Homomorphisms between JC＊-algebras and Lie C＊-algebras

It is shown that every almost ＊-homomorphism h ： A→B of a unital JC＊-algebra A to a unital JC＊-algebra B is a ＊-homomorphism when h（rx） = rh（x） （r 〉 1） for all x∈A, and that every almost linear mapping h ： A→B is a ＊-homomorphism when h（2^nu o y） - h（2^nu） o h（y）, h（3^nu o y） - h（3^nu） o h（y） or h（q^nu o y） = h（q^nu） o h（y） for all unitaries u ∈A, all y ∈A, and n = 0, 1,.... Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings. We prove that every almost ＊-homomorphism h ： A→B of a unital Lie C＊-algebra A to a unital Lie C＊-algebra B is a ＊-homomorphism when h（rx） = rh（x） （r 〉 1） for all x ∈A.     

Hydrogen-bonded systems between monocarboxylic acids and the trinuclear cluster cation [H3Ru3(C6H6)(C6Me6)2(O)]: cold-spray ionisation mass spectroscopic and X-ray crystallographic studies

The hydrogen-bonded systems formed between monocarboxylic acid derivatives and the trinuclear arene-ruthenium cluster cation [H₃Ru₃(C₆H₆)(C₆Me₆)₂(O)]⁺ (1) have been studied in solution by cold-spray ionisation mass spectroscopy (CSI-MS) and in the solid state by single-crystal X-ray structure analysis of the tetrafluoroborate salts. The presence of 1:1 (acid:cluster) adducts in acetone solution has been clearly demonstrated by CSI-MS. Single-crystal X-ray structure analyses of selected acid-cluster complexes show that in every case the hydroxyl of the acid function interacts strongly with the μ₃-oxo ligand of cation 1, the O ? O distance ranging from 2.499(9) to 2.595(11) Å.     

Perturbation method for determining the group of invariance of hierarchical models

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.     

The theoretical study for the perovskite-type manganese fluorides of KMnF3, RbMnF3 and K1−xLixMnF3

We performed the hybrid-density functional theory (DFT) calculations for the strongly correlated perovskite-type manganese fluorides of KMnF₃, RbMnF₃ and K_1?xLi_xMnF₃ In both solids, UBHHLYP, which contains 50% Hartree–Fock exchange term, provided the reasonable effective exchange integral (J_ab) values, in comparison with the experimental ones. In order to investigate the intrinsic roles of counter cations precisely, we examined the variations of the total energy and J_ab value, assuming the displacement of counter cation toward <1 0 0> direction. In KMnF₃ (RbMnF₃), it was found that the steric repulsion between potassium (rubidium) and bottleneck is large, while that between lithium and bottleneck is negligible in K_1?xLi_xMnF₃. Finally, we also showed the possibility of the lithium ion conduction in the antiferromagnetic K_1?xLi_xMnF₃. It was concluded that the lithium ion conduction in RMnF₃ is possible, if the vacancy at R site exists.