On critical exponents of Dowling matroids

The critical problem in matroid theory is the problem to determine the critical exponent of a given representable matroid over a finite field. In this paper, we study the critical exponents of a class of representable matroids over finite fields, called Dowling matroids. Then the critical problem for a Dowling matroid is corresponding to the classical problem in coding theory to determine the maximum dimension k such that there exists an \([n,k,d]_q\) code for given n, d and q. We give a necessary and sufficient condition on the critical exponents of Dowling matroids by using a coding theoretical approach.     

ESR study on photodecomposition mechanism of oxidized poly(vinyl alcohol)

Photolysis behavior of oxidized poly(vinyl alcohol) (PVA) in which carbonyl groups were introduced by oxidation with sodium hypochlorite and periodic acid was investigated by using ESR spectrometry. Increased formation of PVA radicals was observed in the sample with low degree of oxidation, which showed an emphasized formation of triplet component radical. On the other hand, the formation of radicals tended to be depressed in the highly oxidized sample, and a singlet component was dominant in the ESR spectrum. By examining infrared and ultraviolet spectra of the oxidized sample, the sample was found to contain two structures, a saturated ketone group and an α,β-unsaturated group; the latter structure was intensified with increasing degree of oxidation. Based on ESR studies of the photoirradiated acetone and mesityl oxide, the models of saturated and α,β-unsaturated ketone structures in the oxidized PVA, respectively a photodecomposition mechanism of oxidized PVA was proposed.     

New method to characterize mesoscopic range and very small strain with using multi-wave X-ray diffraction

A new technique to observe mesoscopic-range strain fields (up to several hundreds of nm) is proposed, using modulation of the crystal-truncation-rod (CTR) scattering caused by Bragg reflection. This technique is particularly sensitive to small, long-range strain fields near crystal surfaces and interfaces, which are usually difficult to be discriminated by using Bragg reflection. A simple interpretation can be made for the modulation profile: the technique is physically simple with a few parameters fitted to the data and, independently of any model, is able to determine the total displacement due to mesoscopic strain field for depths up to several hundreds of nanometers. We applied this method to a Si(0 0 1) wafer whose surface is covered with a thermal oxide layer 3 nm thick. On the basis of the expressions we obtained for the modulation profile a least-squares fitting was carried out to give a result that under the oxide layer there exists a total displacement of −0.16 Å. It was also revealed from the visibility of the modulation profile that the total displacement has a static fluctuation of at least ±0.13 Å in the lateral direction. The new method can be used for the correction of the errors of the X-ray standing wave (XSW) method produced by strained layers near crystal surfaces.     

Conversion of disilanes to functional monosilanes: XII. The palladium(0)-catalyzed dechlorinative silylation of benzylic chlorides with methylchlorodisilanes. A facile route to benzylmethylchlorosilanes

This paper describes the facile dechlorinative silylation of benzylic chlorides of types XC₆H₄CH₂Cl (X = H, Me and Cl) and ClCH₂C₆H₄CH₂Cl (o-, m- and p-isomers) with methylchlorodisilanes ClMe₂SiSiMe₂Cl, ClMe₂SiSiMeCl₂ and Cl₂MeSiSiMeCl₂ in the presence of Pd(PPh₃)₄ to give the corresponding benzylmethylchlorosilanes in good to high yields.     

Normal integral bases of ∞ -ramified abelian extensions of totally real number fields

LetF be a totally real number field and [ a product of some real primes ofF. J. Brinkhuis gave a necessary condition for a finite abelian extension ofF which is unramified outside [ to have a normal integral basis. We consider the converse of his result and give a necessary and sufficient condition. Furthermore, we concretely express it whenF is a real quadratic field or a cyclic cubic field.     

Gas chromatographic determination for forensic purposes of petroleum fuel inhaled just before fatal burning

The determination of petroleum fuel in the blood of burned bodies was carried out by three different gas chromatographic procedures. Seven components of gasoline (isopentane, n-pentane, 2-methylpentane, benzene, 2-methylhexane, 3-methylhexane and toluene) and five of kerosene (xylene, C9H20, mesitylene, pseudocumene and C11H24) were chosen as indicators with a coefficient of variation of 5-24%. The methods were applied to four autopsy cases with a relatively low carboxyhaemoglobin (HbCO) content. When gasoline exposure had occurred, the blood concentrations determined were almost identical whatever the components selected. Great variations in the components determined were found after kerosene exposure, and hydrocarbons greater than or equal to C14 were hardly inhaled by the victims. A higher content of fuel in the left than in the right ventricular blood observed in the autopsy cases suggests fuel inhalation just before death. The same phenomenon was also observed in the content of blood HbCO. Determinations of petroleum fuel and HbCO in both the right and left ventricular blood would be useful for the forensic diagnosis on burned bodies with a low HbCO content.