Synthesis and characterization of manganese and cobalt pyroborates: M2B2O5 (M = Mn,Co)

The magnetic property of Co₂B₂O₅ and the optical property of M₂B₂O₅ (M = Mn, Co) were investigated. Co₂B₂O₅ showed antiferromagnetic behavior below the Néel temperature of T_N ≈ 45 K, and the Weiss temperature was T_W = +7.7 K. The effective magnetic moment of Co was 4.96 μ_B, which indicated that Co was divalent and in a high-spin state. Absorptions attributed to the d–d transitions in Mn²⁺ and Co²⁺ ions were observed at 250–650 nm in the diffuse reflection spectra. The optical absorption edges of Mn₂B₂O₅ and Co₂B₂O₅ were at 243 nm (5.11 eV) and 299 nm (4.15 eV), respectively.     

β(1,3) Branched heptadeca- and linear hexadeca-saccharides possessing an aminoalkyl group as a strong ligand to dectin-1

In this report, we describe the convergent synthesis of β(1,3) oligosaccharides containing an aminoalkyl group. The branched heptadecasaccharide and linear hexadecasaccharide acted as ligands of dectin-1 whose binding affinity was only 10-fold weaker than that of natural SPG and exhibited dectin-1 agonist activity.     

Unitary representations of the quantum group SU q (1,1): Structure of the dual space ofU q (sl(2))

Real forms of the quantum universal enveloping algebraU _q (sl(2)) and a topological quantum group associated with this algebra are discussed.     

Prediction of the lifetime of nitrile-butadiene rubber by FT-IR.

A quantitative measurement method with FT-IR was proposed for a thermal degradation analysis of nitrile-butadiene rubber (NBR). An NBR film was prepared as a model sample on a barium fluoride (BaF2) crystal plate, which was subjected to a heat treatment. The absorbances of various functional groups were measured directly by FT-IR after thermal degradation at high temperatures. By measuring the absorbances, it was possible to readily determine quantitatively each of the functional groups after the degradation of NBR. By assuming that the NBR lifetime was the point at which the absorbance of a carbon-carbon double bond reaches 45% of that prior to thermal treatment, a method for predicting the lifetime of NBR heated below 150 degrees C was proposed, by using an Arrhenius plot of the heating time versus heating temperature.     

Thermal phase transition of RbMnFe(CN)6 observed by X-ray emission and absorption spectroscopy

The thermal phase transition of RbMnFe(CN)₆ has been observed by Mn and Fe 3p-1s X-ray emission spectroscopy (XES) and 1s X-ray absorption spectroscopy (XAS). The thermal variations of the spin states and the valences of Mn and Fe were determined to be Mn²⁺(S=5/2)-NC-Fe³⁺(S=1/2) for the high-temperature (HT) phase and Mn³⁺(S=2)-NC-Fe²⁺(S=0) for the low-temperature (LT) phase. These transitions are thus caused by charge transfer between Mn and Fe. The temperature dependences of Mn and Fe 3p-1s XES and 1s XAS were observed as the composition of the spectra of the HT and LT phases. The ratios of the HT component in each spectrum show good agreement with the thermal transition curves observed with magnetic susceptibility measurements.     

Excess of a Lattice

 A pair (x,y) of elements in a lattice is mismatching if x is join-irreducible, y is meet-irreducible, and xy. The excess of a lattice L is defined by ex(L):=|L|− min{|V _x |+|I _y |:(x,y) is mismatching}, where V _x (I _y ) is the principal filter (ideal) generated by x(y), respectively. In the first half of this paper, it is shown that a lattice has excess zero (one) if and only if it is isomorphic to a Boolean lattice (one of a chain of length two, a diamond, and a pentagon), respectively. In the second half, we show that for each relatively complemented lattice which is not Boolean, its size is at most five times its excess. Moreover we determine extremal configurations. Received: September 2, 1999 Final version received: July 25, 2000 Acknowledgments. The author thanks the referee for constructive comments. Present address: Bureau of Human Resources, National Personnel Authority, 1-2-3 Kasumigaseki, Chiyoda-ku, Tokyo 100-8913, Japan. e-mail: abetet@jinji.go.jp     

Regularized product expressions of higher Riemann zeta functions

As a generalization of recent work by Kurokawa, Matsuda, and Wakayama (2004) we introduce a higher Riemann zeta function for an abstract sequence. Then we explicitly determine its regularized product expression.