A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Wild ginseng grows in Myanmar

Ginseng, the underground parts of plants of Panax species, has been used in oriental traditional medicine for centuries. Unfortunately, because of extensive exploitation over thousands of years, the natural source of these species has been almost exhausted. Recently, we have found a wild ginseng growing in Myanmar. Here, by a combination of chemical composition study and gene sequence analysis, we unambiguously demonstrate that the wild ginseng is actually P. zingiberensis, commonly known as ginger ginseng. This ginseng was an indigenous to the southwestern China. However, now it is seriously threatened to brink of extinction and is put on the highest level of protection in China. Therefore, an appropriate protection measure is highly recommended to preserve this valuable resource, since this Myanmar ginseng might turn out to be the last P. zingiberensis, which could ever be seen in the planet.     

On the origin of compositional fluctuations in ZnSe1- x S x alloys grown by metal-organic vapour-phase epitaxy

Periodic vertical modulations of the sulphur concentration have been observed in epitaxial layers of ZnSe_{1? x} S _x grown by metal-organic vapour-phase epitaxy. High-spatial-resolution microanalysis has shown that the sulphur variation is of the order of 1 at.% with a period of about 44 ± 0.1 nm. A detailed analysis of the possible causes of this modulation is presented which shows that periodic temperature fluctuations of the substrate are the most likely source.     

Development of novel backwash cleaning technique for reverse osmosis in reclamation of secondary effluent

The objective of the study was to further develop a novel cleaning technique for reverse osmosis in reclamation of municipal secondary effluent. This technique is a new backwash method via direct osmosis (DO) by intermittent injection of the high salinity (HS) solution without stopping of high pressure pump and it is environment and membrane friendly technique. In the study, DO-HS trials were carried out with a UF-RO pilot system which was operated on site with the secondary treated effluent as the raw feed. Different operating conditions for DO-HS treatment in the actual process were investigated. It was found that the operation for implementation of the DO-HS cleaning technique developed was easy. For the first time, the actual profiles of HS concentration, DO backwash flow rate, brine flow rate and permeate pressure during DO-HS treatment have been demonstrated. It was observed that turbidity of the brine stream during DO-HS treatment at 3 NTU was 5 times higher than that before DO-HS treatment. The results from this study have confirmed the previous hypothesis with DO-HS treatment that there would be a strong driving force for DO backwash to lift and sweep the foulants from the membrane surface which would be carried over to the brine. The optimal plant operating conditions in terms of RO feed flow rate, HS concentration and HS injection time are ready for the DO-HS method to be adopted and validated in a long-term continuous plant operation.     

Rapid, sensitive DNT vapor detection with UV-assisted photo-chemically synthesized gold nanoparticle SERS substrates

We report rapid, sensitive, and direct detection of 2,4-dinitrotoluene (DNT) vapor using tailored gold nanoparticles (Au-NPs) as the SERS substrate. The Au-NPs were synthesized using the UV-assisted photo-chemical reduction method and subsequently formed a monolayer on the glass slide through polymer-mediated self-assembly. The SERS substrate such prepared has high SERS enhancement, high affinity towards DNT vapor, and rapid response to the DNT adsorption/desorption. We systematically studied the effect of the Au-NP size and surface density on the SERS performance such as enhancement factor and response time. With the optimized SERS substrate, an enhancement factor over 5.6 × 10(6) was achieved. Furthermore, real-time detection of DNT vapor with only 0.35 second data acquisition time was demonstrated using a 12 mW laser. Compared to previously reported results, we achieved two orders of magnitude reduction in detection time and more than one order of magnitude reduction in excitation laser power. The detection limit is estimated to be 0.4 attogram, which corresponds to a sub-ppb DNT concentration in air. This work will lead to the development of ultra-fast and ultra-sensitive SERS devices for explosive identification and monitoring.     

Calibrated Subbundles in Noncompact Manifolds of Special Holonomy

This paper is a continuation of Math. Res. Lett. 12 (2005), 493–512. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of Sⁿ by looking at the conormal bundle of appropriate submanifolds of Sⁿ. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey–Lawson for submanifolds in Rⁿ in their pioneering paper, Acta Math. 148 (1982), 47–157. We also construct calibrated submanifolds in complete metrics with special holonomy G₂ and Spin(7) discovered by Bryant and Salamon (Duke Math. J. 58 (1989), 829–850) on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy. Mathematics Subject Classification (2000): 53-XX, 58-XX.     

Hybrid Plasma – Prospects for Application in Medicine and Biology

Russian Physics Journal - Different schemes and designs of generators of low-temperature hybrid plasma produced by simultaneous ionization of plasma-generating medium by an electron beam with...     

Carbenylative amination with N-tosylhydrazones

A Pd-catalyzed reaction of vinyl iodides and N-tosylhydrazones that assembles η(3)-allyl ligands through carbene insertion is demonstrated. Intramolecular trapping with nitrogen nucleophiles generates good yields of cinnamyl and pentadienyl amines like those found in alkaloid natural products. Carbenylative amination was the key reaction to complete the synthesis of the alkaloid caulophyllumine B. Migratory insertion was biased to provide allylamines with optical purity up to 64% ee, but in a lower yield.