Dimension of Image Valuables Set up by Fashion Apparel Responsible Designer

Abstract

In our previous paper, we proposed diffusion equation model in behavioral space in order to explain the relationship between power of items and selling power. Behavioral space is the set composed of personal figures in various space of human behavior. Responsible designer of fashion apparels designs items of his brand by extracting subset composed of personal figures of clients of his brand. This study aims to elucidate the dimension of image valuables set up by responsible designer in behavioral space based on the diffusion model described in our previous paper. If the dimension is 1-dimension, it is shown that the total sales numbers of apparel change proportional to the root of time t. On the other hand, it is also shown that the total sales numbers of apparel change proportional to t and t1.5 in cases of 2-dimension and 3dimension, respectively. Further from these results, it is easily understood that the total sales numbers of apparel change proportional to tn/2 in general dimension n. From the data obtained by actual company in Japan, it becomes clear that total sales numbers of men's shirt and women's blouse change proportional to t1.5 and t.

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