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Interior normal lengths on convex configurations. (English) Zbl 0842.90131

The topics of this paper are described in the introduction: “Mr. X is standing on the boundary of an elliptically shaped cricket oval and decides to stroll over the playing surface to the other side. Mr. X is renowned for walking in perfect straight lines and is blessed with incredible speed and superb sense of direction. For the benefit of the local oval drunk, he begins to walk in a straight line, heading from his starting position in a direction normal to the boundary. Once on the other side, he becomes curious to know how far he walked, and, needing to know immediately, decides to call the distance covered ‘the interior normal length’, and then calls for the help of the local mathematician (the local oval drunk):
(i) Provide Mr. X with a mathematical description of his problem;
(ii) Where on the boundary should Mr. X begin so that he walks the least distance”?

MSC:

90C99 Mathematical programming
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[1] Hwang F. K., Annals of Discrete Mathematics, Monograph 53, in: The Steiner Tree Problem (1992)
[2] DOI: 10.1007/BF01758758 · Zbl 0748.05051 · doi:10.1007/BF01758758
[3] DOI: 10.1007/BF02189325 · Zbl 0774.05033 · doi:10.1007/BF02189325
[4] DOI: 10.2307/2324504 · doi:10.2307/2324504
[5] Rao C. R., Generalized Inverse of Matrices and Its Applications (1971) · Zbl 0236.15004
[6] Trenkler G., Praxis der Mathematik 33 pp 183– (1991)
[7] DOI: 10.2307/1427743 · Zbl 0749.60092 · doi:10.2307/1427743
[8] Feller W., An Introduction to Probability Theory audits Applications 1, 3. ed. (1978)
[9] Abel, N. H. 1965.Ouvres Completes, vol. 2, 26–28. New York: Johnson Reprint Corporation.
[10] DOI: 10.1088/0264-9381/9/5/011 · Zbl 0991.83528 · doi:10.1088/0264-9381/9/5/011
[11] Murphy, G. 1960.Ordinary Differential Equations Theory and Solutions, 23–26. Princeton, New Jersey: Van Nostrand.
[12] Eisenhart, L. P. 1949.Riemannian Geometry, Vol. 82/83, 91–93. Princeton University Press. · Zbl 0041.29403
[13] Willmore, T. J. 1964.An Introduction to Differential Geometry, 313Oxford University Press. · Zbl 0086.14401
[14] DOI: 10.1112/blms/22.4.362 · Zbl 0707.26014 · doi:10.1112/blms/22.4.362
[15] Sandor S., On an inequality of Ky Fan, to appear
[16] Wang W. L., Acta. Math. Sinica 27 pp 485– (1984)
[17] Beckenbach, E. F. and Bellman, R. 1961.Inequalities, first edition, 5Berlin: Springer. · Zbl 0097.26502
[18] Berberian S. K., Introduction to Hilbert Space (1961) · Zbl 0121.09302
[19] Ringrose J. R., Compact Non-self-adjoint Operators (1971) · Zbl 0223.47012
[20] DOI: 10.1016/0024-3795(92)90045-C · Zbl 0761.15002 · doi:10.1016/0024-3795(92)90045-C
[21] Aitken, A. C. 1956.Determinants and Matrices, 138Edinburgh and London: Oliver and Boyd. example 27.
[22] Gurland J., Skandinavisk Aktuarietidskr 39 pp 171– (1956)
[23] DOI: 10.2307/2685218 · doi:10.2307/2685218
[24] DOI: 10.2307/1267291 · Zbl 0238.62011 · doi:10.2307/1267291
[25] Stromberg K. R., Introduction to Classical Real Analysis (1981) · Zbl 0454.26001
[26] DOI: 10.1080/0020739920230216 · Zbl 0753.15004 · doi:10.1080/0020739920230216
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