The Many-body problem is very important issue in physics. Usually perturbation calculations based on the Green's function have been used to analyze such a problem, however, infinite orders of perturbation calculations are required to obtain exact solutions, thus resulting in the analytical and numerical difficulties. To overhaul such difficulties, we propose the new calculation method based on the differential forms, which are able to evaluate exact solutions if Hamiltonian is composed of Fermi particles. Since our proposed method is based on time evolution equations, comparisons with the calculations derived from Feynman Kernel is possible, with showing complete agreement. Furthermore we applied this method to the simplest Anderson Hamiltonian to investigate the appearance of magnetic moment. The calculation results show that magnetic moment easily disappears with small Coulomb repulsive energy, possibly implying the spin fluctuations.

Intermetallic compounds (IMCs), known for their hardness, play an important role in the precipitation strengthening of alloys. However, precipitation in excessive amounts or as large particles can result in embrittlement of the material. Thus, controlling the distribution of IMCs among the matrix is crucial for the design of strong and ductile alloys. In this research, a supersaturated Ti-Cu alloy formed by Laser Powder Bed Fusion (L-PBF) was heat-treated at different phase regions to produce lamellar, network, and dispersed distributions of Ti₂Cu IMC precipitates. To comprehensively understand the formation mechanisms of each IMC distribution structure, in-situ microstructure observation was performed during the heat-treatments. The lamellar IMC structure obtained from heat treatment above the beta-transus temperature, was found to derive from the rejection of Cu atoms towards the boundaries of lamellar alpha grains formed during cooling. The network IMC structure obtained from heat-treatment in the α+β phase region involved the formation of a Cu-rich β-Ti layer between α-Ti grains during heating, and subsequent precipitation of Ti₂Cu into an α-encapsulating network upon cooling. Finally, the dispersed structure of IMCs was observed to result from regular nucleation and growth of Ti₂Cu during heat treatment in the α+IMC region.

本誌第69巻第5号に掲載の永瀬丈嗣氏，寺井智之氏，松室光昭氏，武村守氏の研究論「Fe-P-C-Ag液体分離金属ガラスの合金設計と凝固組織」につきまして，著者より訂正の申し出がありました．訂正箇所は下記の通りです．

P. 187. Figure caption, Fig. 2, 引用文献

（正）[46]

（誤）[33]

P. 186. 本文右段5行目

（正）ロール接地面（Wheel-contacted side, WH）と自由表面側（Free Surface side, FS）が明瞭に区別される場合（典型例は文献[48]）と，区別が明確でない場合（典型例は文献[40]）が報告されている．

（誤）ロール接地面（Wheel-contacted side, WH）と自由表面側（Free Surface side, FS）が明瞭に区別される場合と，区別が明確でない場合が報告されている．