Estimating function with asymptotic bias and its estimator

We introduce the estimating function with asymptotic bias and investigate the asymptotic behavior of the estimator based on it by using their relationship. The estimator based on the estimating function with asymptotic bias has the asymptotic normality with asymptotic bias. We show that this theory has several interesting applications in practical statistics.     

A matrix partition problem

In the set of positive definite semi-integral symmetric matrices we propose a partition problem. Then by introducing the notion of “additively prime” we obtain the generating function for this problem. Finally we establish the analyticity of the generating function.     

Zero modes of quantum fluctuations for the instanton

All possible zero eigenvalues for quantum fluctuations in the presence of the BPST instanton are treated in the light of the spontaneous breakdown of conformal symmetry. The zero eigensolution in the fermion equation is automatically given as a consequence of the breakdown of the conformal super-symmetry.     

The reaction of aqua-(ethylenediaminetetra-acetato)ruthenium(III) with o-phenylenediamine under aerobic conditions

An electron-transfer reaction between [Ru(III)(Hedta)(H₂O)] and o-phenylenediamine in the presence of O₂ takes place to give a Ru(II)-edta complex with coordinated (bidentate) o-benzoquinone diimine. The complex obtained has been characterized by analysis, magnetic measurements, electronic, IR, ¹H and ¹³C NMR spectral data.     

Chain conformations of block copolymers

An analytical theory of block copolymer conformations is developed for systematically studying the effects of the chain length, chain architecture, and segment interactions. The main results obtained for AB diblock and ABA triblock chains are as follows: (i) In the absence of AA and BB interactions, both diblock and triblock chains collapse to a dense form if the AB interaction is attractive. In the collapsed coil form, the mean-square end-to-end distance 〈R²〉 is proportional to the square root of the number of segments n^1/2. (ii) The diblock chain has a dumbbell form if AA and BB interactions are attractive and AB interaction repulsive, but the triblock chain collapses. In the dumbbell form, 〈R²〉 is proportional to n.     

Correlation of57Fe hyperfine interactions with Fe-Fe distance in Laves phase compounds RFe2 (R=rare earth)

The⁵⁷Fe Mössbauer isomer shifts and magnetic hyperfine fields in Laves phase compounds RFe₂ (R=Pr, Nd and Sm) are studied with particular reference to the effect of the Fe–Fe interatomic distance on the hyperfine interactions. It is shown that the charge density at the Fe nuclei scales linearly with fractional volume change up to 20%. The⁵⁷Fe hyperfine field corrected for the influence of rare-earth moment shows a systematic variation with the distance, which can be understood in terms of the Bethe-Slater curve arguments. The similarity of the atomic volume dependence of the⁵⁷Fe hyperfine interactions in Lves phase compounds to those in iron with close-packed structure is emphasized.This paper is based on a paper presented at the 5th Int. Conf. on hyperfine interactions, Berlin, July 21–25, 1980.     

Heat capacity of a five-coordinated iron(III) complex,chlorobis(N,N-dimethyldithiocarbamato) iron(III), between 0.4 and 300 k: New finding of a magnetic phase transition

The heat capacity of the title complex, Fe[S₂CN(CH₃)₂]₂Cl, has been measured between 0.4 and 300 K. A λ -type phase transition with a small shoulder arising from magnetic ordering was found at (0.609 ± 0.005) K. The character of the ordered phase has been suggested to be ferromagnetic on the basis of comparison between the methyl- and ethyl-homologues. The magnetic hyperfine structure of the Mössbauer spectra and the line broadening due to electronic relaxation effects at 1.2 K hitherto reported are concluded to result from a critical slowing-down when the magnetic transition temperature is approached from the high-temperature side. A Schottky-type anomaly arising from the zero-field splitting of a single ferric ion was observed around 2 K. The excess entropy beyond the lattice contribution at low temperatures amounts to (14.05 ±0.27) J K^?1mol^?1, which cannot be accounted for solely by the magnetic entropy of Rln 4 (= 11.53 JK^?1mol^?1) for the intermediate spin of $\text{S =}\text{3}\text{2}$. Two possibilities concerning additional conntribution have been discussed; one is a mixing of spin species of $\text{S =}\text{5}\text{2}$ and the other is a tunnel-splitting of the rotational levels of four methyl-constituents. The present study cannot give a definite conclusion as to the existence of dimeric units suggested from Mössbauer spectroscopy.     

Heat capacity of [Ni(OCH3)(acac)(CH3OH)]4 from 0.4 to 285 K: Spin interaction and tunnel-splitting of internal rotation of methyl group

The heat capacity of the tetranuclear nickel cluster complex, tetrakis [μ₃-methoxo-2,4-pentanedionato (methanol) nickel (2)], has been measured from 0.4 to 285 K. Contrary to the previous prediction by Bertrand et al.[6], that this complex exhibits an intercluster ferromagnetic spin coupling, the present heat capacity measurement shows no indication of the spin-ordering effect caused by the intercluster interaction at least down to 0.4 K. Instead, a heat capacity anomaly centered around 1.5 K with a shoulder at 0.5 K has been observed. This anomaly is well accounted for in terms of both a level splitting of the ground S = 4 state due to a uni-axial crystalline anisotropy and a tunnel-splitting of the rotational levels of methyl groups. The intracluster spin exchange constant J and the single-ion zero-field splitting parameter D are determined to be $\text{J}\text{hc}\text{= 7.0 cm}{}^{\mathrm{?1}}$ and $\text{D}\text{hc}\text{= 3.65 cm}{}^{\mathrm{?1}}$ (h being the Planck constant and c the speed of light in a vacuum). The temperature dependence of the effective Bohr magneton [6] is also satisfactorily accounted for on the basis of this model. The tunnel-splitting δ of the lowest rotational level of the four methyl groups belonging to methoxides is estimated to be $\text{δ}\text{hc}\text{= 0.4–0.7 cm}{}^{\mathrm{?1}}$ and the corresponding potential barrier V_o is found to be V_o = 1.9–1.5 kJmol^?1.     

Ion heating and high-energy-particle production by ion-cyclotron heating in the large helical device

Ion-cyclotron heating was applied to the Large Helical Device. When the proton-cyclotron resonance was near the saddle point of the magnetic field-strength plane, strong ion-cyclotron damping occurred. Under these conditions efficient plasma heating was achieved for more than one minute. A high-energy ion tail was observed, and the effective tail temperature was determined by a balance between the wave acceleration and the electron-drag relaxation. There was no apparent sign of particle orbit loss effect in the investigated density range of 0.8-1.3x10(19) m(-3).