A reduction technique in Waring's problem, I
Kent D. Boklan (1993)
Acta Arithmetica
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Kent D. Boklan (1993)
Acta Arithmetica
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Trevor D. Wooley (1993)
Acta Arithmetica
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François Destrempes (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.
N. Macheras, W. Strauss (1994)
Fundamenta Mathematicae
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We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called "self-consistency", which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies.
Béla Bollobás, Paul Erdős, Guoping Jin (1993)
Acta Arithmetica
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Robert S. Coulter (1998)
Acta Arithmetica
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Randrianarivony, Arthur (1994)
Séminaire Lotharingien de Combinatoire [electronic only]
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Myung-Hwan Kim (1993)
Acta Arithmetica
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Rolando Cavazos-Cadena, Raúl Montes-de-Oca (2000)
Applicationes Mathematicae
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This work concerns controlled Markov chains with finite state space and nonnegative rewards; it is assumed that the controller has a constant risk-sensitivity, and that the performance ofa control policy is measured by a risk-sensitive expected total-reward criterion. The existence of optimal stationary policies isstudied within this context, and the main resultestablishes the optimalityof a stationary policy achieving the supremum in the correspondingoptimality equation, whenever the...