Using block designs in crossing number bounds

The crossing number $\mathrm{\text{CR}}\left(G\right)$ of a graph $G=\left(V,E\right)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$‐planar crossing number of $G,{\mathrm{\text{CR}}}_k\left(G\right)$, is defined as the minimum of $\text{CR}\left(G_1\right)+\text{CR}\left(G_2\right)+?+\text{CR}\left(G_k\right)$ over all graphs $G_1,G_2,\dots ,G_k$ with ${\cup }_{i=1}^k{G}_i=G$. Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every $k\ge 1$, we have ${\text{CR}}_k\left(G\right)\le (2/k^2?1/k^3)\text{CR}\left(G\right)$ and that this bound does not remain true if we replace the constant $2/k^2?1/k^3$ by any number smaller than $1/k^2$. We improve the upper bound to $(1/k^2)\left(1+o\left(1\right)\right)$ as $k\to \infty$. For the class of bipartite graphs, we show that the best constant is exactly $1/k^2$ for every $k$. The results extend to the rectilinear variant of the $k$‐planar crossing number.     

The synthesis of 2-amino-4(3H)-quinazolinones and related heterocycles via a mild electrocyclization of aryl guanidines

A new method for the preparation of 2-amino-4(3H)-quinazolinones and similar fused heterocycles is described. Simply warming a mixture of an aryl guanidine and carbonyl diimidazole in acetonitrile results in formation of a putative N-amidinoisocyanate intermediate which undergoes a 6π-electron electrocyclic reaction with the aryl ring to generate the quinazolinone ring system. The mild conditions are compatible with a variety of functional groups, and the reaction is shown to be successful on multigram scale.     

Evaluation of polypyrrole/silver/polyethylene glycol nanocomposite sorbent for electroenhanced direct-immersion solid-phase microextraction of carvacrol and thymol from medicinal plants

The unique features of nanostructured polypyrrole, conductivity enhancement effect of silver nanoparticles and high polar adsorptivity of polyethylene glycol were merged into polypyrrole/silver/polyethylene glycol (PPy/Ag/PEG) nanocomposite. It was synthesized and simultaneously coated on the surface of a stainless-steel fiber using an amended electropolymerization procedure. Before coating, the fiber substrate was made porous and sticky by allocating platinum dots on the surface of the stainless-steel fiber using the electrophoretic method. The prepared fiber was applied for the extraction of carvacrol and thymol (the most important antioxidants in medicinal plants) through an electroenhanced direct-immersion solid-phase microextraction (EE-DI-SPME) sampling strategy, followed by GC-FID quantification. To achieve the best efficiency, the effectual experimental variables including pH of sample solution, applied voltage, extraction temperature and time, stirring rate, and ionic strength were investigated. Under the optimal experimental conditions, the calibration curves were linear over the range of 0.5–30 µg mL^?1 for thymol and 0.01–30 µg mL^?1 for carvacrol. The detection limits (3S_b) and relative standard deviation (RSD%, n?=?6) were obtained to be 0.15, 0.003 µg mL^?1 and 10.2, 8.7% for thymol and carvacrol, respectively. The results demonstrated the priority of the proposed fiber compared with polypyrrole and polyacrylate fibers, in terms of extraction efficiency, durability and stability. The developed method was successfully employed for the analysis of thymol and carvacrol in medicinal plants.     

Thermally Rearranged Polymer Membranes Containing Tröger's Base Units Have Exceptional Performance for Air Separations

The influence of segmental chain motion on the gas separation performance of thermally rearranged (TR) polymer membranes is established for TR polybenzoxazoles featuring Tröger's base (TB) monomer subunits as exceptionally rigid sites of contortion along the polymer backbone. These polymers are accessed from solution‐processable ortho‐acetate functionalized polyimides, which are readily synthesized as high‐molecular‐weight polymers for membrane casting. We find that thermal rearrangement leads to a small increase in d‐spacing between polymer chains and a dramatic pore‐network reconfiguration that increases both membrane permeability and O₂/N₂ selectivity, putting its performance above the 2015 upper bound.     

Decomposition of hexamethyldisilane on a hot tungsten filament and gas-phase reactions in a hot-wire chemical vapor deposition reactor

To study the effect of an Si-Si bond on gas-phase reaction chemistry in the hot-wire chemical vapor deposition (HWCVD) process with a single source alkylsilane molecule, soft ionization with a vacuum ultraviolet wavelength of 118 nm was used with time-of-flight mass spectrometry to examine the products from the primary decomposition of hexamethyldisilane (HMDS) on a heated tungsten (W) filament and from secondary gas-phase reactions in a HWCVD reactor. It is found that both Si-Si and Si-C bonds break when HMDS decomposes on the W filament. The dominance of the breakage of Si-Si over Si-C bond has been demonstrated. In the reactor, the abstraction of methyl and H atom, respectively, from the abundant HMDS molecules by the dominant primary trimethylsilyl radicals produces tetramethylsilane (TMS) and trimethylsilane (TriMS). Along with TMS and TriMS, various other alkyl-substituted silanes (m/z = 160, 204, 262) and silyl-substituted alkanes (m/z = 218, 276, 290) are also formed from radical combination reactions. With HMDS, an increasing number of Si-Si bonds are found in the gas-phase reaction products aside from the Si-C bond which has been shown to be the major bond connection in the products when TMS is used in the same reactor. Three methyl-substituted 1,3-disilacyclobutane species (m/z = 116, 130, 144) are present in the reactor with HMDS, suggesting a more active involvement from the reactive silene intermediates.     

High-throughput synthesis of HepDirect prodrugs of nucleoside monophosphates

A high-throughput phosphoramidite method for HepDirect prodrug synthesis was optimized on seven representative nucleosides, adenosine, inosine, guanosine, uridine, cytidine, AICA-riboside, and thymidine, each on a 5 mg scale. The variables optimized included (1) reaction time, (2) reaction temperature, (3) activating agent, (4) solvent, (5) purification method, and (6) stoichiometry. Preparative HPLC with mass-based fraction collection and yield determination from an ELSD standard curve enabled high-throughput. The optimized conditions for the representative nucleosides required 6 mol equiv of phosphoramidite to nucleoside and resulted in an average HPLC determined yield of 31 +/- 14% and HPLC purity of 93 +/- 3%.     

Interpreting ultrafast molecular fragmentation dynamics with ab initio electronic structure calculations

High-level ab initio electronic structure calculations are used to interpret the fragmentation dynamics of CHBr(2)COCF(3), following excitation with an intense ultrafast laser pulse. The potential energy surfaces of the ground and excited cationic states along the dissociative C-CF(3) bond have been calculated using multireference second order perturbation theory methods. The calculations confirm the existence of a charge transfer resonance during the evolution of a dissociative wave packet on the ground state potential energy surface of the molecular cation and yield a detailed picture of the dissociation dynamics observed in earlier work. Comparisons of the ionic spectrum for two similar molecules support a general picture in which molecules are influenced by dynamic resonances in the cation during dissociation.     

Ultrathin layer chromatography on nanostructured thin films

Ultrathin layer chromatography (UTLC) is a relatively new variant of thin layer chromatography, with a 10mum thick monolithic silica sorbent layer that gives faster separations with lower limits of detection and reduced analyte and solvent volumes. We have produced UTLC plates with controllable nanostructure and thickness, and show that the layer separation characteristics depends on the film nanostructure. We also show that layers made with in-plane anisotropic nanostructures will exhibit a decoupling effect, where the analyte spots do not develop in the same direction as the solvent front movement. The added layer morphology and material selection adds a degree of freedom to UTLC, and may have applications in multi-dimensional TLC.     

Electrochemical Oxidation of Metolazone at a Glassy Carbon Electrode

Metolazone is a diuretic agent used in patients with edematous states and/or hypertension. The electrochemical behavior of metolazone on a glassy carbon electrode was investigated using cyclic, differential pulse, and square‐wave voltammetry at different pHs. The pH dependent oxidation of metolazone occurs in two consecutive steps in a diffusion‐controlled mechanism and involves the formation of a main oxidation product. The first oxidation process is reversible, and involves two electrons and two protons corresponding to the oxidation of nitrogen in the sulfonamide moiety. The second oxidation process is irreversible, also occurs in the sulfonamide moiety, involves a one electron‐transfer, and is followed by deprotonation to produce a cation radical, which reacts with water and yields a hydroxylated product. The diffusion coefficient of metolazone was calculated to be 3.43×10^?6 cm² s^?1 in pH 7.0 0.1 M phosphate buffer.