Ramsey problems in additive number theory
Béla Bollobás, Paul Erdős, Guoping Jin (1993)
Acta Arithmetica
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Béla Bollobás, Paul Erdős, Guoping Jin (1993)
Acta Arithmetica
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Yonutz Stanchescu (1998)
Acta Arithmetica
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Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.
Trevor D. Wooley (1993)
Acta Arithmetica
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Benkart, Georgia, Smirnov, Oleg (2003)
Journal of Lie Theory
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Myung-Hwan Kim (1993)
Acta Arithmetica
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Jonas Koko (2000)
Applicationes Mathematicae
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The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.
Julia Mueller (1993)
Acta Arithmetica
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Foata, Dominique, Zeilberger, Doron (1987)
Séminaire Lotharingien de Combinatoire [electronic only]
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Hong-Quan Liu (1993)
Acta Arithmetica
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M. D. Coleman (1993)
Acta Arithmetica
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