過渡現象の時系列による新代数化理論とその二、三の回路への応用
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概要
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The object of this paper is to construct a new system of theory with the view of treating electromagnetic phenomena more freely with respect to the time parameter. On the transient phenomena of natural circuits, non-linear network problems and time-variable network problems, these analyses generally are treated by the differrential and integral equations, which frequentiy are difficult and sometimes impossible to solve. In such cases, practically, the approximate values of the phenomena are wished to be known. In order to match this demand, the authors introduce the algebraic or arithmetic treatment of these problems by means of the special approximations and the time series determined thereby. If the characteristics of elements in the network are given by the practical measurements, and even if the data can frequently be not written as the functional equations of time 't' and the element constants, the data can usually be used by the authors, treatment with respect to the differrential and integral equations. In this case, the approximated treatment introduced in this paper is one of the most convenient methods Namely, first, by the quantisation of the given time and then by fixing an arbitrary metric of time, the fundamental equations of the given network are established. Next, by the front and the rear approximations the equations of two kinds on time series are determined. Then by knowing the values of every electrical quantity before the transient time the values of these at this transient time can be determined one after another. The solution is the avarage solution about the two approximations, where the metric of time must be adequately small so that the metric error is smaller than the needed value. If the better values in the arbitrary periods are wished to be determined, the metrics of time in these periods must be especially smaller than the others. Namely the metric of time in each period is not necessarily same, and then that may be chosen as the adequate value in each period. It is usually the merit of this treatment that the method holds the physical structure of the given network and this original approxiniation is more effective than the others. Especially, the authors believe that one of the best solutions is determined on the difficult problem by using the adequate computor. Especially, using the adequate camputor on the difficult problem, the method of authors usually is become the better. After all, Kron's diakoptic, the dual one^(-F-Ii) and Poincare process of physical field ploblems are thought to be ”diakoptics” (or ”codiakoptics”) of the 3-dimensional space, then this treatment of authors also is able to be thought to become the generalized diakoptics of the 1-dimensional space (time) in our 4-dimensional space.
- 山形大学の論文
- 1966-01-14
著者
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