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Volume 4 / Issue 1

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DOI:   10.3217/jucs-004-01-0034


On the Algebra of Intervals and Convex Bodies

Svetoslav M. Markov (Bulgarian Academy of Sciences, Bulgaria)

Abstract: We introduce and study abstract algebraic systems generalizing the arithmetic systems of intervals and convex bodies involving Minkowski operations such as quasimodules and quasilinear systems. Embedding theorems are proved and computational rules for algebraic transformations are given.

Keywords: Interval arithmetic, Minkowski operations, commutative semigroups, convex bodies, isomorphic embedding, quasilinear space.

Categories: G.1.m, I.1.m