Experimental results of an N-S junction and analysis of the results using the Arnold theory were reported. Au and Pb were employed as a normal metal and a superconducting material, respectively. The excess current effect due to the Andreev reflection was observed in the current-voltage characteristics of an N-S junction whose normal resistance was 1.603 Ω. The excess current at 4.62 K was about 0.7 mA when the applied voltage was 2 mV. The barrier height and width were estimated to be 1.0169 eV and 0.7 , respectively, by comparing the experimental results and analysis based on the Arnold theory. In the voltage region less than 2 mV, the theory well agreed with the experiment. Moreover, the applied voltage dependence of the supercurrent and quasiparticle current were separately calculated. It was made clear that the supercurrent was larger than the quasiparticle current in the voltage region less than 2Δ/e, where Δ is the superconducting energy gap and e is the absolute value of an electron's charge. The supercurrent began to gradually saturate when the voltage was higher than Δ/e and became constant at the applied voltage greater than 2Δ/e. In our experiment, the excess current larger than expected from the Arnold theory was observed in the voltage region higher than 2Δ/e.

In this letter, a generalized syndrome polynomial is proposed from which several decoding key-equations for Reed-Solomon codes can be derived systematically. These equations are always solved by the extended Euclidean algorithm.

A theoretical conjecture on fractal dimensions of a dendrite distribution in neural networks is presented on the basis of the dendrite tree model. It is shown that the fractal dimensions obtained by the model are consistent with the recent experimental data.