Bounds for point recolouring in geometric graphs

We examine a recolouring scheme ostensibly used to assist in classifying geographic data. Given a drawing of a graph with bi-chromatic points, where the points are the vertices of the graph, a point can be recoloured if it is surrounded by neighbours of the opposite colour. The notion of surrounded is defined as a contiguous subset of neighbours that span an angle greater than 180 degrees. The recolouring of surrounded points continues in sequence, in no particular order, until no point remains surrounded. We show that for some classes of graphs the process terminates in a polynomial number of steps. On the other hand, there are classes of graphs with infinite recolouring sequences.     

On the Nodal Count for Flat Tori

We give an explicit formula for the number of nodal domains of certain eigenfunctions on a flat torus. We apply this to an isospectral but not isometric family of pairs of flat four-dimensional tori constructed by Conway and Sloane, and we show that corresponding eigenfunctions have the same number of nodal domains. This disproves a conjecture by Brüning, Gnutzmann, and Smilansky.     

DNA transport and delivery in thermal gradients near optofluidic resonators

Heat generation and its impact on DNA transport in the vicinity of an optofluidic silicon photonic crystal resonator are studied theoretically and experimentally. The temperature rise is measured to be as high as 57 K for 10 mW of input power. The resulting optical trapping and biomolecular sensing properties of these devices are shown to be strongly affected by the combination of buoyancy driven flow and thermophoresis. Specifically, the region around the electromagnetic hot spot is depleted in biomolecules because of a high free energy barrier.     

Flat Curves

We characterize the sextic trefoil among plane curves of low degree: first as a complex curve with compact, flat geometry; and then as a curve with meromorphic arc length parameterization.     

A Highly Warped Heptagon‐Containing sp2 Carbon Scaffold via Vinylnaphthyl π‐Extension

A new strategy is demonstrated for the synthesis of warped, negatively curved, all‐sp²‐carbon π‐scaffolds. Multifold C?C coupling reactions are used to transform a polyaromatic borinic acid into a saddle‐shaped polyaromatic hydrocarbon ( 2 ) bearing two heptagonal rings. Notably, this Schwarzite substructure is synthesized in only two steps from an unfunctionalized alkene. A highly warped structure of 2 was revealed by X‐ray crystallographic studies and pronounced flexibility of this π‐scaffold was ascertained by experimental and computational studies. Compound 2 exhibits excellent solubility, visible range absorption and fluorescence, and readily undergoes two reversible one‐electron oxidations at mild potentials.     

A Molecular Secret Sharing Scheme

A method for implementing a secret sharing scheme at the molecular level is presented. By creating molecular code generators that are self‐assembled from several molecular components, we established a means for distributing distinct code‐activating elements among several participants. In this way, an authorization code can only be generated when all the participants are present, which ensures that highly secured systems cannot be operated by unauthorized individuals or disloyal users. Additional layers of protection result from the ability to program the security code by replacing one or several molecular components and by subjecting the system to distinct chemical inputs.     

Application of multiple quench parameters for confirmation of radionuclide identity in radioanalytical quality control

Journal of Radioanalytical and Nuclear Chemistry - Robust and reliable radiochemical analysis is the key factor in the appropriate disposal and management of radioactive wastes arising from the...     

Synthesis,Antiprotozoal Activity,and Cheminformatic Analysis of 2-Phenyl-2H-Indazole Derivatives

Indazole is an important scaffold in medicinal chemistry. At present, the progress on synthetic methodologies has allowed the preparation of several new indazole derivatives with interesting pharmacological properties. Particularly, the antiprotozoal activity of indazole derivatives have been recently reported. Herein, a series of 22 indazole derivatives was synthesized and studied as antiprotozoals. The 2-phenyl-2H-indazole scaffold was accessed by a one-pot procedure, which includes a combination of ultrasound synthesis under neat conditions as well as Cadogan’s cyclization. Moreover, some compounds were derivatized to have an appropriate set to provide structure-activity relationships (SAR) information. Whereas the antiprotozoal activity of six of these compounds against E. histolytica, G. intestinalis, and T. vaginalis had been previously reported, the activity of the additional 16 compounds was evaluated against these same protozoa. The biological assays revealed structural features that favor the antiprotozoal activity against the three protozoans tested, e.g., electron withdrawing groups at the 2-phenyl ring. It is important to mention that the indazole derivatives possess strong antiprotozoal activity and are also characterized by a continuous SAR.     

Preparation and Characterization of Forsterite (Mg2SiO4) Xerogels

Mg2SiO4 gels were prepared from alkoxide precursors, and the formation of the forsterite crystal phase was studied after heat treatments up to 1200°C. Prehydrolyzed TEOS in solution with 2-methoxyethanol was mixed with Mg(OEt)2, and the solution was hydrolyzed using excess water. The resultant gels were dried at 100°C to form xerogels which were subsequently powdered. These powders were characterized using thermal analysis (DTA and TGA), surface area analysis (BET), X-ray diffraction (XRD) and transmission electron microscopy (TEM).DTA and XRD indicated that forsterite crystallized at 770°C, and by 1000°C the powders were predominantly crystalline. BET gave powder surface areas between 400 and 550 m2 g–1. TEM revealed angular particles with sizes between 0.2 and 2 m. The low temperature of crystallization of forsterite indicates a high degree of intimate mixing between the precursor alkoxides, although XRD indicated some degree of inhomogeneity.