Publications

Polynomials non-negative on strips and half-strips (with H. Nguyen). J. Pure Appl. Algebra 216 (2012), no. 10, 2225-2232.

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P\'olya's Theorem with zeros. (with M. Castle and B. Reznick). J. Symb. Comp. 46(9) (2011), 1039-1048.

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Rational certificates of positivity for compact semialgebraic sets. Pac. J. Math. 251(2) (2011), 385-391.

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A quantitative P\'olya's Theorem with zeros. (with M. Castle and B. Reznick). J. Symb. Comp. 44 (2009), 1285-1290.

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Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals (with J. Demmel and J. Nie), J. Pure and Appl. Algebra 209 (2007), 189--200.

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A quantitative P\'olya's Theorem with corner zeros. (with B. Reznick). In Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, J.-G. Dumas, editor, New York, NY, ACM Press, pp.285--290.

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A new proof of Hilbert's theorem on ternary quartics. (with B. Reznick, C. Scheiderer, and F. Sottile). C. R. Math. Acad. Sci. Paris 339 (2004), 617-620.

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Polynomials positive on unbounded rectangles. (with Bruce Reznick), in Positive Polynomials in Control (A. Garulli, D. Henrion eds.), Springer Lecture Notes in Control and Information Sciences.

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Positive polynomials and the moment problem for cylinders with compact cross-section. J. Pure Appl. Alg. 188 (2004), 217-226.

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Computational approaches to representation theorems for partially ordered real algebras (with Dionne Bailey), Algorithmic and quantitative real algebraic geometry, 13--21, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 60, Amer. Math. Soc., Providence, RI, 2003.

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The moment problem for non-compact semialgebraic sets (with Claus Scheiderer), Advances in Geometry 1 (2001), 71-88.

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A new bound for P\'olya's Theorem with applications to polynomials that are positive on polyhedra, Effective Methods in Algebraic Geometry, (with Bruce Reznick), J. Pure and Applied Alg. 164 (2001), 221-229.

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Notes towards a constructive proof of Hilbert's theorem on ternary quartics, , (with Bruce Reznick), Quadratic forms and their applications (Dublin 1999), Contemp. Math. 272 (2000),

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Polynomials that are positive on an interval , (with Bruce Reznick), Trans. Amer. Math. Soc. 352 (2000), 4677-4692.

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Deciding positivity of real polynomials , (with E. Becker and T. Woermann), Real algebraic geometry and ordered structures (Baton Rouge, LA, 1996), Contemp. Math. 253 (2000), 19-23.

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An algorithm for sums of squares of real polynomials , (with T. Woermann), J. Pure and Appl. Alg. 127 (1998), 99-104.

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Hilbert's 17th problem and the champagne problem , American Mathematical Monthly 103 (1996), 879-887.

Sums of powers in rings and the real holomorphy ring , (with E. Becker) Journal fu\"r die reine und angewandte Mathematik 480 (1996), 71-103.

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Valuations and higher level orders in commutative rings , J. Algebra 172 (1995), 255-272.

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Higher level form schemes (with M. Marshall) Communications in Algebra 21(11) (1993), 4083-4102.

Holomorphy rings and higher level orders in skew fields J. Algebra 67 (1990), 285-298.

Higher level orders on noncommutative rings J. Pure and Appl. Algebra 67 (1990), 285-298.

Finite spaces of signatures Canadian J. Math. Vol XLI, No. 5 (1989), 808-829.

Higher level reduced Witt rings of skew fields Math. Zeit. 198 (1988), 545-554.

Characterizing reduced Witt rings of higher level Pacific J. Math. 128 (1987), 333-347.