Abstract.

Inspired by circular complex interval arithmetic, an arithmetic for closed balls in ℝⁿ is pursued. In this sense, the properties of certain operations on closed balls in ℝⁿ, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3,7}, are studied. In particular, known results for operations on closed balls in ℂ, which can be identified with ℝ², are extended to closed balls in ℝⁿ.

中文翻译：

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闭球的算术

摘要。

受循环复数区间算术的启发，研究了ℝ ⁿ中闭球的算术。从这个意义上说，研究了 ℝ ⁿ中对封闭球的某些操作的性质，其中一些与向量的 Hadamard 积或当n ∈ {3,7} 时的 2 倍向量叉积有关。特别是，在 ℂ 中的封闭球上的已知结果（可以用 ℝ ²来识别）扩展到 ℝ ⁿ中的封闭球。