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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The volume of a region defined by polynomial inequalities
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by O. S. Rothaus PDF
Proc. Amer. Math. Soc. 42 (1974), 265-267 Request permission

Abstract:

Let $P(x)$ be a polynomial on ${R^n}$ with nonnegative coefficients. We develop a simple necessary and sufficient condition that the set $S = \{ x \in {R^n}|{x_i} \geqq 0,P(x) \leqq 1\}$ shall have finite volume. A corresponding result where $P(x)$ is replaced by a collection of polynomials is an easy corollary. Finally, the necessary and sufficient conditions for the special case that P is a product of linear forms is also given.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 265-267
  • MSC: Primary 52A20
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0331219-0
  • MathSciNet review: 0331219