Minmax problems for fractional parts of real numbers (Q2711476)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minmax problems for fractional parts of real numbers |
scientific article |
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Minmax problems for fractional parts of real numbers (English)
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8 April 2002
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fractional parts of real numbers
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nonlinear extremal problems
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view-obstruction problems
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Diophantine approximation
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0.8656454
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0.8425273
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The classical view-obstruction problem is an optimization problem on simultaneous inhomogeneous Diophantine approximation and can be interpreted as a billiard problem with straight lines in the \(d\)-dimensional unit cube. Problems of this type were first investigated by the reviewer in 1968 [\textit{J. M. Wills}, Monatsh. Math. 72, 254-263, 368-381 (1968); ibid. 74, 166-171 (1970; Zbl 0188.10602)] and \textit{T. W. Cusick} in 1973 [Aequationes Math. 9, 165-170 (1973; Zbl 0265.52003)], and has been generalized in various directions.NEWLINENEWLINENEWLINEThe author investigates nonlinear view-obstruction problems and obtains various number theoretic results with analytic methods and computer algebra. The results are underlined by several figures.
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