First Stereoselective Total Synthesis of FD‐594 Aglycon

Stereocontrolled access to the hexacyclic core of FD‐594 has been achieved. The key steps include the intramolecular S_NAr reaction for construction of the densely functionalized xanthone skeleton, the stereoselective lactone cleavage using a chiral nucleophile to induce the axial stereochemistry, and the SmI₂‐mediated pinacol cyclization for the stereocontrolled conversion of axially chiral biaryl dialdehyde into the corresponding trans diol.

     

Study on Stereochemical Activity of Lone Pair Electrons in Sulfur and Halogen Coordinated Antimony(III) Complexes by 121Sb Mössbauer Spectroscopy

We have measured ¹²¹Sb Mössbauer spectra at 20 K for 52 compounds of antimony(III). An Sb(III) atom with the electron configuration [Kr] 4d ¹⁰5s ² has a lone pair electrons. The stereochemical property of the lone pair has been found to depend very much on the kinds of atoms surrounding the antimony atom and the configurations of the coordinating atoms.     

Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.     

Convergence of general decompositions of exponential operators

A general theorem is proved concerning the convergence of decompositions of exponential operators in a Banach space (or normed space). As a corollary, the convergence of fractal decompositions is proved. The convergence of generalized. Trotter-like formulas is also shown to result from the general theorem.     

The variational theory and rate equation method with applications to relaxation near the instability point

The variational principle of Glansdorff and Prigogine is formulated for stochastic processes and the relation between this method and the rate equation method is discussed in a certain frame-work of variational functions. An application is given to the Fokker-Planck equation to describe the formation process of macroscopic order and to obtain the onset time.     

Monte Carlo simulations of the two-dimensional quantal and classical spin systems — A new type of phase transition with vortices

A new type of phase transition has been found in the two-dimensional XY-model using Monte Carlo simulations, which show a divergence of susceptibility, but no divergence of specific heat. Vortices appear below T_c as was predicted by Kosterlitz and Thouless.