The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

Photoinduced electron accumulation in colloidally dispersed wide band-gap semiconductor nanosheets

We investigated photoinduced electron accumulation in a colloidal system of layered hexaniobate that is known as a photocatalytically active wide band-gap semiconductor, and attempted to control the photoresponse by introducing additives into the colloid. The inorganic nanosheets were obtained by exfoliation of the layered oxide. UV-irradiation of the colloids led to electron accumulation in the nanosheets to generate reduced niobate species. Propylammonium ions introduced as the exfoliating reagent and present as the counter ions of niobate nanosheets were indicated as the electron donor that stabilized the electron-accumulating state. Yield and half-life of the reduced niobate species greatly increased by adding an appropriate amount of photochemically inert clay nanosheets, while they increased only a little by the addition of molecular electron donors such as EDTA and triethanolamine. Moreover, the molecular species diminished the enhancement effect of the clay nanosheets. The results suggested that the photochemical event was not explained by direct interactions between the semiconductor nanosheets and the additives at molecular level but governed by indirect interactions between the colloid components regulated by the colloid structure.     

Synthesis and reduction ability of borane complexes of 2-aminopyridine derivative having a chiral center at the amino nitrogen

A novel method for synthesis of a chiral amine borane is described and selective reductions of carbonyl compounds with the amine borane are investigated.     

Hydrolysis of 4-cyano-1-ethoxypyrimido[1,6-a]benzimidazole: Formation of a ynaminonitrile and benzimidazolidines

The title compound 4 was hydrolyzed to a new type of ynaminonitrile 5 and benzimidazolidines 7 and 9 under acidic or basic conditions. Reaction mechanisms were proposed.     

Indirect determination of sub-ng ml-1 levels of phosphorus in waters by di-isobutyl ketone extraction of reduced molybdoantimonylphosphoric acid an

Reduced molybdoantimonylphosphoric acid is extracted into di-isobutyl ketone (DIBK) and phosphorus in the extract is indirectly determined by inductively-coupled plasma emission spectrometric measurement of the Mo II 202.03-nm or Sb I 206.83-nm line. Washing of the extract with acid is unnecessary because of the low solubility of DIBK in water. Arsenic(III), Si, Ge, Fe(III) and most anions do not cause serious interference but arsenic(V) must be absent. The detection limits are 5.2 and 45 pg P ml^-1, and the relative standard deviations for 1 μg of phosphorus are 2.0% and 2.5%, for molybdenum and antimony measurements, respectively. The method is applied in the analysis of river and seawater.     

sdg boson model in the SU(3) scheme

Basic properties of the interacting boson model with s-, d- and g-bosons are investigated in rotational nuclei. An SU(3)-seniority scheme is found for the classification of physically important states according to a group reduction chain U(15) ? SU(3). The capability of describing rotational bands increases enormously in comparison with the ordinary sd interacting boson model. The sdg boson model is shown to be able to describe the so-called anharmonicity effect recently observed in the ¹⁶⁸Er nucleus.     

Beta-NMR measurement of 58Cu in Si

The β-NMR study of short-lived nucleus ⁵⁸Cu (I ^π ?=?1^?+?, T _1/2?=?3.2 s) in Si has been performed. Spin polarization of ⁵⁸Cu induced by the charge exchange reaction of ⁵⁸Ni was observed in Si at 15 K. The ⁵⁸Cu magnetic moment $|\upmu[^{58}\mbox{Cu}]| = (0.46 \pm 0.03)\upmu_{\rm N}$ deduced from the β-NMR spectrum is consistent with the previous results on the laser spectroscopy. The present result shows that the ⁵⁸Cu nucleus is promising as a new nuclear probe for the microscopic study of Cu impurities in Si.     

Precise nuclear moments of extremely proton-rich nuclus 23 Al

Electric quadrupole coupling constant eqQ/h of the extremely proton-rich ²³Al (I ^π ?=?5/2^?+?, T _1/2?=?0.47 s) nucleus implanted into an Al₂O₃ single crystal has been measured for the first time, using the β-ray detecting nuclear quadrupole resonance method (β-NQR) in a high magnetic field. As a preliminary result, the quadrupole coupling constant was determined as |eqQ/h(²³Al) |?=?2.66±0.77 MHz. Using the quadrupole coupling constant of ²⁷Al in Al₂O₃ as a reference, the Q moment of the ground state of ²³Al was extracted as |Q(²³Al)|?~?160 mb, which is well explained by the shell model calculation in the sd-shell model space with the USD interaction.