THE CATEGORY THEORY OF TIME SYSTEMS

In this paper we show a categorical treatment of general time systems using the categorization method presented in our previous paper. Various concepts about general time systems are categorized in the unified framework. Some category theoretical tools for the investigation of such time systems are presented. Using those tools some basic properties of time systems are explored in our framework. In particular, a conceptual equivalence between the causality and the state space representability is proved in the categorical terms. These results show that our method can be a universal tool for a categorization and a categorical treatment of mathematically defined general systems.     

DESIGN OF MULTIBEAM SATELLITE COMMUNICATIONS NETWORKS REALIZED BY SS/FDMA

In the subchannel switched frequency-division multiple access (SS/FDMA) system, each transponder bandwidth is subdivided into several narrow bands named ‘subchannels’, and interbeam connections are established on a subchannel by subchannel basis. The SS/FDMA system makes it possible to construct a satellite communications network among multiple beams by using only one transponder per beam. This paper presents systematic design methods for such networks. First, a method to determine transmission parameters of the network, such as transmit power levels of respective carriers, is described. Objectives of the design method are to maximize the system capacity, and to minimize the average transmit power for one carrier. Results of example calculations are also presented for power-limited and bandwidth-limited networks. Next, a method to determine the number of subchannels is described for bandwidth-limited networks, which is an important parameter affecting the system capacity of the bandwidth-limited networks. Results of an example calculation taking account of uniform and non-uniform traffic distribution patterns are also presented.     

GAS CHROMATOGRAPHIC DETERMINATION AND CORRELATION OF WEIGHT-FRACTION HENRY'S CONSTANTS FOR HYDROCARBON GASES AND VAPORS IN MOLTEN POLYMERS

In the polymer industry, separation equipment is required to separate unreacted monomers and solvents from polymers. In order to design such equipments, solubilities of gases and vapors in molten polymers are needed as fundamental data. It is very helpful if the weight-fraction Henry's constant, which gives solubilities of a solute at concentrated regions of a polymer, can be estimated by a predictive method.

In the present study, a new expression for the free volume term has been derived and is coupled with the UNIFAC model. The present UNIFAC-FV model was applied to common polymer systems. The weight-fraction Henry's constants were calculated for several volatile hydrocarbons and the calculated results were compared with the experimental data determined by a gas chromatographic technique.

The present UNIFAC-FV model with a new free volume expression was found to be helpful in predicting the weight-fraction Henry's constants of hydrocarbon solutes in molten polystyrene, in polypropylene, and in low-density polyethylene. It is advantageous that our model is applicable both supercritical gases and subcritical vapors with no adjustable parameters.     

MICROSTRUCTURE AND RHEOLOGICAL BEHAVIOR OF WHIPPING CREAM

The mechanism of the formation of a rigid foam structure during whipping of reconstituted whipping cream was investigated. The rheological properties of whipped cream were estimated from an analysis of shear creep curves by a four element model. The values of each element increased exponentially during the process of whipping. From cryo-SEM observation, the surface of air bubbles consisted of a thin membrane which was penetrated by fat globules. Also, fat globules in the serum were joined together by free fat to form a framework structure.
The relationship between the rheological properties and microstructure of whipped cream was deduced from the rheological properties of two model systems. It is believed that whipped cream is a mixed matrix of a SOB O/W structure and a stiffer W/O structure.     

Applications of the Long and Accurate Polymerase Chain Reaction Method in Yeast Molecular Biology: Direct Sequencing of the Amplified DNA and Its Introduction into Yeast

A DNA fragment longer than 10 kb can be amplified by the long and accurate polymerase chain reaction (LA-PCR) method. We demonstrate here applications of this technique in molecular biological studies of Saccharomyces cerevisiae. We have shown that DNA fragments amplified by LA-PCR can be directly used as a template in the chain-termination sequencing protocol, making it possible to quickly identify the DNA insert of yeast genomic library clones. We have also shown that the amplified yeast DNA can easily be introduced into yeast by co-transformation with linearized vector DNA. Overlapping DNA between the amplified yeast fragment and the vector must be more than 20 bp long in order to obtain 90% or more correct recombinant plasmids. These results suggest that simple amplification of yeast clones by LA-PCR can replace the previous procedures of yeast clone recovery, consisting of transformation of Escherichia coli, propagation of plasmids in E. coli and preparation of plasmid DNA. © 1997 John Wiley & Sons, Ltd.     

Rational decision principle and social choice function

In this paper, we treat a social choice function as a decision principle and apply the concept of the rational decision principle to it. Then we derive the concept of the order rational decision principle. We show that the rational decision principle is suitable for an integral framework for a social choice, as well as for decision making under uncertainty and multiobjective decision making. We also show that some decision principles are considered to be models of Arrow's decision principle in a weaker sense.     

ALGEBRAIC FORMULATION OF RELATIONSHIP BETWEEN A GOAL SEEKING SYSTEM AND ITS ENVIRONMENT

The purpose of this paper is, first, to formalize the key concepts for describing the relationship between a goal seeking system and its relevant environment and, then, mainly based on Ashby's Law of Requisite Variety, to develop a formal discussion on the relationship in the framework of mathematical general systems theory. The law, one of the most well-known laws in the general systems theory, intuitively claims that “only the variety can destroy the variety”. Although the claim is so simple and has attracted more and more attention from organization theory, organizational cybernetics and control theory, the concepts involved are used quite loosely. By defining the concepts of the varieties in terms of equivalence relations, we will formulate the basic logic explaining the relationship between a goal seeking system and its relevant environment and explore its meaning and significance. In this process we will also reveal the meaning of the internal model principle, which says that in order to control the environment the system should incorporate an internal model of it.     

THE CANONICAL STRUCTURE AS A MINIMUM STRUCTURE

In this paper a structure of a system is defined as a mathematical structure (?; Σ ), where ? is a first-order logic language and Σ is a set of sentences of the given first-order logic. It is shown that a canonical structure determined by Σ which is similar to those used in proving the Gödei's completeness theorem, satisfies a universality in the sense of category theory when homomorphisms are used as morphisms, and a freeness in the sense of universal algebra when Σ-morphisms, which preserve Σ are used. The universality and the freeness give the minimality of the canonical structure.

As an example, a structure of a stationary system is defined as a pair (?e-sta, Σe-sta)-Its canonical structure is actually constructed. In a sense this canonical structure accords with models constructed by Nerode realization.