From November 15th to 17th, 2013, the 76th Symposium of the Science on Form was held at Aoyama Gakuin University in Shibuya-ku, Tokyo, Japan. The theme of the symposium was "Forms recognized in Economics and Business Administration" (The Society for Science on Form, Japan, 2013). Due to their abstract nature, Economics and Business Administration have not received much attention academically in the .eld of science of form.

Therefore, on this occasion, we found it necessary to take up this theme again to contribute to the advancement of the "Science of Form". At the symposium, oral presentations were given on subjects related to "Economics or Business Administration and form", in which the topics were not limited only to a tangible form, but also included form as an abstract concept.

On the first day of the symposium, Professor Akiko Kamesaka from Aoyama Gakuin University School of Business Administration gave a presentation as an invited lecturer (Kamesaka, 2013). On the second day, Professor Takeshi Yoshida from Aoyama Gakuin University School of Business Administration also gave a presentation as a guest lecturer (Yoshida, 2013), and Professor Hiroki Takada from Fukui University Graduate School of Engineering gave a presentation as a special lecturer (Takada, 2013). In addition, some society members also gave insightful reports during general presentation sessions (Suzuki et al., 2013; Takaki, 2013).

To commemorate these achievements, the editorial board of this journal FORMA of the Society of Science on Form planned to publish an issue specific to this symposium.

From the end of 2014 through 2015, we received six papers from five researchers who are at the forefront of fields relevant to this issue. Three original papers, written by Professor Yoshida, Aoyama Gakuin University, Professor Takayuki Morimoto, Department of Mathematical Sciences, Kwansei Gakuin University, and Professor Takada, Fukui University are included. Two review articles were written by Professor Emeritus Ryuji Takaki, Tokyo University of Agriculture and Technology and Professor Elly Shiozawa, Meiji University School of Commerce. One additional paper was posted by Professor Emeritus Takaki as a forum article, which was related to "the Debate about the Future of Science of the Form" in the symposium.

We hope that these six papers will contribute to the future developments of the Society for Science on Form, Japan.

Several examples of branching structures in the nature, social structures and the human body are introduced, and results of their analyses are given. It is shown that the Horton's law, which is confirmed for river branching structures, is satisfied also in variety of branching structures in the nature and human societies. It is suggested that these structures are constructed owing to mechanisms similar to that for river structure. As for the branching structures in human body some trials are introduced to construct them numerically by the use of mathematical models. The object of this review article is to show that the analyses of branching forms are interesting topics as the science of forms.

Utilizing specific forms of communication will lower health care costs by increasing productivity and efficiency in the health care sector. Firstly, we analyzed the form of communication in the context of risk management. The health care provider was the focus. Specifically we examined the checklist used by surgeons to prevent malpractice incidences; reducing complications after surgery or general treatments will therefore lower the mortality rate and result in lowering health care costs. Secondly, from the potential-patient aspect of health care (preventive medicine), we took up the form of communication in the context of Kotler's social marketing. Through promotional strategies, such as campaigns, the general public will have more knowledge of diseases; people would know what to expect and what would be the consequences. This paper sets the framework for analyzing the two forms of health care communication.

In academic research and practice of management, there are three different and important factors, or three Katas (which represent the Japanese words that denote forms of enterprise, patterns of corporate activity, and methods of business). Certainly, there has been much research on each topic, in an uncoordinated fashion, in both academic investigations and in practical applications. Although we need to consider them altogether, thus far, there is almost no comprehensive research on these factors. This study, therefore, presents preliminary conceptual research on these topics to resolve the associated problems and further advance the research on Katas.

This study investigates European option pricing under fractional Brownian motion (fBm) and applies it to realized volatility (RV). The RV measure is selected because it uniquely exhibits simultaneous stationarity and long-range dependency properties in financial time series, as shown in our empirical study. Meanwhile, the Black-Scholes differential equation is not well defined when the underlying assets follow fBm with the Hurst exponent H ≠ ½ because fBm is not a semimartingale. Thus, we compute the European option prices using a previously proposed fractional Black-Scholes formula. Our empirical study is conducted on Tokyo Stock Price Index data from January 06, 1997 to December 30, 2013 with a sample size of 4177.

Any factor that exert the influence on the process of JP¥/US$ exchanges rate has been discussed widely by researchers in academic and business fields. In some cases, for instance, the cause of changes was explained by many macro-economical factors and they tried to explain by stochastic and statistical model. However, a heavy fall was necessarily expressed. We attempt to express the change of the JP¥/US$ exchange rate in addition to it by a phase transition model with noise. We carried out some empirical studies with a fractal analysis and statistical tests for verifying whether the series are random and generated by the stochastic model. We found that time series on difference of JP¥/US$ exchange rates satisfy these properties. We composed a stochastic differential equation as the model that might describe variability of the difference. We regressed the potential function in the sense of the time average on the stochastic differential equation with use of graphs of polynomials. This paper also presents the necessity of the number of order on the polynomials with consideration on stability of singular points for perturbation, what we call structural stability in Topology. With integration of the series reproduced by our model, we obtained series as numerical simulations of the JP¥/US$ exchange rate. We compare these series with the time series data of the JP¥/US$ exchange rate to evaluate our stochastic differential equation.

This forum article is aimed at introducing the main activities of the Society for Science on Form, Japan since its establishment in 1985, and its relations to friend societies with similar characters. At present, we have two major friend organizations, i.e. the Society for Culture on Form (in Japan) and the International Society for Interdisciplinary Study of Symmetry (ISIS Symmetry). Next, meanings of "Katachi" and "Symmetry" are explained, so that the relations to these friend organizations are convinced. In addition, other small groups with interdisciplinary activities are introduced, i.e. the "Kutachi" group in USA (aiming at development of better artificial systems) and an NPO Interdisciplinary Institute for Science Technology and Art (ISTA), in which the present author is deeply involved. Then, the past and present situations of the journal Forma is mentioned, and some hints are given in order to elevate its status.