The number of homomorphisms from a finite abelian group to a symmetric group

ABSTRACT

We present an algorithm to construct the automorphism group of a finite p-group. The method works down the lower exponent-p central series of the group. The central difficulty in each inductive step is a stabiliser computation; we introduce various approaches designed to simplify this computation.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

Hydrolytic Degradation and Monomer Recovery of Poly(butylene succinate) and Poly(butylene succinate/adipate) in the Melt

Aliphatic dicarboxylic acid/aliphatic diol‐derived polyesters, poly(butylene succinate) and poly(butylene succinate/adipate), have been hydrolytically degraded in the melt in high‐temperature and high‐pressure water over a wide temperature range of 180–300 °C for periods of up to 30 min. The formation/decomposition of succinic acid (SA), adipic acid (AA), and butane‐1,4‐diol (BD), plus the molecular weight change of PBS and PBSA were then investigated. SA and AA were recovered at maximum yields of 65–80%, whereas BD was recovered at a maximum yield of only 30%, probably because of its decomposition. The obtained results were compared with those reported for aliphatic hydroxycarboxylic acid‐derived polyesters and aromatic dicarboxylic acid/aliphatic diol‐derived polyesters.

     

Dielectric anisotropy of a homochiral rare-earth metal complex

A homochiral rare-earth metal Tb complex that exhibited a very large dielectric anisotropic property with a temperature-independent feature is obtained. Our findings on high-dielectric anisotropy will provide a new impetus in this field of materials science.     

Asymmetric cyclization-carbonylation of 2-alkyl-2-propargylcyclohexane-1,3-diones: facile access to optically active hydrindanes

Oxidative cyclization-carbonylation of 2-alkyl-2-propargylcyclohexane-1,3-diones mediated by Pd(TFA)₂/2,2′-isopropylidenebis[(4R)-4-(3,4-dimethoxyphenyl)-2-oxazoline] 28 afforded bicyclic-β-alkoxyacrylates in 51-74% yields with 72-82% ee. The products containing quaternary carbon were converted to optically active hydrindanes 33.