Uniform convexity of ψ-direct sums of Banach spaces

Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕_ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕_ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?_p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?_p,q is the Lorentz sequence space. These results extend the well-known fact for the ?_p-sum . Some other examples are also presented.     

Development of a high-sensitivity chromatographic separation system for pyridylaminated aldopentoses and aldohexoses

A rare sugar is considered to be a monosaccharide rarely found in nature. To investigate their natural distribution and biological roles, a robust analytical system must be used to isolate, identify, and quantify them. Herein, we report the development of such a system that can specifically quantify and chromatographically separate four aldopentoses and eight aldohexoses tagged with 2-aminopyridine. Purified monosaccharides derivatized with a pyridylamino moiety (PA–monosaccharides) are first chromatographed over a high-performance anion-exchange resin. But, because two of the PA–aldohexoses used in this study, PA–talose and PA–idose, co-elute with the common saccharides, PA–glucose and PA–mannose, respectively, a second chromatographic step, reversed-phase high-performance liquid chromatography, is used to completely separate them. Thus, as shown by the results of this study, chromatographic separation of PA–monosaccharides is achievable and provides a quantitative measurement of common and rare isomeric aldopentoses and aldohexoses.     

Facile synthesis of 2-azaazulenes from thiobenzoyl isocyanates using trimethylsilyldiazomethane

The reaction of trimethylsilyldiazomethane with thiobenzoyl isocyanates, in situ generated from thiazole-4,5-diones, yielded diazoketones, which were converted into 2-azaazulenes by the intramolecular Buchner reaction.     

Swelling of poly(ethylene oxide) gel in aqueous solutions of sodium dodecyl sulfate with added sodium chloride

The swelling behavior of poly(ethylene oxide) (PEO) gels in aqueous solutions of sodium dodecyl sulfate (SDS) with and without NaCl was investigated. In the absence of NaCl, PEO gels with different degrees of cross-linking began to swell from a concentration lower than the critical micelle concentration (cmc) of SDS, then showed sigmoidal enhancements of swelling in a higher SDS concentration region until the degrees of swelling reached maximum values. The SDS concentration at which the swelling began to appear was in reasonable agreement with the critical aggregation concentration (cac) value reported for the aqueous PEO system. For the cases where NaCl was present, the swelling behavior of PEO gel was different from that when NaCl was absent in the following way. The concentrations where the swelling begins to appear, and hence those where the degree of swelling rises steeply, decreased with an increase in NaCl concentration. The ultimate degrees of swelling at higher concentration regions also decreased with an increase in the NaCl concentration. The lowering of the SDS concentrations at which the PEO gel began to swell is in line with the decreases in the cmc of SDS solutions containing NaCl and also with the decreases in the cac of PEO solution. Electronic Publication     

Synthesis of β‐Methoxyacrylate Natural Products Based on Box‐PdII‐Catalyzed Intermolecular Methoxycarbonylation of Alkynoles

Bis(oxazoline)‐palladium(II) catalyzed carbonylation of homopropargyl alcohols afforded acyclic methoxyacrylate 2 and 6‐membered lactone 3a , 3b , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k in good combined yield. In the case of propargyl alcohols, 5‐membered lactones 3p , 3q , 16 were obtained in moderate yields. The one‐pot synthesis of kawa lactones 3a , 3r , 3s and formal synthesis of dihydroxycystothiazole A and dihydroxycystothiazole C are presented. To elucidate the stereochemistry of (+)‐annularin G and (?)‐annularin H, the first asymmetric syntheses of these natural products were achieved.     

Analysis of Th, U, Pu, and Am in radioactive metal waste using extraction chromatography

In order to analyze actinide elements in radioactive metal waste, the dissolution and chemical separation conditions were optimized. The surfaces of a type 304 stainless steel plate and of pipe waste sampled from the prototype advanced thermal reactor (Fugen) were dissolved in mixed acid solution (HNO₃:HCl:H₂O = 1:1:4). The resulting solution was evaporated to dryness and dissolved with 2 mol/dm³ of HNO₃ to prepare sample solutions. In order to analyze trivalent actinide elements in the sample solution containing a large amount of Fe(III) (>0.1 g) using TRU resin, the effect of Fe(III) concentration on the recovery of Am(III) and reduction effect of Fe(III) to Fe(II) with ascorbic acid were studied. On the basis of results of this study, chemical separation scheme was constructed and Pu and Am in the sample solutions were separated. Thorium and U in the sample solutions were separated with UTEVA resin. High recoveries for all experimented elements were obtained from the analysis of spiked sample solutions, the effectiveness of the method was confirmed.     

Separation of zeros for source signature identification under reverberant path conditions

This paper presents an approach to distinguishing the zeros representing a sound source from those representing the transfer function on the basis of Lyon's residue-sign model. In machinery noise diagnostics, the source signature must be separated from observation records under reverberant path conditions. In numerical examples and an experimental piano-string vibration analysis, the modal responses could be synthesized by using clustered line-spectrum modeling. The modeling error represented the source signature subject to the source characteristics being given by a finite impulse response. The modeling error can be interpreted as a remainder function necessary for the zeros representing the source signature.