Using theCcomputer to Investigate Cyclic Steiner Quadruple Systems
Mária Guregová, Alexander Rosa (1968)
Matematický časopis
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Mária Guregová, Alexander Rosa (1968)
Matematický časopis
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Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma, Alena Zhukova (2013)
Open Mathematics
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It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open polygonal chains, or robot arms. We introduce the notion of the oriented area for an open polygonal chain, prove that critical points are exactly the cyclic configurations with antipodal endpoints...
Zdzisław Skupień (1999)
Discussiones Mathematicae Graph Theory
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David J. Grynkiewicz (2006)
Acta Arithmetica
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K. T. Phelps (1980)
Colloquium Mathematicae
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Maria Jankiewicz (1974)
Applicationes Mathematicae
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Edjvet, Martin, Hammond, Paul, Thomas, Nathan (2001)
Experimental Mathematics
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K Chikawa, K Iséki, T Kusakabe (1962)
Acta Arithmetica
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Yakovlev, A.V. (2004)
Zapiski Nauchnykh Seminarov POMI
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Ollis, M.A. (2005)
The Electronic Journal of Combinatorics [electronic only]
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M. N. Huxley, S. V. Konyagin (2009)
Acta Arithmetica
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Béla Nagy (2013)
Studia Mathematica
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Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.