Nonlinear interpolation of functions of very many variables

The difficulty is first shown in the nonlinear interpolation of functions defined in a space of very many dimensions. There is a method using a sampling technique [J. ACM, Vol. 17, pp. 420–425, July 1970] that works fairly well in the regime ofk~10?20 (k=number of dimensions). The sampling errors, however, increase exponentially with increasingk, so that fork greater than the above values the computation is no more feasible. This is due to the subtraction between two large sums of about the same magnitude, each of which suffers stochastic fluctuations accompanying the samplings. To avoid this difficulty, a “pairwise” sampling method is devised where one draws two samples at a time when required, one from each of these two sums of terms. With the use of this technique, standard errors are reduced by orders of magnitude. Some details of algorithm are given together with typical computed examples.     

Identification of gas emanated from human skin: methane, ethylene, and ethane.

We investigated whether methane, ethylene and ethane gas can be detected in gas emanating from human skin, which is called skin gas. Skin gas was collected with a homemade stainless-steel trap system, which was cooled with liquid nitrogen, and analyzed with a gas chromatograph fitted with a flame ionization detector (FID). Skin-gas samples were obtained by covering a hand for 30 min with a polyfluorovinyl bag in which pure helium gas was introduced. The bag, the trap system and GC were set up online to avoid any contamination by air. Methane, ethylene and ethane in skin gas were successfully collected at an average amount emanated for 30 min (from ten subjects) of 150 +/- 63, 20 +/- 11 and 17 +/- 8 [mean +/- SD] pg/cm2, respectively.     

The aggregations or crystals of metal-complex dye (C. I. Acid Yellow 161) on wool fibre

Summary The visible absorption spectra of dye crystals and the cross-section of wool fibre dyed with metal complex dye (C. I. Acid Yellow 161) were measured by means of a microspectrophotometer. The spectrum of crystal showed sharp and high maximum at 410 nm referred to as the peak from single crystal of the dye. The spectrum of the cross-section of dyed fibre showed two peaks of 410 nm (crystal-band) and 435 nm (monomeric state of the dye). Also, the electron diffraction pattern of the cross-section of dyed wool fibre showed the reflection ring of chromium. These results suggested that the dye should be present in the wool fibre in the monomeric, aggregate or crystalline state.

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Zusammenfassung Mit Hilfe des Mikrospektrophotometers wurden die Absorptionsspektren im Sichtbaren von Farbstoffkristallen und von Querschnitten der mit Metallkomplex-Farbstoff (C. I. Acid Yellow 161) gefärbten Woll-Fasern gemessen. Die Kristall-Spektren zeigen ein scharfes und hohes Maximum bei 410 nm, das der Bande des Farbstoffkristalls zugeordnet werden muß. Die Spektren der Querschnitte gefärbter Fasern zeigen zwei Banden: seine bei 410 nm (Kristallbande) und eine bei 435 nm (Monomerbande). Auch zeigen die Elektronenbeugungen an Querschnitten gefärbter Fasern die Ring des Chromes. Dies läßt vermuten, daß in den Wollfasern Monomeres, Aggregate oder Kristalle des Farbstoffs existieren.

     

Electronic structure of TiH2

The electronic structure of TiH₂ has been studied using the augmented-plane-wave method and the LCAO interpolation. The density of states and its orbital components show that the conduction band is Ti d-like and that the valence band is largely derived from the hydrogen orbitals with small Ti 3d hybridization. The electronic charges on the hydrogen atom are ～ 1.5 as compared to 1.6–1.7 of the rare-earth metal hydrides.