending vibrations of linear, quasilinear, and bent molecules are qualitatively different phenomena. Each of these cases has been fully described by quantum mechanical formulations in the last half century, but important two-dimensional aspects of all three cases as well as the relationship between the three types of bending behavior remain difficult to visualize. Simple two-dimensional figures can help to provide an introduction to basic spatial and mathematical aspects of the bending problem.     

Interlaboratory comparison of methods for the determination of incurred tilmicosin residues in bovine liver

The objective of this study was to compare 2 methods for the determination of tilmicosin residues in bovine liver samples. Three laboratories participated in the comparison of the 2 methods. The first method was described in a New Animal Drug Application (NADA 140-929), and the second was a modification of that method in which hexane was substituted for carbon tetrachloride in one cleanup step. Each of the 3 laboratories analyzed subsamples of 10 bovine livers containing incurred tilmicosin. Residues ranged from 2.3 to 81 ppm tilmicosin in the 10 liver samples with an 11.8% relative standard deviation obtained by using both methods. In addition, fortified-control liver tissue samples were analyzed concurrently with tissues containing incurred residues by using the modified method in one of the laboratories. The fortification levels ranged from 0.3 to 112 ppm, with recoveries ranging from 76 to 92%. The results from the 3 laboratories were comparable, indicating that the modified method was not only as effective as the original NADA method, but also more desirable because of the change to a less hazardous solvent.     

A transition state analogue for an RNA-editing reaction

Deamination at C6 of adenosine in RNA catalyzed by the ADAR enzymes generates inosine at the corresponding position. Because inosine is decoded as guanosine during translation, this modification can lead to codon changes in messenger RNA. Hydration of 8-azanebularine across the C6-N1 double bond generates an excellent mimic of the transition state proposed for the hydrolytic deamination reaction catalyzed by ADARs. Here, we report the synthesis of a phosphoramidite of 8-azanebularine and its use in the preparation of RNAs mimicking the secondary structure found at a known editing site in the glutamate receptor B subunit pre-mRNA. The binding properties of analogue-containing RNAs indicate that a tight binding ligand for an ADAR can be generated by incorporation of 8-azanebularine. The observed high-affinity binding is dependent on a functional active site, the presence of one, but not the other, of ADAR2's two double-stranded RNA-binding motifs (dsRBMs), and the correct placement of the nucleoside analogue into the sequence/structural context of a known editing site. These results advance our understanding of substrate recognition during ADAR-catalyzed RNA editing and are important for structural studies of ADAR.RNA complexes.     

Self-assembly of a tripodal pseudorotaxane on the surface of a titanium dioxide nanoparticle

This paper describes the self-assembly of a heterosupramolecular system consisting of a tripodal viologen, adsorbed at the surface of a titanium dioxide nanoparticle, that threads a crown ether to form a pseudorotaxane. The viologen, a 1,1'-disubstituted-4,4'-bipyridinium salt with a rigid tripodal anchor group, has been synthesized. This viologen is adsorbed at the surface of a titanium dioxide nanoparticle in solution. As intended, this tripodal viologen is both oriented normal to and displaced from the surface of the nanoparticle and threads a crown ether to form the heterosupramolecular complex. The threading of the crown ether by the tripodal viologen to form the above pseudorotaxane complex at the surface of a titanium dioxide nanoparticle has been studied by (1)H NMR, optical absorption spectroscopy, and cyclic voltammetry.     

Rapid synthesis of tetrahydro-4H-pyrazolo[1,5-a]diazepine-2-carboxylate

Hydrazines condense with dimethyl 2-pyrrolidino-4-oxo-2-pentenedioate in the presence of aq. HCl to form N-substituted pyrazole-3,5-dicarboxylates 2. Complex bicyclic derivatives, such as pyrazolo-oxazine 3a, pyrazolo-oxazepine 3b, pyrazolo-pyrazine 4a, and pyrazolo-diazepine 4b, were generated using 2-hydrazinoethanol, 3-hydrazinopropanol, 2-hydrazinoethylamine, and 3-hydrazinopropylamine.     

Ultra-fast and scalable sidewall functionalisation of single-walled carbon nanotubes with carboxylic acid

A simple and fast method for the functionalisation of single-walled carbon nanotubes with carboxylic acid terminated molecules, at varying molar fractions, is presented.     

Enyne cross-metathesis with strained, geminally-substituted alkenes: direct access to highly substituted 1,3-dienes

Angle strain in methylene cyclobutane was used to drive a cross-enyne metathesis with 1-alkynes, giving 1,1,3-trisubstituted 1,3-dienes in good isolated yields. An extensive survey of Grubbs' second-generation catalysts led to an optimized reaction conducted at 0 degrees C.     

Formation of microcrystals, micropuddles, and other spatial inhomogenieties in surface reactions under ambient conditions: an atomic force microscopy study of water and nitric acid adsorption on MgO(100) and CaCO3(104)

In this study, atomic force microscopy (AFM) is used to image freshly cleaved MgO(100) and CaCO3(104) as these surfaces undergo reaction with water and nitric acid under ambient conditions of temperature, pressure, and relative humidity. The reaction of water and nitric acid results in the formation of hydroxylated and nitrated surfaces, respectively. It is clear from the AFM images that there are spatial inhomogenieties and surface features that form on micrometer and nanometer length scales as these reactions proceed. These features, which include hillocks, patches, microcrystallites, and micropuddles, are due to surface and phase segregation as a result of facile ion mobility in the presence of adsorbed water. In addition, instabilities and oscillations in the AFM images provide an indication of liquid formation and the deliquescence (i.e., a solid to liquid-phase transition) of nitrate salts as a function of relative humidity.     

Linearization, Dold-Puppe stabilization, and Mac Lane's -construction

In this paper we study linear functors, i.e., functors of chain complexes of modules which preserve direct sums up to quasi-isomorphism, in order to lay the foundation for a further study of the Goodwillie calculus in this setting. We compare the methods of Dold and Puppe, Mac Lane, and Goodwillie for producing linear approximations to functors, and establish conditions under which these methods are equivalent. In addition, we classify linear functors in terms of modules over an explicit differential graded algebra. Several classical results involving Dold-Puppe stabilization and Mac Lane's -construction are extended or given new proofs.