By starting with a reaction-diffusion equation a mapping model for the continuous system is proposed. The transition from the uniform state to the non-uniform one occurs at the same value of the diffusion constant for the mapping model as for the original reaction-diffusion equation if the transition exists. The mapping model is further studied by adopting the logistic model in one-dimensional space with a periodic boundary condition. Equal time spectra in wave number space and power spectra for several values of wave numbers are numerically obtained. A comparison of the numerical results of the equal time spectra with a simple theory is made to give a satisfactory agreement for large wave numbers.

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An attempt has been made to understand various results obtained so far in the one-dimensional isotropic antiferromagnetic spin system from the point of view of the Fermi liquid theory. Specific heat thus obtained is very close to the value given by Bonner and Fisher by the numerical calCulation. A brief discussion is. made on the exact solution of the magnetic susceptibility.(2) a connection. with the conventional many-body theory can be examined,

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