Hidefumi Kawakatsu

Methods for Evaluating Pictures and Extracting Music by 2D DFA and 2D FFT

This study proposes the following two methods applying two-dimensional DFA (detrended fluctuation analysis) and two-dimensional FFT (fast Fourier transform) algorithm: (1) a method for finding pleasant photographs of local tourist spots, and (2) a method for generating music from these photographs. We define “pleasant image” as the photograph containing 1/ f noise components since it has been suggested that the 1/ f -noise structure in visual art as well as in music can stimulate the perception of pleasant. The method for extracting music from the picture is developed as follows: (a) the image is divided into some squares and frequency components are extracted from each square by two-dimensional FFT, and then (b) the frequency components of each square are transformed into musical pitches. A method to arrange the music by reflecting features of the image is also provided.

A mathematical model for an optimal appointed delivery date on a home delivery market

In recent years, the home delivery market has rapidly been growing since customers can purchase a variety of products very easily via Internet. At the same time, however, customers tend to switch from a supplier to another seeking for better service for them. For this reason, it is necessary for suppliers to enclose their customers by means of various kinds of service and strategy. An appointed delivery date of a product ordered by a customer is one of important factors of suppliers services. From the suppliers point of view, they hope to make the period from the order date to the delivery date as short as possible to increase their customers, but at the same time they prefer to make this period as long as possible since the risk becomes higher that they cannot deliver products to their consumer by the appointed date under the short period appointed date. This study proposes a stochastic model to determine an optimal appointed delivery date for a supplier. For small values of an appointed delivery date L , the probability that a customer purchases the product becomes larger, but the probability of tardiness increases. In contrast, the purchase probability as well as the penalty of tardiness decreases with L . From this point of view, this study formulates the expected profit for a supplier, which is to be maximized as an objective function. Clarified are the conditions under which an optimal appointed delivery date exists for the case where the purchase probability is expressed by a multinomial logit model. Numerical examples are also presented.

Methods for Classifying Pictures of Tourist Destinations and for Transforming Frequency Components into Musical Chords.

This study develops the following two methods applying the 1D and 2D FFT (fast Fourier transform) algorithms: (1) a method for finding pleasant photographs of local tourist destinations based on observations in our previous study, and (2) a method for generating chord progressions from these photographs considering the two kinds of “intervals”: (a) the difference between the frequency components and (b) the difference between pitches in music theory. Some examples are provided to illustrate the proposed method.

Optimal Models for Adding Relation to an Organization Structure with Different Numbers of Subordinates at Each Level

This study aims at revealing optimal additional relations to a pyramid organization such that the communication of information between every member in the organization becomes the most efficient. This paper proposes models of adding a relation between two members in the same level of the organization structure in which each member of (m)-th level below the top has different number of subordinates, (m+2) in Model-1 and (2m+2) in Model-2. The total shortening distance which is the sum of shortening lengths of shortest paths between every pair of all nodes is formulated and is illustrated with numerical examples to obtain an optimal level of two members between which a relation is added for each of Model-1 and Model-2.

An Optimal Model of Adding Relation Between the Top and a Member of a Linking Pin Organization Structure with K Subordinates

This study considers the addition of relation to an organization structure such that the communication of information between every member in the organization becomes the most efficient. This paper proposes a model of adding relation to a linking pin organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent. When a new edge between the root and a node with a depth N is added, an optimal depth N * is obtained by minimizing the total distance which is the sum of lengths of shortest paths between every pair of all nodes.

A Game Theoretical Analysis for the Quantity Discount Problem with Weibull Ameliorating Items

This paper presents a model for determining optimal all-unit quantity discount strategies in a channel of one seller (poultry farmer) and one buyer (retailer). The poultry farmer’s stock increases due to the growth of items. In contrast, the retailer purchases items as fresh chicken meat from the poultry farmer, the inventory level of the retailer is therefore depleted due to the combined effects of its demand and deterioration. The poultry farmer attempts to increase her profit by controlling the retailer’s ordering schedule through a quantity discount strategy. We formulate the above problem as a Stackelberg game between the poultry farmer and the retailer to analyze the existence of the poultry farmer’s optimal quantity discount pricing policy, which maximizes her total profit per unit of time. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed formulation.

An Inventory Model for Special Display Goods with Seasonal Demand

The present study discusses the retailer’s optimal replenishment policy for seasonal products. The demand rate of seasonal merchandise such as clothes, sporting goods, children’s toys and electrical home appearances tends to decrease with time after reaching its maximum value. In this study, we focus on “Special Display Goods”, which are heaped up in end displays or special areas at retail stores. They are sold at a fast velocity when their quantity displayed is large, but are sold at a low velocity if the quantity becomes small. We develop the model with a finite time horizon (selling period) to determine the optimal replenishment policy, which maximizes the retailer’s total profit. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed model.

Existence of single input rule modules for optimal fuzzy logic control

The nonlinear feedback control whose feedback law is constructed by the SIRMs method is structured and presented mathematically. The set of SIRMs formed from themembership functions, important degrees and some parameters is compact by considering it to be a family of them. And by considering the fuzzy inference calculations as a composite functional on the family of the membership functions, its continuity is proved in functional analysis. Then, the existence of optimal solution of fuzzy feedback control using SIRMs method is derived from these facts.