Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Altered expression of polyhydroxyalkanoate synthase gene and its effect on poly[(R)-3-hydroxybutyrate] synthesis in recombinant Escherichia coli

Polyhydroxyalkanoate (PHA) synthase (PhaC) from Wautersia eutropha was expressed in a wide range of production level in Escherichia coli XL1-Blue cells and its effects on PhaC activity, poly[(R)-3-hydroxybutyrate] [P(3HB)] production and its molecular weights were investigated. The production level of PhaC was controlled both by the amount of chemical inducer (isopropyl-β-d-thiogalactopyranoside, IPTG) added into the medium and the use of different copy number of plasmids. In a flask experiment, as PhaC production level in the cells increased, the PhaC activity also increased in the range of low PhaC concentration. However, PhaC activity did not further increase in the range of high PhaC concentration, probably due to the formation of inclusion body in the cells. The molecular weight of P(3HB) was found to decrease with increasing PhaC activity. This trend was also verified in high cell density cultivation using 10-l jar fermentor. Furthermore, we demonstrated that the use of low copy number plasmid and appropriate induction of PhaC expression were effective in achieving both high productivity and high molecular weight of P(3HB).     

Rapid and sensitive determination of the conversion of UV-cured acrylic ester resins by pyrolysis-gas chromatography in the presence of an organic alkali.

The double-bond conversion of UV-cured resins prepared from pentaerythritol triacrylate (PETA) was determined by pyrolysis-gas chromatography in the presence of an organic alkali, tetramethylammonium hydroxide (TMAH). The pyrogram of the uncured prepolymer compound, consisting of PETA and a photoinitiator, 2,2-dimethoxy-2-phenylacetophenone, contained specific products reflecting the original acrylate structure, such as methyl acrylate (MA) and methyl ethers of pentaerithritol. Meanwhile, in pyrograms of the UV-cured PETA, the yields of MA considerably decreased. The double-bond conversions of the cured resins, irradiated with various UV dosages, were calculated based on the relative yields of MA among specific products in the pyrograms. The conversions determined by this approach were analyzed by comparing them with those estimated by Fourier-transform infrared spectroscopy.     

Simple and rapid determination of trace amounts of gold(III), palladium(II), and platinum(IV) in industrial waste solutions after recovery of noble metals by combined use of GFAAS and anion-exchange separation.

A simple and rapid method for the analysis of trace amounts of gold(III), palladium(II), and platinum(IV) by the combined use of graphite furnace atomic absorption spectrometry and anion-exchange separation was proposed, and successfully applied to the rapid determination of metals in industrial waste solutions obtained from the final process of noble-metal recovery factories, because noble metals can be selectively and quantitatively separated to a high degree by using a small column containing only a 0.7 g-portion of a common anion-exchange resin and a dilute thiourea solution.     

Simple and rapid spectrophotometric determination of iron after preconcentration as its 1,10-phenanthroline complex on the natural polymer "chitin"

Preconcentration by collection of metal complexes on chitin has been applied to the spectrophotometric determination of iron in water. The iron is collected as its 1,10-phenanthroline (phen) complex on a column of chitin in the presence of tetraphenylborate as counter-ion. The iron(II)-phen complex retained on the chitin is eluted with an acetone-1M acetic acid mixture (8:2 v/v), and the absorbance of the eluate is measured at 512 nm. Beer's law is obeyed over the concentration range 1.1-11.2 mug of iron in 10 ml of eluate. In the presence of EDTA as masking agent, Ca, Mg, Al, Mn, Zn, Cd and Pb do not interfere in concentrations up to 100 times that of iron(II) and Co, Ni and Cu do not interfere in concentrations up to 20 times that of iron(II). Common inorganic anions do not interfere in concentrations up to 10,000 times that of iron(II). The proposed method has been applied to determination of iron in tap water.     

Novel ring transformation of thiazolidine to oxazolidine: acyl halide-promoted intramolecular rearrangement of 4(R)-hydroxymethyl-3-methyl-1,3-thiazolidine

An interesting transformation occurs during acylation of 4(R)-hydroxymethyl-3-methyl-1,3-thiazolidine when 4(R)-acylthiomethyl-3-methyl-1,3-oxazolidines are yielded: the reaction competing with O-acylation is controlled by the bulkiness of the acyl group.