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

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

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

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

**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.- PDF, DOI

**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.- PDF, Postscript

**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.- PDF, Postscript DOI

**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.- PDF, Postscript

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

**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.- PDF PostScript,

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

**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.- PDF DOI PostScript,

**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),- PDF PostScript,

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

**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.- PDF PostScript,

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

**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.

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

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

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