Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

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.     

A SENSITIVE METHOD FOR DETERMINING CHLOROPHYLL b IN PLANT EXTRACTS

Abstract— A new method of using hydroxylamine as the reagent was developed to determine the concentrations of chlorophylls a and b in plant extracts accurately and sensitively. The method is based on the principle that hydroxylamine reacts in a short time with the aldehyde group of chlorophyll b in 95 per cent methanol at pH 5.8 to afford a derivative having a red band similar in position to the red band of chlorophyll a , while the spectrum of chlorophyll a is unaffected by the treatment with hydroxylamine. The method includes the measurements of absorbanlce for the mixture of a plant extract with hydroxylamine and for the reagent blank at a single wavelength, 666 mμ, and the concentrations of chlorophylls a and b are calculated from the absorbance value for the reagent blank and the increment of absorbance due to the reaction. By measuring this increment directly by difference photometry, one can determine a low concentration of chlorophyll b relative to chlorophyll a . The contents of chlorophylls in matured and etiolated leaves were determined by the method, and the errors included in this method were shown to be smaller than those in a commonly used technique including the measurements at two different wavelengths.     

Synthesis of pyrimidinopurinophanes

Synthesis and structures of the title compounds 2a–d are described. In spite of non-parallel orientation of the two base rings, fairly large hypochromism was observed for 2a–d.     

Hydrothermal synthesis of potassium molybdenum oxide bronzes: structure-inheriting solid-state route to blue bronze and dissolution/deposition route to red bronze

The hydrothermal syntheses of the alkali metal molybdenum bronzes from starting solids (H_xMoO₃) with structural affinities to the desired products were investigated. Single-phase potassium blue and red bronzes were prepared by the hydrothermal treatments at around 430 K, and characterized by powder X-ray diffraction, IR spectroscopy, and SEM. The formation processes of these two bronzes during the hydrothermal treatments were found to differ. The blue bronze was formed by a structure-inheriting solid-state route from H_xMoO₃ with x<0.3, whereas the red bronze was formed for x>0.3 through a solution dissolution/deposition route via the formation of MoO₃+MoO₂.