一般化破壊の修復

概要

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In this paper, a general idea, "repair of the generalized breakdown", introduced for discussing various breakdown phenomena, is studied, and to denote the idea, an operator called restoration is introduced. Though a category of the restoration basically needs to be evaluated with some proper cost-function as an inverse problem of the generalized breakdown, in this study, as the first step, classification of the restoration, etc. are investigated from inclusion relations in the set theory. The restoration has three kinds : a non-restoration, a partial restoration and a complete restoration. Composite mappings of those kinds, a composite partial restoration etc., are also defined to disscuss a dynamic restoration process statically. It makes clear that the composition of double partial restorations is a composite partial restoration, the composition of a partial restoration and a non-restoration succeeded to it is a composite partial restoration, the partial restoration can not be operated in succession of a complete restoration, etc. Furthermore, the composition of infinite number of partial restorations is not a restoration, under some condition the infinite alternate composition of a generalized partial breakdown and a partial restoration is a composite generalized complete breakdown.
東海大学の論文