Characteristic parameters and classification of one-dimensional cellular automata

We present definitions of characteristic parameters and discuss a classification of one-dimensional cellular automata. The parameters: probability of active sites, capacity dimension and spreading rate of difference patterns are defined on the image of the configuration space of all site states under a rule function of time evolution. On study of 2-state, 3-neighbor cellular automata we propose a new classification scheme of the rules, which gives quantitative grounds for the Wolfram's phenomenological classification.     

On the correlation equalities for the random-bond Ising model

We obtain several equalities of the configurationally averaged spin correlation functions for the random-bond Ising model by means of a gauge transformation. These equalities are shown to be useful to find the exact results for the internal energy, an upper bound of the specific heat, the equality for the zero-field susceptibility and the zero-field spin glass susceptibility, and so on.     

Exactly solvable model of a spin glass

Sherrington and Kirkpatrick presented a solvable model of a spin glass. In the solution, they used a mathematically unwarranted procedure. In the present article, we show that the problem is exactly solved by starting with the virial expansion formula, and confirm the results of Sherrington and Kirkpatrick. The solution is obtained for the random Ising magnet in which the external field of each site and the exchange integral between each pair of sites are random variables. We obtain the exact thermodynamic properties for this system in the limit of n_w→∞, assuming that the exchange integrals of a spin with O(n_w) neighbours are $\text{O(n}{}_{\mathrm{w}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ and the average value of each is O(n_w^?1). The system is found to show the spin-glass state as well as the paramagnetic and the ferromagnetic state.     

Critical properties of XY model on two-layer Villain－ferromagnetic lattice

We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane (J) and a ferromagnetic plane (I), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters (I,J), the system presents three phases: namely, a Kosterlitz－Thouless (KT) phase in which the two planes are critical for I predominant over J, a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of (I,J): the KT transition, the Ising transition and an XY-Ising transition with ν=0.849(3). It turns out that the Ising or XY-Ising transition is associated with the disappearance of the chiral order in the Villain plane.     

Lipase TL®-mediated kinetic resolution of benzoin: facile synthesis of (1R,2S)-erythro-2-amino-1,2-diphenylethanol

The lipase TL®-mediated kinetic resolution of (±)-benzoin (1) proceeded to give the corresponding optically pure benzoin (R)-1. On the other hand, (S)-benzoin-O-acetate (5) could be hydrolyzed without epimerization to give (S)-benzoin (S)-1, under alkaline conditions. Further, (R)-1 was converted to (1R,2S)-2-amino-1,2-diphenylethanol (99:1 er) according to the procedure reported previously.     

Design of a Photocatalytic [2+2] Cycloaddition Reaction Using Redox-Tag Strategy

The design of photocatalytic processes is important for a sustainable society. Key to these photocatalytic reactions is electron transfer. This article is focused on titanium dioxide photocatalyzed organic synthesis and the design of a new [2+2] cycloaddition reaction based on the electron transfer process. Electron transfer - not only between the substrate and the photocatalyst but also inter- and intramolecularly – is crucial for the reaction design. Radical cations were generated by the photocatalyst and trapped by alkenes. The resultant cyclobutyl radical cations were immediately reduced by the aryl rings via intramolecular electron transfer to obtain cyclobutane rings. The outcome of the reaction was controlled by substitution of the aryl ring and the linker connecting the aryl ring to the enol ether. The carefully designed substrates were highly effective for photocatalytic cycloaddition.